Abstract
Calculations of spectral darkening and visibility functions for the brightness oscillations of the Sun resulting from global solar oscillations are presented. This has been done for a broad range of the visible and infrared continuum spectrum. The procedure for the calculations of these functions includes the numerical computation of depth-dependent derivatives of the opacity caused by p modes in the photosphere. A radiative-transport code was used for this purpose to get the disturbances of the opacities from temperature and density fluctuations. The visibility and darkening functions are obtained for adiabatic oscillations under the assumption that the temperature disturbances are proportional to the undisturbed temperature of the photosphere. The latter assumption is the only way to explore any opacity effects since the eigenfunctions of p-mode oscillations have not been obtained so far. This investigation reveals that opacity effects have to be taken into account because they dominate the violet and infrared part of the spectrum. Because of this dominance, the visibility functions are negative for those parts of the spectrum. Furthermore, the darkening functions show a wavelength-dependent change of sign for some wavelengths owing to these opacity effects. However, the visibility and darkening functions under the assumptions used contradict the observations of global p-mode oscillations, but it is beyond doubt that the opacity effects influence the brightness fluctuations of the Sun resulting from global oscillations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Fontenla, J., White, O.R., Fox, P.A., Avrett, E.H., Kurucz, R.L.: 1999, Calculation of Solar irradiances. I. Synthesis of the Solar spectrum. Astrophys. J. 518, 480 – 499.
Fröhlich, C., Bonnet, R.M., Bruns, A.V., Delaboudinière, J.P., Domingo, V., Kotov, V.A., Kollath, Z., Rashkovsky, D.N., Toutain, T., Vial, J.C.: 1988, IPHIR: The helioseismology experiment on the PHOBOS mission. In: Rolfe, E.J. (ed.) Seismology of the Sun and Sun-Like Stars, ESA-SP 286, European Space Agency, Noordwijk, 359 – 362.
Lebedev, N.I., Kuznetsov, V.D., Oraevskii, V.N., Staude, J., Kostyk, R.I.: 2004, The helioseismological CORONAS-F DIFOS experiment. Astron. Rep. 48, 871 – 875. doi:10.1134/1.1809399.
Pozrikidis, C.: 1998, Numerical Computation in Science and Engineering, Oxford University Press, New York.
Rybicki, G.B., Hummer, D.G.: 1991, An accelerated lambda iteration method for multilevel radiative transfer. I. Non-overlapping lines with background continuum. Astron. Astrophys. 245, 171 – 181.
Staude, J., Dzhalilov, N.S., Zhugzhda, Y.D.: 1994, Radiation-hydrodynamic waves and global solar oscillations. Solar Phys. 152, 227 – 239.
Toutain, T., Gouttebroze, P.: 1993, Visibility of solar p-modes. Astron. Astrophys. 268, 309 – 318.
Uitenbroek, H.: 2001, Multilevel radiative transfer with partial frequency redistribution. Astrophys. J. 557, 389 – 398. doi:10.1086/321659.
Vernazza, J.E., Avrett, E.H., Loeser, R.: 1976, Structure of the solar chromosphere. II. The underlying photosphere and temperature-minimum region. Astrophys. J. Suppl. 30, 1 – 60.
Woodard, M.: 1984, Observations of low-degree modes from the solar maximum mission (extended abstract). In: Ulrich, R.K., Harvey, J., Rhodes, E.J. Jr., Toomre, J. (eds.) Solar Seismology from Space, JPL, Pasadena, 195 – 197.
Zhugzhda, Y.D.: 1983, Non-adiabatic oscillations in an isothermal atmosphere. Astrophys. Space Sci. 95, 255 – 275.
Zhugzhda, Y.D.: 2006, Analytical signal as a tool for studying solar p-modes. Astron. Lett. 32, 329 – 343.
Zhugzhda, Y.D., Dzhalilov, N.S., Staude, J.: 1993, Radiation-hydrodynamic waves in an optically non-grey atmosphere. Astron. Astrophys. 278, L9 – L12.
Zhugzhda, Y.D., Staude, J., Bartling, G.: 1996, Spectral darkening functions of solar p-modes – an effective tool for helioseismology. Astron. Astrophys. 305, L33 – L36.
Author information
Authors and Affiliations
Corresponding author
Additional information
Helioseismology, Asteroseismology, and MHD Connections
Guest Editors: Laurent Gizon and Paul Cally.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Nutto, C., Roth, M., Zhugzhda, Y. et al. Calculation of Spectral Darkening and Visibility Functions for Solar Oscillations. Sol Phys 251, 179–188 (2008). https://doi.org/10.1007/s11207-008-9132-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11207-008-9132-9