On adaptive-grid computations of variable stars

Abstract

We show that the use of an implicit adaptive-grid technique is an efficient and up-to-date approach for the calculations of radial oscillations in variable stars. We chose as an illustrative example the radiative envelope of an RR Lyrae variable. For the hydrostatic initial model we compare the Lagrangian ratioed zoning with an adaptive-grid rezoning. We show that the adaptive-grid yields an optimal distribution of the mesh points in the sense that the relevant physical features, the hydrogen and first and second helium ionization zones, are well resolved. For the hydrodynamical evolution we present the full-amplitude model for both the Lagrangian and adaptive-grid computations. We perform a detailed comparison and show that the adaptive-grid method yields limit cycle solutions that are substantially improved over the Lagrangian grid model. This is due to the fact that the Lagrangian mesh sweeps through the ionization zones twice during one oscillation period, whereas the adaptive-mesh resolves them and tracks them continuously. The results are, in particular, smooth radial velocity and light curves. Beyond a physically better defined solution we also observe larger time steps for the convergence towards the limit cycle and for the evolution during one period.