The theoretical red edge of the RR Lyrae gap. I - Dependence of convection on pulsation phase

Two-dimensional conservation equations of mass, momentum, and energy are integrated in time by finite-difference techniques for several pulsating RR Lyrae models. Convective motion is generated naturally in convectively unstable regions from computer roundoff error. Time dependence is governed solely by the integration of the equations. The numerical approach and assumptions are discussed in detail. Here we are primarily concerned with the dependence of convection on the pulsation phase, which is the result most independent of the various approximations. Cases in which convection plays a major role and where its effects are comparatively minor are both considered. From the time dependence we discuss the suppression of radial pulsation and make a preliminary determination of the position of the red edge.