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Author name code: wilson-peter
ADS astronomy entries on 2022-09-14
=author:"Wilson, P.R." OR =author:"Wilson, Peter R."
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Title: Solar and Stellar Activity Cycles
Authors: Wilson, Peter R.
2005ssa..book.....W Altcode:
How do you predict the parameters of future solar cycles? What is the
role of dynamo theory in the cyclic activity of the Sun and similar
stars? And what are the implications of chaos theory for stellar
cycles? This book answers these questions and offers a timely review
of studies in the cyclic activity of the Sun and other stars. This
authoritative reference shows the importance of reliable predictions
of the parameters of future solar cycles, and carefully explains the
methods currently used to determine these (with special reference to
the maximum of cycle 22). Some of the latest research into solar cycles
is clearly presented; this includes helioseismology, observations
of the extended activity cycle and the polar fields reversal, and
contributions from dynamo theory and chaos theory. For graduate students
and researchers, this monograph provides a much-needed synthesis of
our understanding of activity cycles in the Sun and other stars.
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Title: Solar and Stellar Activity Cycles
Authors: Wilson, Peter R.
2005ssac.book.....W Altcode:
1. Introduction; 2. Historical survey; 3. The structure of the Sun and
the phenomena of activity; 4. The equations of magnetohydrodynamics
and magnetostatics; 5. The one-dimensional configuration of the cycle;
6. Heuristic models of the solar cycle; 7. Stellar activity and activity
cycles; 8. The two-dimensional representation of the extended activity
cycle; 9. The origin of the large-scale fields; 10. The reversals of
the polar magnetic fields; 11. The role of dynamo theory in cyclic
activity; 12. Helioseismology and the solar cycle; 13. Chaos and the
cycle; 14. Forecasting the cycle; 15. Summary and conclusion.
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Title: The Mechanism involved in the Reversals of the Sun's Polar
Magnetic Fields
Authors: Durrant, C. J.; Turner, J. P. R.; Wilson, P. R.
2004SoPh..222..345D Altcode:
Models of the polarity reversals of the Sun's polar magnetic fields
based on the surface transport of flux are discussed and are tested
using observations of the polar fields during Cycle 23 obtained by
the National Solar Observatory at Kitt Peak. We have extended earlier
measurements of the net radial flux polewards of ±60° and confirm
that, despite fluctuations of ∼20%, there is a steady decline in
the old polarity polar flux which begins shortly after sunspot minimum
(although not at the same time in each hemisphere), crosses the zero
level near sunspot maximum, and increases, with reversed polarity
during the remainder of the cycle. We have also measured the net
transport of the radial field by both meridional flow and diffusion
across several latitude zones at various phases of the Cycle. We can
confirm that there was a net transport of leader flux across the solar
equator during Cycle 23 and have used statistical tests to show that it
began during the rising phase of this cycle rather than after sunspot
maximum. This may explain the early decrease of the mean polar flux
after sunspot minimum. We also found an outward flow of net flux across
latitudes ±60° which is consistent with the onset of the decline of
the old polarity flux. Thus the polar polarity reversals during Cycle
23 are not inconsistent with the surface flux-transport models but the
large empirical values required for the magnetic diffusivity require
further investigation.
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Title: Observations and Simulations of the Polar Field Reversals in
Cycle 23
Authors: Durrant, C. J.; Wilson, P. R.
2003SoPh..214...23D Altcode:
We have used observations obtained by the National Solar Observatory
at Kitt Peak to study the reversals of the polar magnetic fields in
Cycle 23. We have compared them with corresponding data obtained by the
Mt. Wilson Observatory, when these are available, testing both data sets
against the locations of Hα filaments. Because of the unreliability
of the data at extreme latitudes and because the apparent time of
reversal varies with the degree of smoothing applied to the data, it
is difficult to determine precise reversal time in each hemisphere
from direct observations. However, we show that it is possible to
obtain a better-defined and more precise reversal time using polar
maps derived from simulations of the synoptic fields. These indirect
values, however, depend critically on the diffusivity used in the
simulations. We applied various tests to confirm an empirical value for
the diffusivity parameter of about 600 km<SUP>2</SUP> s<SUP>−1</SUP>
and hence determined empirical reversal times of CR 1976 in the northern
hemisphere and CR 1981 in the south.
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Title: Bipolar Magnetic Fields Emerging at High Latitudes
Authors: Durrant, C. J.; Turner, J.; Wilson, P. R.
2002SoPh..211..103D Altcode:
Three examples of the unusual development of high-latitude large-scale
features during cycle 23 are described. These features are found in
synoptic plots constructed using data obtained at both the NSOKP and
the MWO Observatories. Several properties of these features cannot
be reproduced in direct simulations using a modified form of the
flux-transport equation appropriate for synoptic fields and it is
inferred that their evolution is not due solely to the advection
and diffusion of decaying active region fields. The analysis shows
that one feature may be related to a high-latitude bipolar region
which emerged in an earlier rotation. By imposing the locations
of Hα filaments on enlargements of the NSOKP daily magnetograms,
we can identify the location of the other features and study their
structure at high resolution. This suggests that they are related to
the emergence of small magnetic knots at high latitudes. By repeating
the simulations including overlays of non-random patterns of bipoles
emerging at appropriate times during the simulations, it is possible
to study the effects of different patterns and to reproduce some
of the qualitative properties of these features not present in the
direct simulations. These results support Stenflo's contention that
`quite minute deviations from a random distribution (in the emergence
of small-scale fields) would suffice for these fields to have global
effects'.
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Title: High-resolution Studies of the Polar Magnetic Fields during
Cycle 23
Authors: Varsik, J.; Durrant, C. J.; Turner, J.; Wilson, P. R.
2002SoPh..205..231V Altcode:
High-resolution mosaics of the solar polar magnetic fields have been
constructed using individual magnetograms obtained with the video
magnetograph of the Big Bear Solar Observatory, and the properties
of these mosaics are demonstrated in this paper. The mosaics show
selected regions of the polar fields on several days during the rising
phase of Cycle 23, and are related to the global polar fields (i)
by superposing the mosaic for a given day on to a full-disk SOHO-MDI
magnetogram obtained on the same day, (ii) by plotting the mosaics in
polar projection and using these to identify the approximate regions
reported by the mosaics on the NSOKP polar synoptic plots, and (iii)
by imposing the locations of the Hα filaments on to the mosaics in
order to infer the neutral lines of the large-scale fields. We have
studied the fine structure of the large-scale unipolar fields near the
poles and, in particular, have constructed histograms of the magnetic
field intensities within particular regions of the mosaics and, in
this way, have estimated the ratios of the number of magnetic knots of
opposite polarities within the unipolar plumes. We have also generated
enlargements of the polar regions of the NSOKP daily magnetograms. These
and statistical studies have shown that on days for which the BBSO
mosaics are not available, the NSOKP enlargements may be used to study
the high-resolution polar fields. Time-series of mosaics obtained over
four-hour periods on September 6 and November 18 show that considerable
evolution in the structure of existing flux knots and the formation
of several new knots has taken place during these periods.
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Title: The Evolution of Trailing Plumes from Active Regions
Authors: Durrant, C. J.; Kress, J. M.; Wilson, P. R.
2001SoPh..201...57D Altcode:
We have studied the evolution of several high-latitude flux `plumes',
i.e., unipolar regions, trailing from active regions which emerged
near sunspot maximum in cycle 23. The observed patterns are compared
with simulations using a simple flux transport equation based on the
observed flux for an earlier Carrington rotation. In addition to the
long recognized poleward migration and diffusion of flux from active
regions, it is found that the evolution of the trailing plumes may
be influenced by flux which emerges above latitude 35° over areas of
all scales. We describe two cases in which the emerging flux appears
in the form of bipolar flux patterns which are not obviously related
to sunspots. Further, we find instances in which the observed surface
flux decreases or spreads at rates which cannot be explained solely in
terms of diffusion using the normally accepted rates. Thus in several
cases the poleward migration of flux cannot be described in terms
of passive transport by advection and diffusion as considered here,
and further investigation of the processes that contribute to the
evolution of the polar fields is required.
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Title: Simulations of the Polar Field Reversals during Cycle 22
Authors: Kress, J. M.; Wilson, P. R.
2000SoPh..194....1K Altcode:
The revised Mount Wilson synoptic magnetic data for the period September
1987 through March 1996 are used as the basis of numerical simulations
of the evolution of both the northern and southern polar magnetic
fields during the reversal and declining phases of cycle 22. The
simulations are based on numerical solutions of the flux-transport
equation which involve, as parameters, the maximum meridional flow
speed, v<SUB>0</SUB>, and the supergranule diffusivity, κ. By matching
characteristics of the observed and simulated fields, such as the
observed reversal times, the evolution of the net flux above 60 °, and
the migration of the polar crown, empirical values of these parameters,
i.e., v<SUB>0</SUB>=11 m s<SUP>−1</SUP>,κ=600 km<SUP>2</SUP>
s<SUP>−1</SUP>, may be determined. Further, the observed decrease
in the mean net flux above 60 ° during the late declining phase of
cycle 22 can be simulated only by increasing the diffusivity to 900
km<SUP>2</SUP> s<SUP>−1</SUP>. However, direct observations of the
supergranule velocities yield values of the diffusivity of order 200
km<SUP>2</SUP> s<SUP>−1</SUP>, and we show that the inclusion of
a pattern of emerging bipoles in the simulations can increase the
diffusion of these fields and that, together with a more realistic
value of the diffusivity, it is possible to reproduce qualitatively
the features of the observed polar field reversals.
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Title: Observations of the Polar Magnetic Fields During the Polarity
Reversals of Cycle 22
Authors: Snodgrass, H. B.; Kress, J. M.; Wilson, P. R.
2000SoPh..191....1S Altcode:
The Mount Wilson synoptic magnetic data for the period September 1987
through March 1996 are completely revised and used to provide polar
plots of the solar magnetic fields for both hemispheres. This period,
from Carrington rotations 1793 to 1906, covers the reversals of the
polar magnetic fields in cycle 22. Comparison of our plots with the
presently available Hα filtergrams for this period shows that the
polarity boundaries are consistent in these two data sets where they
overlap. The Mount Wilson plots show that the polar field reversals
involve a complex sequence of events. Although the details differ
slightly, the basic patterns are similar in each hemisphere. First the
old polarity becomes isolated at the pole, then shortly thereafter,
the isolation is broken, and the polar field includes unipolar regions
of both polarities. The old polarity then reclaims the polar region,
but when the isolation of this field is established for a second time,
it declines in both area and strength. We take the reversal to be
complete when the old polarity field is no longer observed in the
Mount Wilson plots. With this criterion we find that the polar field
reversal is completed in the north by CR 1836, i.e., by December 1990,
and in the south by CR 1853, i.e., March 1992.
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Title: The evolution of isolated active regions
Authors: Kress, J. M.; Wilson, P. R.
1999SoPh..189..147K Altcode:
The decay of several active regions which emerged early in cycle
22 has been studied using daily magnetograms and synoptic plots
obtained at the Vacuum Telescope at the National Solar Observatory,
Kitt Peak. The observed patterns are compared with simulations using
the flux transport equation and some discrepancies are noted. For one
region it is shown that, by including the emergence of a non-random
pattern of small magnetic bipoles during the decay, the correspondence
between the observed and simulated patterns may be improved.
---------------------------------------------------------
Title: High-Resolution Studies of the Solar Polar Magnetic Fields
Authors: Varsik, J. R.; Wilson, P. R.; Li, Y.
1999SoPh..184..223V Altcode:
We present high-resolution studies of the solar polar magnetic fields
near sunspot maximum in 1989 and towards sunspot minimum in 1995. We
show that, in 1989, the polar latitudes were covered by several unipolar
regions of both polarities. In 1995, however, after the polar field
reversal was complete, each pole exhibited only one dominant polarity
region.
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Title: Curious Magnetic Changes in a Quiet Region
Authors: Zirin, H.; Wilson, P. R.; Li, Y.
1998SoPh..179..269Z Altcode:
We describe the evolution of weak magnetic fields in a quiet region
observed at the Big Bear Solar Observatory on 1 October 1996. We
observed puzzling changes in which one polarity changed without
corresponding increases or decreases in the other. In the rest of the
same field, no special changes were observed, and a search of nearby
days revealed no similar changes. We do not wish to call Maxwell's
laws into question, we simply state that there are surprising effects
that we cannot understand with current models.
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Title: The Internal Solar Rotation Rate Inferred from Combined GONG
and LOWL Data
Authors: Li, Y.; Wilson, P. R.
1998ApJ...499..504L Altcode:
Frequency splittings derived from the first 4 months of GONG data
and from the 2 yr average of the LOWL data in the form of the
Clebsch-Gordon coefficients are analyzed. The results show that the
equatorial rotation rate is essentially “flat” (i.e., independent of
radius) for 0.2 < R/R<SUB>⊙</SUB> < 0.6. They also indicate an
increase in the rotation rate at high latitudes (of ~15% at latitude
60° for R/R<SUB>⊙</SUB> < 0.4), but it is emphasized that this
result is a property of the data sets and should not be regarded as
a property of the Sun without independent confirmation.
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Title: Is the Solar Rotation Uniform Below the Surface?
Authors: Wilson, P. R.; Li, Y.
1998ESASP.418..857W Altcode: 1998soho....6..857W
For want of reliable data, most analyses of solar frequency splittings
(e.g. Thompson et al. 1996) have assumed that the tachocline layer
connects the differentially rotating convection zone to a uniformly
rotating interior. Yet there is some indication in the first four months
GONG data of an increase in the angular velocity at high latitude below
r = 0.6 (Wilson et al. 1997, and a stronger signal in the two year LOWL
data (Charbonneau et al. 1998, Li and Wilson 1998) suggesting that there
may be an increase of ~15% at latitude 60-circ below r = 0.4. There
is also an indication in the SOHO data of a localized increase at r =
0.6 and latitude ~60-circ (Schou, private communication). The evidence
from these diverse sources is assessed.
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Title: From "down under"
Authors: Wilson, Peter R.
1998ASSL..222..136W Altcode: 1998ream.conf..136W
No abstract at ADS
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Title: The internal rotation rate inferred from LOWL and GONG data
Authors: Li, Y.; Wilson, P. R.
1998IAUS..185..181L Altcode:
A slightly modified forward method (Wilson et al., 1995, 1996) is
applied to the 2-year-average LOWL frequency splitting data recently
provided by Jesper Schou and Steven Tomczyk. In comparison with GONG
data, this data set contains less multiplets at small nu l, but more
at large nu l which probes greater depth into the solar interior. Two
approaches are to be described and the internal rotation profiles
will be shown in this poster. One approach uses a combined data set
of the GONG 4-month-average data and the 2-year-average LOWL data. For
the second, multiplets with nu l > 54.6 are selected from the LOWL
data (for reasons to be given in the paper). We use the rotation rate
previously obtained from the 4-month-average GONG data as the value
for depth from the surface to 0.75R<SUB>odot</SUB>. Below this level
we use the selected LOWL data to constrain the rotation rate. In both
cases, the surface rotation rates are chosen equal to the measured
plasma rotation rates by Snodgrass (1984).
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Title: Coronal Holes and the Polar Field Reversals
Authors: Fox, P.; McIntosh, P.; Wilson, P. R.
1998SoPh..177..375F Altcode:
A description of the reversal of the solar north polar magnetic field
during cycle 22 is provided using polar projections which combine
the large-scale magnetic fields as inferred from Hα synoptic charts
and coronal holes mapped from Hei λ1083 nm spectroheliograms. These
plots are supported by polar plots of the magnetic fields derived from
synoptic magnetic field data from the Mount Wilson Observatory. The
coronal holes showed some unexpected evolutionary patterns in
relation to the polarity reversals, and these patterns appear to be
coordinated with changes in the global patterns of coronal holes and
the heliospheric current sheet, suggesting that the polar reversal
originates from global processes rather than from local magnetic flux
annihilation. Similar patterns have been observed in the reversal of
the southern polar magnetic field in cycle 22 and in both hemispheres
in cycle 21. The consequences of these findings for the solar dynamo
process are discussed.
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Title: The Rotational Structure of the Region below the Solar
Convection Zone
Authors: Wilson, P. R.; Burtonclay, D.; Li, Y.
1997ApJ...489..395W Altcode:
Frequency splittings derived from the first 4 month string of GONG
data in the form of the Clebsch-Gordon coefficients are analyzed with
particular emphasis on the region near the base of and just below
the convection zone. It is found that the greatest changes in angular
velocity occur across the region 0.60 < r = R/R<SUB>⊙</SUB> <
0.72. At equatorial latitudes, the angular velocity increases (outward)
from 416 nHz at r = 0.645 to 455 nHz at r = 0.71, with a maximum
angular velocity gradient dω(λ)/dr of order 2.2 × 10<SUP>-3</SUP>
(in units of nHz km<SUP>-1</SUP>) at r = 0.68 +/- 0.01. At latitude
30°, there are some fluctuations in the angular velocity between r =
0.70 and r = 0.75, but below r = 0.70 the angular velocity is relatively
uniform. At latitude 45°, the angular velocity decreases from 449
nHz at r = 0.645 to 415 nHz at r = 0.71, with a maximum (negative)
gradient of magnitude 1.9 × 10<SUP>-3</SUP> again at r = 0.68 +/-
0.01; while at latitude 60° the angular velocity decreases from
440 nHz at r = 0.67 to 383 nHz at r = 0.775, with a maximum negative
gradient of order 2.4 × 10<SUP>-3</SUP> at r = 0.70 +/- 0.01. Models
exhibiting a discontinuous shear between the convection zone and a
uniformly rotating radiative region are not strongly supported by
these data. A model with a uniformly rotating core below r = 0.58
and with some latitudinal structure in the range 0.58 < r <
0.70 is found to be consistent with the data.
---------------------------------------------------------
Title: New IRIS constraints on the solar core rotation.
Authors: Gizon, L.; Fossat, E.; Lazrek, M.; Cacciani, A.; Ehgamberdiev,
S.; Gelly, B.; Grec, G.; Hoeksema, J. T.; Khalikov, S.; Palle, P. L.;
Pantel, A.; Regulo, C.; Schmider, F. -X.; Wilson, P. R.
1997A&A...317L..71G Altcode:
Four time series of IRIS data (4 to 6 months) have been used to obtain
improved measurements of the low degree (l=1,2,3) rotational splitting
frequencies. Assuming that the rotation law is known in the outer
layers of the Sun, we investigate the implications of IRIS splittings
for the central regions. Both a one-shell and a two-shell rotation
model have been considered in the solar core. A core rotating slightly
faster than the outer radiative envelope provides the best fit to the
data. Some evidence for the reliability of the observations is shown
by the visibility of differential rotation in the l=3 multiplets.
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Title: On the Inference of the Solar Internal Rotation Profile from
Frequency-splitting Data
Authors: Wilson, P. R.; Burtonclay, D.; Li, Y.
1996ApJ...470..621W Altcode:
From the earliest helioseismology data it was inferred that the internal
angular velocity of the Sun is invariant across the convection zone
(i.e., it mimics the surface differential rotation). This result caused
some concern to theoreticians since many dynamo and dynamical models of
the convection zone require that the angular velocity be approximately
constant on cylinders concentric about the rotation axis. <P />Stark and
others have argued that in order to test models of the angular velocity
against frequency- splitting data the uncertainties in these data must
be magnified, and it is shown here that within these uncertainties it is
indeed difficult to exclude some models in which the angular velocity is
independent of radius across a region including the convection zone and
some depths below it. Further, Gough and his colleagues have recently
claimed that the currently available data are not inconsistent with some
models for which the angular velocity is constant on cylinders within
the Sun's convection zone. Thus, inferences from frequency-splitting
data regarding the internal angular velocity of the Sun would seem
to be somewhat uncertain. <P />In this paper, these uncertainties are
discussed and an alternative approach is proposed in which a forward
method is used to find the simplest model for the angular velocity
(i.e., with the least positional variations) consistent with the data,
including the quoted uncertainties. While it is not claimed that such a
model represents the true angular velocity, its features may be said to
"characterize" the essential properties of a particular data set.
---------------------------------------------------------
Title: Some aspects of the interpretation of frequency splitting data
Authors: Wilson, P. R.
1996BASI...24..251W Altcode:
No abstract at ADS
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Title: Book reviews
Authors: Humphreys, R. M.; Kemp, S.; Savonije, G.; van der Hucht,
K. A.; van der Kruit, P. C.; Miley, G.; Bumba, V.; van Nieuwkoop,
J.; van Hoolst, T.; Cox, A.; Rutten, R. J.; Kleczek, J.; de Jager,
Cornelis; Jerzykiewicz, M.; Zwaan, C.; Poedts, S.; Sakai, Jun-Ichi;
Pecker, J. -C.; Heikkila, W.; de Jong, T.; Wilson, P. R.; Müller,
E. A.; Hoyng, P.; Icke, V.; Shore, S. N.; Achterberg, A.; Lucchin, F.;
Butcher, H.; Ne'Eman, Y.; Heidmann, J.; Belton, M. J. S.; de Graauw,
Th.; Waters, L. B. F. M.; Pacini, F.; Hultqvist, B.; Akasofu, S. -I.;
Vial, J. -C.; Schatzman, E.; van der Laan, H.; Cole, K. D.; Vanbeveren,
D.; Southwood, D.; van der Klis, M.; Katgert, Peter
1996SSRv...76..339H Altcode:
No abstract at ADS
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Title: Differential Rotation and Dynamics of the Solar Interior
Authors: Thompson, M. J.; Toomre, J.; Anderson, E. R.; Antia, H. M.;
Berthomieu, G.; Burtonclay, D.; Chitre, S. M.; Christensen-Dalsgaard,
J.; Corbard, T.; De Rosa, M.; Genovese, C. R.; Gough, D. O.; Haber,
D. A.; Harvey, J. W.; Hill, F.; Howe, R.; Korzennik, S. G.; Kosovichev,
A. G.; Leibacher, J. W.; Pijpers, F. P.; Provost, J.; Rhodes, E. J.,
Jr.; Schou, J.; Sekii, T.; Stark, P. B.; Wilson, P. R.
1996Sci...272.1300T Altcode:
Splitting of the sun's global oscillation frequencies by large-scale
flows can be used to investigate how rotation varies with radius
and latitude within the solar interior. The nearly uninterrupted
observations by the Global Oscillation Network Group (GONG) yield
oscillation power spectra with high duty cycles and high signal-to-noise
ratios. Frequency splittings derived from GONG observations confirm
that the variation of rotation rate with latitude seen at the surface
carries through much of the convection zone, at the base of which is
an adjustment layer leading to latitudinally independent rotation at
greater depths. A distinctive shear layer just below the surface is
discernible at low to mid-latitudes.
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Title: High-Resolution Studies of the Solar Polar Magnetic Fields
Authors: Varsik, J. R.; Wilson, P. R.; Li, Y.
1996AAS...188.3504V Altcode: 1996BAAS...28..871V
Most observations of the polar magnetic fields of the Sun have been at
relatively low resolution. High-resolution studies of the polar fields
offer new insight into their evolution. We show that near sunspot
maximum in 1989, the polar regions are covered with several unipolar
regions, each region containing magnetic knots of both polarities. These
knots have average lifetimes greater than 7 hours but less than 24
hours. In 1995, after the polar field reversal was complete, each pole
exhibits one dominant polarity, and the dominant polarity knots are in a
ratio of 5:1 to the opposite polarity. By measuring the displacement of
magnetic knots over a 7 hour period a rotation rate can be determined
which is consistent with the Snodgrass (1982) relation determined by
cross correlations of Mt. Wilson magnetograms. Most knots are not seen
in magnetic bipoles either when the overall polar fields are mixed or
when one polarity is dominant.
---------------------------------------------------------
Title: Calculations of the Solar Internal Angular Velocity for
1986--1990
Authors: Wilson, P. R.; Burtonclay, D.; Li, Y.
1996ApJ...457..440W Altcode:
Frequency splitting data obtained at the Big Bear Solar Observatory for
the years 1986, 1988, 1989, and 1990 are analyzed by a modified forward
calculation in order to find the simplest solutions which embody the
essential features of those data. The solutions are used to identify
the properties of the Sun's internal angular velocity that are common
to all years and to study possible changes from year to year. <P />The
common properties include a maximum in the angular velocity at all
latitudes just below the surface and a shear zone (negative outward),
at high latitudes near the base of the convection zone. Surprisingly,
there is no indication of a shear zone at intermediate latitudes,
and at low latitudes there is only a weak suggestion of a shear in
1989 and 1990. While there is some evidence of other changes in the
internal angular velocity from year to year, they do not appear to be
qualitatively significant.
---------------------------------------------------------
Title: Book-Review - Solar and Stellar Activity Cycles
Authors: Wilson, P. R.; Collier Cameron, A.
1995Obs...115..334W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Crisis in Helioseismology
Authors: Wilson, P. R.; Burtonclay, D.; Li, Y.
1995ESASP.376b.295W Altcode: 1995help.confP.295W; 1995soho....2..295W
No abstract at ADS
---------------------------------------------------------
Title: Calculations of the Solar Internal Rotation Coefficients,
1986-1990
Authors: Wilson, P. R.; Burtonclay, D.
1995ASPC...76...78W Altcode: 1995gong.conf...78W
No abstract at ADS
---------------------------------------------------------
Title: Forward Analysis of the BBSO Frequency-splitting Coefficients
for 1986
Authors: Wilson, P. R.; Burtonclay, D.
1995ApJ...438..445W Altcode:
Frequency-splitting data obtained at the Big Bear Solar Observatory
(BBSO) for 1986 are collated by a method which permits qualitative
inferences regarding the internal rotation profile of the Sun. The data
are analyzed by a recursive forward approach which is first tested by a
'hare and hounds' experiment. The method is then applied to the Big Bear
data yields a solution for the Sun's internal rotation profile for 1986.
---------------------------------------------------------
Title: The Reversal of the Solar Polar Magnetic Fields - Part Five
Authors: Wilson, P. R.; Giovannis, J.
1994SoPh..155...29W Altcode:
The Mount Wilson synoptic magnetic data from CRs 1815 to 1866 are used
to describe the reversal of the solar polar magnetic fields during
the period May 1989-March 1993. These are compared with simulations
based on the observed fields for CR 1815 using the flux transport
equation. Simulations including the emergence of small bipoles with
preferred poleward orientations are also described. It is shown that,
while the former can provide a qualitative account of the evolution
of the southern fields between CRs 1815 and 1860, only the latter can
describe the evolution of the northern fields between CRs 1815 and 1865.
---------------------------------------------------------
Title: Books-Received - Solar and Stellar Activity Cycles
Authors: Wilson, P. R.
1994JBAA..104..240W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Books-Received - Solar and Stellar Activity Cycles
Authors: Wilson, P. R.
1994Sci...265.1902W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar and stellar activity cycles.
Authors: Wilson, P. R.
1994CAS....24.....W Altcode:
This book offers a unique survey of our knowledge of cyclic activity
for the Sun and extends and links this to cycles in other stars. It
provides a valuable review of our basic knowledge of the Sun, of solar
activity cycles and of stellar activity cycles in general. It shows
the importance of reliable predictions of future solar cycles, and
carefully explains the methods currently used to determine the details
of these (with special reference to the maximum of cycle 22). Some of
the latest research into solar cycles is clearly presented, including
helioseismology, observations of the extended activity cycle and the
polar field reversals and theoretical contributions from dynamo theory
and chaos theory.
---------------------------------------------------------
Title: Solar and stellar activity cycles
Authors: Wilson, Peter R.
1994ssac.book.....W Altcode: 1994QB526.C9W55....
No abstract at ADS
---------------------------------------------------------
Title: Real and Virtual Unipolar Regions
Authors: Snodgrass, H. B.; Wilson, P. R.
1993SoPh..148..179S Altcode:
Difficulties in relating magnetograph measurements to the actual
solar magnetic field are discussed. After a brief review both of
problems inherent in the nature of the measurements and of sources
of instrumental error, we show that field measurements taken within
the photosphere can map out large-scale regions of a single magnetic
polarity even though these regions contain no footpoints of large-scale
magnetic structures, but instead only aggregates of small, unresolved
bipoles. This may occur wherever the density of unresolved bipoles has
a preferred orientation and a spatial variation along the direction
of that orientation. We call these regionsvirtual unipolar regions,
as they are not connected to regions of opposite polarity by field
loops or lines passing through the corona. Investigation of these
regions shows that they can arise at widely separated locations, and
that they may evolve into real unipolar magnetic regions which are
connected to the chromospheric and coronal fields. These results can
explain a number of puzzling aspects of magnetograph observations of
the solar background magnetic field.
---------------------------------------------------------
Title: Forward Calculations of Libbrecht's Frequency Splitting
Coefficients
Authors: Wilson, P. R.
1993ASPC...42..209W Altcode: 1993gong.conf..209W
No abstract at ADS
---------------------------------------------------------
Title: The Reversal of the Solar Polar Magnetic Fields - Part Four
Authors: Murray, N.; Wilson, P. R.
1992SoPh..142..221M Altcode:
It is a basic feature of the Babcock-Leighton model of the solar cycle
that the polar field reversal is due to the diffusive decay and poleward
drift of the active region fields. The flux from follower regions moves
preferentially polewards in each hemisphere, where it cancels with,
and then replaces, the previously existing polar fields. A number of
workers have attempted to model this process by numerical solutions
of the flux transport equation, which include the surface effects of
supergranule diffusion, differential rotation and meridional flow,
with conflicting results.
---------------------------------------------------------
Title: Helioseismology Data and the Solar Dynamo
Authors: Wilson, P. R.
1992ApJ...399..294W Altcode:
Some of the difficulties raised by recent helioseismology data for
dynamo wave models of the solar cycle are addressed. These data
have been interpreted as indicating that the latitudinal variations
of angular velocity across the convection zone are approximately
independent of depth. Theoretical frequency splittings are calculated
for several types of model of the sun's internal rotation profile,
and it is confirmed that models in which the rotation rate is constant
on concentric cylinders are incompatible with these data, but only
if parameters for the surface rotation rate are permitted to depart
from those derived from surface spectroscopic data. Another class
of model, in which the rotation rate profiles are not independent of
depth, is investigated, and these models are shown to accommodate the
helioseismology data at least as well as the radial surfaces model. The
implications for dynamo models and for the dynamics of the convection
zone are considered.
---------------------------------------------------------
Title: The Reversal of the Solar Polar Magnetic Fields - Part Three
Authors: Wilson, P. R.
1992SoPh..138...11W Altcode:
Observations of the first major active regions and large-scale magnetic
field patterns of Cycle 22 are presented. These show that, following
the emergence of a trans-equatorial pattern, or cell, of positive flux
related to old cycle activity, the first new cycle active regions of
the longitude range emerged across the neutral lines of this cell,
which continued to grow and expand across the equator for several
rotations. The development of a parallel trans-equatorial band of
flux of opposite (negative) polarity and the emergence of both new
and old cycle active regions across a neutral line of this cell are
also described.
---------------------------------------------------------
Title: Comment on the Discussion of the Extended Activity Cycle
Authors: Wilson, P. R.
1992ASPC...27..376W Altcode: 1992socy.work..376W
No abstract at ADS
---------------------------------------------------------
Title: The Reversal of the North Polar Field
Authors: Wilson, P. R.
1992ASPC...27..116W Altcode: 1992socy.work..116W
No abstract at ADS
---------------------------------------------------------
Title: Theoretical Implications of the Extended Activity Cycle
Authors: Wilson, P. R.
1992ASPC...27..368W Altcode: 1992socy.work..368W
No abstract at ADS
---------------------------------------------------------
Title: The Reversal of the Solar Polar Magnetic Fields - Part Two
Authors: Wilson, P. R.; McIntosh, P. S.
1991SoPh..136..221W Altcode:
Observations of the first large-scale patterns of magnetic fields near
the sunspot minimum of 1986 (the start of cycle 22) are presented using
synoptic magnetic data provided by the National Solar Observatory
and contour maps constructed from data provided by the Mount Wilson
Solar Observatory. The latter are compared with simulated contour maps
derived from numerical solutions of the flux transport equation using
data from particular Carrington rotations as initial conditions.
---------------------------------------------------------
Title: The Reversal of the Solar Polar Magnetic Fields - Part One
Authors: Wilson, P. R.; McIntosh, P. S.; Snodgrass, H. B.
1990SoPh..127....1W Altcode:
Some theoretical difficulties confronting the current model of the
polar magnetic reversal by cancellation with the flux remnants of
decaying active regions are discussed. It is shown that the flux
transport equation does not adequately describe the essential physical
consequences of the transport of large-scale fields, linked to deep
subsurface toroids, over distances comparable with the solar radius. The
possibility that subsurface reconnections may release these fields
to form U-loops is discussed but it is shown that, in this event,
the loops will quickly rise to the surface. Mechanisms whereby the
flux may escape through the surface are considered.
---------------------------------------------------------
Title: An Extended Activity Cycle Picture of the Sun's Polar
Magnetic Fields
Authors: Snodgrass, H. B.; Wilson, P. R.
1990BAAS...22Q.855S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Origin of the Large-Scale Fields
Authors: Wilson, P. R.; McIntosh, P. S.
1990BAAS...22..872W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Cycle Workshop - 3RD Meeting / Sydney, Australia /
1989JAN
Authors: Wilson, P. R.; Donnelly, R. F.; Wilkinson, P.
1990SoPh..125..159W Altcode: 1990SoPh..125..157W
The contributions to the third meeting of the Solar Cycle Workshop are
briefly summarized. The topics discussed at the meeting included (i)
predictions and precursors, (ii) large and small-scale magnetic fields,
(iii) photospheric velocity fields, (iv) coronal phenomena, (v) the Sun
as a star, (vi) limb temperature measurements and helioseismic data,
(vii) theoretical modelling of the cycle, (viii) cyclic activity in
stars, and (ix) the interpretation of the Elatina Sandstone Layers.
---------------------------------------------------------
Title: The buoyancy of U-loops
Authors: Wilson, P. R.
1989PASA....8...32W Altcode: 1989PASAu...8...32W
The problem of the surface migration of solar magnetic fields is
discussed. It is shown that, unless some form of reconnection takes
place below the surface, magnetic tension should effectively prevent
such migration and the possibility of U-loop formation and transport
is considered. As a first step, the buoyancy of a magnetic 'U-loop'
within an isothermal atmosphere is considered. It is shown that
such a configuration may form by the reconnection of the arms of
an Omega-loop associated with an active region, and is likely to be
buoyant initially and rise through the region. However, as it rises,
the net buoyancy decreases and, provided that the temperature within
the loop is even marginally less than that outside, it will reach
a subsurface configuration in which the net buoyancy is zero. The
significance of this result for solar magnetic fields is then assessed.
---------------------------------------------------------
Title: The Solar Dynamo and the Convective Rolls
Authors: Wilson, P. R.
1988SoPh..117..217W Altcode:
The most sophisticated attempts to model the convection zone have
yielded results in which the angular velocity increases outwards and
the largest scales of convection take the form of `banana cells' aligned
with the rotation axis. However, not only does the sign of the angular
velocity gradient present problems for dynamo theory, but attempts to
detect banana type cells have so far been unsuccessful. Although by
no means conclusive, current tracer, spectropic, and radiative data
all tend to support models of azimuthal rolls encircling the axis as
the fundamental mode.
---------------------------------------------------------
Title: Solar Cycle Workshop
Authors: Wilson, P. R.
1988SoPh..117..205W Altcode:
The presentations and discussions which took place during the second
meeting of the Solar Cycle Workshop are summarized under the headings:
sunspot minimum, the extended cycle, the large-scale photospheric
motions, the large-scale magnetic fields and the polar reversal,
the small-scale fields, global cyclic phenomena and the fundamental
processes. The progress achieved so far is assessed and the directions
for future observational and theoretical work are suggested.
---------------------------------------------------------
Title: The extended solar activity cycle
Authors: Wilson, P. R.; Altrocki, R. C.; Harvey, K. L.; Martin, S. F.;
Snodgrass, H. B.
1988Natur.333..748W Altcode:
The solar cycle has been defined in terms of a sequential periodic
variation in sunspot numbers, the period being the interval between
successive minima, currently averaging 11.2 years. But a number of
observations have indicated that the activity cycle may begin at
higher latitudes before the emergence of the first sunspots of the
new cycle. Here we report results from sunspot cycle 21 concerning
the ephemeral active regions, the coronal green-line emission and the
torsional oscillation signal, which confirm the earlier suggestions. In
particular, we report the appearance of a high-latitude population of
ephemeral active regions in the declin-ing phase of sunspot cycle 21,
with orientations that tend to favour those for cycle 22 rather than
21. Taken together, these data indicate that sunspot activity is simply
the main phase of a more extended cycle that begins at high latitudes
before the maximum of a given sunspot cycle and progresses towards
the equator during the next 18-22 yr, merging with the conventional
'butterfly diagram' (the plot of the latitudes of emerging sunspots
against time) as it enters sunspot latitudes. We suggest that this
extended cycle may be understood in the perspective of a model of
giant convective rolls that generate dynamo waves propagating from
pole to equator.
---------------------------------------------------------
Title: Solar torsional oscillations as a signature of giant cells
Authors: Snodgrass, H. B.; Wilson, P. R.
1987Natur.328..696S Altcode:
Although the existence of giant cells<SUP>1</SUP> as the fundamental
mode of solar convection has long been proposed on theoretical grounds,
attempts to detect them observationally have been unsuccessful. During
one search, using Mount Wilson magnetograph data, Howard and
LaBonte<SUP>2,3</SUP> discovered a pattern of latitudinal velocity bands
that move from the poles towards the equator in synchrony with the
sunspot cycle, and they interpreted this pattern as a torsional wave
or 'oscillation' with wavenumber k=2 hemisphere<SUP>-1</SUP>. Here we
suggest that this signal is not in fact an oscillation but represents
a modulation of the mean differential rotation caused by a system of
giant convective rolls which start at the poles at 11-yr intervals and
migrate to the equator in a period of 18-22 yr. Additional evidence
for the presence of these rolls is found in the zero offsets in the
Mount Wilson data<SUP>4</SUP> and in latitude variations of the limb
temperature<SUP>5</SUP>. Thus we argue that the fundamental mode
of giant-cell convection in the sun takes the form of equatorward
migrating azimuthal rolls. This differs from the 'banana cell' mode
suggested by Gilman<SUP>6</SUP>, and from the poleward propagating
rolls reported by Ribes et al.<SUP>7</SUP>.
---------------------------------------------------------
Title: Azimuthal Rolls and the Solar Cycle
Authors: Snodgrass, H. B.; Wilson, P. R.
1987BAAS...19Q.935S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Cycle Workshop
Authors: Wilson, P. R.
1987SoPh..110....1W Altcode:
Clearly there is no concensus or agreement at present about the
nature and mechanism of the solar cycle or, indeed, about many of its
observed features. However, by highlighting these areas of agreement
and disagreement through the presentations and discussions during
this meeting, it is hoped that the work of the Workshop Groups will be
directed to resolving at least some of these questions at or before the
next meeting (planned for August, 1987). In particular, it is hoped
that Group V (The Sun as a Star) will be able to contribute through
studies of the sun in relation to stellar cycles and activity.
---------------------------------------------------------
Title: Solar Rotation and the Giant Cells
Authors: Wilson, P. R.
1987SoPh..110...59W Altcode:
Departures from the mean solar differential rotation rate as a function
of latitude, longitude, and epoch of the solar cycle, together with
variations in the rotation rate as determined by spectroscopic and
tracer measurements are reviewed. It is shown that, if giant convection
cells do exist as predicted, real variations in the subsurface rotation
rate should occur and that this may be responsible for the observed
surface anomalies.
---------------------------------------------------------
Title: Solar Cycle Workshop. Proceedings of the 2nd meeting, held
at Stanford Sierra Lodge, Lake Tahoe, California, 10 - 14 May 1987.
Authors: Wilson, P. R.
1987scwp.book.....W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Cycle Workshop. Proceedings of the first meeting held at
Big Bear Solar Observatory, Pasadena, CA, USA, 17 - 20 August, 1986.
Authors: Wilson, P. R.
1987SoPh..110.....W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A New Definition for the Solar Cycle
Authors: Wilson, P. R.
1986BAAS...18.1010W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Generation of Magnetic Fields in Photospheric Layers
Authors: Wilson, P. R.
1986SoPh..106....1W Altcode:
Recent observations concerning the growth and decay of photospheric
magnetic flux present a challenge to the conventional picture of
the photosphere as a passive medium through which flux tubes emerge
inertly. Rather, they suggest the possibility that interactions between
the magnetic flux and the photospheric velocity fields may give rise
to changes in the observed surface flux.
---------------------------------------------------------
Title: Flux changes in small magnetic regions. II - Further
observations and analysis
Authors: Simon, G. W.; Wilson, P. R.
1985ApJ...295..241S Altcode:
Further examples of flux changes are described in which the flux
associated with small magnetic knots of dimension 2-3 arcsec is
observed to increase or decrease by 50-100 percent during periods
of order 20-40 minutes. Within the same regions both positive and
negative flux knots have been studied. In one case the positive and
negative flux fluctuations appeared to be almost out of phase, but in
another they were roughly in phase. From measurements of the velocity
field within each region, an estimate of the vertical velocity shear has
been calculated, and correlations of order 0.5 between the fluctuations
in this shear and in both the positive and negative flux counts have
been obtained in several, but not all cases. The possibility that
these apparent flux changes are due to instrumental or seeing effects,
changes in the line equivalent width, or vertical velocity gradients
is discussed, but it is concluded that none of these effects provides
a tenable alternative explanation of the observed changes. It is
therefore suggested that these changes may provide examples of the
generation of nonpotential magnetic fields (i.e., electric currents)
within the photospheric layers, as has been proposed by several authors
from time to time.
---------------------------------------------------------
Title: A new model for flux emergence and the evolution of sunspots
and the large-scale fields
Authors: McIntosh, P. S.; Wilson, P. R.
1985SoPh...97...59M Altcode:
Existing models for the evolution of sunspots and sunspot groups,
describing the subsurface structure of the magnetic fields and their
interactions with the convective motions, are briefly reviewed. It is
shown that they are generally unable to account for the most recent data
concerning the relationship between the large-scale solar magnetic field
structures and the magnetic fields of active regions. In particular,
it is shown that the former do not arise directly from the decay of the
latter, as required by the Babcock model and all other models based on
it. Other observations which are not adequately explained by current
models are also cited.
---------------------------------------------------------
Title: The possibility of a photospheric dynamo
Authors: Wilson, P. R.
1985AuJPh..38..911W Altcode:
Several recent observations are discussed which suggest that the
current model for the emergence and decay of photospheric flux does
not provide a complete account of all the processes involved. An
elementary two-dimensional dynamo is discussed and it is shown how
this may be adapted to photospheric conditions in order to provide a
plausible kinematic account of these observations.
---------------------------------------------------------
Title: Photospheric flux changes and the MHD approximation
Authors: Wilson, P. R.
1984PASA....5..500W Altcode: 1984PASAu...5..500W
It is noted that observations of changes in photospheric magnetic
flux present a challenge to the conventional picture of passive
emerging flux tubes. This problem is assessed through an examination
of the MHD approximation; both the pressure gradient term and the
thermoelectric term are considered. It is concluded that, although
they may provide seed fields, the two source terms, of themselves,
seem unable to explain the observed rates of flux growth. However,
observations suggest that regions of rapid growth and decay of flux
are connected with velocity shears; it is thus necessary to consider
the possibility that these nonaxisymmetric motions may give rise to
dynamo action within these local regions.
---------------------------------------------------------
Title: Flux changes in small magnetic regions
Authors: Wilson, P. R.; Simon, G. W.
1983ApJ...273..805W Altcode:
High spatial and temporal resolution observations of continuum,
velocity, and magnetic fields in active regions of the sun have
been obtained which reveal rapid changes in the total magnetic flux
associated with surface magnetic features. Attention is given to two
cases. In the first, during February 1980, the total positive flux
associated with a magnetic feature increased by about 50 percent in
about 90 min without observable negative flux change. The topology
of the feature developed from a single intense core to one exhibiting
several discrete cores, all of like polarity. The second case, during
July 1981, involved large fluctuations in the flux associated with a
small negative feature over 20-min time intervals. Calculations of the
correlation between velocity gradients and magnetic field gradients
show values in the 0.4-0.7 range at times of good seeing, reaching a
peak when the flux is greatest.
---------------------------------------------------------
Title: Free and forced oscillations of a flux tube
Authors: Wilson, P. R.
1981ApJ...251..756W Altcode:
The free oscillations of a magnetic flux tube of finite dimension,
embedded in a nonmagnetic plasma, which may be in uniform motion
relative to the tube, are studied for models in which energy may
propagate laterally away from the tube. Although solutions obtained
using the thin tube approximation yield both real and complex
frequencies, the numerical solutions for effectively thick tubes all
exhibit real frequencies and imaginary external wavenumbers. Thus the
waves propagate parallel to e flux tube with constant amplitude and
are evanescent in the transverse direction. <P />The same general
formulation permits the study of the oscillations set up by an
oscillatory disturbance applied at a point on the axis of the tube. Here
it is found that for weak or moderately intense tubes the wave
amplitudes decrease along the tube away from the disturbance as wave
energy leaks away from the tube in the transverse direction. Intense
tubes, however, tend to focus the wave energy along the tube, and the
wave amplitude increases away from the disturbance. It is suggested
that this effect may be relevant for photospheric flux tubes.
---------------------------------------------------------
Title: Flux Changes in Small Magnetic Regions
Authors: Wilson, P. R.; Simon, G. W.
1981BAAS...13..882W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Faculae, filigree and calcium bright points
Authors: Wilson, P. R.
1981SoPh...69....9W Altcode:
Simultaneous observations of fine structure photospheric features at
several wavelengths are described. The observations, which include
regions near disk center and at the limb, were obtained using a narrow
band calcium filter and selected wavelengths in Mg b<SUB>1</SUB>, the
red wing of Hα and the Hα continuum using the Universal Birefringent
Filter of the Sacramento Peak Observatory.
---------------------------------------------------------
Title: Theories of sunspot structure and evolution
Authors: Wilson, P. R.
1981phss.conf...83W Altcode:
Various attempts to model all or part of the known phenomena associated
with sunspots are reviewed. In summary, sunspots appear and grow
as groups within active regions. Simple prototypes are the leader L
and follower F spots, with the F spots decaying within a week, like a
group, while L spots first form a moat-like structure and then last for
several solar rotations. The magnetic structure stability of a sunspot
is discussed, together with the reasons for the relative coolness,
i.e., 3500-4000 K. A necessity is mentioned for understanding the
subsurface structure of the spots, although the phenomena may in fact
be shallow. Attention is given to the features and deficiencies of
three sunspot models. It is suggested that improvements in modeling
may be obtained from studies of the irradiance variability data, the
growth and decay rates, time-dependent studies of the simultaneous
magnetic and velocity fields and brightness patterns in the region
around sunspots, and observations by the solar orbiting telescope of
the ultrafine structure of the umbrae and penumbrae.
---------------------------------------------------------
Title: The general dispersion relation for the vibration modes of
magnetic flux tubes
Authors: Wilson, P. R.
1980A&A....87..121W Altcode:
The general dispersion relation for wave modes in a magnetic flux tube
embedded in a compressible but unstratified atmosphere is obtained
and is solved numerically for several different sets of atmospheric
parameters. Approximate analytic solutions for the phase velocity are
also recovered in the thin tube approximation and these are compared
with the numerical solutions. The nature of the different modes is
discussed and particular attention is given to the interface or long
wavelength mode, and to the 'taut wire' mode.
---------------------------------------------------------
Title: The interaction of acoustic waves with flux tubes
Authors: Wilson, P. R.
1980ApJ...237.1008W Altcode:
The interaction between a magnetic flux tube and an acoustic wave
front propagating in the nonmagnetic region in which it is embedded
is investigated by expressing the incident wave as a Fourier Bessel
series. Using the velocity and pressure balance conditions at the
interface, one may determine the amplitudes of the reflected and
transmitted waves for each Bessel component. The component of the
energy flux parallel to the field and averaged over azimuth and cycle
is determined at the interface for both internal and external waves. It
is found that when the component of the phase velocity of the incident
wave along the tube approaches AC(i)/square root of (A-squared plus
C/i/-squared) (A is the Alfven speed and C(i) the sound speed),
the wave flux within the tube is concentrated at the interface. The
implications of this for wave propagation in the solar atmosphere are
briefly discussed.
---------------------------------------------------------
Title: Wave propagation in a magnetic flux sheath in the presence
of a velocity field.
Authors: Wilson, P. R.
1979ApJ...230..194W Altcode:
Hydromagnetic-wave propagation in a plane-parallel magnetic flux
sheath embedded in a compressible plasma is studied in the case
where a uniform velocity field exists in either the sheath or the
external plasma. The problem is formulated in the flux-sheath geometry
partly for the mathematical convenience of the Cartesian coordinate
system, and the formulation is generalized to include perturbation
velocities parallel to the flux sheath and perpendicular to the
magnetic field. Variations in the perturbation amplitudes in the
indicated direction are considered in order to elucidate possible
wave modes along supergranule boundaries. Attention is given to
a strictly two-dimensional case, the thin-flux-tube approach, and
the three-dimensional case. The effect of the velocity field on the
stability of the system is evaluated.
---------------------------------------------------------
Title: Hydromagnetic wave modes in magnetic flux tubes.
Authors: Wilson, P. R.
1979A&A....71....9W Altcode:
The vibration modes and stability of a discrete magnetic flux element
(a cylindrical flux tube or a two-dimensional flux sheath) embedded
in an infinite compressible but unstratified plasma are analyzed. It
is shown that the dispersion relation for a thin flux tube takes
two distinct forms, depending on whether the oscillation modes are
symmetrical or asymmetrical, that the m = 0 mode in the cylindrical
geometry is analogous to the pulsation mode of a thin flux sheath, and
that the axis of the flux tube has a finite velocity for the m = 1 mode,
which is analogous to the vibration mode of a taut wire. Comparison
of the results for the thin flux tube and thin flux sheath indicates
that the taut-wire mode of the sheath corresponds to the m = 1 mode
of the tube. The relevance of this analysis to solar magnetic fields
is discussed.
---------------------------------------------------------
Title: Wave modes in magnetic elements in a stratified atmosphere.
Authors: Wilson, P. R.
1978ApJ...225.1058W Altcode:
The vibration modes of a magnetic flux element embedded in a
compressible, gravitationally stratified atmosphere are considered. A
local dispersion relation is first derived for a force-free field
which decreases exponentially with height, and this is applied to
a magnetic flux sheath lying within the local region. The sheath is
embedded in an isothermal, gravitationally stratified plasma for which
the standard dispersion relation applies globally. The velocity and
pressure balance conditions across the interface restrict the possible
vibration modes of the system. For the pulsation or varicose mode,
a modified acoustic mode and a modified fast mode are obtained. The
latter has a cutoff frequency which is greater than the acoustic
cutoff and suggests that waves of shorter periods may occur in the
presence of magnetic elements. For the sinuous or taut wire mode,
complex solutions for the dispersion equation are obtained. For one
of these the real part is large and negative, indicating that, within
the limitations of a linear analysis, waves propagate with increasing
amplitude. The possible significance of this is briefly discussed.
---------------------------------------------------------
Title: Wave modes in a magnetic flux sheath.
Authors: Wilson, P. R.
1978ApJ...221..672W Altcode:
The symmetric wave modes of a two-dimensional magnetic flux sheath
embedded in a compressible isothermal but nongravitational atmosphere
are investigated under more general conditions than those considered
earlier by Cram and Wilson. Both two-dimensional 'taut wire' and
pulsation modes are considered, and explicit solutions are obtained
when the thickness of the flux sheath is small compared with the
transverse scale size of the perturbations. In particular, it is found
that the taut wire or Alfven-type mode may be unstable if the density
within the sheath is less than that outside. The solutions for the
pulsation mode are compared with those obtained by Defouw under similar
conditions. Agreement is obtained only in the limit as the sound speed
in the nonmagnetic region tends to infinity. It is shown that Defouw's
analysis, which neglects all transverse variations in the perturbations,
is unsuitable to the problem and that the approximation which he makes
eliminates the interaction between the magnetic and nonmagnetic plasmas.
---------------------------------------------------------
Title: Structure within a magnetic flux tube.
Authors: Wilson, P. R.
1978PASA....3..225W Altcode: 1978PASAu...3..225W
X-ray observations of the solar corona show the existence of hot flux
loops within which both the pressure and temperature appear to be in
excess of that outside the loops. This paper discusses the structure
within such flux tubes in terms of standard models, the enhancement
of small-scale fields and approximate models of large radius.
---------------------------------------------------------
Title: The stability of a magnetic flux element in a horizontally
stratified compressible plasma.
Authors: Wilson, P. R.
1977SoPh...55...35W Altcode:
The configuration of a magnetic flux element in a static, compressible,
gravitationally stratified plasma is considered. Under isothermal
conditions an exact force-free solution is given for a two-dimensional
cartesian flux sheath but for an axi-symmetric element, i.e. a flux
tube, approximate solutions, applicable only to thin flux tubes,
are obtained.
---------------------------------------------------------
Title: Hydromagnetic Waves in Magnetic Flux Tubes
Authors: Wilson, P. R.
1977PASA....3..173W Altcode: 1977PASAu...3..173W
No abstract at ADS
---------------------------------------------------------
Title: The elementary theory of a twisted flux tube. II. Stability.
Authors: Wilson, P. R.
1977ApJ...214..917W Altcode:
Previously developed models for magnetic flux tubes are used to
calculate the total potential energy of a tube embedded in an isothermal
horizontally stratified compressible atmosphere. By comparing this with
the total energy of a system of n flux tubes having the same total flux
as the original tube, a necessary condition is obtained that the system
is consistent with the adiabatic subdivision of a single untwisted flux
tube. It is shown that under nonadiabatic conditions such as exist in
the solar photosphere, the subdivision process must be endothermic
(i.e., external energy is required) if the temperature within
the original tube is significantly less than its surroundings, but
exothermic if the temperatures are comparable. Thus it is conjectured
that magnetic structures are less susceptible to subdivision if they
are significantly cooler than their surroundings. While a twisted
flux tube cannot subdivide simply like an untwisted tube, it may fray
into several spiral filaments; it is shown that the cooling required
to prevent this is actually greater than for an equivalent untwisted
tube. It is shown that several features of the growth and decay of
sunspots may be explained in terms of this conjecture.
---------------------------------------------------------
Title: The elementary theory of twisted flux tubes. I. Equilibrium
configurations.
Authors: Wilson, P. R.
1977ApJ...214..611W Altcode:
An approximate parametric treatment of the equilibrium of a twisted,
nonisothermal flux tube is given in which third and higher order
terms in the Taylor expansion of the field are neglected. Families of
nonisothermal, nonforce-free solutions are obtained. The equilibrium
and pressure boundary conditions are satisfied correct to second-order
terms, while the zero divergence condition is satisfied exactly. Models
of untwisted flux tubes or of isothermal force-free tubes are obtained
as particular cases of the general formulation. A comparison is
made with Parker's analysis of twisted flux tubes, and it is shown
that Parker's analysis is valid only for small angles of twist. The
possibility of field enhancement by cooling and twisting is considered
in terms of the models obtained.
---------------------------------------------------------
Title: Alfvén waves and Meyer's sunspot model.
Authors: Wilson, P. R.
1975MNRAS.172..535W Altcode:
The recent account of the growth and decay of a sunspot by Meyer,
Schmidt, Weiss and Wilson is compared with models exhibiting a
large emission of Alfven flux. It is shown that a composite model
which involves both modified convection and Alfven waves within the
sub-surface flux rope can overcome some of the difficulties faced
by either type of model independently. It is shown that interactions
between convective motions and the flux tubes may give rise to twists in
these tubes. The significance of these twists in relation to the decay
of the spot magnetic field and the appearance of the moving magnetic
features in the moat is discussed. An approximate distribution of the
radiative, convective and hydromagnetic energy flux in the neighborhood
of a stable l-spot is suggested on the basis of the composite model.
---------------------------------------------------------
Title: Alfvén Waves and the Sunspot Phenomenon
Authors: Wilson, P. R.
1975SoPh...42..333W Altcode:
Parker's explanation of the sunspot phenomenon in terms of the
enhanced emission of Alfvén waves (solar vulcanology) is shown to be
compatible with observation only if ∼ 90% of the waves propagate
downwards. Further difficulties arise if the region of cooling by
Alfvén wave generation is restricted to a depth of 2 Mm. However,
it is shown that, if Alfvén wave generation is included in a recent
model proposed by Meyer, Schmidt, Weiss and Wilson, these difficulties
may be resolved. The problem of the sharp umbra and penumbra boundaries
is discussed and it is shown that features of this combined model are
relevant to the flare phenomenon.
---------------------------------------------------------
Title: Hydromagnetic Waves in Structured Magnetic Fields
Authors: Cram, L. E.; Wilson, P. R.
1975SoPh...41..313C Altcode:
Although the inhomogeneous nature of solar magnetic fields is now
well established, most theoretical analyses of hydromagnetic wave
propagation assume infinite homogeneous fields. Here we reformulate
the hydromagnetic wave problem for magnetic fields which vary in one
direction perpendicular to the field. The permitted modes of small
amplitude hydromagnetic oscillations are considered, first in the case
of a single interface between semi-infinite magnetic and non-magnetic
compressible regions, and secondly for a magnetic flux sheath of
given thickness imbedded in a nonmagnetic region. It is shown that,
for small values of R (the ratio of the Alfvén to the sound speed),
an acoustic or p-mode wave front passes through the flux sheath with
only minor deformation. However, for large R, the transmitted acoustic
wave is attenuated and, depending upon the thickness of the flux sheath
and the angle of incidence, a hydromagnetic wave may be effectively
trapped and guided along the flux sheath.
---------------------------------------------------------
Title: The growth and decay of sunspots.
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.; Wilson, P. R.
1974MNRAS.169...35M Altcode:
Sunspots are formed between supergranules, at junctions in the
chromospheric network. Many spots disappear rapidly. However, some large
spots enter a phase of slow decay: an annular cell develops, centered
on the spot and with a systematic outward velocity directed from the
penumbra toward the nearest faculae. This flow forms a moat around
the spot swept clear of magnetic field except for magnetic features
which migrate from the penumbra to the surrounding network. This
phase may persist for several months before the spot is finally
destroyed. Throughout this period the sunspot area, and hence its flux,
decrease at a constant rate. The evolution of a sunspot is related
to subphotospheric convection, with particular emphasis on a model of
the slow decay phase which explains the steady decay of magnetic flux.
---------------------------------------------------------
Title: The Cooling of a Sunspot. IV: Reply to M. H. Gokhale
Authors: Wilson, P. R.
1974SoPh...37..483W Altcode: 1974SoPh...37..438W
Some criticisms made by Gokhale (1974) on the present author's (1972)
work on the cooling of a sunspot are met. It is agreed that axisymmetric
models of magnetic and velocity fields are inadequate with respect to
the zero divergence conditions, and that nonaxisymmetric models must
be considered even if only in qualitative form. It is pointed out that
the failure of Wilson's (1972) axisymmetric models to satisfy the zero
divergence condition at all points where r is below a critical value
does not invalidate some of the other conclusions. Calculations are
carried showing the existence of a region where the zero divergence
condition is satisfied to first order. It is agreed also that the power
converted to magnetic form during field amplification is not a likely
explanation of the residual energy deficit associated with sunspots.
---------------------------------------------------------
Title: The Cooling of a Sunspot IV: Reply to D. J. Mullan
Authors: Wilson, P. R.
1974SoPh...35..111W Altcode:
This paper considers the recent criticism by Mullan (1973) of sunspot
models and the cooling mechanism which I have proposed in Papers I,
II and III of this series. The discussion of the cooling produced
by an idealized flow cycle has been extended to include vertical
temperature gradients which are consistent with a convectively unstable
atmosphere. This leads to an expression for Mullan's parameter f (the
ratio in which estimates of the energy flux based on an idealized Carnot
cycle should be reduced) which is appropriate to this situation. It is
shown that, for a cycle similar to that of Paper III, f = 0.82, while
for one which has a vertical extent of order 5 Mm, f= 0.4. Hence the
energy flux which, in principle, can be transported away from a sunspot
by such a cycle is conservatively estimated to be 1.1 × 10<SUP>29</SUP>
erg s<SUP>−1</SUP> compared with a typical sunspot energy deficit
of 2.2 × 10<SUP>29</SUP> erg s<SUP>−1</SUP>. Other criticisms
relating to the magnetic field amplification and the `cool one' model
are discussed. It is concluded that the essential features of these
models remain valid and that the modifications suggested by Mullan's
criticism greatly increase their applicability to the sunspot problem.
---------------------------------------------------------
Title: The Stability of a Velocity Shear in the Presence of an
Inhomogeneous Magnetic Field
Authors: Wilson, P. R.
1974Ap&SS..26..363W Altcode:
The stability of a velocity shear in the presence of a parallel
but non-uniform magnetic field is considered in general terms. Two
special cases are then investigated; (i) the well known case of
a plane interface at which a discontinuity in the magnetic field
coincides with the velocity shear; (ii) an axially symmetric flow
in which discontinuities in the magnetic and velocity fields occur
at a cylindrical surface whose axis is parallel to the flow. In the
first case the flow is stabilized if the rms Alfvén velocity of
the magnetic field exceeds the shear velocity; a result consistent
with that obtained by other writers. In the second case it is shown
that the discontinuity in the magnetic field increases the stability
of the system. The significance of this result for the stability of
the flux ropes associated with sunspots in the solar convection zone
is considered.
---------------------------------------------------------
Title: A Theoretical Model for the Convection of Magnetic Flux in
and Near Sunspots
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.; Wilson, P. R.
1974IAUS...56..235M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Stability of a Magnetic Flux Rope and its Relation to
Sunspots, Faculae and Flares
Authors: Wilson, P. R.
1974IAUS...56..301W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Cooling of a Sunspot. III: Recent Observations
Authors: Wilson, P. R.
1973SoPh...32..435W Altcode:
The coordinates of the cooling cycle described in Paper I are re-defined
in order to provide an account in which the part played by the cycle
in cooling the sunspot is separated from the role of the supergranule
cells in transporting energy away from it.
---------------------------------------------------------
Title: Erratum: "The cooling of a sunspot. II" [Sol. Phys., Vol. 27,
p. 363 - 372 (1972)].
Authors: Wilson, P. R.
1973SoPh...30..280W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Cooling of a Sunspot. I: A Carnot Cycle and the
Hydromagnetic Interactions
Authors: Wilson, P. R.
1972SoPh...27..354W Altcode:
A mechanism is proposed to explain the cooling of a sunspot in terms of
the detailed interactions between the magnetic field and the convective
motions. The mechanism provides that an axially symmetric concentration
of magnetic field deforms the normal supergranule cell pattern below
the sunspot into a radial outflow of plasma over a region of diameter
∼ 60 Mm.
---------------------------------------------------------
Title: The Cooling of a Sunspot. II: Convection Zone Models and the
Magnetic Power Supply
Authors: Wilson, P. R.
1972SoPh...27..363W Altcode:
In order to discuss the detailed interactions between the magnetic and
velocity fields below a sunspot, several models of the convection zone
are considered. It is suggested that giant convection cells establish
a pattern of large superadiabatic gradients near the top and bottom
of the zone analogous with the temperature gradients in laboratory
convection. These gradients in turn establish their own eddies or cells
with dimensions typical of the local scale height. Those at the top
correspond to the photospheric granules while overshoot motions from the
bottom of the layer may be related to the surface supergranule motions.
---------------------------------------------------------
Title: Giant Cells and the Solar Cycle
Authors: Wilson, P. R.
1972PASA....2..144W Altcode: 1972PASAu...2..144W
Despite the success of the Babcock-Leighton model in explaining some
phenomena of the solar cycle, e.g. Hale’s polarity law and Maunder’s
butterfly diagram, it has recently encountered a number of observational
and theoretical difficulties. The observational difficulties are
centred around the different behaviour of bi-polar magnetic regions
(BMRs) and uni-polar magnetic regions (UMRs). Babcock explains BMRs
as the surface eruptions of toroidal fields wound by the differential
rotation and it is clear that in their subsequent evolution and decay
they are obviously influenced by this effect. However, UMRs display a
sector structure in which the boundaries between regions of opposite
polarities appear to be quite unaffected by the differential rotation
but closely related to the interplanetary field sectors. Another feature
of solar activity unexplained by the Babcock theory is the tendency
of sunspots, flares, etc. to reappear at the same latitude during a
cycle. Warwick has observed that proton flares show a preference for
particular latitudes which may extend over several cycles. Again Bumba
et al. have observed that new cycle fields tend to appear in longitude
regions where old cycle fields are still visible.
---------------------------------------------------------
Title: Mean Values in Inhomogeneous Atmospheres
Authors: Wilson, P. R.; Williams, N. V.
1972SoPh...26...30W Altcode:
A brief summary of observations of inhomogeneities in the solar
atmosphere and progress in the theoretical analysis of two-dimensional
model atmospheres is given. In particular, it is asserted that
reliable reference models of the mean temperature, pressure, etc. may
be derived only by averaging over the horizontal coordinates of a two-
or three-dimensional model. In discussion of a wide variety of cases
including strong chromospheric lines, weak photospheric lines, and
continuum radiation, it is shown that although the derivation of mean
values by first averaging over the fluctuations in the data and then
applying a one-dimension analysis is an obvious first approximation,
it may lead to errors of a gross qualitative nature. Thus the recent
deductions by several authors of very small temperature gradients in the
upper regions of sunspots are shown to be subject to considerable doubt.
---------------------------------------------------------
Title: High Resolution Spectroscopy of the Disk Chromosphere. II. Time
Sequence Observations of Ca II H and K Emissions
Authors: Wilson, P. R.; Rees, D. E.; Beckers, J. M.; Brown, D. R.
1972SoPh...25...86W Altcode:
Two independent sets of high resolution time series spectra of the
CaII H and K emission obtained at the Solar Tower and at the Big
Dome of the Sacramento Peak Observatory on September 11th, 1971 are
reported. The evolutionary behaviour of the emission first reported
by Wilson and Evans is confirmed but the detail of the evolution is
found to be more complex. In one case, a doubly peaked feature showing
some K<SUB>3</SUB> emission evolves into a single K<SUB>2</SUB> (red)
peak with no K<SUB>3</SUB> emission. Coincidentally, a neighbouring
doubly peaked feature evolves to a very strong blue peak. In an entirely
independent sequence a doubly peaked feature evolves into a single red
peak. The K<SUB>2</SUB> emission then fades completely although the
continuum threads are still strong. Finally a strong K<SUB>2</SUB>
blue peak appears. These developments are confirmed by intensity
profiles obtained from the spectra.
---------------------------------------------------------
Title: Alfvén Waves in Umbral Flux Tubes
Authors: Wilson, P. R.
1972SoPh...22..434W Altcode:
Savage has suggested that an energy flux of 2 × 10<SUP>10</SUP>
erg cm<SUP>−2</SUP> s<SUP>−1</SUP> passes through the umbra of a
sunspot in the form of hydromagnetic waves. In this paper some of the
consequences of this flux are considered. It is first shown that it
is not inconsistent with the energy requirements for the heating of
umbral dots and for solar wind storms, assuming in the latter case
that the flux tubes emerging from about one tenth of the area of a
large spot are open-ended.
---------------------------------------------------------
Title: Facular Models and the Sunspot Energy Deficit
Authors: Wilson, P. R.
1971SoPh...21..101W Altcode:
The problem of the energy deficit in a sunspot is shown to be critically
related to the depth of a given sunspot model. Recent facular models
are discussed and a new model is derived from recent data using a
two-dimensional radiative transfer analysis. The excess non-radiative
energy required by this and other models is evaluated and it is shown
that in some models this may account for a considerable fraction of the
sunspot energy deficit. For these models the Alfvén energy travelling
along the closed flux loops from the sunspot is insufficient to supply
the requirements of the faculae and it is suggested that excess energy
flux from below the faculae is also required. These results provide
further support for `deep' as opposed to `shallow' sunspot models.
---------------------------------------------------------
Title: Center Limb Observations of Inhomogeneities in the Solar
Atmosphere. III: Time Dependent Fine Structure of the Ca II Emission
Authors: Wilson, P. R.; Evans, C. D.
1971SoPh...18...29W Altcode:
High resolution Ca II K-line spectra obtained at Kitt Peak National
Observatory in September 1970 at a dispersion of 20 mm/Å and a spatial
resolution approaching 1 arc sec are described.
---------------------------------------------------------
Title: Center Limb Observations of Inhomogeneities in the Solar
Atmosphere. II: The Na D and Na 5688 Doublets and the MgI 4571 Line
Authors: Cannon, C. J.; Wilson, P. R.
1971SoPh...17..288C Altcode:
Center-limb observations of line-center intensity fluctuations in the Na
D and Na 5688 doublets and the Mg 4571 line are described. For small
scale structures the rms distributions for the photospheric lines
show maxima of 20% at a heliocentric angle of 40° (Mg4571) and 9%
at 20° (Na 5688). The rms values for Na D range between 10 and 13%
but show no significant maximum. Values for large scale structures
are somewhat less.
---------------------------------------------------------
Title: Sunspot Magnetic Fields and Umbral Dots
Authors: Wilson, P. R.
1971IAUS...43..475W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A three-component model for the formation of the chromospheric
Ca ii K line
Authors: Wilson, P. R.
1970SoPh...15..139W Altcode:
A recent two-component model for the formation of the CaII K
line in the solar chromosphere put forward by Beebe and Johnson
is discussed. Although this model is a great advance on existing
one-component models, it is pointed out that observations require a
minimum of three components in order to understand the formation of
the K<SUB>2</SUB> peaks.
---------------------------------------------------------
Title: Center-Limb Observations of Inhomogeneities in the Solar
Atmosphere. I: The Mg b Lines
Authors: Cannon, C. J.; Wilson, P. R.
1970SoPh...14...29C Altcode:
Center-limb observations of line-center intensity and velocity
fluctuations in the Magnesium b lines are described. Autocorrelation
and power spectral analyses indicate small scale brightness structures
having periodicities of 3000 km and 8000 km and large scale structures
of 22000 km. Corresponding velocity structures are 6000 km and 30000 km.
---------------------------------------------------------
Title: On the Properties of Umbral Dots
Authors: Wilson, P. R.
1969SoPh...10..404W Altcode:
On the basis of a three-dimensional radiative transfer analysis of
several models it is shown that bright structures in sunspot umbrae
which have horizontal diameters of 300 km or less cannot extend more
than 300 km down into the umbra. Thus, such models are inconsistent
with the hypothesis that the bright features are due to convection from
the deep regions of the umbra. No such restrictions can be applied if
the surface diameter is of order 500 km, but a model of this type is
shown to be inconsistent with the available data. Thus a convective
explanation of these bright features appears to be ruled out.
---------------------------------------------------------
Title: Structure of a Sunspot. V: What is the Wilson Effect?
Authors: Wilson, P. R.; McIntosh, P. S.
1969SoPh...10..370W Altcode:
From enlargements of patrol photographs of the disk passage of the
sunspot of July 20 - August 2, 1966, intensity profiles across the spot
are obtained at several positions near the disk-center and at each
limb. It is found that these profiles show asymmetric features near
each limb (increasingly sharp limb-side penumbra and poorly resolved
disk-side penumbra) which are similar to those reported in Paper III
of this series. It is suggested that these profile asymmetries are the
essential feature of the center-limb variations in the appearance of
a sunspot which have become known as the Wilson effect.
---------------------------------------------------------
Title: The Mean Temperature Gradient in the Umbra
Authors: Wilson, P. R.
1969SoPh....9..391W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Temperature Fluctuations in the Solar Photosphere. II: The
Mean Limb-Darkening and the Second Maximum
Authors: Wilson, P. R.
1969SoPh....9..303W Altcode:
In paper I of this series it was shown that Edmonds' center-limb rms
intensity fluctuation data provided strong evidence for the existence of
a maximum in the horizontal temperature fluctuation near 250 km (optical
depth 0.7). The data also gave a much less reliable indication of a
second temperature fluctuation maximum approximately 100 km below this
level. Two models, model 1 exhibiting a single temperature fluctuation
maximum and model 2 which has two temperature fluctuation maxima,
were put forward as worthy of further investigation.
---------------------------------------------------------
Title: On Granulation Models
Authors: Wilson, P. R.
1969SoPh....8...20W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Temperature Fluctuations and Convection in the Solar
Photosphere
Authors: Wilson, P. R.
1969BAAS....1R.296W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Temperature Fluctuations and Convective Modes in the Solar
Photosphere
Authors: Wilson, P. R.
1969PASA....1..195W Altcode: 1969PASAu...1..195W
Recently I have carried out a two-dimensional radiative-transfer
analysis of the data given by Edmonds on centrelimb relative rms
intensity fluctuations in terms of horizontal temperature fluctuations
in the solar photosphere. Edmonds himself attempted an analysis of his
data and found a ΔT <SUB>rms</SUB> which increased monotonically from
about 300°K at unit mean optical depth (i.e. at a given physical depth)
to 500°K at optical depth 3.
---------------------------------------------------------
Title: Temperature Fluctuations in the Solar Photosphere
Authors: Wilson, P. R.
1969SoPh....6..364W Altcode:
The general problem of interpreting granulation data, in particular
Edmonds' r.m.s. intensity fluctuation distribution against heliocentric
angle θ, is discussed.
---------------------------------------------------------
Title: On the Solution of the Transfer Equation for Continuum
Radiation in Inhomogeneous Atmospheres
Authors: Wilson, P. R.
1969ApJ...155..715W Altcode:
A successful method of solving the equation of radiative transfer for
a spectral line formed in a two- dimensionally varying atmosphere is
adapted to continuum radiation. An important modification to the method,
necessitated by the large horizontal intensity fluctuations found near
the boundaries of large solar granules and sunspots, is described
---------------------------------------------------------
Title: The Structure of a Sunspot. IV: A Two-Dimensional Radiative
Transfer Analysis of Center-Limb Intensity Profiles
Authors: Wilson, P. R.
1968SoPh....5..338W Altcode:
Typical intensity profiles across a sunspot at several heliocentric
angles are selected from recent observations of the Wilson Effect. In
addition, the profile of the mean intensity at the surface of the spot
is inferred from these observed profiles.
---------------------------------------------------------
Title: The Structure of a Sunspot. III: Observations of the Wilson
Effect
Authors: Wilson, P. R.; Cannon, C. J.
1968SoPh....4....3W Altcode:
White-light photographs of a fairly regular sunspot have been obtained
for all but one day of its passage across the disk. From microphotometer
tracings across these photographs, intensity profiles across the spot
have been obtained at several heliocentric angles, θ.
---------------------------------------------------------
Title: The Structure of a Sunspot. II: The Magnetohydrodynamics of
the Penumbra
Authors: Wilson, P. R.
1968SoPh....3..454W Altcode:
It is shown that horizontal radial flow in the penumbra is not
inconsistent with a vertical component of the penumbral magnetic
field. The magnetic amplification produced by the stretching of the
magnetic-flux tubes in this velocity field yields a resultant field
whose typical inclination to the horizontal is about 20°. It is shown
that the thermal convection forces can balance the magnetic forces
restraining this flow and that the magnetic energy produced by the
stretching of the flux tubes is of the same order of magnitude as the
sunspot-energy deficit. Finally, a mechanism is suggested for dispersing
this magnetic energy over a large region of the solar surface.
---------------------------------------------------------
Title: Spectral-Line Formation in Inhomogeneous Atmospheres
Authors: Wilson, P. R.
1968ApJ...151.1029W Altcode:
A method is presented for solving the three-dimensional Eddington
approximation of the radiative transfer equation for the spectral line
formed by a two-level atom in an atmosphere exhibiting horizontal
fluctuations in its physical properties. The method is demonstrated
in two simple cases in which (i) the electron temperature is assumed
to fluctuate sinusoidally in one direction parallel with the surface,
and (ii) similar fluctuations are postulated for the density. Criteria
for the stability of the solution and for assessing the accuracy of the
results are discussed. In case (i) the opacity is arbitrarily assumed to
be constant, since accurate methods are available for the solution of
problems of this type, and the accurate and approximate solutions are
compared. It is found that, although the source function fluctuations
below the surface are comparable in each case, the computed emergent
intensity fluctuations are much greater in case (i) than in case (ii)
where the opacity fluctuations greatly reduce the effect of the source
function fluctuations
---------------------------------------------------------
Title: On the Three-Dimensional Form of the Eddington Approximation
Authors: Wilson, P. R.
1968ApJ...151.1019W Altcode:
Derivations of the three-dimensional form of the Eddington approximation
by Giovanelli and by Unno and Spiegel are examined and shown to
be equivalent. They are compared with an earlier form obtained by
Chandrasekhar for stellar interiors and shown to be superior near the
surface. A third derivation is given which permits one to obtain a
mathematically consistent boundary condition for zero incident flux on
a plane surface This is similar to Krook's boundary condition for the
one-dimensional problem. This derivation also permits the investigation
of the accuracy of this approximation in a three-dimen- sional
atmosphere. While in general agreement with Unno and Spiegel's claims
for the value of the ap- proximation in astrophysical investigation,
this paper disagrees with their general conclusions for opti- cally
thin atmospheres and discusses several examples where errors are
found. Finally, the importance of the three-dimensional approximation
is emphasized in applications to atmospheres in which both in- tensity
and opacity fluctuate generally
---------------------------------------------------------
Title: The Structure of a Sunspot. I: The Birth and Development of
a Sunspot
Authors: Wilson, P. R.
1968SoPh....3..243W Altcode:
A new model for the structure of a sunspot is put forward. The features
of the model are (i) the deep inhibition of convection by magnetic
fields, (ii) the formation of a `cool cone' above the region of
inhibition of convective transfer by the energy diverted around this
region, and (iii) the development of the penumbra by the interaction
of strong magnetic field with thermal forces in a region where the
opacity prevents the transport of energy by radiation alone. A clear
distinction is made between a pore, which results from the inhibition
of deep convection across an area considerably greater than that of
the pore, and isolated penumbral filaments, which result from strong
local fields in the surface regions.
---------------------------------------------------------
Title: A Radiative Transfer Analysis of Wilson Effect Observations.
Authors: Wilson, P. R.
1968AJS....73R..84W Altcode:
Typical intensity profiles across a sunspot are selected from
recent observations of the Wilson effect (previously reported at
the Philadelphia meeting of the AAS and to appear in Solar Physics)
at the heliocentric angles 00, 580, 710. In addition, at 0=54044
(cos 0 = 1/~) a mean profile (i.e. asymmetries are averaged out) is
inferred from observed profiles at 0 = 580 and 520 since, within the
limits of the Eddington approximation, the emergent intensity at 0 =
cos-1 (1/W3) is equal to the mean intensity at the surface of a plane
parallel atmosphere. Starting from these data the transfer equation
is solved for the two-dimensional source function distribution within
the sunspot for several models of the opacity distribution. It is
found that only for an opacity model in which unit optical depth in
the umbra occurs at least 700 km below unit optical depth in the
mean photosphere do we obtain increases in the limb-side apparent
penumbral width and decreases in the apparent umbral diameter which
are qualitatively similar to the observed behavior but much smaller in
magnitude. However, when some further assumptions are made regarding
the release of convected heat in the penumbra near the umbra-penumbra
boundary, it is possible to reproduce all the features of the observed
profiles. Although no assumption is made about the shape of the umbra
below the surface, these solutions clearly show that at a depth of 700
km below unit optical depth in the penumbra the diameter of the umbral
region, which is 10 000 km. at the surface, has increased to about 11
500 km. Thus the shape of the umbral region below the surface is part
of an inverted cone of semivertical angle about 450
---------------------------------------------------------
Title: Recent Observations of the Wilson Effect in a Sunspot.
Authors: Wilson, P. R.
1968AJS....73R..40W Altcode:
White light photographs of a fairly regular sunspot have been obtained
for all but one day of its passage across the disk. From microphotometer
tracings across these photographs, intensity profiles across the spot
have been obtained at several heliocentric angles. Apparent sunspot,
umbral, and penumbral widths, have been obtained from these profiles
and an examination of these reveals that the well-known Wilson effect
(Wilson, A., Phil. Trans. 64, 1, 1774) is more complex than an earlier
account by Loughhead and Bray (Australian J. Phys. 11, 177,1958)
indicates. In particular, it appears that the apparent increase in
the width of the limb-side penumbra as the spot approaches the limb is
accompanied by an almost complementary decrease in the apparent umbral
diameter. Further, these changes in apparent widths occur only at
heliocentric angles greater than about 600. A model for the structure
of a sunspot, which qualitatively explains these observations, is
suggested. Its particular feature is the conical shape of the umbral
region below the solar surface. Unlike most existing models, however,
the vertex of the cone is upward so that the abnormally cool region
at a given physical depth below the surface covers a large area than
at the surface.
---------------------------------------------------------
Title: The Interpretation of Limb Intensity Profiles
Authors: Wilson, P. R.
1966ApJ...146..241W Altcode:
Limb intensity profiles at the center of Ha (i.e.,intensity distribution
against distance perpendicular to the limb and to the line of sight of
the observer) are calculated for several simple models of the absorption
coefficient at the line center. It is found that an abrupt change
of gradient, which appears in many observed profiles, also appears
in the calculated profiles, and in the latter this corresponds to a
total tangential optical thickness of 2.6 + 0.6 for a wide variety of
models. Thus one relation between the parameters of the model may be
obtained directly from observations.
---------------------------------------------------------
Title: On the Height of Formation of H-Alpha in the Solar Chromosphere
Authors: White, O. R.; Wilson, P. R.
1966ApJ...146..250W Altcode:
Several features of Ha limb spectra, including the line emission beyond
the continuum limb, are analyzed to yield information about the height
of formation of Ha in the solar chromosphere. It is concluded that
de Jager's suggested value for the height of unit optical depth at
the line center (5000 km) is too high. For the chromospheric features
in these spectra the height of formation lies in a range from 1500 km
(above a sunspot) to 2700 km. This is consistent with the limb profile
analysis which yields a range from 1600 to 3000 km for a hypothetical
mean chromosphere.
---------------------------------------------------------
Title: A Note on Deinzer's "theory of Sunspots"
Authors: Wilson, P. R.
1966ApJ...143..993W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On Photospheric Mean Values.
Authors: Wilson, P. R.
1965ApJ...142.1195W Altcode:
It is shown that, because the physical processes in the solar
photosphere are non-linear, calculations of mean values of the source
function must take into account not only the limb-darkening data
but also the magnitude of the observed instensity fluctuations. An
approximate iterative method is given for calculating mutually
consistent mean values and horizontal fluctuations for the source
function A discussion of physical considerations indicates that
results obtained for model atmospheres may well apply to the solar
atmosphere. Mean values of the source function against depth are
obtained that are on the average 8 per cent higher than existing mean
values. Mean values at fixed optical depth are also calculated, and
the role of the optical depth coordinate in a fluctuating atmosphere
is discussed.
---------------------------------------------------------
Title: The Wilson Effect and Sunspot Structure.
Authors: Wilson, P. R.
1965ApJ...142..773W Altcode:
A method is described for interpreting sunspot-intensity profiles at
different heliocentric angles in terms of the attenuation coefficient
distribution in the spot. Since the currently available data on sunspot
profiles at various angles are qualitative rather than quantitative,
the method cannot be applied in detail at present. However, it is
hoped that the availability of such a method will encourage observers
in the admittedly difficult task of obtaining such data. In order
to demonstrate what may be done at present, a simplified form of the
method is applied to Loughhead and Bray's photographs of a sunspot as
it passed across the disk of the Sun from limb to limb. It is shown that
the mean attenuation coefficient in the umbra of this spot is between 1
and 2 orders of magnitude less than in the surrounding photosphere. A
difference of 1 order of magnitude is shown to be consistent with the
assumption that the umbra of the spot is in radiative equilibrium.
---------------------------------------------------------
Title: Astrophysics: Summary and Discussion. (Book Reviews: Sunspots)
Authors: Wilson, P. R.
1965Sci...149...46W Altcode: 1965Sci...149...46B
No abstract at ADS
---------------------------------------------------------
Title: Photospheric Structure and RMS Fluctuation Data.
Authors: Wilson, P. R.
1964ApJ...140.1148W Altcode:
A new model approach to the interpretation of photospheric fluctuation
data is developed by calculating the attenuation coefficient
corresponding to any given value of the source function using the
assumption of LTE and the absorption properties of the negative
hydrogen ion and the neutral hydrogen atom. Application of this method
to Edmonds' recent rms fluctuation data shows it to be inconsistent with
a variety of simple columnar models of photospheric structure. Various
photospheric models are examined to determine the features of model
photospheric structures which affect the shape of calculated rms
fluctuation distributions. Finally a qualitative interpretation is
suggested for the appearance of the large-scale granulation pattern
toward the limb, as observed by Edmonds.
---------------------------------------------------------
Title: On Methods of Interpreting Solar Fluctuation Data.
Authors: Wilson, P. R.
1964ApJ...139..929W Altcode:
Existing methods of interpreting solar fluctuation data are compared,
and some major difficulties as[ated with the "empirical approach" of
, Edmonds, and others are shown to be more readily dled by the model
approach. Particular reference is made to the interpretation of the
maximum in onds' distribution of rms intensity fluctuations against
heliocentric angle. Difficulties in the existmodel method are also
mentioned and a new approach is suggested.
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Title: The Wilson effect and sunspot structure
Authors: Wilson, P. R.
1964susp.conf..146W Altcode:
No abstract at ADS
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Title: An Interpretation of Edmonds' Granulation Data.
Authors: Wilson, P. R.
1963ApJ...137..606W Altcode:
Edmonds' recent data on granulation contrast is interpreted in terms
of solutions of the equation of transfer in non-uniform media. It
is shown, first, that his results cannot be readily explained in
terms of atmospheres which are in radiative equilibrium, or even
of non-equilibrium atmospheres in which emission varies only with
depth. However, using a simple model representing emission from
convective cells, it is possible to reproduce an essential feature
of his results and to make some progress toward a photospheric model
based on his observations.
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Title: Three-dimensional solutions of the transfer equation
Authors: Wilson, P. R.
1963MNRAS.126..393W Altcode:
Methods of solving the equation of radiative transfer are obtained
sultable for media whose diffLtsing and absorbing properties vary
generally in three dimensions. The existing two-dimensional solutions
are then deduced as special cases. As an illustration of the second
and more important method, a model problem is solved.
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Title: Radiative transfer in media exhibiting large horizontal
variations
Authors: Wilson, P. R.
1962MNRAS.124..383W Altcode:
A method of solution of the equation of transfer is established
in media where the emitted radiation exhibits large horizontal
variations. Attenuation coefficient distributions are calculated for
two given intensity distributions, one of which is relevant to the
solar photosphere, and the interpretation of data concerning intensity
variations across photospheric granules is discussed. The general form
of the solution is also obtained for an axially symmetric medium such
as an idealized sunspot, and the need for data regarding the directional
intensity near a sunspot is stressed.
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Title: Spectral line profiles in emitting layers
Authors: Wilson, P. R.
1962MNRAS.124..231W Altcode:
Line emission profiles are calculated for a finite uniform layer in
which scattering is completely non-coherent, using a power series
solution of the equation of transfer in Eddington's approximate
form. The results obtained are in satisfactory agreement with those
obtained by Giovanelli using an independent method. The extension of
the method to non-uniform media is also discussed.
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Title: The application of the equation of transfer to the
interpretation of solar granulation
Authors: Wilson, P. R.
1962MNRAS.123..287W Altcode:
of The interpretation of solar granulation is discussed in terms
of the equation radiative transfer. This is solved for non-uniform
two-dimensional media in the absence of radiative equilibrium. The
solution is obtained as a functional relation for the attenuation
coefficient K in terms of the total intensity J and the emission
function E, and estimates of some of the parameters of simple models
are made by fitting mean values of J and K to tabulated values of
Sykes (4) and Plaskett (3). Typical data concerning the horizontal
variations in intensity at normal emergence are discussed in terms of
the remaining parameters of the models, and the need is indicated for
similar information at other angles of emergence.
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Title: On Solving the Equation of Radiative Transfer for Conservative
Non-uniform Media
Authors: Wilson, P. R.
1961AuJPh..14...57W Altcode:
No abstract at ADS
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Title: The Constant Flux Problem in Non-uniform Exponential Media
Authors: Wilson, P. R.
1960AuJPh..13..461W Altcode:
No abstract at ADS
