Table Of ContentSCORe '96:
SOLAR CONVECTION AND OSCILLATIONS AND THEIR RELATIONSHIP
ASTROPHYSICS AND
SPACE SCIENCE LIBRARY
VOLUME 225
Executive Committee
W. B. BURTON, Sterrewacht, Leiden, The Netherlands
J. M. E. KUIJPERS, Faculty 0/ Science, Nijmegen, The Netherlands
E. P. 1. VAN DEN HEUVEL, Astronomical Institute, University 0/ Amsterdam,
The Netherlands
H. VAN DER LAAN, Astronomical Institute, University 0/ Utrecht,
The Netherlands
Editorial Board
I. APPENZELLER, Landessternwarte Heidelberg-Konigstuhl, Germany
J. N. BAHCALL, The Institute/or Advanced Study, Princeton, U.S.A.
F. BERTOLA, Universita di Padova, Italy
W. B. BURTON, Sterrewacht, Leiden, The Netherlands
J. P. CASSINELLI, University o/Wisconsin, Madison, U.S.A.
C. J. CESARSKY, Centre d' Etudes de Saclay, Gif-sur·Yvette Cedex, France
O. ENGVOLD, Institute o/Theoretical Astrophysics, University o/Oslo, Norway
J. M. E. KUIJPERS, Faculty 0/ Science, Nijmegen, The Netherlands
R. McCRAY, University o/Colorado, JILA, Boulder, U.S.A.
P. G. MURDIN, Royal Greenwich Observatory, Cambridge, U.K.
F. PACINI, Istituto Astronomia Arcetri, Firenze, Italy
V. RADHAKRISHNAN, Raman Research Institute, Bangalore, India
K. SATO, School of Science, The University of Tokyo, Japan
F. H. SHU, University of California, Berkeley, U.S.A.
B. V. SOMOV, Astronomical Institute, Moscow State University, Russia
R. A. SUNYAEV, Space Research Institute, Moscow, Russia
S. TREMAINE, CfTA, University of Toronto, Canada
Y. TANAKA, Institute of Space & Astronautical Science, Kanagawa, Japan
E. P. J. VAN DEN HEUVEL, Astronomical Institute, University ofA msterdam,
The Netherlands
H. VAN DER LAAN, Astronomical Institute, University of Utrecht,
The Netherlands
N. O. WEISS, University o/Cambridge, U.K.
SCORe '96:
SOLAR CONVECTION
AND OSCILLATIONS
AND THEIR RELATIONSHIP
Edited by
F. P. PUPERS,
J. CHRISTENSEN-DALSGAARD
and
C. S. ROSENTHAL
Theoretical Astrophysics Center,
Institute ofA stronomy,
Aarhus University,
Arhus, Denmark
SPRINGER-SCIENCE+BUSINESS MEDIA, BV.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-6172-8 ISBN 978-94-011-5167-2 (eBook)
DOI 10.1007/978-94-011-5167-2
Printed on acid-free paper
AII Rights Reserved
© 1997 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1997
Softcover reprint of the hardcover 1 st edition 1997
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any mformation storage and
retrieval system, without written permis sion from the copyright owner.
TABLE OF CONTENTS
Preface
VII
Part I : Global Structure
Effects of convection on the mean solar structure ................................................ 3
J¢rgen Christensen-Dalsgaard
Convective Overshooting and Mixing ........................................................... 23
Ian W. Roxburgh
Effect of turbulent pressure on solar oscillation frequencies ...................................... 51
II.M. Antia, S. Basu
Parameters of the solar convection zone in evolutionary and seismic models ..................... 55
V. Baturin, S.V. Ayukov
A calibration of mixing length theory based on RHD simulations of solar-type convection ........ 59
H.-G. Ludwig, B. Freytag, M. Steffen
A precision-controlled solar model with realistic subatmospheric stratification ................... 65
H. Schlattl, A. Weiss, H.-G. Ludwig, J. Bernkopf
Solar models with convective overshoot ........................................................ 69
M. Stix, M. Kiefer
Near-surface constraints on the structure of stellar convection zones ............................. 73
R. Trampedach, J. Christensen-Dalsgaard, A. Nordlund, R.F. Stein
Part II : Basic Properties of Convection
Stellar Convection; General Properties .......................................................... 79
Ake Nordlund, Bob Stein
Compressible Turbulence ...................................................................... 105
Vittorio M. Canuto
Sound speed variations near the photosphere due to entropy perturbations
in 3d numerical experiments ............................ . ............................... 127
D. Georgobiani, J.R. Kuhn, R.F. Stein
A hydrodynamic simulation of the radiation-convection transition region ...................... 131
Y.-C. Kim, K.L. Chan
Photospheric Downflows: How deep, how coherent, how important? ........................... 135
M.P. Rast
"Mesogranulation" - A Convective Or An Oscillatory Phenomenon'? .......................... 139
Th. Straus
Part III : Convective Effects on Oscillations
Convective Effects on Mode Frequencies ...................................................... 145
Colin S. Rosenthal
Excitation and Damping of Solar Acoustic Oscillations ........................................ 161
Pawan Kumar
On Nonlinear Solar Oscillations .............................. 171
H.P. Singh, M.K. Das, M.K. Patra
Effects of Convection on Solar p Modes ......................................... In
M. Swisdak, E. Zweibel
v
vi
The theory of Anisotropic P~mode Propagation in the Solar Convection Zone .................. 181
Yu.D. Zhugzhda
Part IV : Rotation and Magnetic Fields
Rotation and angular momentum transport .................................................... 187
Jean-Paul Zahn
The Solar Dynamo Problem ................................................................... 201
Fausto Cattaneo
Differential rotation in turbulent compressible convection ...................................... 223
N.H. Brummell, J. Toomre, N.E. Hurlburt
The effects of rotation on the global dynamics of turbulent convection .......................... 227
K. Julien, J. Werne, S. Legg, J. McWilliams
The effects of rotation on convective overshoot ................................................. 231
K. Julien, J. Werne, S. Legg, J. McWilliams
Two-dimensional measurements of Sunspot Oscillations ........................................ ~5
J. Staude, T. Horn
Part V : Local Properties of Convection
Acoustic Tomography of Solar Convective Flows and Structures ............................... 241
Alexander G. Kosovichev, Tom L. Duvall, Jr.
Dynamic Behavior of the Solar Atmosphere ................................................... 261
Robert F. Stein, Mats Carlsson
The influence of radiative damping on the modes of a magnetized isothermal atmosphere ....... 277
D. Banerjee, S.S. Hasan, J. Christensen-Dalsgaard
Dynamical Relations between Photosphere and Chromosphere ................................. 281
N. M. Hoekzema
Photospheric flows as measured by SOI/MDI .................................................. 285
N. Hurlburt, Z. Frank, R. Shine, T. Tarbell, A. Title, G. Simon
The Dutch Open Telescope .................................................................... 289
R.,J. Rutten, R.H. Hammerschlag, F.M. Bettonvil
The Magneto-Optical Filter in Napoli: Perspectives and Test Observations ..................... 293
P.F. Moretti, G. Severino, G. Cauzzi, K. Reardon, T. Straus, A. Cacciani, C. Marmolino,
M. Oliviero, L.A. Smaldone
Part VI : Synthesis
Synthesis Convection, Structure and Evolution ......................................... 299
Evry Schatzman
Index of Authors 311
Index of Keywords 313
PREFACE
This volume contains the reviews and poster papers presented at the workshop Solar Convection
and Oscillations and their Relationship: SCORe '96, held in Arhus, Denmark, May 27 - 31, 1996.
The aim of this workshop was to bring together experts in the fields of convection and helioseismology,
and to stimulate collaborations and joint research. The participation to this workshop was purposely
kept limited in order to provide optimal conditions for informal discussions.
In autumn of 199,5 the long-awaited GONG network of solar telescopes became fully operational
and the first data already show significant improvement over existing datasets on solar oscillations.
Furthermore, in December of 1995 the satellite SOHO was launched which, together with GONG,
provides a major step forward in both the quantity and the quality of available solar oscillation data.
It is with this in mind that we decided to organize the workshop to prepare for the optimal use of this
wealth of data, with which to deepen our understanding of solar structure and specifically, of one of
the longest-standing problems in solar and stellar modelling: the treatment of convection.
We feel that the workshop succeeded in this goal: The review talks provided overviews of the
current status of the observational and theoretical aspects of the fields, while the time after lunch was
spent in general discussion of the topics raised in the reviews and the material presented in the relevant
posters. We found this format very helpful. In particular, outstanding problems could be identified
during the discussions and thus directions of future research, both theoretical and observational, laid
out. The Synthesis that summarizes the workshop captures the spirit of the workshop very well,
in presenting the questions that theory poses for helioseismic observations, and the problems that
helioseismic results raise in our understanding of the physical processes governing global and local
properties of the Sun.
The organizers of the workshop could not have achieved this success without the generous
financial support of the Theoretical Astrophysics Center (TAC) : a research center established by the
Danish National Research Foundation as a collaboration between Copenhagen University and Aarhus
University. Furthermore, we are most grateful to Anette Skovgaard and Anette Uhl for the very
substantial time and effort they spent on the large variety of practical problems usually encountered
in organizing scientific meetings, not least of which was ensuring the smooth and timely processing of
"isa applications.
Frank P. Pijpers Jorgcn Christ,ensen-Dalsgaard Colin S. Rosenthal
va
Part I Global Structure
Something in me was born before the stars
and saw the sun begin from far away
F. Pessoa Sonnet XXIV, (1918)
EFFECTS OF CONVECTION
ON THE MEAN SOLAR STRUCTURE
J0RGEN CHRISTENSEN-DALSGAARD
Teoretisk Astrofysik Center, Danmarks Grundforskningsfond,
and
Institut for Fysik og Astronomi, Aarhus Universitet,
DK-8000 Aarhus C, Denmark
Abstract. The overall framework for the study of solar convection and
oscillations is the spherically symmetric component of solar structure. I
discuss those properties of the solar interior which depend on convection
and other possible hydrodynamical motion and the increasingly detailed
information about the structure which is provided by helioseismic data.
The most basic dependence of solar models on convection is the calibration
to fix the solar radius. The dominant causes for differences in oscillation
frequencies between the Sun and solar models seem to be located near the
top of the convection zone. However, there is also evidence for possible
weak mixing below the convection zone and perhaps in the solar core. The
former, at least, might be induced by penetration of convective motion into
the stable layers below.
Key words: solar structure, convection, helioseismology
1. Introduction
The outer solar convection zone extends over 29 % of the solar radius and
contains about 2 % of the mass of the Sun (e.g. Christensen-Dalsgaard,
Gough & Thompson 1991; Kosovichev & Fedorova 1991). Within most
of this region, energy transport is dominated by convection, leading to a
temperature gradient which only deviates slightly from being adiabatic. In
particular, the structure of the convection zone is essentially independent
of the local value of the opacity. Furthermore, matter is mixed on a time
scale of months and hence the composition may be assumed to be uniform.
3
F. P. Pijpers et al. (eds.), SCORe '96: Solar Convection and Oscillations and their Relationship, 3-22.
© 1997 Kluwer Academic Publishers.
4 J0RGEN CHRISTENSEN-DALSGAARD
In earlier phases of solar evolution, the convection zone has extended con
siderably more deeply: thus it is normally assumed that the Sun was fully
convective before arriving on the main sequence, justifying the assumption
that the early Sun was chemically homogeneous.
Motion induced by convection is likely to extend beyond the boundaries
of the convection zone. This can be observed in the solar atmosphere and
has a significant effect on the atmospheric structure. Penetration beneath
the lower boundary of the convection zone can only be inferred indirectly,
but is potentially far more important for overall solar structure and evolu
tion. It may affect the temperature stratification in the upper parts of the
radiative interior and cause mixing and transport of angular momentum, ei
ther through direct motion in the form of penetrating convective plumes or
through convectively induced gravity waves (e.g. Schatzman, these proceed
ings; Zahn, these proceedings). Clear evidence for such mixing is provided
by the solar surface abundances of lithium and beryllium which are con
siderably reduced (by factors of about 140 and 2, respectively; Anders &
Grevesse 1989), relative to the initial composition of the solar system; this
indicates that matter has been mixed to a temperature considerably higher
than the maximum temperature at the base of the convectively unstable
region during the main-sequence life of the Sun.
Here I am concerned with the effects of convection on the spherically
symmetric stellar structure and evolution, and how these effects can be in
vestigated through observations of solar oscillations. Many of these issues
will be addressed in more detail in later papers in the present volume; how
ever, I hope to provide a general framework, as well as a basic impression
of the data now available for testing the solar models.
Gough & Weiss (1976) pointed out that the properties of the convection
zone is essentially controlled by the thin, substantially superadiabatic re
gion at its top. The integral of the superadiabatic gradient over this region
determines the adiabat of the nearly adiabatic part of the convection zone
and hence its overall structure. Provided the treatment of the superadi
abatic region is adjusted, e.g. by varying suitable parameters, such as to
yield the same adiabat, the overall structure is insensitive to the details
of that treatment. Here I consider two simple parametrized treatments of
convection. One is the mixing-length theory of B6hm-Vitense (1958; in the
following MLT), with a mixing length proportional to the pressure scale
height. The second is the formulation by Canuto & Mazzitelli (1991; CM),
with a characteristic scale related to the distance to the top of the con
vection zone. A potentially more realistic description of the superadiabatic
region can in principle be based on appropriate averages of numerical so
lutions of the time-dependent hydrodynamical equations of convection. I
shall consider results of simulations carried out by Nordlund, Stein and
