Dissipation effects in nonlinear Cepheid models

We examine the effects of very small dissipation on radial modes of numerical Cepheid models, by means of increasing the numerical resolution. The active region of the star is taken to be that between the ``core'' (at appx 10^5 K) and the Hydrogen ionization region (at appx 10^4 K). By increasing the numerical resolution in this interior region we also decrease the overall dissipation, as is the case for any model using viscosity of von-Neumann Richtmeyer type. Other tests verify that models are insensitive to changes in resolution which occur in the regions interior to the core or exterior to the Hydrogen partial ionization region. The increased resolution changes the temporal light-curves of the fundamental, first- and second-overtone modes, producing strong secondary features (minima and maxima) which have repercussion on the Fourier decomposition parameters that are at odds with observations. The features can be identified as signatures of internal shock waves that develop for different conditions depending on the mode of the pulsation. They therefore cannot be attributed to a particular property of the increased resolution in the stellar model. By looking also at the radius-velocity limit cycles, it becomes clear that the development of the shocks is correlated with the rapid growth of pulsational amplitude that accompanies highly-resolved low dissipation models.

Under adaptive rezoning, resolution can be further increased in active regions, and tests with adaptive models confirm that amplitudes and secondary features are more distinct in this case.

Tests with a von-Neumann Richtmeyer viscosity scaled to be resolution independent confirm that it is this dissipation which determines the limiting nonlinear amplitude, but such a scheme is not robust enough to be used in many pulsational settings.

Turning to turbulent viscosity, we implement a nonlocal time dependent scheme of turbulent convection, common for stellar problems over the past thirty years, and find that the associated dissipation serves to limit the amplitude. With increased resolution then, the turbulent viscosity solves the amplitude problem and therefore the problem of secondary features as well.