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NON-GREY RADIATIVE TRANSFER IN THE PHOTOSPHERIC CONVECTION : VALIDITY OF THE EDDINGTON APPROXIMATION
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 Title & Authors
NON-GREY RADIATIVE TRANSFER IN THE PHOTOSPHERIC CONVECTION : VALIDITY OF THE EDDINGTON APPROXIMATION
BACH, KIEHUNN;
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 Abstract
The aim of this study is to describe the physical processes taking place in the solar photosphere. Based on 3D hydrodynamic simulations including a detailed radiation transfer scheme, we investigate thermodynamic structures and radiation fields in solar surface convection. As a starting model, the initial stratification in the outer envelope calculated using the solar calibrations in the context of the standard stellar theory. When the numerical fluid becomes thermally relaxed, the thermodynamic structure of the steady-state turbulent flow was explicitly collected. Particularly, a non-grey radiative transfer incorporating the opacity distribution function was considered in our calculations. In addition, we evaluate the classical approximations that are usually adopted in the onedimensional stellar structure models. We numerically reconfirm that radiation fields are well represented by the asymptotic characteristics of the Eddington approximation (the diffusion limit and the streaming limit). However, this classical approximation underestimates radiation energy in the shallow layers near the surface, which implies that a reliable treatment of the non-grey line opacities is crucial for the accurate description of the photospheric convection phenomenon.
 Keywords
Sun:photosphere;atmospheres;granulation;numerical:hydrodynamics;radiative transfer;
 Language
English
 Cited by
 References
1.
Asplund, M., Grevesse, N., & Sauval, A. J. 2005, The Solar Chemical Composition, ASPC, 336, 25

2.
Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, The Chemical Composition of the Sun, ARA&A, 47, 481 crossref(new window)

3.
Bach, K., & Kim, Y.-C. 2012, Hydrodynamical Comparison Test of Solar Models, Astron. Nachr., 333, 934 crossref(new window)

4.
Bahcall, J. N., & Loeb, A. 1990, Element Diffusion in Stellar Interiors, ApJ, 360, 267 crossref(new window)

5.
Baran, O. A., & Stodilka, M. I. 2014, Specifics of the Solar Photospheric Convection at Granulation, Mesogranulation, and Supergranulation Scales, Sol. Phys., 30, 173

6.
Basu, S., & Antia, H. M. 2008, Helioseismology and Solar Abundances, Phy. Rep., 457, 217 crossref(new window)

7.
Böhm-Vitense, E. 1958, Über Die Wasserstoffkonvektionszone in Sternen Verschiedener Effektivtemperaturen und Leuchtkräfte. Mit 5 Textabbildungen, Z. Astrophys., 46, 108

8.
Cannon, C. J. 1973, Angular Quadrature Perturbations in Radiative Transfer Theory, J.QSRT, 13, 627

9.
Cannon, C. J. 1973, Frequency-Quadrature Perturbations in Radiative-Transfer Theory, ApJ, 185, 621 crossref(new window)

10.
Castelli, F., Gratton, R. G., & Kurucz, R. L. 1997, Notes on the convection in the ATLAS9 model atmospheres, A&A, 318, 841

11.
Chan, K. L., & Wolff, C. L. 1982, ADI on Staggered Mesh - A Method for the Calculation of Compressible Convection, J. Comp. Phys., 47, 109 crossref(new window)

12.
Chan, K. L., & Sofia, S. 1987, Validity Tests of the Mixing-Length Theory of Deep Convection, Science, 235, 465 crossref(new window)

13.
Deardorff, J. W. 1970, A Numerical Study of Three-dimensional Turbulent Channel Flow at Large Reynolds Numbers, J. Fluid Mechanics, 41, 453 crossref(new window)

14.
Dravins, D. 1987, Stellar Granulation II: Stellar Photospheric Line Asymmetries, A&A, 172, 211

15.
Ferguson, J. W., Alexander, D. R., Allard, F., et al. 2005, Low- Temperature Opacities, ApJ, 623, 585 crossref(new window)

16.
Freytag, B., Ludwig, H.-G., & Steffen, M. 1996, Hydrodynamical Models of Stellar Convection. The Role of Overshoot in DA White Dwarfs, A-Type Stars, and the Sun, A&A, 313, 497

17.
Grevesse, N., & Sauval, A. J. 1998, Standard Solar Composition, SSRv, 85, 161

18.
Hathaway, D. H., Teil, T., Norton, A. A., & Kitiashvili, I. 2015, The Sun’s Photospheric Convection Spectrum, ApJ, 811, 105 crossref(new window)

19.
Hubeny, I. 2003, Stellar Atmosphere Modeling, ASPC, 288, 17

20.
Iglesias, C. A., & Rogers, F. J. 1996, Updated Opal Opacities, ApJ, 464, 943 crossref(new window)

21.
Kim, Y. -C., Fox, P. A., Sofia, S., & Demarque, P. 1995, Modeling of Shallow and Inefficient Convection in the Outer Layers of the Sun Using Realistic Physics, ApJ, 442, 422 crossref(new window)

22.
Kim, Y. -C., Fox, P. A., Demarque, P., & Sofia, S. 1996, Modeling Convection in the Outer Layers of the Sun: A Comparison with Predictions of theMixing-Length Approximation, ApJ, 461, 499 crossref(new window)

23.
Kurucz, H. L. 1995, Laboratory and Astronomical High Resolution Spectra, ASPC, 81, 17

24.
Kurucz, R. L. 1996, Model Atmospheres and Spectrum Synthesis, ASPC, 108, 160

25.
Ludwig, H. G., Freytag, B., & Steffen, M. 1999, A Calibration of theMixing-Length for Solar-Type Stars Based on Hydrodynamical Simulations, A&A, 346, 111

26.
Mihalas, D. 1978, Stellar Atmospheres 2nd edn, Freeman and Co. (San Francisco: Freeman and Co.)

27.
Nordlund, A. 1982 Numerical Simulations of the Solar Granulation. I - Basic Equations and Methods, A&A, 107, 1

28.
Nordlund, A., & Dravins, D. 1990, Stellar Granulation. III - Hydrodynamic Model Atmospheres, A&A, 228, 155

29.
Peaceman, D. W., & Rachford, Jr. H. H. 1955, The Numerical Solution of Parabolic and Elliptic Differential Equations, J. Soc. Ind. Appl. Math, 3, 28 crossref(new window)

30.
Robinson, F. J., Demarque, P., Li, L. H., Sofia, S., Kim, Y.-C., Chan, K. L., & Guenther, D. B. 2003, Three-Dimensional Convection Simulations of the Outer Layers of the Sun Using Realistic Physics, MNRAS, 340, 923 crossref(new window)

31.
Robinson, F. J., Demarque, P., Li, L. H., Sofia, S., Kim, Y.-C., Chan, K. L., & Guenther, D. B. 2004, Three-Dimensional Simulations of the Upper Radiation-Convection Transition Layer in Subgiant Stars, MNRAS, 347, 1208U crossref(new window)

32.
Robinson, F. J., Demarque, P., Guenther, D. B. Kim, Y.-C., & Chan, K. L. 2005, Simulating the Outer Layers of Procyon A : A Comparison with the Sun, MNRAS, 362, 1031 crossref(new window)

33.
Rogers, F. J., Swenson, F. J., & Iglesias, C. A. 1996, OPAL Equation-of-State Tables for Astrophysical Applications, ApJ, 456, 902 crossref(new window)

34.
Sbordone, L., Bonifacio, P., Castelli, F., & Kurucz, R. L. 2004, ATLAS and SYNTHE under Linux, MSAIS, 5, 93

35.
Smagorinsky, J. 1963, General Circulation Experiments with the Primitive Equations I. The Basic Experiment, Monthly Weather Rev., 91, 99 crossref(new window)

36.
Spiegel, E. A. 1957, The Smoothing of Temperature Fluctuations by Radiative Transfer, ApJ, 126, 202 crossref(new window)

37.
Steffen, M., Ludwig, H.-G., & Kruess, A. 1989, A Numerical Simulation Study of Solar Granular Convection in Cells of Different Horizontal Dimension, A&A, 213, 371

38.
Stein, R. F., & Nordlund, Å. 1989, Topology of Convection Beneath the Solar Surface, ApJL, 342, 95 crossref(new window)

39.
Tanner, J. D., Basu, S., & Demarque, P. 2014, The Effect of Metallicity-dependent T-tau Relations on Calibrated Stellar Models, ApJL, 785, 13 crossref(new window)

40.
Thoul, A. A., Bahcall, J. N., & Loeb, A. 1994, Element Diffusion in the Solar Interior, ApJ, 421, 828 crossref(new window)

41.
Trampedach, R., & Stein, R. F. 2011, The Mass Mixing Length in Convective Stellar Envelopes, ApJ, 731, 78 crossref(new window)

42.
Trampedach, R., Stein, R. F., Christensen-Dalsgaard, J., Nordlund, Å., & Asplund, M. 2014, Improvements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations - I. T(τ) Relations, MNRAS, 442, 805 crossref(new window)

43.
Trampedach, R., Stein, R. F., Christensen-Dalsgaard, J., Nordlund, Å., & Asplund, M. 2014, Improvements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations - II. Calibrating theMixing-length Formulation, MNRAS, 445, 4366 crossref(new window)

44.
Unno, W., & Spiegel, E. A. 1966, The Eddington Approximation in the Radiative Heat Equation, PASJ, 18, 85

45.
Vögler, A., Bruls, J. H. M. J., & Schüssler, M. 2004, Approximations for Non-grey Radiative Transfer in Numerical Simulations of the Solar Photosphere, A&A, 421, 741 crossref(new window)