Pulsation and Stability of RR Lyrae Stars. I. Instability Strip
Abstract
In order to provide a detailed analysis of RR Lyrae instability strip topology, an extensive grid of nonlinear, nonlocal, and timedependent convective models of RR Lyrae stars has been computed at fixed mass (M = 0.65 solar mass) and chemical composition (Y = 0.299, Z = 0.001). Four series of envelope models at different luminosity levels (log(L/solar luminosity) = 1.81, 1.72, 1.61, 1.51) and on a large range of effective temperatures (5700 K less than T_{e} less than 8000 K) have been investigated. The nonlinear modal stability has been evaluated at limiting amplitude for both the fundamental and the first overtone. The equations governing both dynamical and convective interactions have been integrated in time until the initial perturbations and the nonlinear fluctuations due to superposition of higher order modes settled down. The theoretical observables obtained by the present survey (radius, luminosity, velocity and temperature amplitudes, periods) describe the pulsation characteristics of the models at full amplitude, hence they can be properly compared with observations. A linear, nonadiabatic survey of the first three modes of RR Lyrae models has been also computed to supply the static structure of the envelope to the nonlinear stability analysis. Several numerical simulations have been performed to test both the numerical accuracy (boundary conditions, timestep size, zoning) and the adequacy of the physical assumption (efficiency of the turbulent regime, artificial viscosity dependence, convective structure initialization) adopted to describe the coupling between dynamical and convective fields. The structure of the instability strip shows several striking features concerning the width in temperature of the region where only the first overtone is unstable. Indeed, the fundamental blue edge, moving from higher to lower luminosity levels, becomes redder, in contrast to previous findings but in agreement with globular clusters observed data. Moreover, using an improved treatment of the convective transport, the firstovertone red edge has been directly evaluated and hence also the width of the 'eitheror' region (i.e., the region where both the fundamental and the first overtone are simultaneously unstable). It has been found that the periods of the nonlinear convective models are systematically smaller than the corresponding periods of both linear and nonlinear radiative models. The differences between linear and nonlinear results are smaller than 2% of the period, however. This effect has been explained as a consequence of the changes induced during the phases of maximum compression by the convective transport on the adiabatic exponent, and on the density inversion located in coincidence with the hydrogen ionization reigon.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 July 1994
 DOI:
 10.1086/192054
 Bibcode:
 1994ApJS...93..233B
 Keywords:

 Stellar Convection;
 Stellar Interiors;
 Stellar Models;
 Stellar Oscillations;
 Stellar Physics;
 Variable Stars;
 Mathematical Models;
 Nonlinear Systems;
 Stellar Evolution;
 Stellar Luminosity;
 Stellar Temperature;
 Astrophysics;
 STARS: EVOLUTION;
 STARS: INTERIORS;
 STARS: OSCILLATIONS;
 STARS: VARIABLES: OTHER RR LYRAE