Abstract
We study the relationship between full-disk solar radiative flux at different wavelengths and average solar photospheric magnetic-flux density, using daily measurements from the Kitt Peak magnetograph and other instruments extending over one or more solar cycles. We use two different statistical methods to determine the underlying nature of these flux – flux relationships. First, we use statistical correlation and regression analysis and show that the relationships are not monotonic for total solar irradiance and for continuum radiation from the photosphere, but are approximately linear for chromospheric and coronal radiation. Second, we use signal theory to examine the flux – flux relationships for a temporal component. We find that a well-defined temporal component exists and accounts for some of the variance in the data. This temporal component arises because active regions with high magnetic-field strength evolve, breaking up into small-scale magnetic elements with low field strength, and radiative and magnetic fluxes are sensitive to different active-region components. We generate empirical models that relate radiative flux to magnetic flux, allowing us to predict spectral-irradiance variations from observations of disk-averaged magnetic-flux density. In most cases, the model reconstructions can account for 85 – 90% of the variability of the radiative flux from the chromosphere and corona. Our results are important for understanding the relationship between magnetic and radiative measures of solar and stellar variability.
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References
Bernstein, R.: 1999, Schaum’s Outline of Theory and Problems of Elements of Statistics II: Inferential Statistics, McGraw-Hill, New York.
Bracewell, R.: 1965, The Fourier Transform and Its Applications, McGraw-Hill, New York.
de Toma, G., White, O.R.: 2006, Solar Phys. 236, 1.
DeLand, M.T., Cebula, R.P., Hilsenrath, E.: 2004, J. Geophys. Res. (Atmospheres) 109, 6304.
Fisher, G.H., Longcope, D.W., Metcalf, T.R., Pevtsov, A.A.: 1998, Astrophys. J. 508, 885.
Fligge, M., Solanki, S.K., Unruh, Y.C.: 2000, Astron. Astrophys. 353, 380.
Fröhlich, C.: 2000, Space Sci. Rev. 94, 15.
Fröhlich, C.: 2006, Space Sci. Rev. 125, 53.
Haisch, B., Schmitt, J.H.M.M.: 1996, Publ. Astron. Soc. Pac. 108, 113.
Harvey, K.L., White, O.R.: 1999, Astrophys. J. 515, 812.
Klimchuk, J.A.: 2006, Solar Phys. 234, 41.
Krivova, N.A., Solanki, S.K.: 2004, Astron. Astrophys. 417, 1125.
Krivova, N.A., Solanki, S.K., Fligge, M.: 2002, In: Wilson, A. (ed.) From Solar Min to Max: Half a Solar Cycle with SOHO SP-508, ESA, Noordwijk, 155.
Krivova, N.A., Solanki, S.K., Fligge, M., Unruh, Y.C.: 2003, Astron. Astrophys. Lett. 399, L1.
Livingston, W., Wallace, L., White, O.R., Giampapa, M.S.: 2007, Astrophys. J. 657, 1137.
Lockwood, M.: 2005, In: Haigh, J.D., Lockwood, M., Giampapa, M.S., Rüedi, I., Güdel, R.M., Schmutz, W. (eds.) The Sun, Solar Analogs and the Climate, Saas-Fee Advanced Course 34, Springer, Berlin, 109.
Nandy, D.: 2004, Solar Phys. 224, 161.
Nandy, D., Martens, P.C.H.: 2007, Adv. Space Res. 40, 891.
Ortiz, A., Rast, M.: 2005, Mem. Soc. Astron. Ital. 76, 1018.
Pevtsov, A.A., Acton, L.W.: 2001, Astrophys. J. 554, 416.
Pevtsov, A.A., Fisher, G.H., Acton, L.W., Longcope, D.W., Johns-Krull, C.M., Kankelborg, C.C., Metcalf, T.R.: 2003, Astrophys. J. 598, 1387.
Preminger, D., Walton, S.: 2005, Geophys. Res. Lett. 32, L14109.
Preminger, D.G., Walton, S.R.: 2006, Solar Phys. 235, 387.
Preminger, D.G., Walton, S.R.: 2007, Solar Phys. 240, 17.
Preminger, D.G., Walton, S.R., Chapman, G.A.: 2002, J. Geophys. Res. (Space Phys.) 107, 6-1.
Saar, S.H.: 1988, Astrophys. J. 324, 441.
Schrijver, C.J.: 1983, Astron. Astrophys. 127, 289.
Schrijver, C.J.: 1987, Astron. Astrophys. 180, 241.
Schrijver, C.J.: 1988, Astron. Astrophys. 189, 163.
Schrijver, C.J.: 2001, Astrophys. J. 547, 475.
Schrijver, C.J., Harvey, K.L.: 1989, Astrophys. J 343, 481.
Schrijver, C.J., Title, A.M., Hagenaar, H.J., Shine, R.A.: 1997, Solar Phys. 175, 329.
Viereck, R., Puga, L., McMullin, D., Judge, D., Weber, M., Tobiska, W.K.: 2001, Geophys. Res. Lett. 28, 1343.
Wenzler, T., Solanki, S.K., Krivova, N.A.: 2005, Astron. Astrophys. 432, 1057.
Wenzler, T., Solanki, S.K., Krivova, N.A., Fluri, D.M.: 2004, Astron. Astrophys. 427, 1031.
Wenzler, T., Solanki, S.K., Krivova, N.A., Fröhlich, C.: 2006, Astron. Astrophys. 460, 583.
Woods, T.N., Tobiska, W.K., Rottman, G.J., Worden, J.R.: 2000, J. Geophys. Res. 105, 27195.
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Preminger, D., Nandy, D., Chapman, G. et al. Empirical Modeling of Radiative versus Magnetic Flux for the Sun-as-a-Star. Sol Phys 264, 13–30 (2010). https://doi.org/10.1007/s11207-010-9560-1
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DOI: https://doi.org/10.1007/s11207-010-9560-1