P-modes and temperature waves in photosphere

1. P-modes and temperature waves in photosphere Yuzef D. Zhugzhda Puskov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation of Russian Academy of Sciences

2. Darkening and visibility functions of p-modes • Local approximation • Inverse problem • True visibility and darkening function • Explorations of Stodilka and Hidalgo et al • Temperature waves in stratified atmosphere • Brightness fluctuations of the Sun and stars and temperature waves

4. P-modes produce small disturbances of the solar photosphere that makes possible to use expansion of intensity only up to the first order. Expansion of intensity darkening function Opacity disturbances due to temperature and density fluctuations Adiabatic approximation polar angle

5. Local approximation makes possible to take out of the integral temperature disturbance After integration over the whole disk of the star we arrive to relative visibility function normalized on relative temperature disturbances The advantage of the local approximation is that relative visibility function depends only on parameters of undisturbed atmosphere

6. Derivative of opacity with respect to temperature Derivative of opacity with respect to density Solid line – absolute visibility, long-dashed line –Plank function contribution, medium-dashed and short-dashed lines – contributions of opacity fluctuations due to temperature and density fluctuation

7. Inverse problem Multi-channel photometer DIFOS Circles –DIFOS, squares –SPM(SOHO)

9. Darkening functions

10. Temperature waves Quasi-adiabatic approximation Quasi-isothermal approximation

12. Coupling of p-modes and temperature waves Optically thick atmosphere Optically thin atmosphere Isothermal atmosphere H-pressure scale Temperature waves Wave coupling It was found out analytical exact solution of the problem in terms of Generalized Hypergeometrical functions P-modes