Simulations of Solar Granulation. I. General Properties

Numerical simulations provide information on solar convection not available by direct observation. We present results of simulations of near surface solar convection with realistic physics: an equation of state including ionization and three-dimensional, LTE radiative transfer using a four-bin opacity distribution function. Solar convection is driven by radiative cooling in the surface thermal boundary layer, producing the familiar granulation pattern. In the interior of granules, warm plasma ascends with ≈ 10% ionized hydrogen. As it approaches and passes through the optical surface, the plasma cools, recombines, and loses entropy. It then turns over and converges into the dark intergranular lanes and further into the vertices between granulation cells. These vertices feed turbulent downdrafts below the solar surface, which are the sites of buoyancy work that drives the convection. Only a tiny fraction of the fluid ascending at depth reaches the surface to cool, lose entropy, and form the cores of these downdrafts. Granules evolve by pushing out against and being pushed in by their neighboring granules, and by being split by overlying fluid that cools and is pulled down by gravity. Convective energy transport properties that are closely related to integral constraints such as conservation of energy and mass are exceedingly robust. Other properties, which are less tightly constrained and/or involve higher order moments or derivatives, are found to depend more sensitively on the numerical resolution. At the highest numerical resolution, excellent agreement between simulated convection properties and observations is found. In interpreting observations it is crucial to remember that surfaces of constant optical depth are corrugated. The surface of unit optical depth in the continuum is higher above granules and lower in the intergranular lanes, while the surface of optical depth unity in a spectral line is corrugated in ways that are influenced by both thermal and Doppler effects.

[1]  A. Malagoli,et al.  Turbulent compressible convection , 1991 .

[2]  J. Toomre,et al.  Two Dimensional Compressible Convection Extending Over Multiple Scale Heights , 1984 .

[3]  L. J. November,et al.  Precise Proper Motion Measurement of Solar Granulation , 1986 .

[4]  Ian W. Roxburgh,et al.  Challenges to theories of the structure of moderate mass stars , 1991 .

[5]  J. Toomre,et al.  Challenges to theories of the structure of moderate-mass stars : proceedings of a conference held at the Institute for Theoretical Physics, University of California, Santa Barbara, CA, USA, 19-22 June 1990 , 1991 .

[6]  E. Spiegel,et al.  Problems of stellar convection , 1977 .

[7]  A. Hanslmeier,et al.  Evidence for transonic flows in the solar granulation , 1992 .

[8]  A. M. Title,et al.  Statistical Properties of Solar Granulation Derived from the Soup Instrument on Spacelab 2 , 1988 .

[9]  G. Scharmer,et al.  On the differences between plage and quiet sun in the solar photosphere , 1992 .

[10]  T. Berger,et al.  On the Dynamics of Small-Scale Solar Magnetic Elements , 1996 .

[11]  R. Rutten,et al.  Solar and stellar granulation , 1989 .

[12]  E. Böhm-Vitense.  Introduction to Stellar Astrophysics , 1989 .

[13]  D. G. Hummer,et al.  Stellar Atmospheres: Beyond Classical Models , 1991 .

[14]  Å. Nordlund,et al.  3-D simulations of solar and stellar convection and magnetoconvection , 1990 .

[15]  Robert F. Stein,et al.  Topology of Convection beneath the Solar Surface , 1989 .

[16]  G. Scharmer,et al.  Constraints Imposed by Very High Resolution Spectra and Images on Theoretical Simulations of Granular Convection , 1989 .

[17]  Å. Nordlund,et al.  Convection and Its Influence on Oscillations , 1991 .

[18]  Hermance J. Hagenaar,et al.  On the Patterns of the Solar Granulation and Supergranulation , 1997 .

[19]  R. Shine,et al.  Evolution and advection of solar mesogranulation , 1992, Nature.

[20]  Å. Nordlund,et al.  Dynamics of and Radiative Transfer in Inhomogeneous Media , 1991 .

[21]  A. Kosovichev.  Tomographic Imaging of the Sun's Interior , 1996 .

[22]  E. J. Rolfe,et al.  Seismology of the Sun and Sun-Like Stars , 1988 .

[23]  I. Mazzitelli,et al.  Stellar Turbulent Convection: A New Model and Applications , 1991 .

[24]  A. Malagoli,et al.  Turbulent supersonic convection in three dimensions , 1990 .

[25]  J. Toomre,et al.  Turbulent Compressible Convection with Rotation. I. Flow Structure and Evolution , 1996 .

[26]  Hard turbulence in rotating Rayleigh-Bénard convection. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  A. Vincent,et al.  The dynamics of vorticity tubes in homogeneous turbulence , 1994, Journal of Fluid Mechanics.

[28]  A. M. Title,et al.  New Observations of Subarcsecond Photospheric Bright Points , 1995 .

[29]  A. Libchaber,et al.  Coherent structures in turbulent convection, an experimental study , 1990 .

[30]  A. M. Title,et al.  TIME-DISTANCE HELIOSEISMOLOGY WITH THE MDI INSTRUMENT: INITIAL RESULTS , 1997 .

[31]  Robert McDougall Kerr,et al.  Rayleigh number scaling in numerical convection , 1996, Journal of Fluid Mechanics.

[32]  P. Matthews,et al.  Nonlinear Compressible Convection in Oblique Magnetic Fields , 1996 .

[33]  R. Noyes,et al.  VORTICITY AND DIVERGENCE IN THE SOLAR PHOTOSPHERE , 1995 .

[34]  Paul R. Woodward,et al.  High-resolution simulations of compressible convection using the piecewise-parabolic method , 1994 .