wolff

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Author name code: wolff
ADS astronomy entries on 2022-09-14
author:"Wolff, Charles. L."

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Title: Building the Foundation for Field Research | Interactive Online
Training in Instrumentation and Measurement of Atmospheric Parameters
Authors: Rockwell, A.; Clark, R. D.; Page, E. M.; Stevermer, A.;
Bol, A.; Campos, T. L.; Cooper, W. A.; Haggerty, J. A.; Wolff, C.;
Voemel, H.
2020AGUFMSY0020002R Altcode:
A series of ten online learning modules on topics related to
instrumentation and measurement of atmospheric parameters are
now published through a collaborative effort between the National
Center for Atmospheric Research Earth Observing Laboratory, The
COMET Program, and Millersville University. These open-source,
interactive, multimedia educational modules are positioned to enhance
traditional pedagogies and supplement blended instruction on topics
such as instrument types, measurement techniques, site selection, and
measurement uncertainty. The target audience includes early graduate
students and upper-level undergraduates in atmospheric and related
sciences fields, but the content is extensible to other disciplines
where treatment of these topics is relevant. Foundations of
Meteorological Instrumentation and Measurements Meteorological
Instrument Performance Characteristics Instrumentation and
Measurement of Atmospheric Temperature Instrumentation and
Measurement of Atmospheric Pressure Instrumentation and Measurement
of Atmospheric Humidity Instrumentation and Measurement of
Surface Precipitation Instrumentation and Measurement of Wind
Instrumentation and Measurement of Atmospheric Trace Gases
Instrumentation and Measurement of Atmospheric Radiation Instrumentation and Measurement of Clouds and Airborne Particles
The content of these modules is of the highest caliber as it
has been developed by subject matter experts who are scientists and
engineers at the forefront of the field of observational science. It
is expected that this effort will fulfill the expressed need for
contemporary, interactive, multimedia guided education and training
modules integrating the latest instructional design and assessment
tools in observational science. Thousands of undergraduate and graduate
students will benefit, while course instructors will value a set
of high-quality lessons to use as supplements in their courses. For
schools that may lack the resources to stage a field project or offer
laboratory-based instrument/measurement experiences, the modules
can fill the void and serve as an alternative to observational and
laboratory research training.

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Title: Solar Irradiance Variability, Influenced by r Modes
Authors: Wolff, Charles L.
2019ApJ...870...20W Altcode:
A spectrum of the four-decade solar irradiance record has a prominent
cluster of power for periodicities near 1 yr. Correlating irradiance
with a bandpass filter showed that periodicity values were not constant,
but varied sinusoidally with each cycle lasting 14 ± 1 yr. The large
modulation amplitude makes solar frequencies ≥1 yr-1
hard to detect at the solar surface. After removing the modulation,
a Lomb-Scargle spectrum exposed two true periodicities: 1.006 and
0.920 yr. They are interpreted as the synodic rotation periods of r
modes of lowest angular degree (ℓ = 1). The first propagates in the
stable interior and the second in the convective envelope perturbed by
its several flow fields. The rotational beat period of the two modes is
about 10.9 yr. This is close to the average length of a solar cycle and
possibly controls this average. The 1.006 yr periodicity dominates most
of the filtered irradiance record but an abrupt change to about 0.8 yr
occurs in mid-2010. Also found was evidence for higher-degree r modes
(ℓ = 2 to 8) and a curious sawtooth modulation with a recurrence
period of 2.6 yr.

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Title: Are Pulsing Solitary Waves Running inside the Sun?
Authors: Wolff, Charles L.
2012ApJ...756..125W Altcode:
A precise sequence of frequencies—detected four independent ways—is
interpreted as a system of solitary waves below the Sun's convective
envelope. Six future observational or theoretical tests of this idea are
suggested. Wave properties (rotation rates, radial energy distribution,
nuclear excitation strength) follow from conventional dynamics of
global oscillation modes after assuming a localized nuclear term strong
enough to perturb and hold mode longitudes into alignments that form
"families." To facilitate future tests, more details are derived
for a system of two dozen solitary waves 2 &lt;= l &lt;= 25. Wave
excitation by 3He and 14C burning is complex. It
spikes by factors M 1 &lt;= 103 when many waves
overlap in longitude but its long-time average is M 2 &lt;=
10. Including mixing can raise overall excitation to ~50 times that
in a standard solar model. These spikes cause tiny phase shifts that
tend to pull wave rotation rates toward their ideal values vprop[l(l +
1)]-1. A system like this would generate some extra nuclear
energy in two spots at low latitude on opposite sides of the Sun. Each
covers about 20° of longitude. Above a certain wave amplitude,
the system starts giving distinctly more nuclear excitation to some
waves (e.g., l = 9, 14, and 20) than to neighboring l values. The
prominence of l = 20 has already been reported. This transition begins
at temperature amplitudes ΔT/T = 0.03 in the solar core for a typical
family of modes, which corresponds to δT/T ~ 0.001 for one of its
many component oscillation modes.

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Title: Astrocaching as an Outreach Tool for Schools
Authors: Khalisi, E.; Wolff, C.
2011epsc.conf..957K Altcode: 2011DPS....43..957K
We tried a scavenger hunt as an outreach tool to inspire 10-13 aged
pupils for astronomical issues. The game was inherited from the
"Geocaching" activities which employ GPS or other mobile devices to
hide and seek repositories anywhere in the world. We altered the rules
such that the itinerary was based on astronomical instructions, and the
repositories contained related items. The realization was successful,
however, some difficulties arose in the specification required from
the young students.

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Title: A New Way that Planets Can Affect the Sun
Authors: Wolff, Charles L.; Patrone, Paul N.
2010SoPh..266..227W Altcode: 2010SoPh..tmp..166W
We derive a perturbation inside a rotating star that occurs when
the star is accelerated by orbiting bodies. If a fluid element has
rotational and orbital components of angular momentum with respect to
the inertially fixed point of a planetary system that are of opposite
sign, then the element may have potential energy that could be released
by a suitable flow. We demonstrate the energy with a very simple
model in which two fluid elements of equal mass exchange positions,
calling to mind a turbulent field or natural convection. The exchange
releases potential energy that, with a minor exception, is available
only in the hemisphere facing the barycenter of the planetary system. We
calculate its strength and spatial distribution for the strongest case
("vertical") and for weaker horizontal cases whose motions are all
perpendicular to gravity. The vertical cases can raise the kinetic
energy of a few well positioned convecting elements in the Sun's
envelope by a factor ≤7. This is the first physical mechanism
by which planets can have a nontrivial effect on internal solar
motions. Occasional small mass exchanges near the solar center and in a
recently proposed mixed shell centered at 0.16Rs would carry
fresh fuel to deeper levels. This would cause stars like the Sun with
appropriate planetary systems to burn somewhat more brightly and have
shorter lifetimes than identical stars without planets. The helioseismic
sound speed and the long record of sunspot activity offer several bits
of evidence that the effect may have been active in the Sun's core,
its envelope, and in some vertically stable layers. Additional proof
will require direct evidence from helioseismology or from transient
waves on the solar surface.

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Title: Effects of a Deep Mixed Shell on Solar g-Modes, p-Modes,
and Neutrino Flux
Authors: Wolff, Charles L.
2009ApJ...701..686W Altcode:
A mixed-shell model that reflects g-modes away from the Sun's center
is developed further by calibrating its parameters and evaluating a
mixing mechanism: buoyancy. The shell roughly doubles g-mode oscillation
periods and would explain why there is no definitive detection of their
periods. But the shell has only minor effects on most p-modes. The
model provides a mechanism for causing short-term fluctuations in
neutrino flux and makes plausible the correlations between this flux
and solar activity levels. Relations are derived for a shell heated
asymmetrically by transient increases in nuclear burning in small
"hot spots." The size of these spots and the timing of a heating
event are governed by sets(ell) of standing asymptotic g-modes,
coupled by a maximal principle that greatly enhances their excitation
and concentrates power toward the equator, assisting the detection of
higher-ell sets. Signals from all sets, except one, in the range 2 &lt;=
ell &lt;= 8 are identified by difference periods between consecutive
radial states using the method of Garcia et al. and reinterpreting
their latest spectrum. This confirms two detections of sets in a similar
range of ell by their rotation rates. The mean radius of shell mixing
is rm = 0.16 R sun, which improves an earlier
independent estimate of 0.18 by the author. The shell may cause the
unexplained dip in measured sound speed at its location. Another sound
speed error, centered near 0.67 R sun, and reversing flows
in the same place with a period originally near 1.3 yr suggest that the
g-modes are depositing there about 3% of the solar luminosity. That
implies the shell at rm is receiving a similar magnitude
of power, which would be enough energy to mix the corresponding shell
in a standard solar model in Lt107 yr.

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Title: Correspondence between Solar Variability (0.6 - 7.0 Years)
and the Theoretical Positions of Rotating Sets of Coupled g Modes
Authors: Juckett, David A.; Wolff, Charles L.
2009SoPh..257...13J Altcode:
Recently, Juckett and Wolff (Solar Phys.252, 247, 2008) showed that the
timing and longitude of sunspot patterns has some correspondence with
a model based on coupled g modes. The model maximizes the nonlinear
coupling of those g modes sharing harmonic degree ℓ to generate a
"set(ℓ)" that assists its own excitation by locally enhancing nuclear
burning. Each set(ℓ) has oscillatory power concentrated at two
longitudes, on opposite sides of the Sun and drifts slowly retrograde
within the radiative zone (RZ) at a rate that depends on ℓ. When
the strong longitudes of two or more sets overlap, wave dissipation
adds extra energy to that locality at the base of the convective
envelope increasing convection and then sunspot activity. We compare
the main subdecadal sunspot frequencies with the intersections of sets
derived from ℓ=2 - 11 and G, where G represents unresolvable high-ℓ
modes that rotate similarly to the RZ. After determining the set(ℓ)
spatial phases, we show that 17 subdecadal oscillations with periods
in the range 0.6 to 7.0 years (4.5 to 50 nHz), generated by 23 unique
intersections of the 11 sets, are synchronous with 17 corresponding
frequencies in the sunspot time series. After optimizing parameters,
we find a mean correlation of 0.96 for synchrony among the 17 waveform
pairs. These 17 frequencies constitute the bulk of the non-noise
subdecadal frequency domain of the sunspot variation. We conclude
that the sunspot series contains oscillatory components with the same
temporal phases and frequencies as various set(ℓ) intersections
spanning the past ≈ 100 years. This additional evidence for the role
of coupled g modes in sunspot dynamics suggests that more of sunspot
variability can be understood with nonmagnetic fluid mechanics than
popularly thought.

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Title: Evidence for Long-term Retrograde Motions of Sunspot Patterns
and Indications of Coupled g-mode Rotation Rates
Authors: Juckett, David A.; Wolff, Charles L.
2008SoPh..252..247J Altcode: 2008SoPh..tmp..168J
Solar g-modes are global oscillations that would exist primarily in the
radiative zone (RZ) and would be excited by either convective overshoot
or nuclear burning in the core. Wolff and O'Donovan (Astrophys. J.661,
568, 2007) proposed a non-linear coupling of g-modes into groups that
share the same harmonic degree ℓ. Each group (denoted set(ℓ))
exhibits a unique retrograde rotation rate with respect to the RZ that
depends mainly on ℓ. The coupling yields a standing wave (nearly
stationary in longitude) that has two angularly defined hot spots offset
from the equator on opposite sides of the Sun that would deposit energy
asymmetrically in the lower convective envelope (CE). It is anticipated
that when two or more groups overlap in longitude, an increase in local
heating would influence the distribution of sunspots. In this paper,
we scanned a multitude of rotational reference frames for sunspot
clustering to test for frames that are concordant with the rotation
of these g-modes sets. To achieve this, spherical harmonic filtering
of sunspot synoptic maps was used to extract patterns consistent
with coalesced g-modes. The latitude band, with minimal differential
rotation, was sampled from each filtered synoptic map and layered
into a stackplot. This was progressively shifted, line-by-line, into
different rotational reference frames. We have detected long-lived
longitudinal alignments, spanning 90 years of solar cycles, which are
consistent with the rotation rate of the deep solar interior as well as
other rotational frames predicted by the coupled g-mode model. Their
sidereal rotation rates of 370.0, 398.8, 412.7, 418.3, 421.0, 424.2
and 430.0 nHz correspond, respectively, to coupled g-modes for ℓ =
2 through 7 and G, where G is a set with high ℓ values or a group
of such sets (unresolved) that rotate almost as fast as the RZ. While
the clustering in these reference frames offers new approaches for
studying the longitudinal behavior of solar activity, it tentatively
leads to the more profound conclusion that a portion of the driving
force for sunspot occurrence is linked to energy extracted from the
solar core and deposited at the top of the RZ by solar g-modes.

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Title: The QBO as potential amplifier and conduit to lower altitudes
of solar cycle influence
Authors: Mayr, H. G.; Mengel, J. G.; Wolff, C. L.; Huang, F. T.;
Porter, H. S.
2007AnGeo..25.1071M Altcode:
In several papers, the solar cycle (SC) effect in the lower atmosphere
has been linked observationally to the Quasi-biennial Oscillation (QBO)
of the zonal circulation. Salby and Callaghan (2000) in particular
analyzed the QBO wind measurements, covering more than 40 years, and
discovered that they contain a large SC signature at 20 km. We present
here the results from a study with our 3-D Numerical Spectral Model
(NSM), which relies primarily on parameterized gravity waves (GW)
to describe the QBO. In our model, the period of the SC is taken to
be 10 years, and the relative amplitude of radiative forcing varies
exponentially with height, i.e., 0.2% at the surface, 2% at 50 km, and
20% at 100 km and above. Applying spectral analysis to identify the SC
signature, the model generates a relatively large modulation of the
QBO, which reproduces the observations qualitatively. The numerical
results demonstrate that the QBO modulation, closely tracking the
phase of the SC, is robust and persists at least for 70 years. The
question is what causes the SC effect, and our analysis shows that
four interlocking processes are involved: (1) In the mesosphere
at around 60 km, the solar UV variations generate in the zonal
winds a SC modulation of the 12-month annual oscillation, which
is hemispherically symmetric and confined to equatorial latitudes
like the QBO. (2) Although the amplitude of this equatorial annual
oscillation (EAO) is relatively small, its SC modulation is large
and extends into the lower stratosphere under the influence of, and
amplified by, wave forcing. (3) The amplitude modulations of both EAO
and QBO are essentially in phase with the imposed SC heating for the
entire time span of the model simulation. This indicates that, due to
positive feedback in the wave mechanism, the EAO apparently provides
the pathway and pacemaker for the SC modulation of the QBO. (4) Our
analysis demonstrates that the SC modulations of the QBO and EAO are
amplified by tapping the momentum from the upward propagating gravity
waves. Influenced and amplified by wave processes, the QBO thus acts as
conduit to transfer to lower altitudes the larger SC variations in the
UV absorbed in the mesosphere. Our model produces in the temperature
variations of the QBO and EAO measurable SC modulations at polar
latitudes near the tropopause. The effects are apparently generated
by the meridional circulation, and planetary waves presumably, which
redistribute the energy from the equatorial region where the waves
are very effective in amplifying the SC influence.

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Title: Soliton Properties of Coupled g-Mode Oscillations
Authors: Wolff, Charles L.
2007AAS...210.4505W Altcode: 2007BAAS...39..160W
Several features typical of solitons are also exhibited by stellar
g-modes when coupled into families that maximize the release of
nuclear energy. Each family is held together against dispersion of its
members by enhanced nuclear burning in small portions of the stellar
core where amplitudes reach nonlinear levels. Since each family has a
different rotation rate somewhat slower than the star, its nonlinear
regions drift past those of others causing complex interactions
(shown in a video). Yet each region emerges from this with its
original wave form. Other similarities with solitons are mentioned,
including the physical origin of a phase shift in longitude due to
the interaction. These similarities suggest that a fully nonlinear
derivation of g-mode sets may be able to show that their large amplitude
regions approach true solitons.

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Title: Coupled Groups of g-Modes in a Sun with a Mixed Core
Authors: Wolff, Charles L.; O'Donovan, Adam E.
2007ApJ...661..568W Altcode:
Groups of linear g-modes can sum to create nonlinear motion in small
“hot volumes” (diameter ~10 Mm) near the solar center that help
drive the modes. We explore the consequences of coupling only in the
hot volumes where the time-averaged rate of 3He burning
can double if temperature oscillations exceed 10%. Anticipating large
local motions in the core, we impose a mixed shell r=(0.10+/-0.03)
Rsolar on an otherwise standard solar model before computing
g-mode solutions. Mixing is rapid (&lt;&lt;106 yr) in
this shell, with slower mixing somewhat beyond. If l is the principal
spherical harmonic index, a set of g-modes for any single l&lt;=5 with
six consecutive radial harmonics can be excited with nearly linear
thermal amplitudes AT&lt;=0.05 throughout the star. But far
smaller thresholds for excitation are actually expected when sets for
many values of l can be computed simultaneously. This is a new kind
of stellar instability whose effectiveness rises with the number of
active modes. Each set rotates rigidly and maximizes the release of
nuclear energy from its hot volumes. There is some evidence for their
rotation rates in the long solar activity record. The upward wave flux
powered by the hot volumes has also been suggested to explain the 1.3
yr reversing flows tentatively detected below the Sun's convective
envelope. An analog using uncoupled modes is also investigated based on
an observation that indicates g-mode activity up to l~=20. If all modes
in that range had linear amplitudes of only AT~=0.0015,
their combined effect would give positive growth rates to dozens of
low harmonic g-modes.

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Title: QBO as potential amplifier of solar cycle influence
Authors: Mayr, Hans G.; Mengel, John G.; Wolff, Charles L.; Porter,
Hayden S.
2006GeoRL..33.5812M Altcode:
The solar cycle (SC) effect in the lower atmosphere has been linked
observationally to the quasi-biennial oscillation (QBO) of the zonal
circulation. Salby and Callaghan (2000) in particular analyzed the
QBO covering more than 40 years and found that it contains a large SC
signature at 20 km. We discuss a 3D study in which we simulate the
QBO under the influence of the SC. For a SC period of 10 years, the
relative amplitude of radiative forcing is taken to vary with height:
0.2% (surface), 2% (50 km), 20% (100 km and above). This model produces
in the lower stratosphere a relatively large modulation of the QBO,
which appears to come from the SC and qualitatively agrees with the
observations. The modulation of the QBO, with constant phase relative
to the SC, is shown to persist at least for 50 years, and it is induced
by a SC modulated annual oscillation that is hemispherically symmetric
and confined to low latitudes (Mayr et al., 2005).

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Title: Wave-driven equatorial annual oscillation induced and modulated
by the solar cycle
Authors: Mayr, Hans G.; Mengel, John G.; Wolff, Charles L.
2005GeoRL..3220811M Altcode:
Our 3-D model for the solar cycle (SC) effect on the QBO (H. G. Mayr et
al., The QBO as potential amplifier of solar cycle influence, submitted
to Geophysical Research Letters, 2005, hereinafter referred to as
Mayr et al., submitted manuscript, 2005) produces a hemispherically
symmetric 12-month Annual Oscillation (AO) in the zonal winds,
which is largely confined to low latitudes. This Equatorial Annual
Oscillation (EAO) is generated through nonlinear interaction between
the dominant anti-symmetric AO and the anti-symmetric component of
the SC response. Due to wave-mean-flow interaction from small-scale
gravity waves (GW), the SC-modulated EAO is amplified and propagates
down through the stratosphere as does the QBO. The amplitude of the
EAO is relatively small, but its SC modulation is large and is in phase
with that of the QBO. Although the EAO is concentrated at low latitudes,
prominent signatures appear in the polar regions where the SC produces
measurable temperature variations. At lower altitudes, the GW-driven
downward propagation of the EAO affects the phase of the annual cycle
and causes the SC effect to be different in the two hemispheres.

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Title: The Sun's Reversing Flows and Heat Spike as Caused by g-Modes
Authors: Wolff, Charles L.; Mayr, Hans G.
2004ApJ...606L.163W Altcode:
The reversing east-west flows centered near 0.675 Rsolar
have not been explained by gravity waves from the convection zone
because suitable wavelengths do not penetrate deeply enough to drive
the observed flow. An alternative is explored using g-modes, many
of whose rotation rates have already been detected. Simple formulas
for the radial drift of the flow and for angular momentum transfer
from asymptotic g-modes are expressed in terms of local oscillation
amplitudes and dissipation rates. The main loss mechanism is horizontal
turbulence caused by the flow. It exceeds that due to gravity
waves for which Schatzman estimated a diffusivity ~108
m2 s-1. Our proposed flow has a peak zonal
speed of 50 m s-1, consistent with the observations at
current resolving power. An array of g-modes with amplitudes near the
detectable limit at the solar surface can cause the flow to replace
itself about every 1.3 yr, as observed, if there are ~103
high harmonic modes. Since the flow occupies the same thin layer where
the sound speed is anomalous, heat dissipated in driving the flow acts
to reduce that solar modeling error.

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Title: Rotational Sequences of Global Oscillations inside the Sun
Authors: Wolff, Charles L.
2002ApJ...580L.181W Altcode:
A very simple mathematical sequence is detected in a half-century of
thermal radio flux from the Sun. Since the only known solar source
for the sequence is global oscillations trapped in the nonconvecting
interior, g-modes and probably r-modes are active. If so, their
rotation frequencies are detected and some previously reported
difference frequencies are confirmed with high confidence. All angular
harmonics for 2&lt;=l&lt;=7 are detected as well as some others up to
the limit l&lt;=14 resolvable by the observations (a Fourier spectrum
of the 10.7 cm flux time series). The mean sidereal rotation rate of the
nonconvecting interior is 428.2 nHz as averaged by g-modes and 429.8 nHz
by the r-modes, indicating that g-mode energy is a bit more centrally
concentrated. Helioseismology measures such rotation rates near 0.36R
(R = solar radius), so the global modes would have about half their
kinetic energy above and below that level. This, and the known log
(r) energy dependence of most modes, implies that these oscillations
are significantly reflected near 0.18R, the same level at which sound
speed measurements display a maximum departure from theoretical models.

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Title: Model of Wave Driven Flow Oscillation for Solar Cycle
Authors: Mayr, H. G.; Wolff, C. L.
2001AGUSM..SP31A16M Altcode:
At low latitudes in the Earth's atmosphere, the observed
zonal flow velocities are dominated by the semi-annual and
quasi-biennial oscillations with periods of 6 months and 20 to 32
months respectively. These equatorial oscillations, the SAO and QBO
respectively, are driven by wave-mean flow interactions due to upward
propagating planetary-scale waves (periods of days) and small-scale
gravity waves (periods of hours). We are proposing (see also Mayr,
Wolff, Hartle, GRL, 28, 2001) that such a mechanism may drive
long period oscillations (reversing flows) in stellar and planetary
interiors, and we apply it to the Sun. The reversing flows would occur
below the convective envelope where waves can propagate. We apply a
simplified, one dimensional, analytical flow model that incorporates
a gravity wave parameterization due to Hines (1997). Based on this
analysis, our estimates show that relatively small wave amplitudes &lt;
10 m/s can produce zonal flow amplitudes of 20 m/s, which should be
sufficient to generate the observed variations in the magnetic field. To
produce the 22-year period of oscillation, a low buoyancy frequency
must be chosen, and this places the proposed flow in a region that
is close to (and below) the base of the convective envelope. Enhanced
turbulence associated with this low stability should help to generate
the dynamo currents. With larger stability at deeper levels in the
solar interior, the model can readily produce also oscillations
with much longer periods. To provide an understanding of the fluid
dynamics involved, we present numerical results from a 2D model for
the terrestrial atmosphere that exemplify the non-linear nature of
the wave interaction for which a mechanical analog is the escapement
mechanism of the clock.

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Title: Wave driven non-linear flow oscillator for the 22-year
solar cycle
Authors: Mayr, Hans G.; Wolff, Charles L.; Hartle, Richard E.
2001GeoRL..28..463M Altcode:
In the Earth's atmosphere, a zonal flow oscillation is observed with
periods between 20 and 32 months, the Quasi Biennial Oscillation. This
oscillation does not require an external time dependent source but
is maintained by non-linear wave momentum forcing. We propose that
such a mechanism also drives long-period oscillations in planetary and
stellar interiors, and we apply it here to generate a flow oscillation
for the 22-year solar cycle. The oscillation would occur just below the
convective envelope—in a region where gravity waves can propagate. We
present results from a simplified analytical model that incorporates
Hines' gravity wave parameterization. Wave amplitudes &lt;10 m/s can
produce reversing zonal flows of 20 m/s that should be sufficient to
generate a corresponding oscillation in the poloidal magnetic field. The
low buoyancy frequency and associated increase in turbulence help
produce the desired oscillation period of the flow and should help
generate the currents for the reversing magnetic field.

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Title: Linear r-Modes below the Sun's Convective Envelope
Authors: Wolff, Charles L.
2000ApJ...531..591W Altcode:
Theoretical properties of linear r-modes in a standard solar interior
are computed, and the excitation of some by convective overshoot is
estimated. The modes oscillate in a resonant cavity usually occupying
most of the nonconvecting interior. Most modes concentrate their
kinetic energy toward the center of the Sun. Over half the energy
usually lies below 0.15 Rsolar with an asymptotic limit of
0.11 Rsolar for high radial harmonics (Rsolar
is the solar radius). The oscillation frequencies are very close to the
well-known toroidal frequency, σt=2Ωm[l(l+1)]-1,
deviating by fractional amounts ~10-6+/-1 which are
roughly 3 orders of magnitude smaller than deviations found earlier
for r-modes in convective layers. An explicit formula for the ratio of
divergent motion to curl motion is derived. It shows how rapidly the
compressible component changes as a function of r. Compressibility is
only ~10-6 of the total motion for low l-modes and declines
proportionally to ml-3 for high l. A small subset of modes
(the lowest radial harmonic of angular states |m|=l) avoid the core
which makes them sensitive to convective overshoot. Just one of the
giant convection cells detected by Beck et al. can excite such modes
to kilometer-size amplitudes with the possibility that far larger
displacement amplitudes can accumulate in the mode over time if the
interaction between cells and r-modes is found to be strong.

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Title: Linear r-Mode Oscillations in a Differentially Rotating Star
Authors: Wolff, Charles L.
1998ApJ...502..961W Altcode:
Differential rotation of a stellar envelope lifts the degeneracy of
r-mode rotation rates and can prohibit some modes. It also reduces
the physical distinction between the two branches of r-modes: slow
(retrograde) and fast (geostrophic). One mode in each branch is
dominated by a given spherical harmonic (l, m), and, for increasing
rotational shear in the star, their characteristics approach each
other until both modes simultaneously cease to exist. Only about
half of the 60 r-modes with l &lt;= 5 and a given radial harmonic can
survive as global, linear modes in the Sun. Each of these has at least
70%, and typically 90%, of its energy in a single toroidal component
of motion. Among solar survivors are all modes where | m | = l &gt;
1. All results apply to linear, adiabatic oscillations of a spherical
fluid shell exhibiting steady, axisymmetric rotation, Ω(r, θ). Since
terms ~Ω2 are small in the Sun, spheroidal motions are
neglected. A generalization of classical perturbation theory was used to
treat “perturbations” of large size and to avoid the need for special
treatment of oscillation frequencies that are zero or degenerate.

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Title: Large Convective Events and Their Aftermath in a Rotating Star
Authors: Wolff, Charles L.
1997ApJ...486.1058W Altcode:
The 35 most exceptional, deep convective events that have occurred
since the year 1750 are identified using Fj, an index of
solar activity. The average event lasted 38 days and was followed by
several years of lesser eruptions in a repeatable time sequence. This
contradicts the common assumption that stellar convection is
random. Deep convective events, which have lifetimes comparable to the
stellar rotation period, will accumulate a net azimuthal motion relative
to the ambient fluid. In the Sun, the rising portion of such an event
moves in longitude ~1° day-1 as it partially conserves
initial angular momentum. Its kinetic energy, ~1029 J, in
azimuthal motion amounts to a pulse that is available to excite global
oscillations (r-modes). Following the pulse, signatures of r-modes can
be traced for 1000 days in the lesser solar eruptions, which is evidence
that the r-modes are causing or modulating convection. A successful,
nonlinear model of this is constructed in which magnetic fields play
no role.

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Title: Convection: Periodic Due to r-Modes
Authors: Wolff, Charles L.
1996ApJ...459L.103W Altcode:
Convection in a rotating fluid can acquire a periodic component where
the convective timescale becomes comparable to or longer than the
rotation period. Then, each local convective event becomes a source
of Rossby-like oscillations. They carry off information that, in a
spherical shell, can sum much later to stimulate an echo of the initial
convective event. The two series of echos most likely to be detectable
occur at intervals of six and 30 rotation periods and apply to events
of large horizontal size. The waves can also impose other periodicities
on the convection, and about a dozen in the range 75--800 days are
clearly identified by comparing known regularities in solar activity
with theoretical beat frequencies of global oscillations (r-modes).

---------------------------------------------------------
Title: Oscillation-Convection Coupling: Cause of Supergranulation?
Authors: Wolff, C.
1995ApJ...443..423W Altcode:
A semianalytic method is derived for dealing simultaneously with
large numbers of linear stellar oscillation modes trapped in
a cavity (a shell) of fluid which is rotating and convecting. A
simple generalization of mixing-length theory shows how convection
is modulated by weak rotational effects and by the horizontal wind
fields of linear r-mode oscillations. The modulated convection is then
used to compute the energy lost to turbulent viscosity by a family
of nondegenerate oscillations. Viscosity terms of fourth degree in
the wind shear can be included if they are a perturbation affecting
only a small portion of the r-mode. Viscous energy loss strengthens
convection in a narrow layer near the base of the H and He ionization
zone. In the Sun, this layer is about 7 Mm thick and centered at 0.932
of a solar radius where convection cells have a typical size of about
20 Mm and a lifetime of 0.3 Ms, both similar to what is observed in
supergranules. If the rms velocity of r-modes at the surface exceeds
5 m/s, then energy is deposited inside the Sun at a sufficient rate to
power the supergranulation and impose on it a weak latitude dependence.

---------------------------------------------------------
Title: Equidistribution of Energy and Other Quantities in Oscillating
Systems
Authors: Wolff, Charles L.
1993ApJ...414..892W Altcode:
Energy of a high harmonic standing wave tends to be distributed equally
over the whole wave even in a stratified medium where the wave's peak
amplitude can be much larger near the upper boundary than the lower
one. This fact is generalized to the many diverse physical problems
which solve second-order differential equations of Sturm-Liouville
type. For any such solution y(z) whose sign fluctuates along the
z-axis, quantities are found which have the same value between any
two neighboring zeros of y. One of the equidistributed quantities
for an oscillating fluid sphere is similar to kinetic energy but is
identical only in limiting cases. The acoustic midpoint of a cavity
can be a unique place where some nonlinear perturbations have extra
strength. This may apply to the puzzling solar phenomenon called
supergranulation.

---------------------------------------------------------
Title: Solar Supergranulation: Driven by Solar Oscillations
Authors: Wolff, C. L.
1993AAS...182.4802W Altcode: 1993BAAS...25..879W
No abstract at ADS

---------------------------------------------------------
Title: `Intermittent' solar periodicities
Authors: Wolff, Charles L.
1992SoPh..142..187W Altcode:
The signal from a stable periodicity can seem to be intermittent when
it is partially masked by an unmodelled window function or when the
data set is too short to resolve closely spaced periodicities. By
taking this into account, short-lived periodicities in solar data can
be reinterpreted as evidence for continuously periodic behavior. The
periodic sources are located in the solar interior and caused by
global oscillation modes. The convective envelope acts as the window
for these sources. Recent reports of seven periodicities from 100
to 1000 days are compared with this model. Precise long-term values
for the periodicities are predicted and they agree closely with
observations. Some elements are suggested that might explain the
well-documented 155-day periodicity. Conventional filtering methods
to suppress effects of the 11-year cycle are criticized as inadequate.

---------------------------------------------------------
Title: Solar irradiance observed from PVO and inferred solar rotation.
Authors: Wolff, Charles L.; Hoegy, Walter R.
1990NASCP3086...57W Altcode: 1990cisv.nasa...57W
Solar irradiance in the EUV has been monitored for 11 years by the
Pioneer Venus Orbiter (PVO). Since the experiment moves around the
Sun with the orbital rate of Venus rather than that of Earth, the
measurement gives us a second viewing location from which to begin
unravelling which irradiance variations are intrinsic to the Sun,
and which are merely rotational modulations whose periods depend on
the motion of the observer. The authors confirm an earlier detection,
made with only 8.6 years of data, that EUV irradiance is modulated by
rotation rates of two families of global oscillation modes. One family
is assumed to be r-modes occupying the convective envelope and sharing
its rotation, while the other family (g-modes) lies in the radiative
interior which has a slower rotation. Measured power in r-modes of
low angular harmonic number (l≤7) indicates that the Sun's envelope
rotated about 0.7% faster near the last solar maximum (1979 thru 1982)
than it did during the next rise to maximum (1986 thru 1989). No change
was seen in the g-mode family of lines, as would be expected from the
much greater rotational inertia of the radiative interior.

---------------------------------------------------------
Title: A seven-month solar cycle observed with the Langmuir probe
on Pioneer Venus Orbiter
Authors: Hoegy, W. R.; Wolff, C. L.
1989JGR....94.8663H Altcode:
An approximately 7-month solar cycle has been observed in the
photoelectron current measured by the Langmuir probe on Pioneer
Venus Orbiter over the time period from 1979 through 1987. The
probe photoelectron current, Ipe, is obtained when the
spacecraft is outside the Venus ionosphere, and the measured current
is due to photoelectron emission caused by EUV solar radiation in the
wavelength range from about 30 nm to 121.6 nm. About one half of the
Ipe is due to solar Lyman alpha emission. The Ipe
data from mid-1984 through 1987 are dominated by a 7-month or 216-day
cycle. Spectral analysis of the 1980-1988 data shows that this cycle
dominates the spectrum for periods less than 300 days; the second most
dominant cylce is at 155 days, a 5-month period. The Ipe
data were spectrally analyzed with three different methods. The
2800-MHz radio flux, observed from Earth over the same time range,
exhibits a similar 7-month cycle at about 234 days which is stronger
than a 5-month (158-day) cycle. Solar Mesosphere Explorer (SME) Lyman
alpha observations for the time period mid-1981 through mid-1988 also
have cycles near 5 and 7 months. Since the 7-month and 5-month cycles
are observed from Venus (Ipe) and from Earth (2800-MHz
radio flux and SME Lyman alpha), the observations suggest that they
are intrinsic frequencies, independent of the orbital frequency of
the observer. The 7- and 5-month cycles are believed to be caused by
long-lived flux enhancements from nonlinear interactions of global
oscillation modes in the Sun's convective envelope (r modes) and
radiative interior (g modes).

---------------------------------------------------------
Title: Periodic Solar Extreme Ultraviolet Flux Monitored Near Venus
Authors: Wolff, Charles L.; Hoegy, Walter R.
1989SoPh..123....7W Altcode:
A detector sharing the orbital rate of Venus has a unique perspective
on solar periodicities. Fourier analysis of the 8.6 year record of
solar EUV output gathered by the Langmuir probe on Pioneer Venus
Orbiter shows the influences of global oscillation modes located in
the convective envelope and in the radiative interior. Seven of the
eight lowest angular harmonic r-mode families are detected by their
rotation rates which differ almost unmeasurably from ideal theoretical
values. This determines a mean sidereal rotation rate for the envelope
of 457.9 ± 2.0 nHz which corresponds to a period of 25.3 days. Many
frequencies are aliased at ± 106 nHz by modulation from the lowest
angular harmonic r-mode in the envelope. The rotation of this mode seems
slightly retrograde, -1.5 ± 2.0 nHz, but small positive values are
not excluded. We confirm that the rotation of the radiative interior,
381 nHz, is slower than the envelope by detecting g-mode frequencies
for angular harmonics, 2 ≤ l ≤ 6, and a possible first detection
of the rotation rate for the l = 1 case. Solar EUV lacks the sudden
darkenings (dips) shown by visible irradiance; vortex cores in the
photosphere and below are again suggested as a possible explanation.

---------------------------------------------------------
Title: Angular Momentum of Stellar Oscillations, and Stellar Rotation
Authors: Wolff, C. L.
1989BAAS...21..745W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Solar Irradiance Change and Special Longitudes Due to γ -Modes
Authors: Wolff, Charles L.; Hickey, John R.
1987Sci...235.1631W Altcode:
Sluggish global oscillations, having a periodicity of months and trapped
in the sun's convection zone, modulate the amount of energy reaching
Earth and seem to impose some large-scale order on the distribution
of solar surface features. These recently recognized oscillations (γ
-modes) increase the predictability of solar changes and may improve
understanding of rotation and variability in other stars. Most of the 13
periodicities ranging from 13 to 85 days that are caused by γ -modes
can be detected in Nimbus 7 observations of solar irradiance during
3 years at solar maximum. These modes may also bear on the classical
question of persistent longitudes of high solar activity.

---------------------------------------------------------
Title: Multiperiodic Irradiance Changes Caused by R-Modes and G-Modes
Authors: Wolff, Charles L.; Hickey, John R.
1987SoPh..109....1W Altcode:
More than 20 real periodicities ranging from 20 days to 2 years modulate
the solar irradiance data accumulated since November 1978 by Nimbus
7. Many are quite strong during the first three years (solar maximum)
and weak after that. There is a high correspondence between periods in
irradiance and 28 periods predicted from the rotation and beating of
global solar oscillations (r-modes and g-modes). Angular states ℓ = 1,
2, and 3 are detected as well as some unresolved r-mode power at higher
ℓ. The prominence of beat periods implies a nonlinear system whose
effective nonlinear power was measured to be about 2. This analysis
constitutes a detection of r-modes in the Sun and determines from them
a mean sidereal rotation rate for the convective envelope of 459 ± 4
nHz which converts to a period of 25.2 days (27.ld, synodic).

---------------------------------------------------------
Title: R-mode oscillations in the sun
Authors: Blizard, Jane B.; Wolff, Charles L.
1987LNP...274..318B Altcode: 1987stpu.conf..318B
The relationship between solar r-modes (long-period oscillations
dominated by the Coriolis force) and solar activity cycles is
investigated statistically. FFT power spectra of the daily Zurich
sunspot numbers (R) and of the Greenwich Photoheliographic projected
whole sunspot area (A) are obtained for the high-activity years of solar
cycles 14 through 21. Both R and A are found to exhibit periods of 22 +
or - 1 d, 34 + or - 1.5 d, and 43 + or - 2 d, corresponding to r-modes
with (l,m) angular harmonics (2,2), (3,1), and (2,1), respectively.

---------------------------------------------------------
Title: Short Periods in the Power Spectrum of Sunspot Number -
16-DAYS to One-Year and R-Mode Oscillations on the Sun
Authors: Blizard, J. B.; Wolff, C. L.
1986PASP...98.1100B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: r-Modes Influencing the Solar Irradiance
Authors: Wolff, C. L.
1986BAAS...18..933W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Properties of R-Modes in the Sun
Authors: Wolff, C. L.; Blizard, J. B.
1986SoPh..105....1W Altcode:
Global oscillations of the Sun (r-modes) with very long periods ∼
1 month are reviewed and studied. Such modes would be trapped in an
acoustic cavity formed either by most of the convective envelope or by
most of the radiative interior. A turning point frequency giving cavity
boundaries is defined and the run of eigenvalues for angular harmonics
l ≤ 3 are plotted for a conventional solar convection zone. The
r-modes show equipartition of oscillatory energy among shells which
each contain one antinode in the radial dimension. Toroidal motion is
dominant to at least the 14th radial harmonic mode. Viscosity
from convective turbulence is strong and would damp any mode in just
a few solar rotations if it were the only significant nonadiabatic
effect. `Radial fine splitting' which lifts the degeneracy in n is very
small (20 nHz or less) for all n ≤ 14 trapped in the envelope. But,
if splitting could be detected, we would have a valuable new constraint
on solar convection theories.

---------------------------------------------------------
Title: Solar Irradiance &amp;g-modes
Authors: Wolff, C. L.; Hickey, J. R.
1984BAAS...16..978W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Solar irradiance changes caused by g-modes and large scale
convection
Authors: Wolff, C. L.
1984SoPh...93....1W Altcode:
Solar irradiance measurements from the ACRIM experiment show a clear
response to the rotation periods of g-mode oscillations (l = 1, 2,
and 3) and their first harmonics. Peaks in the ACRIM spectrum at
16.6, 18.3, 20.7, 36.5, and ≃- 71 days all lie within about 1%
of periods arising from g-mode rotation. This means that the g-modes
are a fundamental cause of irradiance fluctuations. On time scales of
months and less they modulate the irradiance by means of transient
flows of global scale which they stimulate in the Sun's convective
envelope. Dimensional arguments indicate that the flows carry up heat
at an average rate ∼ 10-3L⊙ which is not in
conflict with observed changes in the irradiance. Five additional tests
for g-modes and large-scale convection are given. An instability is
described which undermines diffusion models of sunspot energy storage.

---------------------------------------------------------
Title: On the clock mechanisms and the implausibility of the 35 day
precessing disk in HZ Herculis/Hercules X-1.
Authors: Kondo, Y.; van Flandern, T. C.; Wolff, C. L.
1983ApJ...273..716K Altcode:
The concept of the precessing accretion disk in HZ Her/Her X-1 in
its varied forms, to account for the 35 day periodicity in the X-ray
flux, has met many objections from a number of workers on various
grounds, but it is still being invoked in current publications. These
objections are reviewed and additional arguments are presented against
the precessing accretion disk model. The implausibility of the disk
models is demonstrated. An alternate clock mechanism, based on nonlinear
oscillations in the normal star, which provides the modulation of the
mass flow is discussed.

---------------------------------------------------------
Title: Solar Irradiance, g-modes, and Convection
Authors: Wolff, C. L.
1983BAAS...15..950W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The rotational spectrum of g-modes in the sun
Authors: Wolff, C. L.
1983ApJ...264..667W Altcode:
Observations and calculations are presented which strongly suggest that
the unique sequence of rotation rates due to g-modes is active in the
sun. It is found that all angular harmonics from 1 = 2-11 appear to
be resolved, while higher harmonics up to at least 1 = 20 also seem
to be active. The extreme narrowness of many of the spectral lines
indicates that the g-modes are locked in sets of constant 1 by a local
mechanism which excites the modes and possibly regulates the long-term
precision of their rotation. These sets act as a system of resonant,
or nearly resonant, clocks which impose a degree of periodicity upon
solar activity and measure the mean solar interior rotation

---------------------------------------------------------
Title: Turbulent compressible convection in a deep
atmosphere. I. Preliminary two-dimensional results.
Authors: Chan, K. L.; Sofia, S.; Wolff, C. L.
1982ApJ...263..935C Altcode:
The turbulent convection of a compressible fluid in a deep atmosphere
is simulated by two-dimensional numerical computations, displaying
coexisting 'cells' whose sizes range from the total depth of the
convection zone to the smallest scale height at the top. While the
largest cells traverse the entire zone, smaller ones are clustered near
the top. The vertical correlation length of the vertical velocity is
proportional to the local pressure or density scale height, in a way
reminiscent of the concept of mixing length.

---------------------------------------------------------
Title: Is the "Mixing Length" Physically Meaningful?
Authors: Chan, K. L.; Sofia, S.; Wolff, C. L.
1982BAAS...14Q.665C Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Synoptic studies of chromospheric variability in F - K dwarfs
with the IUE.
Authors: Hallam, K. L.; Wolff, C. L.; Sewall, J. R.
1982NASCP2238..227H Altcode: 1982auva.nasa..227H; 1982NASCP2338..227H; 1982IUE82......227H
Time-sequential series of IUE spectra for ten F, G and K dwarfs
were obtained in 1980 and 1981 to study the rotational dependence of
chromospheric flux in the ultraviolet. An interactive computational
method using unbiased estimators was developed to measure emission
line fluxes free of arbitrary judgement concerning the behavior of
the underlying spectrum and shapes of the line profiles. Due to the
limited number of observational samples per star, we have used special
techniques to analyze the sparsely and anharmonically sampled emission
line flux data. Two different autocorrelation measures were computed
for each emission line as a function of temporal frequency. Examples and
results of this analysis now in progress are given for several stars.

---------------------------------------------------------
Title: Rotation of dwarf star chromospheres in the ultraviolet.
Authors: Hallam, K. L.; Wolff, C. L.
1981ApJ...248L..73H Altcode:
Periodic variations in the ultraviolet fluxes of chromospheric emission
line multiplets are investigated for F, G and K stars as evidence of
rotational modulation. Vacuum ultraviolet spectra were obtained with
the IUE spacecraft for six stars as many as 11 times over the period
April 23 to December 3, 1980. Variations in the emission fluxes of the
hydrogen Lyman-alpha, Si II and Mg II lines are observed with periods
up to 47 days. The periodicity, which is identified with rotational
modulation, is found to persist over many rotational cycles, although
the periods and time dependences of the fluxes from the different ionic
species are not identical, probably due to differential rotation and
global distributions. The spread of the UV periods is observed to be
within 10%, with one or two peaks per cycle and a ratio of modulated
to umodulated flux ranging from 1.1 to 3.0, analogous to solar behavior.

---------------------------------------------------------
Title: A variable mixing-length ratio for convection theory
Authors: Chan, K. L.; Wolff, C. L.; Sofia, S.
1981ApJ...244..582C Altcode:
It is argued that a natural choice for the local mixing length in the
mixing-length theory of convection has a value proportional to the local
density scale height of the convective bubbles. The resultant variable
mixing-length ratio (the ratio between the mixing length and the
pressure scale height) of this theory is enhanced in the superadiabatic
region and approaches a constant in deeper layers. Numerical tests
comparing the new mixing length successfully eliminate most of the
density inversion that typically plagues conventional results. The
new approach also seems to indicate the existence of granular motion
at the top of the convection zone.

---------------------------------------------------------
Title: Large Scale Order in the Sun
Authors: Wolff, C. L.
1981BAAS...13..878W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The collective excitation of g-modes in the sun
Authors: Wolff, C. L.
1980LNP...125..252W Altcode: 1980nnsp.work..252W
Oscillations of the solar interior (linear g-modes) may be strongly
driven by the collective influence of all the modes upon the nuclear
reactions in the core. This heretofore neglected effect could
couple the modes, reduce the effective amplitudes near the center,
and spatially concentrate most of the oscillation energy into just a
portion of the radiative interior. If operating at sufficient strength,
this can reverse the conventional conclusion, drawn from single mode
calculations, that almost all solar g-modes are damped. Furthermore, it
would put the theory into rough harmony with three otherwise troubling
observations: (1) the 'low' neutrino flux measured by Davis (1978),
(2) the high correspondence found by Wolff (1976) between recurrence
periods in solar activity and the rotational beat periods of g-modes,
and (3) the fluctuations in the sun's diameter which imply g-mode
activity at high angular harmonics (Hill and Caudell 1979). A nonlinear
expression is derived for the local rate of work done on an array of
oscillation modes by the nuclear reactions. Three additional tests of
the model are suggested.

---------------------------------------------------------
Title: Some simple properties of stellar pulsation modes.
Authors: Wolff, C. L.
1979ApJ...227..943W Altcode:
Except for the lowest harmonics, small-amplitude stellar pulsation
modes possess many simple properties whose evaluation does not require
numerical integration of the fourth-order equations of motion. All
antinodes tend to have the same total kinetic energy except for
those lying near physical or geometric boundaries. However, when
kinetic energy per unit volume is considered, order-of-magnitude
enhancements are seen in antinodes lying near the center of the star,
and factor-of-2 enhancements occur near the polar axis. The nodes are
distributed very regularly along the radius. They follow an exponential
law in g-regions, and their separation is proportional to the sound
travel time in p-regions. A simple graphical procedure is described
for surveying the oscillation frequencies of a new stellar model. A
precise condition is derived giving the division of energy between
radial and angular motion. Another condition gives the fractional
contribution to the velocity field of its two sources, the divergence
and the curl. Certain simplifying results of weak coupling among the
linear modes are briefly described.

---------------------------------------------------------
Title: Hercules X-1 = HZ Herculis: a multiperiod variable?
Authors: Wolff, C. L.; Kondo, Y.
1978ApJ...219..605W Altcode:
Fundamental rotation properties of the free modes of oscillation of
a star are employed to account for the various periodicities observed
in the X-ray binary system HZ Her/Her X-1. The various rotation rates
may be taken as defining a set of beat periods associated with the
quasiregular flareups of HZ Her. This analysis, involving only one
free parameter, provides a single physical mechanism to explain five
observed periods of the binary system, including periods of 1.7 days,
35 days and 10 to 12 years.

---------------------------------------------------------
Title: White-dwarf variability and the rotation g-modes.
Authors: Wolff, C. L.
1977ApJ...216..784W Altcode:
The multiperiodic behavior clearly evident after Fourier analysis
of many DA white-dwarf light curves is interpreted as arising from
outbursts whose timing is regulated by the rotation and oscillation of
the star. A model is proposed on the basis of three main assumptions:
(1) a broad array of g-mode oscillations is taking place all the
time in DA white-dwarf variables; (2) slow rotation permits most
of the g-modes to couple and form a small group of nonlinear modes,
each characterized by one of the indices of the spherical harmonic
functions involved; and (3) the observed brightenings of the star are
produced by upwelling of convection on a large horizontal scale when
the antinodes of the nonlinear oscillation patterns periodically rotate
into alignment and cause a temporary local enhancement of energy per
unit volume. This model is used to match precisely almost every strong
periodicity observed in the complex light curves of the DA white dwarfs
G207-9, G38-29, G29-38, and HL Tau 76. If the model has been applied
correctly, the results indicate that all four of these variables are
rotating slowly with periods in the range from 250 to 500 sec.

---------------------------------------------------------
Title: White Dwarf Variable Stars and Their Oscillations.
Authors: Wolff, C. L.
1976BAAS....8Q.558W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Timing of solar cycles by rigid internal rotations.
Authors: Wolff, C. L.
1976ApJ...205..612W Altcode:
The so-called 11-year cycle of solar activity is really more complex
and contains many periods of greatly different lengths. Periods as
long as 178 years and as short as 3.1 years are predicted by a theory
based on beats between rigidly rotating, inertially oscillating g-modes
inside the sun. Most of the beat periods are then confirmed to about
1 percent accuracy in sunspot observations. Since the agreement is
of high statistical significance, one can conclude that approximate
alignment of major solar oscillation modes contributes to high solar
activity. The theory receives further support when tested against an
independent class of observations - the large-scale magnetic sector
structure. Predicted rotation rates of at least four solar oscillation
modes are detected in the sector data with discrepancies all less than
0.3 percent. As a by-product of these successful fits to observation,
the mean rotation of the entire solar mass becomes known. Its rotation
frequency is 4.49 by 10 to the -7th power Hz, which is a sidereal period
of 25.8 days. Magnetic fields have played no role in calculating the
length of any of these solar cycles.

---------------------------------------------------------
Title: Interplanetary gas. XXI. Validity of the Chapman-Enskog
description of the solar wind for protons.
Authors: Price, J. C.; Brandt, J. C.; Wolff, C. L.
1975ApJ...199..756P Altcode:
Measured velocity distribution functions for solar-wind protons are used
to estimate the validity of the Chapman-Enskog description, and it is
found to be the best description presently in use. Subject headings:
interplanetary medium - solar wind

---------------------------------------------------------
Title: An Anticorrelation between Polar and Equatorial Rotation of
the Solar Photosphere
Authors: Wolff, C. L.
1975SoPh...41..297W Altcode:
Published spectroscopic measurements of solar rotation are analyzed
to show that when the rotation velocity increases at high latitudes
it tends to decrease at low latitudes, and conversely. The high
latitude velocities typically vary over only 20% of the range of
those near the equator and the smallest variations of all occurred near
latitude 60° during the rising portion of the previous solar cycle. The
anticorrelation is consistent with a recent suggestion that differential
rotation on the sun arises from photospheric wind systems whose strength
is determined, ultimately, by oscillations within the Sun.

---------------------------------------------------------
Title: An Anticorrelation Between Polar &amp;Equatorial Rotation Rates
Authors: Wolff, C. L.
1975BAAS....7..364W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Rigid and differential rotation driven by oscillations within
the sun.
Authors: Wolff, C. L.
1974ApJ...194..489W Altcode:
Long-period oscillations involving the entire mass of the sun
rotate like rigid bodies, and their oscillatory power is distributed
nonuniformly across the solar surface. A mostly qualitative theory is
constructed showing how the oscillations drive convective flows of
global scale, which then organize photospheric and coronal magnetic
fields into patterns which rotate rigidly. The convection rises along
long graceful curves, creating the magnetic-arcade structures in
the corona and unipolar photospheric regions on each side by dynamo
action. These are thought to be the origin of the sector structure in
the solar wind. The rigid patterns of convective upwelling also force
nonrigid horizontal winds on the solar surface. Under the action of
the Coriolis force, the main horizontal motions are converted into
polar and equatorial wind currents which have the proper directions
to drive the differential rotation long observed on the sun's surface.

---------------------------------------------------------
Title: Distinctive patterns on the surface of two slowly rotating
stars whose oscillations are nonlinearly coupled.
Authors: Wolff, C. L.
1974ApJ...193..721W Altcode:
Slowly rotating stars which are oscillating at small amplitude in a
broad spectrum of g-modes should display strong surface nonuniformities
if even weak nonlinear coupling exists between the modes. Oscillatory
power will be concentrated into distinctive patterns which rotate
rigidly in spite of differential rotation in the outer stellar
layers. Each pattern rotates at a constant rate slower than the star
as a whole according to a very simple law of rotation. Virtually all
the rotation rates are within 9 per cent of the stellar rate. Evidence
is cited that the sun may be oscillating, so other stars along the
main sequence may be oscillating, also. If zones obeying the predicted
rotation law can be detected in a star, then the rotation rate of the
stellar interior becomes known, and differential rotation is negligible
over most of the stellar mass.

---------------------------------------------------------
Title: What is the Horizontal Scale of the 5-min Oscillations?
Authors: Wolff, Charles L.
1973SoPh...32...31W Altcode:
If wrong, all the early reports of a small horizontal scale (≈
2000 km) for the 5-min oscillations may be due to unfortunate
similarities between the velocity and overturning time of the solar
granule convection and the corresponding velocity and period typical
of the oscillations. A large horizontal scale (≈ 30000 km) for the
oscillations seems consistent with the old data and almost required
by more recent measurements. The large scales recently measured would
imply that a sizeable fraction of the solar volume is involved in the
oscillation and would cast some doubt on all the old theories of the
5-min oscillations which were based on plane parallel atmospheres.

---------------------------------------------------------
Title: Interplanetary Gas. XVIII. The Mean Free Path of Protons at
i Astronomical Unit
Authors: Brandt, John C.; Nichols Thayer, Nina; Wolff, Charles L.;
Hundhausen, A. J.
1973ApJ...183.1037B Altcode:
Velocity distribution functions of solar-wind protons obtained by
the Vela 3 satellites have been analyzed to obtain a microscopic
determination of the momentum flux along magnetic field lines with
respect to a reference frame moving at the bulk speed. The determination
from macroscopic parameters allows the calculation of an effective
mean free path for protons at 1 a.u. which averages 0.06 a.u. and is
relatively independent of solar-wind velocity w. For quiet times when
300 km 1 &lt; w &lt; 400 km s ', the experimental mean free path is
2 to 3 times smaller than the value from plasma theory. For w &gt;
400 km s', the experimental value is 10 to 100 times smaller than the
theoretical value. The shorter mean free path for quiet times has been
incorporated into the model by Wolff, Brandt, and Southwick by use
of a coefficient of viscosity reduced by a factor of 3 at Earth. The
resulting model is in better agreement with the values of the quiet
solar wind at Earth suggested by Hundhausen than is the model with
full viscosity. Subject headings: interplanetary medium - solar wind

---------------------------------------------------------
Title: A Theory for the 5-Minute Oscillations of Large Horizontal
Scale.
Authors: Wolff, C. L.
1973BAAS....5...20W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Comments on Paper by E. Leer and T. E. Holzer, ‘Collisionless
solar wind protons: A comparison of kinetic and hydrodynamic
descriptions’
Authors: Brandt, John C.; Wolff, Charles L.
1973JGR....78.3197B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Five-Minute Oscillations as Nonradial Pulsations of the
Entire Sun
Authors: Wolff, Charles L.
1972ApJ...177L..87W Altcode:
Calculations of the stability coefficient show that the Sun should be
pulsating as a unit in nonradial modes of high order. The pulsations
are driven by the superadiabatic gradient of the low photosphere
and by the same sensitive changes in opacity that are known to be
iniportant in variable stars. The existence of solar pulsations can
explain many of the large scale features observed in the well known
5-ininute oscillations of the solar atmosphere.

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Title: Free Oscillations of the Sun and Their Possible Stimulation
by Solar Flares
Authors: Wolff, Charles L.
1972ApJ...176..833W Altcode:
A large solar flare can raise the temperature of the underlying
photosphere by 10 percent. The resulting thermal expansion exerts upon
the solar interior a mechanical impulse whose kinetic energy is 1025
ergs. This will stimulate free modes of oscillation of the entire Sun,
and the initial amplitudes of the more easily observable modes are
calculated. Preliminary estimates of the effects of radiation damping
and turbulent viscosity indicate that damping times will typically he
longer than 1 day for the modes of most interest.

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Title: Solar wind heating.
Authors: Barnes, A.; Brandt, J. C.; Hartle, R. E.; Wolff, C. L.
1972CosEl...3..254B Altcode:
No abstract at ADS

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Title: Gegenschein-Moulton Region Photography from Lunar Orbit
Authors: Dunkelman, L.; Wolff, C. L.; Mercer, R. D.
1972NASSP.315..161D Altcode:
No abstract at ADS

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Title: Theoretical Oscillations of the Entire Sun.
Authors: Wolff, Charles L.
1971BAAS....3..462W Altcode:
No abstract at ADS

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Title: A Two-Component Model of the Quiet Solar Wind with Viscosity,
Magnetic Field, and Reduced Heat Conduction
Authors: Wolff, Charles L.; Brandt, John C.; Southwick, Robert G.
1971ApJ...165..181W Altcode:
Previous models of the quiet solar wind based on steady-state plasma
theory do not satisfactorily reproduce the observed properties
at Earth. The addition of non thermal heating cannot provide
agreement. Most earlier models neglected viscosity, and we find that
viscosity plays the major role in heating the protons. We present a
model, including viscosity, in which steady-state theory is altered
only by the reduction of the electron mean free path-a semiempirical
method for including the effects of plasma instabilities. At 1 a.u.,
this model has radial and azimuthal velocities of about 300 and 2 km
sec ', respectively; the electron and proton temperatures are 200000
and 40000 K; the electron density is 9 All are in good agreement with
quiet-time observations.

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Title: Are the Libration Clouds Real?
Authors: Roosen, R. G.; Wolff, C. L.
1969Natur.224..571R Altcode:
IT is disconcerting that the existence of dust cloud satellites at the
L4 and L5 libration points in the Earth-Moon
system, first reported by Kordylewski1, is so widely
accepted2-6, in view of negative radar results3,
and optical results7-11, some of which report no clouds even
to a limit twenty to thirty times fainter than the brightness claimed
by Kordylewski. Other discussions12,13 have also argued
against the existence of libration clouds. While there undoubtedly
exist patches of brightness in the night sky, their connexion with
the libration points is unproven.

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Title: A Solar-Wind Model with Two Temperatures, Viscosity, Rotation,
and Magnetic Field
Authors: Wolff, C. L.; Brandt, J. C.; Southwick, R. G.
1969BAAS....1S.369W Altcode:
No abstract at ADS

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Title: Interplanetary Gas. XVI. a Calculation of the Angular Momentum
of the Solar Wind
Authors: Brandt, John C.; Wolff, Charles; Cassinelli, Joseph P.
1969ApJ...156.1117B Altcode:
A model of the quiet solar wind with magnetic field has been calculated
numerically using the momen- tum equations developed by Weber and Davis,
but with energy transport governed by the first law of thermodynamics
with heat conduction. The model is close to observed densities of
coronal electrons for r &gt; 2 Ro. Near the Earth, the model has N. =
6 cm3, w = 315 km sec', T = 325000° K, and a garden- hose angle of
55°; the Alfvén point is at r = 31.4 Ro, and the angular momentum
per unit mass in the solar equator is L = 1.4 X 1019 cm2 sec', a value
which gives an e-folding time for solar rotational braking of 5 X 1O~
yr. The azimuthal velocity (w~) of the plasma near Earth is 2.5 km
sec', and this value is consistent with the determination for quiet
times from Type I comet tails

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Title: A Calculation of the Angular Momentum of the Solar Wind
Authors: Brandt, John C.; Wolff, Charles; Cassinelli, Joseph P.
1969BAAS....1T.183B Altcode:
No abstract at ADS

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Title: Optical Environment about the OGO-III Satellite
Authors: Wolff, Charles
1967Sci...158.1045W Altcode:
An upper limit to the brightness of the daytime sky near a large
unmanned satellite has been obtained; it is some 30 times less than
the darkest daytime sky yet reported by an astronaut. However, there
still remains the danger that this background light (less than 5 ×
10-13 as bright as the sun) will interfere with observations
of the solar corona and zodiacal light.

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Title: Brightness of Possible Cloud Surrounding the OGO-IlI Satellite.
Authors: Wolff, C. L.
1967AJ.....72R.838W Altcode:
The fact that orbiting astronauts have great difficulty seeing stars
in the daytime has been discussed in the literature (Xey, E. P., and
Huch, W. F., Sc?ence 153, 297,1966; Roach, Dunkelman, Gill, and Mercer,
NASA Pubi. SP-121, Gemini Mid-Program Conference, 1966, p. 315) and
has led to speculation about a possible cloud of material surrounding
the spacecraft and scattering sunlight. Experience with a well-shielded
photometer on the OGO-IlI satellite cannot rule out the possibility of
there being a similar problem of daytime background light near large
unmanned satellites; however, if there is, the brightness is 30 times
less than the darkest daytime sky yet reported by an astronaut. A
measured upper limit of 1000 visual tenth magnitude stars per square
degree can be set upon the brightness, in full sunlight, of any cloud
of debris that might surround OGO-I I I. Any such high background of
scattered sunlight will be of concern to some astronomers. G. Xewkirk
(Planetary Space Sc?., to be published) has studied the problem of
a cloud about the Gemini spacecraft and this is compared, here, with
what might be expected for an unmanned satellite.

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Title: Photography of the Earth's Cloud Satellites from an Aircraft
Authors: Wolff, C.; Dunkelman, L.; Haughney, L. C.
1967Sci...157..427W Altcode:
Under astronomically favorable circumstances, photographs do not reveal
excess light near the triangular libration points of the earth-moon
system. We find that the visible surface brightness of anomalous dust
populations, if these populations do exist, is less than 10-9
candela per square centimeter.

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Title: Schreiben des Herrn Wolff an den Herausgeber
Authors: Wolff
1873AN.....82..279W Altcode:
No abstract at ADS

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Title: Beobachtung der Sonnenfinsterniß vom 15ten May 1836 von den
Herren Clüver und Wolff zu Bremen
Authors: Clüver; Wolff
1836AN.....13..381C Altcode:
No abstract at ADS