P-modes and P-modes and temperature waves temperature waves

in photospherein photosphereYuzef D. ZhugzhdaYuzef D. Zhugzhda

Puskov Institute of Terrestrial Puskov Institute of Terrestrial Magnetism, Ionosphere and Magnetism, Ionosphere and Radiowave Propagation of Radiowave Propagation of

Russian Academy of SciencesRussian Academy of Sciences

•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

Expansion of intensity

P-modes produce small disturbances of the solar photosphere that makes possible to use expansion of intensity only up to the first order.

Opacity disturbances due to temperature and density

fluctuations

Adiabatic approximation

polar angle

darkening function

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

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

Inverse problem

Multi-channel photometer DIFOS

Circles –DIFOS, squares –SPM(SOHO)

Darkening functions

Temperature waves

Quasi-adiabatic approximation

Quasi-isothermal approximation

|||| aT kk

|||| aT kk

Coupling of p-modes and temperature waves

Optically thick

atmosphere

Optically thin

atmosphere

Isothermal atmosphere H-pressure

scale

It was found out analytical exact solution of the problem in terms of Generalized

Hypergeometrical functions

Wave coupling

P-

mod

es

Temperature waves