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.
Bibcode: 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.

Title: Solar and Stellar Activity Cycles
Authors: Wilson, Peter R.
Bibcode: 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.

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.
Bibcode: 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.

Title: Observations and Simulations of the Polar Field Reversals in
    Cycle 23
Authors: Durrant, C. J.; Wilson, P. R.
Bibcode: 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.

Title: Bipolar Magnetic Fields Emerging at High Latitudes
Authors: Durrant, C. J.; Turner, J.; Wilson, P. R.
Bibcode: 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'.

Title: High-resolution Studies of the Polar Magnetic Fields during
    Cycle 23
Authors: Varsik, J.; Durrant, C. J.; Turner, J.; Wilson, P. R.
Bibcode: 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.

Title: The Evolution of Trailing Plumes from Active Regions
Authors: Durrant, C. J.; Kress, J. M.; Wilson, P. R.
Bibcode: 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.

Title: Simulations of the Polar Field Reversals during Cycle 22
Authors: Kress, J. M.; Wilson, P. R.
Bibcode: 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.

Title: Observations of the Polar Magnetic Fields During the Polarity
    Reversals of Cycle 22
Authors: Snodgrass, H. B.; Kress, J. M.; Wilson, P. R.
Bibcode: 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.

Title: The evolution of isolated active regions
Authors: Kress, J. M.; Wilson, P. R.
Bibcode: 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.
Bibcode: 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.

Title: Curious Magnetic Changes in a Quiet Region
Authors: Zirin, H.; Wilson, P. R.; Li, Y.
Bibcode: 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.

Title: The Internal Solar Rotation Rate Inferred from Combined GONG
    and LOWL Data
Authors: Li, Y.; Wilson, P. R.
Bibcode: 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 &lt; R/R<SUB>⊙</SUB> &lt; 0.6. They also indicate an
  increase in the rotation rate at high latitudes (of ~15% at latitude
  60° for R/R<SUB>⊙</SUB> &lt; 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.

Title: Is the Solar Rotation Uniform Below the Surface?
Authors: Wilson, P. R.; Li, Y.
Bibcode: 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.

Title: From "down under"
Authors: Wilson, Peter R.
Bibcode: 1998ASSL..222..136W
Altcode: 1998ream.conf..136W
  No abstract at ADS

Title: The internal rotation rate inferred from LOWL and GONG data
Authors: Li, Y.; Wilson, P. R.
Bibcode: 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 &gt; 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).

Title: Coronal Holes and the Polar Field Reversals
Authors: Fox, P.; McIntosh, P.; Wilson, P. R.
Bibcode: 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.

Title: The Rotational Structure of the Region below the Solar
    Convection Zone
Authors: Wilson, P. R.; Burtonclay, D.; Li, Y.
Bibcode: 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 &lt; r = R/R<SUB>⊙</SUB> &lt;
  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 &lt; r &lt;
  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.
Bibcode: 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.

Title: On the Inference of the Solar Internal Rotation Profile from
    Frequency-splitting Data
Authors: Wilson, P. R.; Burtonclay, D.; Li, Y.
Bibcode: 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.
Bibcode: 1996BASI...24..251W
Altcode:
  No abstract at ADS

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
Bibcode: 1996SSRv...76..339H
Altcode:
  No abstract at ADS

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.
Bibcode: 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.

Title: High-Resolution Studies of the Solar Polar Magnetic Fields
Authors: Varsik, J. R.; Wilson, P. R.; Li, Y.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1995Obs...115..334W
Altcode:
  No abstract at ADS

Title: The Crisis in Helioseismology
Authors: Wilson, P. R.; Burtonclay, D.; Li, Y.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1994JBAA..104..240W
Altcode:
  No abstract at ADS

Title: Books-Received - Solar and Stellar Activity Cycles
Authors: Wilson, P. R.
Bibcode: 1994Sci...265.1902W
Altcode:
  No abstract at ADS

Title: Solar and stellar activity cycles.
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 1994ssac.book.....W
Altcode: 1994QB526.C9W55....
  No abstract at ADS

Title: Real and Virtual Unipolar Regions
Authors: Snodgrass, H. B.; Wilson, P. R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1992ASPC...27..376W
Altcode: 1992socy.work..376W
  No abstract at ADS

Title: The Reversal of the North Polar Field
Authors: Wilson, P. R.
Bibcode: 1992ASPC...27..116W
Altcode: 1992socy.work..116W
  No abstract at ADS

Title: Theoretical Implications of the Extended Activity Cycle
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1990BAAS...22Q.855S
Altcode:
  No abstract at ADS

Title: The Origin of the Large-Scale Fields
Authors: Wilson, P. R.; McIntosh, P. S.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1987BAAS...19Q.935S
Altcode:
  No abstract at ADS

Title: Solar Cycle Workshop
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1987SoPh..110.....W
Altcode:
  No abstract at ADS

Title: A New Definition for the Solar Cycle
Authors: Wilson, P. R.
Bibcode: 1986BAAS...18.1010W
Altcode:
  No abstract at ADS

Title: The Generation of Magnetic Fields in Photospheric Layers
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1981BAAS...13..882W
Altcode:
  No abstract at ADS

Title: Faculae, filigree and calcium bright points
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1974IAUS...56..301W
Altcode:
  No abstract at ADS

Title: The Cooling of a Sunspot. III: Recent Observations
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1969SoPh....8...20W
Altcode:
  No abstract at ADS

Title: Temperature Fluctuations and Convection in the Solar
    Photosphere
Authors: Wilson, P. R.
Bibcode: 1969BAAS....1R.296W
Altcode:
  No abstract at ADS

Title: Temperature Fluctuations and Convective Modes in the Solar
    Photosphere
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1966ApJ...143..993W
Altcode:
  No abstract at ADS

Title: On Photospheric Mean Values.
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1965Sci...149...46W
Altcode: 1965Sci...149...46B
  No abstract at ADS

Title: Photospheric Structure and RMS Fluctuation Data.
Authors: Wilson, P. R.
Bibcode: 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.
Bibcode: 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.

Title: The Wilson effect and sunspot structure
Authors: Wilson, P. R.
Bibcode: 1964susp.conf..146W
Altcode:
  No abstract at ADS

Title: An Interpretation of Edmonds' Granulation Data.
Authors: Wilson, P. R.
Bibcode: 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.

Title: Three-dimensional solutions of the transfer equation
Authors: Wilson, P. R.
Bibcode: 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.

Title: Radiative transfer in media exhibiting large horizontal
    variations
Authors: Wilson, P. R.
Bibcode: 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.

Title: Spectral line profiles in emitting layers
Authors: Wilson, P. R.
Bibcode: 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.

Title: The application of the equation of transfer to the
    interpretation of solar granulation
Authors: Wilson, P. R.
Bibcode: 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.

Title: On Solving the Equation of Radiative Transfer for Conservative
    Non-uniform Media
Authors: Wilson, P. R.
Bibcode: 1961AuJPh..14...57W
Altcode:
  No abstract at ADS

Title: The Constant Flux Problem in Non-uniform Exponential Media
Authors: Wilson, P. R.
Bibcode: 1960AuJPh..13..461W
Altcode:
  No abstract at ADS

