explanation blue bibcodes open ADS page with paths to full text
Author name code: bogdan
ADS astronomy entries on 2022-09-14
author:"Bogdan, Thomas J."
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Title: EMResearch/EvoMaster:
Authors: Arcuri, Andrea; ZhangMan; Asmab89; Bogdan; Gol, Amid;
Galeotti, Juan Pablo; Seran; Martín López, Alberto; Aldasoro,
Agustina; Panichella, Annibale; Niemeyer, Kyle
2022zndo...6651631A Altcode:
The first open-source AI-driven tool for automatically generating
system-level test cases (also known as fuzzing) for web/enterprise
applications. Currently targeting whitebox and blackbox testing of
REST APIs.
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Title: Drifting inwards in protoplanetary discs. II. The effect of
water on sticking properties at increasing temperatures
Authors: Pillich, C.; Bogdan, T.; Landers, J.; Wurm, G.; Wende, H.
2021A&A...652A.106P Altcode: 2021arXiv210808034P
In previous laboratory experiments, we measured the temperature
dependence of sticking forces between micrometer grains of chondritic
composition. The data showed a decrease in surface energy by a factor
~5 with increasing temperature. Here, we focus on the effect of surface
water on grains. Under ambient conditions in the laboratory, multiple
water layers are present. At the low pressure of protoplanetary
discs and for moderate temperatures, grains likely only hold a
monolayer. As dust drifts inwards, even this monolayer eventually
evaporates completely in higher temperature regions. To account for
this, we measured the tensile strength for the same chondritic material
as was prepared and measured under normal laboratory conditions in our
previous work, but now introducing two new preparation methods: drying
dust cylinders in air (dry samples), and heating dust pressed into
cylinders in vacuum (super-dry samples). For all temperatures up to 1000
K, the data of the dry samples are consistent with a simple increase
in the sticking force by a factor of ~10 over wet samples. Up to 900 K
super-dry samples behave like dry samples. However, the sticking forces
then exponentially increase up to another factor ~100 at about 1200
K. The increase in sticking from wet to dry extends a trend that is
known for amorphous silicates to multimineral mixtures. The findings
for super-dry dust imply that aggregate growth is boosted in a small
spatial high-temperature region around 1200 K, which might be a sweet
spot for planetesimal formation.
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Title: Drifting inwards in protoplanetary discs I Sticking of
chondritic dust at increasing temperatures
Authors: Bogdan, T.; Pillich, C.; Landers, J.; Wende, H.; Wurm, G.
2020A&A...638A.151B Altcode: 2020arXiv200700997B
Sticking properties rule the early phases of pebble growth in
protoplanetary discs in which grains regularly travel from cold,
water-rich regions to the warm inner part. This drift affects
composition, grain size, morphology, and water content as grains
experience ever higher temperatures. In this study we tempered
chondritic dust under vacuum up to 1400 K. Afterwards, we measured the
splitting tensile strength of millimetre-sized dust aggregates. The
deduced effective surface energy starts out as γ<SUB>e</SUB> = 0.07
J m<SUP>-2</SUP>. This value is dominated by abundant iron-oxides as
measured by Mössbauer spectroscopy. Up to 1250 K, γ<SUB>e</SUB>
continuously decreases by up to a factor five. Olivines dominate
at higher temperature. Beyond 1300 K dust grains significantly grow
in size. The γ<SUB>e</SUB> no longer decreases but the large grain
size restricts the capability of growing aggregates. Beyond 1400 K
aggregation is no longer possible. Overall, under the conditions probed,
the stability of dust pebbles would decrease towards the star. In view
of a minimum aggregate size required to trigger drag instabilities it
becomes increasingly harder to seed planetesimal formation closer to
a star.
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Title: Hinks, Arthur Robert
Authors: Bogdan, Thomas J.
2014bea..book..961B Altcode:
No abstract at ADS
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Title: Belopolsky, Aristarkh Apollonovich
Authors: Bogdan, Thomas J.
2014bea..book..193B Altcode:
No abstract at ADS
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Title: Menzel, Donald Howard
Authors: Bogdan, Thomas J.
2014bea..book.1457B Altcode:
No abstract at ADS
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Title: Robertson, Howard Percy
Authors: Bogdan, Thomas J.
2014bea..book.1848B Altcode:
No abstract at ADS
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Title: A Space Weather Mission to the Earth's 5th Lagrangian Point
(L5)
Authors: Howard, R. A.; Vourlidas, A.; Ko, Y.; Biesecker, D. A.;
Krucker, S.; Murphy, N.; Bogdan, T. J.; St Cyr, O. C.; Davila, J. M.;
Doschek, G. A.; Gopalswamy, N.; Korendyke, C. M.; Laming, J. M.;
Liewer, P. C.; Lin, R. P.; Plunkett, S. P.; Socker, D. G.; Tomczyk,
S.; Webb, D. F.
2012AGUFMSA13D..07H Altcode:
The highly successful STEREO mission, launched by NASA in 2006,
consisted of two spacecraft in heliocentric orbit, one leading and
one trailing the Earth and each separating from Earth at the rate
of about 22.5 degrees per year. Thus the two spacecraft have been
probing different probe/Sun/Earth angles. The utility of having remote
sensing and in-situ instrumentation away from the Sun-Earth line was
well demonstrated by STEREO. Here we propose the concept of a mission
at the 5th Lagrangian "point" in the Earth/Sun system, located behind
Earth about 60 degrees to the East of the Sun-Earth line. Such a mission
would enable many aspects affecting space weather to be well determined
and thus improving the prediction of the conditions of the solar wind
as it impinges on geospace. For example, Coronal Mass Ejections can
tracked for a significant distance toward Earth, new active regions
can be observed before they become visible to the Earth observer, the
solar wind can be measured before it rotates to Earth. The advantages
of such a mission will be discussed in this presentation.
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Title: Propagation of different components of cosmic rays from
Centaurus A in the Galactic magnetic fields
Authors: Kobzar, O.; Hnatyk, B.; Marchenko, V.; Bogdan, T.
2011ysc..conf...47K Altcode:
Propagation of different chemical composition ultrahigh energy cosmic
rays in the galactic magnetic fields was simulated. The simulation for
the ultra high energy events, registered by the AUGER observatory in
the sky region near Centaurus A was performed. It is shown that some
of these events could originate from Centaurus A.
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Title: The influence of extragalactic magnetic fields on the
propagation of cosmic rays from Centaurus A
Authors: Sushchov, O.; Kobzar, O.; Hnatyk, B.; Marchenko, V.;
Bogdan, T.
2011ysc..conf...50S Altcode:
The motion of different chemical composition of ultra high energy
cosmic rays in the galactic magnetic fields with taking into account
the extragalactic magnetic field was considered. The ultra high
energy events registered by the AUGER observatory in the sky region
near Centaurus A were investigated. It is shown that in the case when
the extragalactic magnetic field is taken into account some of these
events could originate from Centaurus A, but it leads to expanding of
sky region of possible source localization.
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Title: The Future of IHY Campaigns: Transition to the International
Space Weather Initiative
Authors: Raulin, Jean-Pierre; Davila, Joseph M.; Bogdan, Thomas;
Yumoto, Kiyohumi; Leibacher, John
2010HiA....15..501R Altcode:
We will present the relevant activities performed during the
International Heliophysical Year (IHY) program during the 5 year
period 2004 - 2008. The IHY was a major international effort that
involved the deployment of new instrumentation, new observations from
the ground and in space, and a strong education component. Under the
United Nations Office for Outer Space program called Basic Space
Science Initiative (UNBSSI), instrument arrays have been deployed
to provide global measurements of heliophysical phenomena. As
a result, significant scientific and educational collaborations
emerged between the organizing groups and the host country teams. In
view of the great successes achieved by the IHY during these years,
we propose to continue the highly successful collaboration with the
UN program to study the universal processes in the solar system
that affect the interplanetary and terrestrial environments, and
to continue to coordinate the deployment and operation of new and
existing instrumentation arrays aimed at understanding the impacts of
Space Weather on Earth and the near-Earth environment. To this end,
we propose a new program, the International Space Weather Initiative
(ISWI). The ISWI strongly complements the International Living With a
Star (ILWS) program, providing more attention nationally, regionally,
and internationally for the ILWS program. Based on a three-year program
activity, the ISWI would provide the opportunity for scientists around
the world to participate in this exciting quest to understand the
effect of space disturbances on our Earth environment.
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Title: Space weather: Challenges and Opportunities (Invited)
Authors: Bogdan, T. J.
2009AGUFMSA34A..01B Altcode:
The Space Weather Prediction Center (SWPC) has the following legal
mandates to: a) Continuously monitor, measure, and specify the
space environment, b) Provide timely and accurate space weather data,
operational forecasts, alerts, and warnings of hazardous space weather
phenomena, c) Provide scientific stewardship of, and public access
to, space weather data and products, d) Understand the processes that
influence space weather and develop applications for the user community
and e) Develop new and improved products and transition them into
operations to meet evolving space weather user needs. This presentation
will discuss the challenges and opportunities that NOAA and the SWPC
face in addressing these mandates. This includes coordination of
space environment activities across federal agencies and the strategic
planning for NOAA's space weather services, integration of space weather
activities as well as critical dependencies of space weather services
on current and future operational environmental satellites.
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Title: Introduction to heliophysics
Authors: Bogdan, Thomas J.
2009hppl.book...21B Altcode:
No abstract at ADS
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Title: Commission 12: Solar Radiation and Structure
Authors: Martínez Pillet, Valentin; Kosovichev, Alexander;
Mariska, John T.; Bogdan, Thomas J.; Asplund, Martin; Cauzzi, Gianna;
Christensen-Dalsgaard, Jørgen; Cram, Lawrence E.; Gan, Weiqun; Gizon,
Laurent; Heinzl, Petr; Rovira, Marta G.; Venkatakrishnan, P.
2009IAUTA..27..104M Altcode:
Commission 12 encompasses investigations on the internal structure
and dynamics of the Sun, mostly accessible through the techniques of
local and global helioseismology, the quiet solar atmosphere, solar
radiation and its variability, and the nature of relatively stable
magnetic structures like sunspots, faculae and the magnetic network. A
revision of the progress made in these fields is presented. For some
specific topics, the review has counted with the help of experts
outside the Commission Organizing Committee that are leading and/or
have recently presented relevant works in the respective fields. In
this cases the contributor's name is given in parenthesis.
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Title: f-Mode Interactions with Thin Flux Tubes: The Scattering Matrix
Authors: Hanasoge, S. M.; Birch, A. C.; Bogdan, T. J.; Gizon, L.
2008ApJ...680..774H Altcode: 2007arXiv0711.2076H
We calculate the scattering effects associated with the interaction of
a surface gravity or f-mode with a thin magnetic flux tube embedded in
a realistically stratified medium. We find that the dominant scattered
wave is an f-mode with amplitude and phase of 1.17% and around 50°
relative to the incident wave, compared to the values of 0.13% and 40°
estimated from observations. The extent of scattering into high-order
acoustic p-modes is too weak to be accurately characterized. We
recover the result that the degree of scattering is enhanced as (1)
the frequency of the incident wave increases and (2) the flux tube
becomes magnetically dominated.
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Title: Division II: Sun and Heliosphere
Authors: Webb, David F.; Melrose, Donald B.; Benz, Arnold O.; Bogdan,
Thomas J.; Bougeret, Jean-Louis; Klimchuk, James A.; Martinez-Pillet,
Valentin
2007IAUTB..26..101W Altcode:
Division II provides a forum for astronomers studying a wide range of
problems related to the structure, radiation and activity of the Sun,
and its interaction with the Earth and the rest of the solar system.
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Title: Spectropolarimetric Inversions of the Ca II 8498 and 8542 Å
Lines in the Quiet Sun
Authors: Pietarila, A.; Socas-Navarro, H.; Bogdan, T.
2007ApJ...670..885P Altcode:
We study non-LTE inversions of the Ca II infrared triplet lines
as a tool for inferring physical properties of the quiet Sun. The
inversion code is successful in recovering the temperature, velocity,
and longitudinal magnetic flux density in the photosphere and
chromosphere, but the height range where the inversions are sensitive
is limited, especially in the chromosphere. We present results of
inverting spectropolarimetric observations of the lines in a quiet-Sun
region. We find three distinct ranges in chromospheric temperature: low
temperatures in the internetwork, high temperatures in the enhanced
magnetic network, and intermediate temperatures associated with
low magnetic flux regions in the network. The differences between
these regions become more pronounced with height as the plasma-β
decreases. These inversions support the picture of the chromosphere,
especially close to the magnetic network, being highly inhomogeneous
in both the vertical and horizontal directions.
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Title: Spectropolarimetric Observations of the Ca II λ8498 and
λ8542 in the Quiet Sun
Authors: Pietarila, A.; Socas-Navarro, H.; Bogdan, T.
2007ApJ...663.1386P Altcode: 2007arXiv0707.1310P
The Ca II infrared triplet is one of the few magnetically sensitive
chromospheric lines available for ground-based observations. We present
spectropolarimetric observations of the 8498 and 8542 Å lines in a
quiet Sun region near a decaying active region and compare the results
with a simulation of the lines in a high plasma-β regime. Cluster
analysis of Stokes V profile pairs shows that the two lines,
despite arguably being formed fairly close, often do not have similar
shapes. In the network, the local magnetic topology is more important in
determining the shapes of the Stokes V profiles than the phase of the
wave, contrary to what our simulations show. We also find that Stokes
V asymmetries are very common in the network, and the histograms of
the observed amplitude and area asymmetries differ significantly from
the simulation. Both the network and internetwork show oscillatory
behavior in the Ca II lines. It is stronger in the network, where
shocking waves, similar to those in the high-β simulation, are seen
and large self-reversals in the intensity profiles are common.
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Title: The Ca II Infrared Triplet Lines as Diagnostics of
Chromospheric Magnetism
Authors: Pietarila, A.; Socas-Navarro, H.; Bogdan, T.
2007ASPC..368..139P Altcode:
The Ca II infrared (IR) triplet lines are a promising candidate for
studying chromospheric magnetism and dynamics. To study how good
of a diagnostic the lines are for chromospheric magnetism in the
quiet Sun we have constructed a MHD simulation in the high plasma-β
regime, analyzed quiet Sun spectropolarimetric data of the lines and
used a non-local thermodynamic equilibrium (nLTE) inversion code on
the observations. In the simulation, where shocking acoustic waves
dominate the dynamics, the Ca lines show a time-varying pattern of
disappearing and reappearing Stokes V lobes. Waves are seen in the
observations as well, but the dynamics are more complex. Unlike in
the simulation, the observed Ca lines do not have similar shapes
and the Stokes V asymmetries are determined by the local magnetic
topology, not the phase of the wave. The fundamental differences
between the observations and the simulation lead one to conclude that
a 1D plane parallel atmosphere is not a valid approximation for the
chromosphere. Nor can the effects of magnetic fields on the dynamics
be neglected. This is further supported by the inversions failure to
reproduce line profile asymmetries caused by gradients in the velocity
and/or magnetic field. To explain the asymmetries, 3D structures and
strongly localized gradients need to be included. The work presented
here will be published in more detail elsewhere.
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Title: Spectropolarimetric observations of the Ca II 8498 A and 8542
A lines in the quiet Sun
Authors: Pietarila, A.; Socas-Navarro, H.; Bogdan, T.
2007arXiv0704.0617P Altcode:
The Ca II infrared triplet is one of the few magnetically sensitive
chromospheric lines available for ground-based observations. We present
spectropolarimetric observations of the 8498 A and 8542 A lines in a
quiet Sun region near a decaying active region and compare the results
with a simulation of the lines in a high plasma-beta regime. Cluster
analysis of Stokes V profile pairs shows that the two lines,
despite arguably being formed fairly close, often do not have similar
shapes. In the network, the local magnetic topology is more important in
determining the shapes of the Stokes V profiles than the phase of the
wave, contrary to what our simulations show. We also find that Stokes
V asymmetries are very common in the network, and the histograms of
the observed amplitude and area asymmetries differ significantly from
the simulation. Both the network and internetwork show oscillatory
behavior in the Ca II lines. It is stronger in the network, where
shocking waves, similar to those in the high-beta simulation, are seen
and large self-reversals in the intensity profiles are common.
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Title: Commission 12: Solar Radiation & Structure
Authors: Bogdan, Thomas. J.; Martínez Pillet, Valentin; Asplund,
M.; Christensen-Dalsgaard, J.; Cauzzi, G.; Cram, L. E.; Dravins, D.;
Gan, W.; Henzl, P.; Kosovichev, A.; Mariska, J. T.; Rovira, M. G.;
Venkatakrishnan, P.
2007IAUTA..26...89B Altcode:
Commission 12 covers research on the internal structure and dynamics
of the Sun, the "quiet" solar atmosphere, solar radiation and its
variability, and the nature of relatively stable magnetic structures
like sunspots, faculae and the magnetic network. There is considerable
productive overlap with the other Commissions of Division II as
investigations move progressively toward the fertile intellectual
boundaries between traditional research disciplines. In large part,
the solar magnetic field provides the linkage that connects these
diverse themes. The same magnetic field that produces the more subtle
variations of solar structure and radiative output over the 11 yr
activity cycle is also implicated in rapid and often violent phenomena
such as flares, coronal mass ejections, prominence eruptions, and
episodes of sporadic magnetic reconnection.The last three years have
again brought significant progress in nearly all the research endeavors
touched upon by the interests of Commission 12. The underlying causes
for this success remain the same: sustained advances in computing
capabilities coupled with diverse observations with increasing levels
of spatial, temporal and spectral resolution. It is all but impossible
to deal with these many advances here in anything except a cursory and
selective fashion. Thankfully, the Living Reviews in Solar Physics; has
published several extensive reviews over the last two years that deal
explicitly with issues relevant to the purview of Commission 12. The
reader who is eager for a deeper and more complete understanding of
some of these advances is directed to http://www.livingreviews.org
for access to these articles.
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Title: Division II: Sun and Heliosphere
Authors: Webb, David F.; Melrose, Donald B.; Benz, Arnold O.; Bogdan,
Thomas J.; Bougeret, Jean-Louis; Klimchuk, James A.; Martinez Pillet,
Valentin
2007IAUTA..26...69W Altcode:
Division II of the IAU provides a forum for astronomers studying a wide
range of phenomena related to the structure, radiation and activity
of the Sun, and its interaction with the Earth and the rest of the
solar system. Division II encompasses three Commissions, 10, 12 and
49, and four working groups. During the last triennia the activities
of the division involved some reorganization of the division and its
working groups, developing new procedures for election of division and
commission officers, promoting annual meetings from within the division
and evaluating all the proposed meetings, evaluating the division's
representatives for the IAU to international scientific organizations,
and participating in general IAU business.
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Title: Low-frequency magneto-acoustic waves in the solar chromosphere
Authors: Jefferies, S. M.; McIntosh, S. W.; Armstrong, J. D.; Bogdan,
T. J.; Cacciani, A.; Fleck, B.
2006ESASP.624E..16J Altcode: 2006soho...18E..16J
No abstract at ADS
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Title: Magnetoacoustic Portals and the Basal Heating of the Solar
Chromosphere
Authors: Jefferies, Stuart M.; McIntosh, Scott W.; Armstrong, James
D.; Bogdan, Thomas J.; Cacciani, Alessandro; Fleck, Bernhard
2006ApJ...648L.151J Altcode:
We show that inclined magnetic field lines at the boundaries of
large-scale convective cells (supergranules) provide “portals”
through which low-frequency (<5 mHz) magnetoacoustic waves can
propagate into the solar chromosphere. The energy flux carried by
these waves at a height of 400 km above the solar surface is found
to be a factor of 4 greater than that carried by the high-frequency
(>5 mHz) acoustic waves, which are believed to provide the dominant
source of wave heating of the chromosphere. This result opens up
the possibility that low-frequency magnetoacoustic waves provide a
significant source of energy for balancing the radiative losses of
the ambient solar chromosphere.
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Title: Low-frequency magneto-acoustic waves in the solar chromosphere
Authors: Jefferies, S. M.; McIntosh, S. W.; Armstrong, J. D.; Cacciani,
A.; Bogdan, T. J.; Fleck, B.
2006IAUJD...3E..62J Altcode:
We demonstrate that low-frequency (< 5 mHz) propagating
magneto-acoustic waves provide a larger source of energy for balancing
the radiative losses of the solar chromosphere than their high-frequency
(> 5 mHz) counterparts. The low-frequency waves, which are normally
evanescent in the solar atmosphere, are able to propagate through
"acoustic portals" that exist in areas of strong, significantly
inclined (> 30° with respect to the vertical), magnetic field. Such
conditions are found both in active regions and at the boundaries of
supergranules. The latter implies that acoustic portals are omnipresent
over the solar surface and throughout the magnetic activity cycle,
an essential prerequisite for any baseline heating mechanism.
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Title: The Ca Ir Triplet As A Diagnostic For Chromospheric Magnetism
Authors: Pietarila, Anna M.; Socas-Navarro, H.; Bogdan, T. J.
2006SPD....37.1902P Altcode: 2006BAAS...38..247P
The Ca IR triplet lines are a good candidate for observing chromospheric
magnetic fields. Simulations of the lines in the high-beta regime,
spectropolarimetric observations and inversions of observations give
insight to their usability\suitability in observing QS magnetic fields
and dynamics. Propagating waves are clearly visible in the simulations,
both in Stokes V and I. Observed line profiles are found to be more
complicated, though they do indicate the presence of waves. We present
both simulated and observed profiles and analyze the ability of the
NLTE inversion algorithm to retrieve the underlying physics in the
solar atmosphere.
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Title: Low-frequency Magneto-acoustic Waves In The Solar Chromosphere
Authors: Fleck, Bernard; Jefferies, S. M.; McIntosh, S. W.; Armstrong,
J. D.; Cacciani, A.; Bogdan, T. J.
2006SPD....37.0206F Altcode: 2006BAAS...38..662F
We demonstrate that low-frequency (< 5 mHz) propagating
magneto-acoustic waves provide a larger source of energy for balancing
the radiative losses of the solar chromosphere than their high-frequency
(> 5 mHz) counterparts. The low-frequency waves, which are normally
evanescent in the solar atmosphere, are able to propagate through
"acoustic portals” that exist in areas of strong, significantly
inclined (> 30° with respect to the vertical), magnetic field. Such
conditions are found both in active regions and at the boundaries of
supergranules. The latter implies that acoustic portals are omnipresent
over the solar surface and throughout the magnetic activity cycle,
an essential prerequisite for any baseline heating mechanism.
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Title: Effect of Thermal Conduction on Acoustic Waves in Coronal Loops
Authors: Bogdan, T. J.
2006ApJ...643..532B Altcode:
The influence of classical (Spitzer) thermal conduction on longitudinal
acoustic waves in a coronal loop is determined through an idealized
but exactly solvable model. The model consists of an isothermal,
stratified (constant gravity) atmosphere in which a monochromatic
acoustic wave, traveling in the direction of decreasing density,
is imposed throughout the lower half of the atmosphere. Based on the
linearized equations of motion, the complete steady state (t-->∞)
solution is obtained. In addition to the imposed driving wave, the
solution also contains reflected and transmitted acoustic and thermal
conduction waves. The mode transformation and mixing occurs in the
vicinity of the atmospheric layer where the gas pressure passes through
a critical value set by the magnitude of the thermal conduction and
other model parameters. For 5 minute waves in a million degree loop,
this critical pressure is on the order of 8×10<SUP>-4</SUP> in cgs
units. Since the apex gas pressure of many coronal loops of current
interest is thought to be comfortably in excess of this value, mode
mixing and transformation is not likely to be a relevant factor for
understanding acoustic waves in these structures. On the other hand,
enhanced thermal conductivity as a result of plasma instabilities,
for example, could revive the importance of this mechanism for coronal
loops. If this mixing layer is present, the calculations show that
the pair of thermal conduction waves invariably gains the overwhelming
majority of the energy flux of the incoming acoustic wave. This energy
is rapidly dissipated in the neighborhood of the mixing layer.
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Title: Simulation of Quiet-Sun Waves in the Ca II Infrared Triplet
Authors: Pietarila, A.; Socas-Navarro, H.; Bogdan, T.; Carlsson, M.;
Stein, R. F.
2006ApJ...640.1142P Altcode: 2005astro.ph.10744P
The Ca II infrared triplet lines around 8540 Å are good candidates
for observing chromospheric magnetism. Model spectra of these lines
are obtained by combining a radiation hydrodynamic simulation with a
Stokes synthesis code. The simulation shows interesting time-varying
behavior of the Stokes V profiles as waves propagate through the
formation region of the lines. Disappearing and reappearing lobes
in the Stokes V profiles as well as profile asymmetries are closely
related to the atmospheric velocity gradients.
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Title: Numerical modelling of MHD waves in the solar chromosphere
Authors: Carlsson, Mats; Bogdan, Thomas J.
2006RSPTA.364..395C Altcode:
No abstract at ADS
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Title: Observational aspects of sunspot oscillations
Authors: Bogdan, T. J.; Judge, P. G.
2006RSPTA.364..313B Altcode:
No abstract at ADS
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Title: Influence of Thermal Conduction on Acoustic Waves in Coronal
Loops
Authors: Bogdan, T. J.
2005AGUFMSH11A0245B Altcode:
Observations of intensity oscillations along coronal loops have sparked
considerable interest for their potential contributions to the nascent
field of coronal seismology. The prevailing interpretation is that
magnetic field-guided longitudinal acoustic waves are responsible
for the loop intensity oscillations. This contribution assesses the
influence of classical (Spitzer) thermal conduction on longitudinal
acoustic waves in the solar corona through an idealized but exactly
solvable model. The model consists of an isothermal, stratified
(g=constant) atmosphere in which a vertically propagating acoustic
wave of prescribed frequency and amplitude, traveling in the direction
of decreasing density, is imposed throughout the lower half of the
atmosphere. Based on the linearized equations of motion the complete
steady-state solution is obtained. In addition to the imposed acoustic
wave, this solution contains reflected acoustic and thermal conduction
waves in the lower half of the atmosphere, and transmitted acoustic
and conduction waves in the upper half of the atmosphere. The acoustic
waves in the lower half of the atmosphere have almost no entropy
fluctuations, while the transmitted acoustic wave in the upper half of
the atmosphere has almost no temperature fluctuations. The boundary
between the two halves of the atmosphere is located where the gas
pressure passes through a critical value determined by the thermal
conductivity. This critical pressure is proportional to the wave
period and the three-halves power of the temperature. In c.g.s. units,
the critical pressure is 4.1 10-4 for a 5-minute oscillation in a
million degree plasma. Except in the immediate vicinity of the coronal
acoustic cutoff frequency (0.43-0.47 mHz) the energy flux carried by
the reflected wave is negligible. The fraction of the energy flux
carried by the transmitted acoustic wave (relative to that carried
by the imposed acoustic wave) has a maximum value of 44% for a wave
period of approximately 29 min, and it decreases to zero as the wave
frequency approaches infinity and the cutoff frequency. The remainder
of the incident wave energy flux is dissipated by the two conduction
waves. The transmitted conduction wave causes the entire upper
half of the atmosphere to oscillate uniformly about the equilibrium
temperature with the prescribed incident wave frequency, while the
transmitted acoustic wave is nearly isothermal. This raises the curious
possibility that intensity oscillations in coronal loop tops---where
the gas pressure is much less than the critical value---might be the
transmitted conduction waves, while any transmitted acoustic waves
would only be detectable through their Doppler shifts.
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Title: Parker Lecture: Waves in the Magnetized Solar Atmosphere
Authors: Bogdan, T. J.
2005AGUSMSH11C..02B Altcode:
Over the last few decades there has been tremendous progress in
determining the detailed structure of solar and stellar interiors and
envelopes through the observation and interpretation of the properties
of p-modes (helioseismology) and g-modes (asteroseismology). These
low-frequency modes derive from the broadband `noise' emitted by
the star's turbulent convection zone. The high-frequency tail of
the convective acoustic emission is not trapped within the stellar
envelope, but is instead able to venture out into the optically
thin atmosphere. There these waves encounter, amongst other things,
the ambient magnetic field (also a by product of the turbulent
convection). Close to the stellar surface, where the magnetic field is
weak in the sense that the magnetic pressure is small compared to the
thermal pressure, or equivalently, the Alfvén speed is much less than
the sound speed, the high-frequency acoustic waves propagate freely
with little regard for the magnetic field. However, at sufficiently
high altitudes these waves will encounter surfaces where the two
pressures and characteristic propagation speeds become comparable. In
passing through these canopy or equipartition surfaces the incident
acoustic waves are transformed into roughly equal amounts of the
three magneto-acoustic gravity (MAG) waves. The transmitted MAG waves
propagate at different phase speeds and along distinct trajectories
through the overlying magneto-atmosphere. They leave distinct imprints
on absorption line profiles and the continuum emission, and pave the
way for seismology of the solar, and perhaps even stellar, atmospheres.
---------------------------------------------------------
Title: Mode Conversion in Magneto-Atmospheres
Authors: Bogdan, T. J.; Carlsson, M.; Hansteen, V.; Heggland, L.;
Leer, E.; McMurry, A. D.; Stein, R. F.
2004AGUFMSH13A1162B Altcode:
Numerical simulations of wave propagation in a simple magneto-atmosphere
are employed to illustrate the complex nature of wave transformation
and conversion taking place in solar and stellar atmospheres. An
isothermal atmosphere threaded by a potential poloidal magnetic
field, and a superposed uniform toroidal field, is treated in a local
cartesian approximation. Spatial variations are restricted to the
two poloidal dimensions, but the toroidal field ensures that all
three MHD waves are present in the simulation. As in our previous
purely two-dimensional simulations (Bogdan et al. ApJ 599, 626-60,
2003), mode mixing and transformation take place at surfaces where
the magnetic and thermal pressures are equal. In the present case,
the upward propagating acoustic-gravity (MAG) wave is converted into
roughly equal parts transmitted fast, intermediate (Alfven), and
slow magneto-acoustic-gravity waves in passing through this mixing
layer. Unlike the fast and slow waves, the Alfven wave is weakly
damped, and is able to deposit its energy and momentum in the upper
chromosphere and corona. The fast and slow MAG waves are decoupled
on either side of mixing layer owing to their disparate propagation
speeds. Under certain fortuitous circumstances, the Alfven wave also
decouples from the fast and slow MAG waves.
---------------------------------------------------------
Title: From the Inside of the Sun to its Atmosphere
Authors: Bogdan, T. J.
2004AGUFMSH52A..01B Altcode:
Charles Greeley Abbot was correct in predicting the solar constant is
decidedly inconstant. Indeed, the solar irradiance exhibits pronounced
variations on nearly all currently accessible observational time
scales. There is overwhelming evidence for a tight correlation between
the Sun's magnetic activity cycle and broadband spectral irradiance in
the sense that greater magnetic activity implies excess irradiance and
vice-versa. Global dynamical and evolutionary processes determine the
time-averaged solar luminosity. In this realm the variable magnetic
field is of no consequence. It is therefore of interest to ask how deep
within the solar envelope and interior do the irradiance fluctuations
persist, and from where do they originate. Observational and theoretical
evidence will be presented to suggest that an answer to this fundamental
question may soon be in hand.
---------------------------------------------------------
Title: Solar Physics at Evergreen
Authors: Zita, E. J.; Bogdan, T. J.; Carlsson, M.; Judge, P.; Heller,
N.; Johnson, M.; Petty, S.
2004APS..NWS.C1005Z Altcode:
We have recently established a solar physics research program at
The Evergreen State College. Famed for its cloudy skies, the Pacific
Northwest is an ideal location for solar physics research activities
that do not require local observations. Collaborators from the High
Altitude Observatory (HAO) at the National Center for Atmospheric
Research have shared solar data from satellite-borne instruments such
as TRACE and SUMER. HAO colleagues also share data from computer
simulations of magneto-hydrodynamics (MHD) in the chromosphere,
generated by the Institute for Theoretical Astrophysics (ITA) at
the University of Oslo. Evergreen students and faculty learned to
analyze data from satellites and simulations, in Boulder and Oslo, and
established an infrastructure for continuing our analyses in Olympia. We
are investigating the role of magnetic waves in heating the solar
atmosphere. Comparing data from satellites and simulations shows that
acoustic oscillations from the photosphere cannot effectively propagate
into the chromosphere, but that magnetic waves can carry energy up
toward the hot, thin corona. We find that acoustic waves can change into
magnetic waves, especially near the magnetic "canopy," a region where
the sound speed is comparable to magnetic wave speeds. Understanding
MHD wave transformations and their role in energy transport can help
answer outstanding questions about the anomalous heating of the solar
atmosphere. Ref: Waves in the magnetized solar atmosphere II: Waves
from localized sources in magnetic flux concentrations. Bogdan et al.,
2003, ApJ 597
---------------------------------------------------------
Title: Erratum: Continuum analysis of an avalanche model for solar
flares [ Phys. Rev. E 66, 056111 (2002)]
Authors: Liu, Han-Li; Charbonneau, Paul; Pouquet, Annick; Bogdan,
Thomas; McIntosh, Scott
2004PhRvE..69e9904L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Theory and Simulations of Solar Atmosphere Dynamics
Authors: Stein, R. F.; Bogdan, T. J.; Carlsson, M.; Hansteen, V.;
McMurry, A.; Rosenthal, C. S.; Nordlund, Å.
2004ESASP.547...93S Altcode: 2004soho...13...93S
Numerical simulations are used to study the generation and propagation
of waves in the solar atmosphere. Solar p-mode oscillations are excited
by turbulent pressure work and entropy fluctuations (non-adiabatic gas
pressure work) near the solar surface. Interactions between short and
long period waves and radiative energy transfer control the formation of
shocks. The magnetic structure of the atmosphere induces coupling among
various MHD wave modes, with intense coupling and wave transformation
at the beta equal one surface, which likely is the location of the
so-called "magnetic canopy".
---------------------------------------------------------
Title: Waves in the Magnetized Solar Atmosphere. II. Waves from
Localized Sources in Magnetic Flux Concentrations
Authors: Bogdan, T. J.; Carlsson, M.; Hansteen, V. H.; McMurry, A.;
Rosenthal, C. S.; Johnson, M.; Petty-Powell, S.; Zita, E. J.; Stein,
R. F.; McIntosh, S. W.; Nordlund, Å.
2003ApJ...599..626B Altcode:
Numerical simulations of wave propagation in a two-dimensional
stratified magneto-atmosphere are presented for conditions that
are representative of the solar photosphere and chromosphere. Both
the emergent magnetic flux and the extent of the wave source are
spatially localized at the lower photospheric boundary of the
simulation. The calculations show that the coupling between the
fast and slow magneto-acoustic-gravity (MAG) waves is confined to
thin quasi-one-dimensional atmospheric layers where the sound speed
and the Alfvén velocity are comparable in magnitude. Away from this
wave conversion zone, which we call the magnetic canopy, the two MAG
waves are effectively decoupled because either the magnetic pressure
(B<SUP>2</SUP>/8π) or the plasma pressure (p=Nk<SUB>B</SUB>T)
dominates over the other. The character of the fluctuations observed
in the magneto-atmosphere depend sensitively on the relative location
and orientation of the magnetic canopy with respect to the wave source
and the observation point. Several distinct wave trains may converge
on and simultaneously pass through a given location. Their coherent
superposition presents a bewildering variety of Doppler and intensity
time series because (1) some waves come directly from the source while
others emerge from the magnetic canopy following mode conversion, (2)
the propagation directions of the individual wave trains are neither
co-aligned with each other nor with the observer's line of sight, and
(3) the wave trains may be either fast or slow MAG waves that exhibit
different characteristics depending on whether they are observed in
high-β or low-β plasmas (β≡8πp/B<SUP>2</SUP>). Through the
analysis of four numerical experiments a coherent and physically
intuitive picture emerges of how fast and slow MAG waves interact
within two-dimensional magneto-atmospheres.
---------------------------------------------------------
Title: MHD Waves in Magnetic Flux Concentrations
Authors: Bogdan, T. J.; Carlsson, M.; Hansteen, V.; Zita, E. J.;
Stein, R. F.; McIntosh, S. W.
2003AGUFMSH42B0535B Altcode:
Results from 2D MHD simulations of waves in a stratified isothermal
atmosphere will be presented and analyzed. The waves are generated
by a localized piston source situated on the lower, photospheric,
boundary of the computational domain. A combination of fast and slow
magneto-atmospheric waves propagates with little mutual interaction
until they encounter the surface where the sound speed and the Alfven
speed are comparable in magnitude. The waves couple strongly in this
region and emerge with different amplitudes and phases. Owing to
this mode mixing and the large variation in the Alfven speed in the
magneto-atmosphere, the fluctuations observed at a given location are
often a superposition of both fast and slow waves which have traversed
different paths and have undergone different transformations during
their journies.
---------------------------------------------------------
Title: The Development of the Western Hemisphere's First Coronagraph
Authors: Bogdan, Thomas J.
2003ANS...324R..95B Altcode: 2003ANS...324..K11B
No abstract at ADS
---------------------------------------------------------
Title: Continuum analysis of an avalanche model for solar flares
Authors: Liu, Han-Li; Charbonneau, Paul; Pouquet, Annick; Bogdan,
Thomas; McIntosh, Scott
2002PhRvE..66e6111L Altcode:
We investigate the continuum limit of a class of self-organized
critical lattice models for solar flares. Such models differ from the
classical numerical sandpile model in their formulation of stability
criteria in terms of the curvature of the nodal field, and are known
to belong to a different universality class. A fourth-order nonlinear
hyperdiffusion equation is reverse engineered from the discrete model's
redistribution rule. A dynamical renormalization-group analysis of the
equation yields scaling exponents that compare favorably with those
measured in the discrete lattice model within the relevant spectral
range dictated by the sizes of the domain and the lattice grid. We
argue that the fourth-order nonlinear diffusion equation that models
the behavior of the discrete model in the continuum limit is, in fact,
compatible with magnetohydrodynamics (MHD) of the flaring phenomenon
in the regime of strong magnetic field and the effective magnetic
diffusivity characteristic of strong MHD turbulence.
---------------------------------------------------------
Title: Waves in magnetic flux concentrations: The critical role of
mode mixing and interference
Authors: Bogdan, T. J.; Rosenthal, C. S.; Carlsson, M.; Hansteen, V.;
McMurry, A.; Zita, E. J.; Johnson, M.; Petty-Powell, S.; McIntosh,
S. W.; Nordlund, Å.; Stein, R. F.; Dorch, S. B. F.
2002AN....323..196B Altcode:
Time-dependent numerical simulations of nonlinear wave propagation
in a two-dimensional (slab) magnetic field geometry show wave mixing
and interference to be important aspects of oscillatory phenomena in
starspots and sunspots. Discrete sources located within the umbra
generate both fast and slow MHD waves. The latter are compressive
acoustic waves which are guided along the magnetic field lines and
steepen into N-waves with increasing height in the spot atmosphere. The
former are less compressive, and accelerate rapidly upward through the
overlying low-beta portion of the umbral photosphere and chromosphere
(beta equiv 8pi p/ B<SUP>2</SUP>). As the fast wave fronts impinge
upon the beta ~ 1 penumbral “magnetic canopy" from above, they
interfere with the outward-propagating field-guided slow waves, and
they also mode convert to (non-magnetic) acoustic-gravity waves as
they penetrate into the weak magnetic field region which lies between
the penumbral canopy and the base of the surrounding photosphere. In
a three-dimensional situation, one expects additional generation,
mixing and interference with the remaining torsional Alfvén waves.
---------------------------------------------------------
Title: Donald Menzel and the beginnings of the high altitude
observatory
Authors: Bogdan, Thomas J.
2002JHA....33..157B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Geometrical properties of avalanches in self-organized critical
models of solar flares
Authors: McIntosh, Scott W.; Charbonneau, Paul; Bogdan, Thomas J.;
Liu, Han-Li; Norman, James P.
2002PhRvE..65d6125M Altcode:
We investigate the geometrical properties of avalanches in
self-organized critical models of solar flares. Traditionally, such
models differ from the classical sandpile model in their formulation of
stability criteria in terms of the curvature of the nodal field, and
belong to a distinct universality class. With a view toward comparing
these properties to those inferred from spatially and temporally
resolved flare observations, we consider the properties of avalanche
peak snapshots, time-integrated avalanches in two and three dimensions,
and the two-dimensional projections of the latter. The nature of the
relationship between the avalanching volume and its projected area is
an issue of particular interest in the solar flare context. Using our
simulation results we investigate this relationship, and demonstrate
that proper accounting of the fractal nature of avalanches can bring
into agreement hitherto discrepant results of observational analyses
based on simple, nonfractal geometries for the flaring volume.
---------------------------------------------------------
Title: Waves in the Magnetized Solar Atmosphere. I. Basic Processes
and Internetwork Oscillations
Authors: Rosenthal, C. S.; Bogdan, T. J.; Carlsson, M.; Dorch,
S. B. F.; Hansteen, V.; McIntosh, S. W.; McMurry, A.; Nordlund, Å.;
Stein, R. F.
2002ApJ...564..508R Altcode:
We have modeled numerically the propagation of waves through magnetic
structures in a stratified atmosphere. We first simulate the propagation
of waves through a number of simple, exemplary field geometries in
order to obtain a better insight into the effect of differing field
structures on the wave speeds, amplitudes, polarizations, direction
of propagation, etc., with a view to understanding the wide variety of
wavelike and oscillatory processes observed in the solar atmosphere. As
a particular example, we then apply the method to oscillations in the
chromospheric network and internetwork. We find that in regions where
the field is significantly inclined to the vertical, refraction by
the rapidly increasing phase speed of the fast modes results in total
internal reflection of the waves at a surface whose altitude is highly
variable. We conjecture a relationship between this phenomenon and the
observed spatiotemporal intermittancy of the oscillations. By contrast,
in regions where the field is close to vertical, the waves continue
to propagate upward, channeled along the field lines but otherwise
largely unaffected by the field.
---------------------------------------------------------
Title: Avalanche models for solar flares (Invited Review)
Authors: Charbonneau, Paul; McIntosh, Scott W.; Liu, Han-Li; Bogdan,
Thomas J.
2001SoPh..203..321C Altcode:
This paper is a pedagogical introduction to avalanche models of solar
flares, including a comprehensive review of recent modeling efforts and
directions. This class of flare model is built on a recent paradigm in
statistical physics, known as self-organized criticality. The basic
idea is that flares are the result of an `avalanche' of small-scale
magnetic reconnection events cascading through a highly stressed coronal
magnetic structure, driven to a critical state by random photospheric
motions of its magnetic footpoints. Such models thus provide a natural
and convenient computational framework to examine Parker's hypothesis
of coronal heating by nanoflares.
---------------------------------------------------------
Title: Wave Propagation in a Magnetized Atmosphere
Authors: Bogdan, T. J.; Rosenthal, C. S.; Carlsson, M.; McIntosh,
S.; Dorch, S.; Hansteen, V.; McMurry, A.; Nordlund, Å; Stein, R. F.
2001AGUSM..SH41A01B Altcode:
Numerical simulations of MHD wave propagation in plane-parallel
atmospheres threaded by non-trivial potential magnetic fields will be
presented, and their implications for understanding distinctions between
intranetwork and internetwork oscillations will be discussed. Our
findings basically confirm the conjecture of McIntosh et al. (2001,
ApJ 548, L237), that the two-dimensional surface where the Alfvén
and sound speeds coincide (i.e., where the plasma-β , the ratio of
gas to magnetic pressure, is of order unity) plays a fundamental
role in mediating the conversion between the fast-, intermediate-
(Alfvén), and slow-Magneto-Atmospheric-Gravity (MAG) waves. For
example, upward-propagating acoustic waves generated at the base of
the internetwork photosphere suffer significant downward reflection
when they encounter this β ≈ 1 surface. Close to the network, this
surface descends from the upper chromosphere and low corona (which
pertains in the internetwork cell interiors) down into the photosphere,
and so chromospheric oscillation `shadows' are predicted to surround
the network. In the network, strong vertical magnetic fields further
depress the β ≈ 1 surface below the surface layers where the
(magnetic field-aligned) acoustic waves (i.e., slow MAG-waves) are
generated. For frequencies in excess of the cutoff frequency, these
acoustic waves suffer little reflection from the overlying atmosphere
and they steepen as they progress upward.
---------------------------------------------------------
Title: Analysis of an avalanche model in the continuum limit
Authors: Liu, H.; Charbonneau, P.; Bogdan, T. J.; Pouquet, A.;
McIntosh, S. W.; Norman, J. P.
2001AGUSM..SP51C03L Altcode:
It is shown that in the continuum limit, the avalanche system postulated
by Lu and Hamilton (1991) (LH91) can be described by a hyper-diffusion
equation in regions where every lattice is in avalanche, and the
overall system can be approximated by a randomly forced system with
a anomalous hyper-diffusion term and a cubic nonlinear transport
term. The LH91 is equivalent to a finite difference approximation to
the the equation with 2nd order center differencing in space and simple
forward time integration, and is numerically unstable. The modified rule
by Lu et al. (1993) (LH93) actually overcame the numerical stability
problem by essentially reducing the diffusion coefficient. We apply a
dynamical renormalization group analysis to the continuum system. The
frequency power spectrum scaling behavior of the "dissipating energy"
and "falling-off energy" derived from this analysis is in reasonable
agreement with the results from the LH93 avalanche model.
---------------------------------------------------------
Title: An Observational Manifestation of Magnetoatmospheric Waves
in Internetwork Regions of the Chromosphere and Transition Region
Authors: McIntosh, S. W.; Bogdan, T. J.; Cally, P. S.; Carlsson, M.;
Hansteen, V. H.; Judge, P. G.; Lites, B. W.; Peter, H.; Rosenthal,
C. S.; Tarbell, T. D.
2001ApJ...548L.237M Altcode:
We discuss an observational signature of magnetoatmospheric waves in
the chromosphere and transition region away from network magnetic
fields. We demonstrate that when the observed quantity, line or
continuum emission, is formed under high-β conditions, where β is
the ratio of the plasma and magnetic pressures, we see fluctuations in
intensity and line-of-sight (LOS) Doppler velocity consistent with the
passage of the magnetoatmospheric waves. Conversely, if the observations
form under low-β conditions, the intensity fluctuation is suppressed,
but we retain the LOS Doppler velocity fluctuations. We speculate that
mode conversion in the β~1 region is responsible for this change in
the observational manifestation of the magnetoatmospheric waves.
---------------------------------------------------------
Title: Waves in the Magnetised Solar Atmosphere
Authors: Rosenthal, C. S.; Carlsson, M.; Hansteen, V.; McMurry,
A.; Bogdan, T. J.; McIntosh, S.; Nordlund, A.; Stein, R. F.; Dorch,
S. B. F.
2001IAUS..203..170R Altcode:
We have simulated the propagation of magneto-acoustic disturbances
through various magneto-hydrostatic structures constructed to mimic
the solar magnetic field. As waves propagate from regions of strong
to weak magnetic field and vice-versa different types of wave modes
(transverse and longitudinal) are coupled. In closed-field geometries
we see the trapping of wave energy within loop-like structures. In
open-field regions we see wave energy preferentially focussed away
from strong-field regions. We discuss these oscillations in terms
of various wave processes seen on the Sun - umbral oscillations,
penumbral running waves, internetwork oscillations etc.
---------------------------------------------------------
Title: Division II: Sun and Heliosphere
Authors: Benz, Arnold O.; Bogdan, T.; Foukal, P. V.; Melrose, D. B.;
Solanki, S.; Vandas, M.; Webb, D. F.
2001IAUTB..24..110B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Sunspot Oscillations and Seismology
Authors: Bogdan, T.
2000eaa..bookE2299B Altcode:
Sunspots are known to host a wide variety of waves and oscillatory
phenomena. The coupling between these oscillations and the 5 min
acoustic oscillations of the surrounding quiet Sun provides a useful
diagnostic probe of the magnetic and thermodynamic structure of the
spot....
---------------------------------------------------------
Title: On the Disposition of Maunders' Origninal Butterfly Diagram
Authors: Bogdan, T. J.
2000AAS...196.2407B Altcode: 2000BAAS...32..708B
On 21 May 1940, Annie S. D. Maunder mailed the original drawing
of the celebrated “Maunder Butterfly Diagram" to Stephen A., and
his daughter Margaret L., Ionides. Later that same year Stephen and
Margaret gave the diagram “on indefinite loan" to Walter Orr Roberts,
then the Superintendent of Fremont Pass Station of the Harvard College
Observatory. The framed diagram remains on display today at the scion
of that organization, the High Altitude Observatory of the National
Center for Atmospheric Research, in Boulder Colorado. Drawing upon
the original correspondences, this contribution recounts the story
behind the travels of the “Maunder Butterfly" during the second World
War. The National Center for Atmospheric Research is sponsored by the
National Science Foundation.
---------------------------------------------------------
Title: Sunspot Oscillations: A Review - (Invited Review)
Authors: Bogdan, T. J.
2000SoPh..192..373B Altcode:
The current state of our knowledge, and ignorance, of the nature of
oscillations in sunspots is surveyed. An effort is made to summarize the
robust aspects of both the observational and theoretical components of
the subject in a coherent, and common, conceptual framework. Detailed
discussions of the various controversial issues are avoided except
in instances where new viewpoints are advanced. Instead, extensive
references are made to the growing literature on the subject, and
generous explanatory remarks are made to guide the reader who wishes
to delve more deeply into the underpinnings of the subject matter.
---------------------------------------------------------
Title: Studying Solar MHD Wave Propagation in Two Dimensions
Authors: McIntosh, S. W.; Bogdan, T. J.
1999AAS...194.7810M Altcode: 1999BAAS...31..962M
We present preliminary results on simulations of Magnetohydrodynamic
(MHD) wave propagation in a two dimensional stratified model of the
upper solar atmosphere. The simulations presented are obtained using
the High-Order Godunov scheme of Zachary, Malagoli & Colella
(1994). These simulations allow us to analyze quantitatively the
coupling, resonances and absorption of MHD waves in a stratified
plasma such as that of the Sun. In particular, we are able to observe
the dynamic evolution of energy and momentum balances of the model
atmosphere in response the wave propagation. In addition, we are able to
study the phenomenology of MHD wave passage through particular regions
of interest. We will concentrate mostly upon the physical manifestation
of MHD waves propagating in “network” and “internetwork” regions and
study the effect on physical parameters and the basic field structure
imposed at outset. We believe that such simulations are important
in that they compliment the high quality/temporal resolution data
currently being acquired by the SOHO and TRACE spacecraft.
---------------------------------------------------------
Title: The Solar-B Solar Optical Telescope Focal Plane Package
Authors: Levay, M.; Berger, T.; Rosenberg, W.; Tarbell, T.; Title,
A.; Bogdan, T.; Elmore, D.; Lites, B.
1999AAS...194.7610L Altcode: 1999BAAS...31R.957L
The primary goal of the Solar-B mission is to understand the physical
processes responsible for dynamics and heating of the outer solar
atmosphere. The Focal Plane Package (FPP) instrument for the 50-cm Solar
Optical Telescope provides precise measurements of the vector magnetic
field, vertical and horizontal flows, and thermal conditions in the
photosphere and low chromosphere with spatial resolution as high as
0.16 arcsec and a field-of-view as large as 320 x 160 arcsec. The FPP
can measure continuously and at high cadence to follow the evolution
of solar features. The FPP consists of broad ( 8 Angstroms) and narrow
( 100 m Angstroms) filters and a spectro-polarimeter that provides
precise polarimetry with high spectral resolution ( 25 m Angstroms). A
correlation tracker and tip-tilt mirror ensure that all focal planes
are stable to better than 0.01 arcsec. A major design consideration
of the FPP is cooperative science operations with the other Solar-B
instruments. Solar-B is a Japanese mission with US and UK partners;
S. Tsuneta is the PI of the Solar Optical Telescope and A. Title the
US PI of the FPP. It is scheduled to launch in Japanese FY 2004.
---------------------------------------------------------
Title: Interaction of P-Modes with Sunspots
Authors: Bogdan, T. J.; Barnes, G. K.; Cally, P. S.; Crouch, A. D.
1999AAS...194.5607B Altcode: 1999BAAS...31R.912B
We report on our ongoing efforts to model the interaction of
the solar acoustic oscillations with solar surface magnetic flux
concentrations. The simulation code employs a finite difference
discretization of the linearized MHD wave equations written in
conservative form. A staggered grid is used to ensure strict numerical
conservation, and the time-stepping is based on a Lax-Wendroff-type
two-step method that yields negligible numerical diffusion. Analysis
of the results from these computations indicates that a significant
fraction of the incident acoustic wave flux is converted into MHD waves
which propagate along the magnetic lines of force. The efficiency
of this coupling increases as the magnetic flux concentration is
endowed with a more pronounced penumbra, wherein the magnetic field
is highly inclined with respect to the local surface gravity. Intense
small-scale fluid motions accompany this enhancement, particularly in
the super-penumbral canopy that surrounds the flux concentration. Such
a wave-coupling process provides an excellent qualitative explanation
of the observed absorption of solar p-modes by sunspots, and is in
basic accord with the excess in the penumbral Doppler signal relative
to that recorded in the sunspot umbra. The versatility of our numerical
simulations permits a sensible quantitative comparison between the model
predictions and these observations, opening the potential to diagnose
certain aspects of the hidden subsurface structure of sunspots. The
National Center for Atmospheric Research is sponsored by the National
Science Foundation.
---------------------------------------------------------
Title: An Expansion Method for Computing Axisymmetric Sunspot
Oscillations
Authors: Bogdan, T. J.
1999ApJ...512..471B Altcode:
A method is proposed to solve for the linear axisymmetric
oscillations of a general, axisymmetric, potential, magnetostatic
sunspot equilibrium. The basic approach is to express the solution as a
series of terms that are products of a prescribed radial planform times
an unknown function of the vertical spatial coordinate and time. If
the potential sunspot magnetic field is strictly uniform and aligned
with the prevailing gravitational stratification, then a single term
in the proposed series solution suffices, and the familiar problem
first considered by Ferraro & Plumpton is readily recovered. For
less trivial magnetic fields, which possess both vertical and radial
gradients, the proposed series solution does not truncate after a
finite number of terms, but the equations that determine the unknown
functions of the vertical coordinate and time enjoy the advantage of
being separable partial differential equations, which can be attacked
through the solution of subordinate ordinary differential equations
by the method of separation of variables. It is also demonstrated
that the proposed series solution encompasses the thin flux tube
expansion. Consequently, a rigorous mathematical basis is provided
for this popular method employed to describe the dynamics of slender
magnetic flux tubes, which proves useful in understanding the intrinsic
astrophysical limitations of the approach. Whether this proposed method
of solution is also a practical and efficient means to calculate the
oscillation modes of axisymmetric sunspot equilibria is not answered
here but will be addressed in a forthcoming companion paper.
---------------------------------------------------------
Title: Axisymmetric Sunspot Oscillations
Authors: Bogdan, T.
1999ASPC..183...78B Altcode: 1999hrsp.conf...78B
No abstract at ADS
---------------------------------------------------------
Title: Sunspot Structure and Wave Propagation
Authors: Bogdan, T. J.
1999soho....9E..17B Altcode:
Oscillatory motions that are observed in sunspots offer unique insights
on the underlying thermodynamic and magnetic structure of spots. Sunspot
seismology differs from helioseismology in that the basic equilibria
are at best axisymmetric (as opposed to spherically symmetric), and
that the magnetic field cannot be treated perturbatively. These two
points conspire to render the construction of sunspot oscillation
eigenfunctions challenging and rich in physical detail. Owing to the
prominent role played by the spot's magnetic field, the detection
of sunspot oscillations is best pursued through spectropolarimetry
where one obtains time series of the full Stokes vector across
Zeeman-sensitive line profiles. Since the Zeeman splitting varies as
l2 while the Doppler width only increases as l, infrared lines offer
the brightest prospect of the simultaneous detection of magnetic
and velocity field fluctuations. A survey of current developments in
theory and observation will be presented. A brief outlook on future
advances will focus on the potential capabilities of the filtergraph
and spectrograph components of the Solar-B focal plane instrumentation
package.
---------------------------------------------------------
Title: Oscillations in a sunspot umbra from the inversion of infrared
Stokes profiles
Authors: Bellot Rubio, Luis R.; Collados, Manuel; Ruiz Cobo, Basilio;
Rodríguez Hidalgo, Inés; Bogdan, Thomas J.
1999AGM....15..A07B Altcode:
We report on the detection of magnetic field strength and velocity
oscillations in the photosphere of a sunspot umbra. Our analysis is
based on the inversion of the full Stokes profiles of three Fe I lines
at 15650 Å, from which the stratification with optical depth of the
different atmospheric parameters has been derived. This allows us to
estimate the amplitude of the oscillations and the phase lag between
the fluctuations in the line-of-sight velocity and field strength. Our
results suggest that the inferred magnetic field oscillations are caused
by opacity fluctuations that move upward and donward the region where
the spectral lines are sensitive to magnetic fields.
---------------------------------------------------------
Title: Sunspot magnetic oscillations: Comparison between observations
and models
Authors: Rüedi, I.; Solanki, S. K.; Bogdan, T.; Cally, P.
1999ASSL..243..337R Altcode: 1999sopo.conf..337R
No abstract at ADS
---------------------------------------------------------
Title: Velocity and Magnetic Field Fluctuations in the Photosphere
of a Sunspot
Authors: Lites, Bruce W.; Thomas, John H.; Bogdan, Thomas J.; Cally,
Paul S.
1998ApJ...497..464L Altcode:
We use a data set of exceptionally high quality to measure oscillations
of Doppler velocity, intensity, and the vector magnetic field at
photospheric heights in a sunspot. Based on the full Stokes inversion
of the line profiles of Fe I 630.15 and 630.25 nm, in the sunspot umbra
we find upper limits of 4 G (root mean square [rms]) for the amplitude
of 5 minute oscillations in magnetic field strength and 0.09d (rms)
for the corresponding oscillations of the inclination of the magnetic
field to the line of sight. Our measured magnitude of the oscillation
in magnetic field strength is considerably lower than that found in
1997 by Horn, Staude, & Landgraf. Moreover, we find it likely
that our measured magnetic field oscillation is at least partly due to
instrumental and inversion cross talk between the velocity and magnetic
signals, so that the actual magnetic field strength fluctuations are
even weaker than 4 G. In support of this we show, on the basis of the
eigenmodes of oscillation in a theoretical model of the sunspot umbra,
that magnetic field variations of at most 0.5 G are all that is to
be expected. The theoretical model also provides an explanation of
the shift of power peaks in Doppler velocity to the 3 minute band in
chromospheric umbral oscillations, as a natural consequence of the
drastic change in character of the eigenmodes of oscillation between
frequencies of about 4.5 and 5.0 mHz due to increased tunneling through
the acoustic cutoff-frequency barrier. Using measurements of the
phase of velocity oscillations above the acoustic cutoff frequency,
we determine the relative velocity response height in the umbra of
four different photospheric spectral lines from the phase differences
between velocities in these lines, assuming that the oscillations
propagate vertically at the local sound speed. In spacetime maps of
fluctuations in continuum intensity, Doppler velocity, magnetic field
strength, and field inclination, we see distinct features that migrate
radially inward from the inner penumbra all the way to the center of
the umbra, at speeds of a few tenths of a kilometer per second. These
moving features are probably a signature of the convective interchange
of magnetic flux tubes in the sunspot, although we failed to find any
strong correlation among the features in the different quantities,
indicating that these features have not been fully resolved.
---------------------------------------------------------
Title: On the Asymmetry of Solar Acoustic Line Profiles
Authors: Rast, Mark P.; Bogdan, Thomas J.
1998ApJ...496..527R Altcode:
We study a simplified model of solar acoustic oscillations and show how
asymmetries in spectral lines depend both on the acoustic source depth,
as previously recognized, and on the acoustic source type. We provide
a unified description of modal line asymmetries and high-frequency
pseudomode locations, suggesting an inversion on power spectra minima to
determine source properties and a correction to Lorentzian line shapes
based upon the relative locations of spectral peaks and valleys. We
also consider nonadiabatic effects due to Newtonian cooling and
demonstrate that these do not lead to notable differences between
velocity and intensity power spectral line shapes. We argue more
generally that it is unlikely that any nonadiabatic effect can be
responsible for the observed differences. Finally, we discuss the
importance of both multiplicative and additive background power to
the spectra and show how additive noise can reduce the apparent line
asymmetry of a mode. We note that information on solar convective
motions can be potentially extracted from three components of the
acoustic power spectra: the additive background yielding information on
the spectrum of nonoscillatory motions at the height of observation,
the multiplicative background reflecting the source spectrum, and
the power minima providing the source depth and physical nature. For
stochastically excited linear waves only the first of these contributes
significantly to spectral differences between observed variables.
---------------------------------------------------------
Title: The Seismology of Sunspots: A Comparison of Time-Distance
and Frequency-Wavenumber Methods
Authors: Bogdan, T. J.; Braun, D. C.; Lites, B. W.; Thomas, John H.
1998ApJ...492..379B Altcode:
A pair of formulae are developed that relate the absorption coefficient
and partial-wave phase shift concepts of frequency-wavenumber local
helioseismology to the center-annulus cross-correlation function
of time-distance helioseismology, under the general circumstances
that both induced and spontaneous sunspot oscillations may be
present. These formulae show that spontaneous emission of p-modes
by magnetic and Reynolds stresses within the spot and the mode
mixing between incoming and outgoing p-modes affect only the
outgoing center-annulus cross-correlation time τ<SUP>+</SUP>,
and they caution that real or spurious phase lags of the umbral
oscillation signal lead to differences in the incoming and outgoing
correlation times, resulting in τ<SUP>-</SUP> ≠ τ<SUP>+</SUP>. The
application of these methods to actual helioseismic data obtained
by the Global Oscillation Network Group (GONG) project is carried
out in order to provide a tangible illustration of how time-distance
and frequency-wavenumber ideas can profitably be combined to yield
deeper insight into the seismic probing of sunspots. <P />By using the
helioseismic GONG data in conjunction with concurrent observations of
Doppler velocities and vector magnetic fields obtained by the High
Altitude Observatory/National Solar Observatory (HAO/NSO) Advanced
Stokes Polarimeter (ASP) for the 1995 October disk passage of active
region NOAA 7912, we demonstrate that the inferred GONG umbral
signal actually originates from the umbra-penumbra boundary about 6
Mm distant from the center of the spot. Further, the ASP observations
show that the 5 minute oscillations at the umbra-penumbra boundary lag
behind those in the center of the umbra by approximately 1 minute,
which is precisely the difference between the incoming and outgoing
correlation times for NOAA 7912 recently determined by Braun. This
remarkable result underscores the perils of using umbral oscillations
in time-distance helioseismology, and it calls into question previous
claims that correlation time differences constitute direct evidence
for the existence of a steady downflow in and around sunspots. Taken
together, the observational and theoretical evidence suggest that
the p-mode forcing of the spot leads to the generation of upwardly
propagating slow magnetoatmospheric waves. These waves are in turn
responsible for the decreased amplitudes of the outwardly propagating
p-modes in the surrounding quiet Sun, and the dispersion in their travel
times between the hidden subsurface layer where they are forced and
the overlying level where the Doppler signals originate leads to the
observed phase lag between the umbral and penumbral oscillations and
the corresponding correlation time differences. <P />This work utilizes
data obtained by the Global Oscillations Network Group (GONG) project,
managed by the National Solar Observatory, a Division of the National
Optical Astronomy Observatories, which is operated by AURA, Inc.,
under a cooperative agreement with the National Science Foundation.
---------------------------------------------------------
Title: Simulation of f- and p-Mode Interactions with a Stratified
Magnetic Field Concentration
Authors: Cally, P. S.; Bogdan, T. J.
1997ApJ...486L..67C Altcode:
The interaction of f- and p-modes with a slab of vertical magnetic
field of sunspot strength is simulated numerically in two spatial
dimensions. Both f-modes and p-modes are partially converted to
slow magnetoatmospheric gravity (MAG) waves within the magnetic slab
because of the strong gravitational stratification of the plasma along
the magnetic lines of force. The slow MAG waves propagate away from
the conversion layer guided by the magnetic field lines, and the
energy they extract from the incident f- and p-modes results in a
reduced amplitude for these modes as they exit from the back side of
the slab. In addition, the incident p-modes are partially mixed into
f-modes of comparable frequency, and therefore larger spherical harmonic
degree, when they exit the magnetic flux concentration. These findings
have important implications for the interpretation of observations
of p-mode absorption by sunspots, both in terms of the successes and
failures of this simple numerical simulation viewed in the sunspot
seismology context.
---------------------------------------------------------
Title: Waves in magnetized polytropes.
Authors: Bogdan, T. J.; Cally, P. S.
1997RSPSA.453..943B Altcode: 1997RSPSA.453..943J
The authors consider the linear oscillations of a plane-parallel
semi-infinite electrically conducting atmosphere with a constant
temperature gradient, subjected to an imposed uniform gravitational
acceleration and uniform magnetic field. The oscillations are treated
in the ideal (dissipationless) limit and the uniform gravitational
acceleration and magnetic field are taken to be co-aligned with the
prevailing temperature gradient. It is demonstrated that atmospheric
motions with prescribed horizontal variations of the form exp(ikx),
with k real, possess both a discrete set of complex eigenfrequencies
w<SUB>n</SUB>, n=0, 1, 2,..., and a continuous spectrum. These
two behaviours derive from a particular fourth-order ordinary
differential equation that arises in the solution of the initial value
problem via an integral transform and describes the coupled fast-
and slow-magnetoatmospheric waves. The authors devote considerable
efforts to document how the discrete spectrum varies in response to
incremental changes in the horizontal wavenumber k and they compare
and contrast this behaviour with that found by Lamb for the same
atmosphere, but with the magnetic field being absent. Implications
for the helioseismology of sunspots are discussed.
---------------------------------------------------------
Title: A Search for large-scale Symmetries in the Emergence of
active Regions
Authors: Charbonneau, Paul; Bogdan, Thomas J.
1997SPD....28.0253C Altcode: 1997BAAS...29..902C
Recent models of the stability, destabilization and subsequent rise
of toroidal flux ropes stored immediately beneath the base of the
solar convective envelope indicate that the zonal order of the most
unstable mode is a function of storage latitude and magnetic field
strength. Taken at face value, this would suggest that large-scale
symmetries should be apparent in the distribution of longitudes of
emergence for active regions. We are using the Mt Wilson sunspot dataset
(coverage extending from 1917 to 1985) to establish observational
support (or lack thereof) for this conjecture. In this contribution
we discuss our method of analysis, and present preliminary results
for a few activity cycles.
---------------------------------------------------------
Title: Velocity and Magnetic Field Fluctuations in the Photosphere
of a Sunspot
Authors: Thomas, J. H.; Lites, B. W.; Bogdan, T. J.
1997SPD....28.0236T Altcode: 1997BAAS...29..899T
We use a data set of exceptionally high quality, obtained with
the HAO/NSO Advanced Stokes Polarimeter, to measure oscillations
of Doppler velocity, intensity, and the vector magnetic field at
photospheric heights in a sunspot. We find an upper limit of 4 G
(rms) for 5-min oscillations in magnetic field strength in the
umbra, based on the full Stokes inversion of the line profiles of
Fe I 6301.5 and 6302.5. This magnitude of the oscillation in field
strength is considerably lower than that found recently by Horn,
Staude, and Landgraf (1997). We show, on the basis of the eigenmodes
of oscillation in a simple theoretical model of the sunspot umbra,
that magnetic field variations of order 1 G are all that is to be
expected. Using measurements of velocity oscillations above the acoustic
cutoff frequency, we determine the relative heights of formation in
the umbra of four different photospheric spectral lines from the phase
differences between velocities in these lines, assuming the oscillations
propagate vertically at the local sound speed. In space-time maps of
fluctuations in continuum intensity, Doppler velocity, magnetic field
strength, and field inclination we see distinct features that migrate
radially inward from the inner penumbra all the way to the center of the
umbra. These moving features are probably a signature of the convective
interchange of magnetic flux tubes in the sunspot, although we failed
to find any strong correlation among the features in the different
quantities, indicating that these features have not been fully resolved.
---------------------------------------------------------
Title: The Seismology of Sunspots: A Comparison of Time-Distance
and Frequency-Wavenumber Methods
Authors: Bogdan, T. J.; Braun, D. C.; Lites, B. W.; Thomas, J. H.
1997SPD....28.0210B Altcode: 1997BAAS...29..894B
A pair of formulae are developed which relate the absorption coefficient
and partial wave phase-shift concepts of frequency-wavenumber local
helioseismology to the center- annulus cross correlation function
of time-distance helioseismology, under the general circumstances
that both induced and spontaneous sunspot oscillations may be
present. These formulae caution that real or spurious phase lags of
the umbral oscillation signal lead to differences in the incoming and
outgoing correlation times for sunspots, as first observed by Duvall
et al. (1996, Nature, 379, 430) and recently confirmed by Braun (1997,
ApJ, submitted). By using helioseismic data obtained by the GONG project
in conjunction with concurrent observations of Doppler velocities and
magnetic fields obtained by the HAO/NSO Advanced Stokes Polarimeter
for the October 1995 disk passage of active region NOAA 7912, we
demonstrate that the inferred GONG umbral oscillation signal actually
originates from the umbra-penumbra boundary some 6 Mm distant from the
center of the spot. Further, the ASP observations show that the 5-min
oscillations at the umbra-penumbra boundary lag those in the center of
the umbra by approximately 1 min, which is precisely the difference
between the incoming and outgoing cross correlation times for NOAA
7912 recently determined by Braun. The evidence suggests that p-mode
forcing of the spot results in the generation of upward propagating
slow MAG waves. These waves are responsible for the absorption of
the p-modes, and the dispersion in their travel times between the
subsurface layer where they are forced and the overlying level where
the Doppler signals originate leads to the observed phase lag between
the umbral and penumbral oscillations, and the corresponding correlation
time differences.
---------------------------------------------------------
Title: A Comment on the Relationship between the Modal and
Time-Distance Formulations of Local Helioseismology
Authors: Bogdan, T. J.
1997ApJ...477..475B Altcode:
The relationship between the time-distance and modal-decomposition
approaches to solar active region seismology is clarified through
the consideration of the oscillations of a plane-parallel, isentropic
polytrope. It is demonstrated by direct construction that a wave packet
formed through the superposition of neighboring p-modes interferes
constructively along a ray bundle that follows the appropriate WKBJ
ray path obtained by using the eikonal approximation. Because the
actual power envelope of the solar 5 minute oscillations restricts
the excited p-modes to rather low radial orders, the ray bundles are
diffuse and sample portions of the solar envelope that are some ~10-30
Mm distant from the nominal WKBJ ray path. This behavior is consistent
with the fact that the eikonal approximation becomes valid only in the
limiting case of large radial orders (n >> 1). The p-mode wave
packets that are isolated by employing the time-distance methods must
therefore be described either as a superposition of individual p-modes
(a wave packet), or as a sum of ray paths (a ray bundle), depending upon
which representation proves to be optimal for the given circumstances.
---------------------------------------------------------
Title: Absorption of p-Modes by Slender Magnetic Flux Tubes and
p-Mode Lifetimes
Authors: Bogdan, T. J.; Hindman, B. W.; Cally, P. S.; Charbonneau, P.
1996ApJ...465..406B Altcode:
The presence of a fibril magnetic field in the solar envelope not only
induces shifts in the p-mode resonant frequencies, but also contributes
to the line width of the modes. The augmentation of the line widths
results from two related physical processes: the excitation of tube
mode oscillations on the individual magnetic fibrils and the attendant
mode mixing between p-modes with identical oscillation frequencies. We
assay the magnitude of the contribution from the former physical
process based upon an idealized model consisting of vertical, slender,
magnetic flux tubes embedded in a plane-parallel isentropic polytrope
of index m. We restrict our attention to axisymmetric flux tubes
that are in mechanical and thermal equilibrium with their immediate
nonmagnetic surroundings. For low p-mode oscillation frequencies,
ω, this model predicts that the line width, F, varies as <P />Γ
∝ fωM<SUP>-½</SUP> ∝fω<SUP>m+2</SUP>, <P />where M the mode
mass, and f is the magnetic filling factor reckoned at the surface
of the polytrope. This scaling is in better overall agreement with
the observations (Γ ∝ ω<SUP>4.2</SUP>) than previous predictions
based on the excitation and damping of solar p-modes by turbulent
convection (which yields Γ ∝ γ<SUP>2</SUP> M<SUP>-1</SUP>
∝ω<SUP>2m+4</SUP>), or the scattering of p-modes by convective
eddies (which yields Γ ∝ ω<SUP>(4/3)m+3)</SUP>, and it suggests
that tube mode excitation on fibril magnetic fields may be a dominant
and detectable (through its solar cycle variation) component of the
low-frequency p-mode line widths.
---------------------------------------------------------
Title: The effect of p-modes on thin magnetic flux tubes
Authors: Hasan, S. S.; Bogdan, T. J.
1996BASI...24..125H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Time-Distance vs. Modal-Decomposition Formulations of Local
Helioseismology
Authors: Bogdan, T. J.
1996AAS...188.6912B Altcode: 1996BAAS...28R.937B
The relationship between the time-distance and modal-decomposition
approaches to solar active region seismology is clarified through
the consideration of the oscillations of a plane-parallel, isentropic
polytrope. It is demonstrated by direct construction that a wave packet
formed through the superposition of neighboring p-modes interferes
constructively along a ray bundle that basically follows the appropriate
WKBJ ray path obtained by using the eikonal approximation. Because
the ~ 10(7) solar p-modes populate k-omega ridges with only rather
modest radial orders, these ray bundles are rather diffuse and sample
portions of the solar envelope that are some ~ 10--30 Mm distant from
the nominal WKBJ ray path. This lack of localization along the ray
path for solar p-modes is consistent with the fact that the eikonal
approximation becomes valid only in the limiting case of large radial
orders (n >> 1). Thus the p-mode wave packets that are isolated by
employing the time-distance methods developed by Duvall et al (1993,
Nature, 362, 430) must be described either as a sum of individual
p-modes (a wave packet), or as a superposition of ray paths (a ray
bundle), depending upon which representation proves to be optimal for
the given circumstances.
---------------------------------------------------------
Title: Waves in Radiating Fluids
Authors: Bogdan, T. J.; Knoelker, M.; MacGregor, K. B.; Kim, E. -J.
1996ApJ...456..879B Altcode:
We derive from first principles the equations which govern the behavior
of small-amplitude fluctuations in a homogeneous and isotropic
radiating fluid. Products of the fluctuating quantities are shown
to obey a wave-energy conservation law from which it follows that
all perturbations must ultimately decay in time. Under fairly general
circumstances the governing equations may be solved through the use of
integral transforms which affords an accounting of the various wave
modes supported by the radiating fluid. In addition to the familiar
radiatively modified acoustic mode, the radiation-diffusion mode, the
radiative-relaxation mode, and the isotropization and exchange modes
which constitute the discrete spectrum of the differential equation,
we find a continuous spectrum of wave modes associated with the
"collisionless" nature of the photons on timescales short compared
to the photon lifetime. This continuous spectrum is eliminated
if an Eddington approximation is used to close the hierarchy of
equations that relate the fluctuating angular moments of the radiation
field. Quantitative results are obtained for the simple case in which
the opacity may be regarded as being independent of the frequency of
the photon and the source function may be approximated by the (local)
Planck function.
---------------------------------------------------------
Title: Jacket Modes: Solar Acoustic Oscillations Confined to Regions
Surrounding Sunspots and Plage
Authors: Bogdan, T. J.; Cally, P. S.
1995ApJ...453..919B Altcode:
It is demonstrated by the application of classical eigenfunction
expansion techniques that the interaction of an incident solar acoustic
oscillation, or p-mode, with a scattering obstacle-such as a sunspot
involves not only the scattering of the incident p-mode into other
p-modes of like frequency (mode mixing), but also the generation of an
acoustic halo localized like a "jacket" about the scatterer. This halo
oscillates at the same frequency as the incident p-mode and is composed
of a superposition of a continuous spectrum of modes referred to as
jacket modes. It is pointed out that these jacket modes should appear
as a broad enhancement to the background power underlying the p-mode
ridges in κ-ω diagrams for regions in close proximity to sunspots and
the boundaries of plage The basic results draw upon a remarkable analogy
between the oscillations of an adiabatically stratified plane-parallel
polytrope and the wave functions for the hydrogen atom: the laterally
propagating p-modes that participate in the mode mixing correspond
to the negative-energy bounds states of the hydrogen atom, while the
continuous spectrum of jacket modes corresponds to the continuum of
positive-energy states in which the electron is not bound to the proton.
---------------------------------------------------------
Title: Active Region Seismology
Authors: Bogdan, T. J.; Braun, D. C.
1995ESASP.376a..31B Altcode: 1995heli.conf...31B; 1995soho....1...31B
Active region seismology is concerned with the determination and
interpretation of the interaction of the solar acoustic oscillations
with near-surface target structures, such as magnetic flux
concentrations, sunspots, and plages. Observations with high spatial
resolution and long temporal duration have enabled the measurement
of the scattering matrix for sunspots and solar active regions as a
function of the mode properties (wavenumber, frequency and azimuthal
order). From this information one may determine the amount of p-mode
absorption, partial-wave phase shift, and mode mixing introduced by
the sunspot. In addition, the possibility of detecting the presence of
completely submerged magnetic fields has been raised and new procedures
for performing acoustic holography of the solar interior are being
developed. The accumulating evidence points to the mode conversion of
p-modes to various magneto-atmospheric waves within the magnetic flux
concentration as the unifying physical mechanism responsible for these
diverse phenomena.
---------------------------------------------------------
Title: Umbral Oscillations in Sunspots: Absorption of p-Modes and
Active Region Heating by Mode Conversion
Authors: Cally, P. S.; Bogdan, T. J.; Zweibel, E. G.
1994ApJ...437..505C Altcode:
The linear adiabatic oscillations of an infinite, stratified,
perfectly conducting atmosphere pervaded by a uniform vertical magnetic
field are computed. The stratification is chosen to approximate the
conditions appropriate for a sunspot umbra where strong reflection
of the fast magnetoacoustic-gravity waves from the rapid increase
of the Alfven speed with height and the sound speed with depth is
anticipated. Since the umbral oscillations are presumably excited by
external p-mode forcing, the angular frequency omega is prescribed --
being set by the p-modes -- and it is required to solve for the allowed
eigenvalues assumed by the horizontal wavenumber k and the corresponding
displacement eigenfunctions. We term these allowed solutions pi-modes
in recognition of the crucial influence of the imposed magnetic
field and to distinguish them from their p-mode cousins present in
the surrounding nonmagnetic quiet Sun. The wavenumber eigenvalues are
complex and are consistent with the spatial decay of the pi-modes inward
toward the center of the sunspot from the umbral boundary. This spatial
attenuation is a consequence of the slow magnetoacoustic-gravity waves
that propagate along the magnetic field lines and extract energy from
the trapped fast waves through mode coupling in the layers where the
sound and Alfven speeds are comparable. Through the consideration of
several ancillary computations we argue that this salient attribute
of the pi-modes may be essential both in explaining the observed
absorption of (the forcing) p-modes by sunspots and in providing a
source of mechanical energy for the overlying active regions. However,
more realistic calculations are clearly called for before these notions
may be confirmed.
---------------------------------------------------------
Title: Multiple Scattering and Resonant Absorption of p-Modes by
Fibril Sunspots
Authors: Keppens, R.; Bogdan, T. J.; Goossens, M.
1994ApJ...436..372K Altcode:
We investigate the scattering and absorption of sound waves by
bundles of magnetic flux tubes. The individual flux tubes within the
bundle have thin nonuniform boundary layers where the thermodynamic
and magnetic properties change continuously to their photospheric
levels. In these nonuniform layers, resonant absorption converts some
of the incident acoustic wave energy into heat and thus the flux-tube
bundle appears as a sink of acoustic power. For a fixed amount of
magnetic flux, we find that composite ('spaghetti') sunspots absorb
much more wave energy than their monolithic counterparts, although
both sunspots scatter comparable amounts of the incident acoustic wave
energy. The extra energy drainage results from the interplay of the
wave scattering back and forth between the tubes and the incremental
loss of acoustic power at each interaction with an individual tube due
to the resonant absorption in its boundary layer. The scattering cross
section is not similarly enhanced because the multiply scattered waves
generally interfere destructively in the far field. Another interesting
consequence of the lack of axisymmetry is that composite sunspots may
show acoustic emission for some multipole components, and absorption
for others. The net absorption cross section is however never negative,
and is nonzero only when the projection of the wave phase speed along
the flux-tube bundle is less than the maximal value of the Alfven
speed. Whereas composite sunspots composed of uniformly magnetized
flux tubes posses narrow scattering resonances, the analogous bundle
of nonuniform fibrils instead exhibits corresponding broad absorption
resonances, resulting from the incremental loss of power on successive
scatters. These broad absorption resonances correspond to leaky (MHD
radiating) eigenmodes of the composite structure. When progressively
more flux tubes are clustered, additional oscillation eigenmodes appear
grouped in a complicated band structure characterized by a (nearly)
common speed of propagation along the bundle.
---------------------------------------------------------
Title: Magneto-atmospheric waves subject to Newtonian cooling
Authors: Bunte, M.; Bogdan, T. J.
1994A&A...283..642B Altcode:
We present a new class of analytic solutions for linear
magneto-atmospheric waves in a stratified, isothermal atmosphere. This
new class spans from the solutions found by Yu (1965) for a constant
Alfven speed atmosphere to those of Nye & Thomas (1967 a,b) for an
atmosphere with exponentially increasing Alfven speed. The inclusion
of radiative dissipation in magneto-atmospheric wave problems - even
in the over-simplified Newtonian cooling approximation - is of great
importance in many applications. We show how the effects of Newtonian
cooling can be incorporated in any isothermal magneto-atmospheric
wave problem by letting the ratio of specific heats, gamma, be a
complex, frequency dependent quantity. This technique is discussed
in the context of the new solutions presented here. In particular, we
discuss its application to the case studied by Souffrin (1966, 1972)
and to the more general case of a constant Alfven speed atmosphere,
where now three, rather than two regions of mainly propagating modes
are found. In the case studied by Nye & Thomas, Newtonian cooling
leads to a fast temporal decay of the eigenmodes.
---------------------------------------------------------
Title: Sunspot seismology: using acoustic waves to probe sunspots
(Invited Review)
Authors: Bogdan, T. J.
1994smf..conf..229B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Modelling magnetoacoustic oscillations in sunspots: a
progress report
Authors: Charbonneau, P.; Cally, P. S.; Bogdan, T. J.
1994smf..conf..251C Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the Generation of Sound by Turbulent Convection. I. A
Numerical Experiment
Authors: Bogdan, Thomas J.; Cattaneo, Fausto; Malagoli, Andrea
1993ApJ...407..316B Altcode:
Motivated by the problem of the origin of the solar p-modes, we study
the generation of acoustic waves by turbulent convection. Our approach
uses the results of high-resolution 3D simulations as the experimental
basis for our investigation. The numerical experiment describes the
evolution of a horizontally periodic layer of vigorously convecting
fluid. The sound is measured by a procedure, based on a suitable
linearization of the equations of compressible convection that allows
the amplitude of the acoustic field to be determined. Through this
procedure we identify unambiguously some 400 acoustic modes. The
total energy of the acoustic field is found to be a fraction of a
percent of the kinetic energy of the convection. The amplitudes of the
observed modes depend weakly on (horizontal) wavenumber but strongly on
frequency. The line widths of the observed modes typically exceed the
natural linewidths of the modes as inferred from linear theory. This
broadening appears to be related to the (stochastic) interaction
between the modes and the underlying turbulence which causes abrupt,
episodic events during which the phase coherence of the modes is lost.
---------------------------------------------------------
Title: The Absorption of p-Modes by Sunspots: Variations with Degree
and Order
Authors: Bogdan, Thomas J.; Brown, Timothy M.; Lites, Bruce W.;
Thomas, John H.
1993ApJ...406..723B Altcode:
A spherical harmonic decomposition of the p-modes into inward and
outward propagating waves is employed to investigate the absorption
of solar p-modes by an isolated sunspot. The absorption coefficient
(averaged over frequency and azimuthal order) is found to increase
with increasing horizontal wavenumber k over the range 0-0.8/Mm. For
larger horizontal wavenumbers, in the range 0.8-1.5/Mm, the absorption
coefficient decreases with increasing k. The absorption along each
individual p-mode ridge tends to peak at an intermediate value of the
spherical harmonic degree in the range 200-400. The highest absorption
is found along the p(1) ridge, and the absorption decreases with
increasing radial order.
---------------------------------------------------------
Title: Solar p-Modes in a Vertical Magnetic Field: Trapped and Damped
pi -Modes
Authors: Cally, P. S.; Bogdan, T. J.
1993ApJ...402..721C Altcode:
The study addresses the question of whether the polytropic atmosphere
with an imposed uniform vertical magnetic field possesses normal
modes of oscillation despite the potential for the s-modes to drain
energy from the resonant cavity created by the favorable vertical
stratification. This question is answered in the affirmative via
direct numerical construction of these eigenfunctions for the complete
uniformly magnetized polytrope. The basic equilibrium atmosphere
is discussed, and the relevant linearized equations and boundary
conditions are provided. The properties of the trapped pi-modes are
considered. It is suggested that they play a role in the magnetized
sunspot atmosphere analogous to that played by the p-modes in the
unmagnetized surrounding quiet sun. Oscillations in sunspots and sunspot
seismology are reassessed in light of the discovery of the natural modes
of oscillation of unbounded atmospheres with vertical magnetic fields.
---------------------------------------------------------
Title: Evidence for Transonic Flows in the Solar Granulation
Authors: Nesis, A.; Bogdan, T. J.; Cattaneo, F.; Hanslmeier, A.;
Knoelker, M.; Malagoli, A.
1992ApJ...399L..99N Altcode:
High-resolution observations of the solar granulation are interpreted
in the light of recent numerical simulations of compressible
convection. The observations show a negative correlation between
the width of suitably chosen, nonmagnetic lines and the continuum
intensity. This result is consistent with a model of granular convection
where regions of supersonic horizontal flow form intermittently in
the vicinity of the downflow lanes. We conjecture that the observed
line broadening in the regions of low intensity is caused by enhanced
turbulent fluctuations generated by the passage of shock fronts bounding
the regions of supersonic motion.
---------------------------------------------------------
Title: Localized Sources of Propagating Acoustic Waves in the Solar
Photosphere
Authors: Brown, Timothy M.; Bogdan, Thomas J.; Lites, Bruce W.;
Thomas, John H.
1992ApJ...394L..65B Altcode:
A time series of Doppler measurements of the solar photosphere with
moderate spatial resolution is described which covers a portion of the
solar disk surrounding a small sunspot group. At temporal frequencies
above 5.5 mHz, the Doppler field probes the spatial and temporal
distribution of regions that emit acoustic energy. In the frequency
range between 5.5 and 7.5 mHz, inclusive, a small fraction of the
surface area emits a disproportionate amount of acoustic energy. The
regions with excess emission are characterized by a patchy structure
at spatial scales of a few arcseconds and by association (but not
exact co-location) with regions having substantial magnetic field
strength. These observations bear on the conjecture that most of the
acoustic energy driving solar p-modes is created in localized regions
occupying a small fraction of the solar surface area.
---------------------------------------------------------
Title: The Conversion of p-Modes to Slow Modes and the Absorption
of Acoustic Waves by Sunspots
Authors: Spruit, H. C.; Bogdan, T. J.
1992ApJ...391L.109S Altcode:
The study considers the possibility that the acoustic absorption by
sunspots and the surrounding plage, reported by Braun et al. (1988,
1990), is a consequence of the conversion of p-modes to slow modes
(s-modes) by the principally vertical magnetic fields within these
structures. It is found that for the f-mode, the absorption coefficient
increases monotonically from small to large horizontal wavenumbers, and,
along the nth p-mode ridge, this same general trend is modulated by
the presence of n localized absorption minima. These characteristic
signatures of acoustic absorption by p-mode/s-mode conversion
distinguish this mechanism from other competing processes and afford
the diagnostic possibility of determining the sunspot magnetic field
strength from the location in wavenumber of the predicted absorption
minima.
---------------------------------------------------------
Title: Flux tube sizes and temporal evolution
Authors: Bogdan, T. J.
1992AIPC..267....1B Altcode: 1992ecsa.work....1B
The present observational knowledge of the size distributions of
solar surface magnetic structures-sunspots, sunspot groups and active
regions-and their temporal evolution, is reviewed in the context of
how such information may provide important clues to the nature of
the solar dynamo and the underlying causes of solar variability. The
ability of such information to distinguish between the competing
theoretical mechanisms of flux tube fragmentation and coalescence is
briefly discussed.
---------------------------------------------------------
Title: Sunspot Seismology - the Interaction of a Sunspot with
Solar P-Modes
Authors: Bogdan, T. J.
1992ASIC..375..345B Altcode: 1992sto..work..345B
This article surveys developments in 'sunspot seismology' from the
decade following the original suggestion of Thomas et al. (1982) that
observations of solar acoustic oscillations in and about sunspots
could be used to probe the internal structure of the sunspot with
depth. Both the theoretical and observational components of sunspot
seismology are considered at length. A large part of this review is
devoted to a discussion of important sunspot seismology paradigms.
---------------------------------------------------------
Title: Multiple Scattering of Acoustic Waves by a Pair of Uniformly
Magnetized Flux Tubes
Authors: Bogdan, Thomas J.; Fox, David C.
1991ApJ...379..758B Altcode:
The interaction of an acoustic plane wave with a pair of uniformly
magnetized flux tubes of circular cross section is considered to
determine whether sunspot seismology can distinguish between the
competing monolithic flux-tube and spaghetti sunspot models. It
is shown that this interaction falls within one of three distinct
categories depending upon the separation of the magnetic flux tubes
and their individual scattering strengths. Estimates suggest that the
interaction of the solar acoustic oscillations with a spaghetti sunspot
will almost surely show coherent phasing of the scattered waves and
will probably exhibit multiple scattering effects.
---------------------------------------------------------
Title: Coupled quasi-linear wave damping and stochastic acceleration
of pickup ions in the solar wind
Authors: Bogdan, Thomas J.; Lee, Martin A.; Schneider, Peter
1991JGR....96..161B Altcode:
Coupled spatially homogeneous quasilinear kinetic equations are derived
which describe the evolution of the energetic ion omnidirectional
distribution function and the intensities of magnetohydrodynamic waves
propagating parallel and antiparallel to the ambient magnetic field. The
energetic ions are assumed to be nearly isotropic and possess speeds
much greater than the Alfvén speed. For application to pickup ions
the equations may also include an energetic ion injection rate and wave
excitation or damping caused by isotropization of the newborn ions. The
wave kinetic equations may be integrated to yield explicit expressions
for the wave intensities, which may be substituted into the ion kinetic
equations to yield a single self-consistent energy diffusion equation
for the energetic ions. The theory represents the first treatment of
stochastic (second-order Fermi) acceleration in which the back reaction
of the ions on the turbulence is included self-consistently. Numerical
solutions of the kinetic equations are presented for four cases of
pickup ions in the solar wind which illustrate the essential features of
the evolution: (1) interstellar pickup helium near a heliocentric radial
distance of 1 AU; (2) interstellar pickup hydrogen near 10 AU; (3) water
group pickup ions downstream of the bow wave of Comet Giacobini-Zinner
for parameters observed during the International Cometary Explorer
flyby; (4) water group pickup ions downstream of the bow wave of Comet
Halley for parameters observed during the Giotto flyby. <P />The helium
calculation reveals some modification of the solar wind wave spectrum
and energy diffusion of the ions; although adiabatic deceleration is
not included, acceleration rates are qualitatively consistent with
the observed spectrum at 1 AU (Möbius et al., 1985). The hydrogen
calculation shows extreme damping of the solar wind wave spectrum
in the cyclotron-resonant frequency range and a reduction in the
acceleration rate of most of the ions. It is suggested that this
behavior is responsible for an underabundance of hydrogen relative to
the minor ions in the anomalous cosmic ray component, which is thought
to originate from pickup ions accelerated at the solar wind termination
shock. Wave damping is small at comet G-Z, and the calculated energy
spectra do not appear to be in quantitative agreement with the observed
spectra (Richardson et al., 1987). At Comet Halley, on the other hand,
wave damping is substantial and the calculated spectra appear to be in
general agreement with the observations (McKenna-Lawlor et al., 1989).
---------------------------------------------------------
Title: Energetic Particle Acceleration in Spherically Symmetric
Accretion Flows: Importance of a Momentum-dependent Diffusion
Coefficient
Authors: Schneider, P.; Bogdan, T. J.
1989ApJ...347..496S Altcode:
We study the transport of suprathermal particles in steady spherical
accretion flows under the assumption that the flow velocity V(r) ∝ -
r<SUP>-α</SUP>, and that the spatial diffusion coefficient κ(r, p)
∝ r<SUP>β</SUP>p<SUP>γ</SUP>, can be expressed as power laws. We
derive the solution of the transport equation for arbitrary combinations
of the parameters (α, β, γ), thereby generalizing previous work on
this subject. In addition, a collisional loss term is also taken into
account. Two different boundary conditions are considered: either,
there is a monoenergetic injection of particles into the flow, or
there are no sources at finite radius, but the distribution function is
required to match smoothly onto a prescribed ambient energetic particle
population at infinity. We find that the parameter space (α, β, γ)
divides naturally into three regions that reflect the nature of the
particle transport in the vicinity of the singularity located at the
origin. If α + β &lt 1 then all injected particles are absorbed
by the singularity at the origin. If α + β > 1 and γ exceeds the
critical value y<SUB>*</SUB> = y<SUB>*</SUB>(α, β), then no particles
are absorbed by the origin. In the remainder of the parameter space
some fraction of the particles are advected into the origin and the
remainder escape to infinity. <P />The emergent particle flux is a
power law for large momenta, with the hardest spectra being obtained
for γ ∼ γ<SUB>*</SUB>. In contrast with the previously studied
Comptonization case where (in the nonrelativistic limit) γ = 0 and the
compression of the accretion flow amplifies the emergent luminosity
by only a small factor, drastic enhancements are possible when γ is
asymptotically equal to γ<SUB>*</SUB>. The possible implication of our
results for cosmic-ray acceleration in our Galaxy is briefly discussed.
---------------------------------------------------------
Title: On the Resonance Scattering of Sound by Slender Magnetic
Flux Tubes
Authors: Bogdan, T. J.
1989ApJ...345.1042B Altcode:
The impact of excited tube modes (resonances) on the acoustic
scattering properties of slender flux tubes, which is relevant to the
interaction of the solar five-minute oscillations with the thin intense
magnetic flux tubes that dot the solar surface, is theoretically
discussed. Quantitative examples are given which take into account
the influence of the finite size of the flux tube on the resonance
locations and widths. The practical implications of the theory for
observations are considered.
---------------------------------------------------------
Title: The Normal Modes of a Resonant Cavity Containing Discrete
Inhomogeneities: The Influence of Fibril Magnetic Fields on the
Solar Acoustic Oscillations
Authors: Bogdan, Thomas J.; Cattaneo, Fausto
1989ApJ...342..545B Altcode:
Motivated by considerations of the interaction between fibril magnetic
fields and solar p-modes, the acoustic spectrum of a cylindrical
cavity filled with ideal gas in which a number of magnetic flux
tubes are embedded is studied. A formalism, based on the T-matrix
approach to acoustic scattering, is developed which can be used to
determine the eigenfrequencies and eigenfunctions for any arbitrary
distribution of flux tubes. For weak scatterers, the frequency shifts
and velocity eigenfunctions are calculated using perturbation theory
for the cases of a single flux tube and a random distribution of up to
100 flux tubes. The results of this 'exact' approach are used to give
a critical appraisal of the predictions of theories based on some form
of averaging, such as the one discussed recently by Bogdan and Zweibel
(1987).
---------------------------------------------------------
Title: On the Interaction of the Solar Acoustic Oscillations with
Convection. I. Scattering of Sound by Steady Vorticity
Authors: Bogdan, T. J.
1989ApJ...339.1132B Altcode:
A general analytic solution is presented that describes the scattering
of sound of wavelength lambda and frequency omega, from a steady
laminar compact vortex of radius a and a uniform vorticity of 2
Omegas. There are no restrictions on the magnitude of the values of
a or Omega relative to those of lambda and omega. The generality of
this solution provides a complete picture of the steady state acoustic
scattering properties of an isolated cylindrical vortex column. Some
inferences are made for the scattering of p-modes by eddies in the
solar convection zone.
---------------------------------------------------------
Title: On the Progagation of Compressive Waves in a Radiating
Magnetized Fluid
Authors: Bogdan, T. J.; Knoelker, M.
1989ApJ...339..579B Altcode:
Using the Mihalas and Mihalas (1983) treatment of the radiation field,
the dispersion relation for linear compressive plane waves in a
homogeneous, unstratified, uniformly magnetized, radiating fluid has
been obtained. In the opticallly thick limit, the present relation
is shown to predict two weakly damped anisotropic radiation-modified
magnetoacoustic modes and a strongly damped radiation-diffusion
mode. The theory has been applied to the example of the interaction
of the solar acoustic oscillations with discrete photospheric magnetic
structures such as sunspots, pores, and knots.
---------------------------------------------------------
Title: Particle acceleration in spherically symmetric accretion flows.
Authors: Schneider, P.; Bogdan, T. J.
1989BAPS...34.1283S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Acoustic spectroscopy of solar magnetic flux concentrations.
Authors: Bogdan, T. J.
1989ftsa.conf..101B Altcode:
The discipline of acoustic spectroscopy of magnetic flux tubes
ultimately strives to answer the following two questions. (1) Given (at
best, incomplete) information about the incident and scattered p-modes
in the neighborhood of a magnetic flux concentration, what (if anything)
can be determined about the internal structure of the flux tube? (2)
Given the unavoidable uncertainties inherent in the measurements of the
incident and scattered acoustic waves, how accurately can the internal
structure of the flux tube be determined? Taken together, these two
questions define a canonical "inverse problem". It is well known that
success in solving inverse problems is invariably predicated upon a
good working knowledge of the related "forward problem". The author
summarizes the progress that has been made in this area and indicates
classes of problems where immediate progress can be achieved.
---------------------------------------------------------
Title: On the radiative damping of p-modes in solar magnetic flux
concentrations.
Authors: Knoelker, M.; Bogdan, T. J.
1988ESASP.286..265K Altcode: 1988ssls.rept..265K
In a generalization of a work by Mihalas and Mihalas (1983) describing
the propagation of compressive disturbances in a radiating fluid,
the authors include the dynamical influence of a uniform magnetic
field. The radiating fluid is treated to be gray, in LTE and assumed
to obey the Eddington approximation. The authors apply these results
to the interaction of solar p-modes with sunspots in the context of
a simple model developed by Abdelatif and Thomas (1987). For physical
conditions representative of the solar envelope and for a variety of
embedded magnetic structures, the temperature fluctuations associated
with compressive waves are reduced inside the magnetic regions. Hence,
radiative damping of these disturbances is suppressed to an extent that
depends upon the nature of the mode (fast or slow magnetoacoustic)
and the propagation direction relative to the uniform background
field. This conclusion raises some interesting predictions concerning
the observational signatures of compressive waves in the solar envelope.
---------------------------------------------------------
Title: Distribution of Sunspot Umbral Areas: 1917--1982
Authors: Bogdan, T. J.; Gilman, Peter A.; Lerche, I.; Howard, Robert
1988ApJ...327..451B Altcode:
Over 24,000 measurements of individual sunspot umbral areas taken from
the Mount Wilson white-light plate collection covering the period
1917-1982 are used to determine the relative size distribution
of sunspot umbras. In the range 1.5-141 millionths of a solar
hemisphere, the sunspot umbral areas are found to be distributed
lognormally. Moreover, the same distribution is obtained for all phases
of the solar cycle (maximum, minimum, ascending, descending), as well
as for various individual cycles, between 1917 and 1982. Both the mean
and the geometric logarithmic standard deviation of this distribution
appear to be intrinsically constant over the entire data set; only
the number of spots exhibits the familiar solar cycle variations. If
the observed lognormal umbral size distribution is not a particular
attribute of the sunspot umbras but is instead of a more fundamental
property of emerging magnetic flux, then the data would predict a
maximum in the size spectrum of photospheric magnetic structures
for flux tubes with radii in the range 500-800 km. The absence of
solar cycle variations in the relative distribution of umbral areas
and especially the lognormal character of this distribution may both
argue for the fragmentation of magnetic elements in the solar envelope.
---------------------------------------------------------
Title: First-order Fermi acceleration in the two-stream limit
Authors: Bogdan, T. J.; Webb, G. M.
1987MNRAS.229...41B Altcode:
A study of the first-order Fermi mechanism for accelerating cosmic-rays
at relativistic and nonrelativistic shocks is carried out by using
the two-stream approximation. Exact steady-state analytic solutions
illustrating the shock acceleration process in the test-particle limit
in which monoenergetic (relativistic) seed particles enter the shock
through an upstream free-escape boundary are obtained. The momentum
spectrum of the shock accelerated particles consists of a series
of Dirac delta distributions corresponding to particles that have
undergone an integral number of acceleration cycles. Since particles
in the model have a finite fixed escape probability from the shock and
the particle momenta p are equally spaced in log p, the envelope of the
delta functions series is a power law in momentum. The solutions are
used to discuss time-dependent aspects of the shock acceleration process
in terms of the finite cycle time, escape probability, and momentum
change per cycle that can be deduced from the steady-state model. The
length-scale over which the accelerated particles extend upstream of
the shock is shown to depend upon the particle energy, with the higher
energy particles extending further upstream. This effect is shown to
be intimately related to the kinematic threshold requirement that the
particle speed exceed the fluid speed in order for particles to swim
upstream of the shock and participate in the shock acceleration process.
---------------------------------------------------------
Title: Energetic Particle Acceleration in Spherically Symmetric
Accretion Flows and Shocks
Authors: Webb, G. M.; Bogdan, T. J.
1987ApJ...320..683W Altcode:
Steady state, spherically symmetric solutions of the cosmic-ray
transport equation describing the acceleration of energetic particles in
galactic accretion flows onto neutron stars, black holes, white dwarfs,
and protostars are studied. The results indicate that astrophysical
accretion flows can be partitioned into distinct classes depending
upon whether the accretion rate lies above or below a critical value
of a few times 10 to the -7th stellar masses/yr. When the particle
transport is convection-dominated, both classes of accretion flows
exhibit a spectral index appropriate for first-order Fermi acceleration
at a plane shock in the absence of losses. As the particle transport
becomes diffusion-dominated, both classes show a break and precipitous
falloff in the particle spectrum due to the escape of these particles
from the accretion flow. The precise nature of the spectrum depends
on the relationship between the particle momentum and the spatial
diffusion coefficient.
---------------------------------------------------------
Title: Propagation of Compressive Waves through Fibril Magnetic
Fields. III. Waves that Propagate along the Magnetic Field
Authors: Bogdan, T. J.
1987ApJ...318..896B Altcode:
An isothermal fibril magnetic field composed of a uniform distribution
of parallel magnetic flux tubes embedded in an unmagnetized fluid
is shown to support compressive modes that propagate along the flux
tube axes with phase velocities below the sound speed. These modes
are simply the familiar tube waves of a single isolated magnetic flux
tube that are modified by the presence of the many individual flux
tubes that constitute the fibril magnetic field. This modification is
worked out for an ensemble of randomly placed parallel magnetic flux
tubes distributed uniformly throughout all space. The net effect is to
reduce the phase velocity to a value below that of a single isolated
flux tube. These modes derive their existence from the presence of
the many interfaces that separate the magnetic and nonmagnetic media,
and are obviously absent in a uniformly magnetized medium that is free
of inhomogeneities. It is suggested that observations of oscillation
spectra at the solar surface may provide an important indirect direction
of unresolved magnetic fibrils in active regions and plage on the Sun.
---------------------------------------------------------
Title: Propagation of Compressive Waves through Fibril Magnetic
Fields. II. Scattering from a Slab of Magnetic Flux Tubes
Authors: Bogdan, T. J.
1987ApJ...318..888B Altcode:
The reflection/transmission of an acoustic plane wave from/through a
slab of parallel, randomly distributed, magnetic flux tubes is worked
out in the long wavelength (thin flux tube) limit. These results are
then contrasted with the reflection/transmission problem for (i) a
uniformly magnetized homogeneous slab and (ii) an infinite half-space
of parallel, randomly distributed, flux tubes. A thin slab of magnetic
fibrils possesses properties that are qualitatively similar to those
of the uniformly magnetized slab. The slab of magnetic fibrils does
not, however, exhibit the total reflection or complete transmission
of the incident wave that are possible for the uniformly magnetized
slab. A thick slab of magnetic fibrils behaves more nearly like the
infinite half-space of fibrils: the amplitude of the reflected wave is
more-or-less independent of the width of the slab, and the amplitude
of the transmitted wave is vanishingly small. The distinction between
thin and thick slabs of randomly placed fibrils depends critically upon
the properties of the composite magnetic medium the magnetic volume
filling factor and the mean flux tube separation and the wavelength
of the incident acoustic plane wave.
---------------------------------------------------------
Title: Distribution of Sunspot Umbral Areas: 1917-1982
Authors: Bogdan, T. J.; Gilman, P. A.; Lerche, I.; Howard, R.
1987BAAS...19..924B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Cosmic-ray acceleration in accretion flows and shocks.
Authors: Webb, G. M.; Bogdan, T. J.
1987ICRC....2..195W Altcode: 1987ICRC...20b.195W; 1987ICRC....2..195B
Steady state spherically symmetric solutions of the cosmic-ray transport
equation describing the acceleration of cosmic-rays in accretion flows
are studied.
---------------------------------------------------------
Title: Propagation of Compressive Waves through Fibril Magnetic Fields
Authors: Bogdan, T. J.; Zweibel, Ellen G.
1987ApJ...312..444B Altcode:
The surface effects of interactions between the solar 5-min p-modes and
the large-scale fibril magnetic field are discussed using a multiple
scattering approach. Attention is given to the propagation of linear
disturbances in a two-dimensional, highly conducting magnetized
plasma with many parallel flux tubes in pressure equilibrium with a
surrounding stationary field-free plasma. Multiple scattering in the
fibril half-space is shown to generate acoustic waves that cascade to
ever-smaller length scales. The scale reduction, proportional to the
depth into the fibril magnetic field, is responsible for the damping
of p-mode oscillations observed in plages.
---------------------------------------------------------
Title: Three-dimensional magnetostatic models of the large-scale
corona.
Authors: Bogdan, T. J.; Low, B. C.
1986NASCP2442..275B Altcode: 1986copp.nasa..275B
A special class of magnetostatic equilibria is described, which are
mathematically simple and yet sufficiently versatile so as to fit any
arbitrary normal magnetic flux prescribed at the photosphere. With
these solutions, the corona can be modeled with precisely the same
mathematically simple procedure as has previously been done with
potential fields. The magnetostatic model predicts, in addition to the
coronal magnetic field, the three dimensional coronal density which
can be compared with coronagraph observations.
---------------------------------------------------------
Title: On the formation of active region prominences (Hα filaments).
Authors: Rompolt, Bogdan; Bogdan, Thomas
1986NASCP2442...81R Altcode: 1986copp.nasa...81R
Analysis of sequential Hα images of active region prominence formation
suggests that simple large-scale photospheric mass-motions may play
a key role in the formation of these long, thin, Hα filaments.
---------------------------------------------------------
Title: Effects of Fibril Magnetic Fields on Solar
p-Modes. II. Calculation of Mode Frequency Shifts
Authors: Zweibel, E. G.; Bogdan, T. J.
1986ApJ...308..401Z Altcode:
The influence of magnetic flux tubes embedded in the solar convection
zone on the observed p-mode oscillation frequencies are estimated
by WKB ray tracing in a model of the solar interior. For randomly
distributed but parallel magnetic fibrils with radii small compared
to the wavelength of the mode, a local correction to the acoustic
dispersion relation can be calculated exactly. The results show that
if the observed photospheric flux remains vertically oriented deep into
the convection zone, then only modes which are confined to within 0.5%
R_sun; of the solar surface are shifted in frequency by as much as 0.1%.
---------------------------------------------------------
Title: The Three-dimensional Structure of Magnetostatic
Atmospheres. II. Modeling the Large-Scale Corona
Authors: Bogdan, T. J.; Low, B. C.
1986ApJ...306..271B Altcode:
Employing the formalism developed in the first paper in this series,
a class of magnetostatic atmospheres is constructed in a 1/r-squared
gravity. These solutions possess electric current densities distributed
continuously in space and directed perpendicular to the gravitational
force. A self-consistent treatment of the energy balance equation is
omitted, but the problem is treated in fully three-dimensional geometry,
allowing for an arbitrary prescription of the normal magnetic flux at
some fixed spherical surface. The prospects of modeling real coronal
structures in approximate magnetostatic equilibrium with observational
inputs from magnetographs and coronographs will be evident from the
illustrative examples presented.
---------------------------------------------------------
Title: Magnetohydrodynamic Stability of an Axisymmetric, Line-tied,
Diamagnetic Plasmoid Embedded in a Uniform Magnetic Field: Erratum
Authors: Bogdan, T. J.
1986ApJ...305..954B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The determination of coronal potential magnetic fields using
line-of-sight boundary conditions
Authors: Bogdan, T. J.
1986SoPh..103..311B Altcode:
Previous efforts to construct solar coronal fields using surface
magnetograph data have generally employed a least squares minimization
technique in order to determine the spherical harmonic expansion
coefficients of the magnetic scalar potential. Provided there is
no source surface high up in the corona, we show that knowledge
of the line-of-sight component of the surface magnetic field,
B<SUB>i</SUB> = B<SUB>r</SUB> sin θ + B<SUB>θ</SUB> cos θ, is
sufficient to uniquely determine the potential coronal magnetic field
by an explicit construction of the magnetic scalar potential for an
arbitrary B<SUB>l</SUB>(θ, φ).
---------------------------------------------------------
Title: Diffusive transport and in situ coalescence of magnetic flux
tubes. I - Steady state solutions
Authors: Bogdan, T. J.
1985ApJ...299..510B Altcode:
There is increasing evidence of fibril character in astrophysical
magnetic fields. The solar photosphere is an obvious example. The author
suggests that the hierarchy of magnetic structures observed in the
photosphere may be synthesized through the coalescence of the thin (R
≈ 2 - 3×10<SUP>2</SUP>km), intense (B ≈ 1-2×10<SUP>3</SUP>gauss)
magnetic fibrils seen to be threading the solar surface. Indeed,
the distribution of magnetic flux tube sizes in a large-scale fibril
magnetic field is likely to result from the interplay between flux
coalescence and fragmentation. To illustrate this point, the author
considers the diffusion, and in situ coalescence, of parallel twisted
magnetic flux tubes through a slab. The present paper concentrates on
steady state solutions for the diffusive transport.
---------------------------------------------------------
Title: Effect of a fibril magnetic field on solar p-modes
Authors: Bogdan, T. J.; Zweibel, E. G.
1985ApJ...298..867B Altcode:
The dispersion relation is obtained for acoustic plane waves that
scatter coherently from an ensemble of parallel magnetic flux tubes
when the wave vector is perpendicular to the flux-tube axis. When the
magnetic flux tubes are distributed uniformly and possess radii that
are small compared with the wavelength, the frequency can be calculated
exactly. The waves are damped slightly due to a loss of coherence and
are shifted downward or upward in frequency relative to a medium devoid
of magnetic fibrils, depending primarily on whether the flux tubes are
more or less dense than their surroundings. It is suggested that the
influence of the fibril magnetic fields observed at the solar surface
cannot be ignored in the interpretation of high-1 surface p-mode data.
---------------------------------------------------------
Title: Dynamical evolution of large-scale, two-dimensional, fibril
magnetic fields
Authors: Bogdan, T. J.; Lerche, I.
1985ApJ...296..719B Altcode:
The dynamical behavior of a large-scale, two-dimensional, fibril
magnetic field embedded in an ideal fluid of infinite electrical
conductivity is considered. The field is treated statistically as
a dilute gas composed of parallel, twisted, magnetic flux tubes in
specified velocity and gravitational fields. The salient physical
processes are the annihilation/coalescence of flux tubes through binary
collisions and flux-tube precipitation, diffusion, and advection caused
by their motions. The purpose is to study the size distribution,
temporal, and latitudinal variations of emerging solar flux with a
fibril magnetic field throughout the solar convection zone. The analysis
suggests that the transport and in situ coalescence/annihilation of
magnetic flux tubes through the solar convection zone may be responsible
for the size spectrum, temporal, and latitudinal variations observed
in the emerging magnetic flux during the solar cycle. Such a scenario
is consistent with the previous works of Speigel and Weiss (1980), and
Schmitt and Rosner (1984), which suggest that solar toroidal fields are
produced near the base of the convection zone and are shredded into
thin magnetic fibrils through a doubly diffusive magnetic buoyancy
instability.
---------------------------------------------------------
Title: Onion-Shell Model of Cosmic Ray Electrons and Radio Synchrotron
Emission in Supernova Remants
Authors: Beck, R.; Drury, L. O.; Voelk, H. J.; Bogdan, T. J.
1985ICRC....3..140B Altcode: 1985ICRC...19c.140B
The spectrum of cosmic ray electrons, accelerated in the shock front
of a supernova remnant (SNR), is calculated in the test-particle
approximation using an onion-shell model. Particle diffusion within the
evolving remnant is explicity taken into account. The particle spectrum
becomes steeper with increasing radius as well as SNR age. Simple
models of the magnetic field distribution allow a prediction of the
intensity and spectrum of radio synchrotron emission and their radial
variation. The agreement with existing observations is satisfactory
in several SNR's but fails in other cases. Radiative cooling may
be an important effect, especially in SNR's exploding in a dense
interstellar medium.
---------------------------------------------------------
Title: Diffusive Electron Acceleration at SNR Shock Fronts and the
Observed SNR Radio Spectral Indices
Authors: Bogdan, T. J.; Lee, M. A.; Lerche, I.; Webb, G. M.
1985ICRC....3..144B Altcode: 1985ICRC...19c.144B
No abstract at ADS
---------------------------------------------------------
Title: Stochastic Particle Acceleration in Flaring Stars
Authors: Bogdan, T. J.; Schlickeiser, R.
1985ICRC....3..250B Altcode: 1985ICRC...19c.250B
The acceleration of electrons by the Fermi-Parker mechanisms in a
quasistationary turbulent plasma of dimension l, mean magnetic field
strength B, and mean number density n are considered. The electrons
suffer radiative and ionization losses and have a scattering mean free
path that increases linearly with their momentum. Analytic solutions
for the steady-state electron energy spectra are presented. The spectra
are characterized by an exponential cutoff above a given momentum
determined by the synchrontron or the confinement time, depending on
the physical characteristics of the accelerating region.
---------------------------------------------------------
Title: Diffusive electron acceleration at SNR shock fronts and the
observed SNR radio spectral indices
Authors: Bogdan, T. J.; Lee, M. A.; Lerche, I.; Webb, G. M.
1985ICRC....9..543B Altcode: 1985ICRC...19i.543B
The radio synchrotron emission from relativistic electrons in shell
supernova remnants (SNRs) provides a unique opportunity to probe
the energy distribution of energetic electrons at their acceleration
site (SNR shock fronts). This information provides insight into the
acceleration mechanism(s). Here the authors discuss the implications of
these observations for the diffusive (first-order Fermi) acceleration
of electrons at the SNR shock fronts.
---------------------------------------------------------
Title: Momentum-dependent diffusive particle acceleration in modified
shock fronts
Authors: Webb, G. M.; Bogdan, T. J.; Lee, M. A.; Lerche, I.
1985MNRAS.215..341W Altcode:
In the presently derived analytic solutions of the steady transport
equation for diffusive particle acceleration in a modified, planar shock
front having free escape boundaries, the fluid velocity profile through
the shock transition decreases monotonically between the upstream
and downstream boundaries. The spatial diffusion coefficient's spatial
dependence is linked to that of the fluid velocity profile. Attention is
given to the solution corresponding to monoenergetic particle injection
at the shock front, with free particle escape at finite distances
both upstream and downstream of the shock. The accelerated particle
spectrum is dominated at high energies by an exponential cutoff,
due to the competition between acceleration by the first-order Fermi
mechanism and particle loss through the free escape boundaries.
---------------------------------------------------------
Title: Stochastic Electron Acceleration in Stellar Coronae
Authors: Bogdan, T. J.; Schlickeiser, R.
1985ASSL..116...33B Altcode: 1985rst..conf...33B
When coupled with a realistic acceleration model, the radiative
signature of flare events in late-type stars is capable of giving
additional, and more accurate, information concerning the nature of
the accelerating regions than when the radiative signature is used
alone. Here the authors consider the second-order Fermi, or stochastic
acceleration mechanism.
---------------------------------------------------------
Title: Three-dimensional magnetostatic models of coronal structures.
Authors: Bogdan, T. J.; Low, B. C.
1985BAAS...17Q.632B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Magnetohydrodynamic Stability of an Axisymmetric, Line-tied,
Diamagnetic Plasmoid Embedded in a Uniform Magnetic Field
Authors: Bogdan, T. J.
1985ApJ...288..672B Altcode:
The stability of a line-tied, axisymmetric, hemispherical plasmoid
embedded in a uniform magnetic field is investigated by using the
MHD energy principle (Bernstein et al., 1958). The equilibrium
configuration studied resembles the magnetic field topology of an
isolated sunspot or of a newly emerged region of magnetic flux in
the solar photosphere, and provides insight into the properties of
these features. This analysis extends previous work on the ideal MHD
stability of equilibrium structures with an axis of translational
symmetry to include structures with only an axis of rotational symmetry.
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Title: Diffusive shock acceleration in modified shocks
Authors: Bogdan, T. J.; Lerche, I.
1985MNRAS.212..413B Altcode:
The authors investigate the effects of shock substructure on the
diffusive shock acceleration of energetic particles by solving the
steady-state transport equation for a unidirectional, inhomogeneous,
flow through a stationary shock front, in the test-particle
approximation. Far downstream from the shock front, the accelerated
particle distribution function is a power law at high momentum. The
spectral index is a smoothly varying function of the ratio l/λ,
where l is the length scale of the shock substructure, and λ is the
accelerated particle scattering mean free path. Possible application to
the non-linear (accelerated particle back reaction) diffusive shock
acceleration problem, and implications for particle (cosmic ray)
acceleration in radiating shocks are briefly discussed.
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Title: Propagation of axisymmetric disturbances on a twisted magnetic
flux tube
Authors: Bogdan, T. J.
1984ApJ...282..769B Altcode:
The propagation of axisymmetric disturbances on a twisted magnetic
flux tube in an inviscid, incompressible, unstratified atmosphere of
infinite electrical conductivity is considered. Dispersion effects
due to twist appear quickly only on highly twisted flux tubes for a
superposition of the lowest radial eigenmodes and wavelengths comparable
to the flux tube radius. These radial profiles become distorted and
show focusing effects after propagating on the order of ten flux tube
radii. This suggests twist effects on hydromagnetic wave propagation
may be important where the flux tubes come up through the surface and
expand into the tenuous atmosphere.
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Title: The turbulent twisted magnetic flux tube gas
Authors: Bogdan, T. J.
1984PhFl...27..994B Altcode:
The kinematic behavior of a dilute, two-dimensional 'gas' of
parallel twisted magnetic flux tubes in a highly conducting fluid is
considered. Collisions between flux tubes with the same sense of twist
are inelastic due to the reconnection of their oppositely directed
azimuthal magnetic field components at impact. In some collisions,
the tension in the reconnected magnetic flux is sufficient to bind
the two flux tubes together. Collisions between flux tubes with the
opposite sense of twist are elastic. It is shown that a tenuous gas of
individual twisted flux tubes condenses into two large-scale regions
of magnetic field with opposite twists. This calculation illustrates
the results of Montgomery and co-workers on the migration of magnetic
energy towards small wavenumbers in two-dimensional magnetohydrodynamic
(MHD) turbulence. In particular, this problem illustrates the dynamical
nonequilibrium of the relaxation phase in turbulent MHD systems.
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Title: Onion-Shell Model of Cosmic Ray Acceleration in Supernova
Remnants
Authors: Bogdan, T. J.; Volk, H. J.
1983ICRC....2..305B Altcode: 1983ICRC...18b.305B
No abstract at ADS
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Title: Onion-shell model of cosmic ray acceleration in supernova
remnants
Authors: Bogdan, T. J.; Volk, H. J.
1983A&A...122..129B Altcode:
A method is devised to approximate the spatially averaged momentum
distribution function for the accelerated particles at the end of
the active lifetime of a supernova remnant. The authors confine
themselves to the test particle approximation and oversimplify
adiabatic losses, but include unsteady shock motion, evolving shock
strength, and non-uniform gas flow effects on the accelerated particle
spectrum. Monoenergetic (T<SUB>0</SUB> = 1 keV) protons are injected at
the shock front. It is found that the dominant effect on the resultant
accelerated particle spectrum is a changing spectral index with
shock strength. High energy particles are produced in early phases,
and the resultant distribution function is a slowly varying power
law αT<SUP>-μ</SUP>, (T = kinetic energy), 2.1 ≤ μ ≤ 2.3 over
several orders of magnitude, independent of the specific details of
the supernova remnant.
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Title: One-dimensional periodic flows with a shock transition -
Application to the density wave theory of spiral structure
Authors: Bogdan, T. J.
1983ApJ...267..109B Altcode:
The problem of one-dimensional gas flow through a sinusoidal
gravitational potential with a series of equally spaced shock fronts
is considered. For time-independent and spatially periodic flows,
an integral equation relates the flow velocity to the gravitational
potential and source functions of energy and momentum densities. It is
suggested that this problem simulates some of the dynamical effects of
the azimuthal flow on a parcel of gas at a fixed radius in a galactic
disk that supports a spiral density wave structure. It omits the radial
motions. In this context, a typical azimuthal velocity across a spiral
arm is specified and the resultant source functions are obtained. The
implications of this calculation suggest heating of the gaseous disk by
O and B stars behind the shock front, and subsequent interarm cooling
is a plausible mechanism for maintaining the periodic cycling of the
gaseous component of the galactic disk.
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Title: Magnetic monopoles and the survival of galactic magnetic fields
Authors: Turner, Michael S.; Parker, E. N.; Bogdan, T. J.
1982PhRvD..26.1296T Altcode:
The most stringent, mass-independent limit on the flux of magnetic
monopoles is based upon the survival of the galactic magnetic
fields, the so-called "Parker limit": F<~10<SUP>-16</SUP>
cm<SUP>-2</SUP>sr<SUP>-1</SUP>sec<SUP>-1</SUP>. We reexamine this limit,
taking into account the monopole's mass and velocity distribution,
and the observed structure of the galactic magnetic field. We derive
flux limits which depend upon the monopole's mass and velocity,
and the strength, coherence length, and regeneration time of the
galactic magnetic field. The largest monopole flux consistent with
both the survival of the galactic magnetic field and the bounds from
the mass density contributed by monopoles is F~=10<SUP>-12</SUP>
cm<SUP>-2</SUP>sr<SUP>-1</SUP>sec<SUP>-1</SUP>, arising for monopoles
of mass ~= 10<SUP>19</SUP> GeV with velocity ~=3×10<SUP>-3</SUP>c
which cluster with the Galaxy. An observed flux greater than this
would have profound implications for our understanding of the galactic
magnetic field, and we briefly explore some exotic possibilities. Of
course, this bound is not applicable to a local source (e.g., the Sun,
atmospheric cosmic-ray production, etc.).
