Modeling of pulsating atmospheres: comparison with observations

Abstract

Nonlinear modeling of pulsating stars has two features. Firstly, a self-consistent time-dependent model must includenot only the optically thin atmospheric region, but also the sub-photospheric envelope, where the instability regions are located.The physical conditions and spatial scales of these regions are verydifferent, while the accuracy of calculations should be as high as possible,especially for the radiative shock waves.As show numerical experiments, the loss of accuracy in the description of theatmospheric dynamics may seriously affect the calculatedmotions in the inner region,and vice versa, to say nothing of the synthetic line spectrum which is one ofthe main goals of the atmosphere modelling. Secondly, to obtain the limit cycle we must run the hydromodel forabout 10³ to 10⁴ pulsational cycles. It isthus clear that we have to simplify the problem of the radiativehydrodynamics in order to obtain reliable resultin a reasonable CPU time. In the presenttalk we describe one of possible approaches which gives good results at least in a semi-quantitative way.