Transitory Tidal Heating and Its Impact on Cluster Isochrones

Abstract

The kinetic energy in tidal flows, when converted into heat, can affect the internal structure of a star and shift its location on a color–magnitude diagram from that of standard models. In this paper we explore the impact of injecting heat into stars with masses near the main-sequence turnoff mass (1.26 M ⊙) of the open cluster M67. The heating rate is obtained from the tidal shear energy dissipation rate, which is calculated from first principles by simultaneously solving the equations that describe orbital motion and the response of a star’s layers to the gravitational, Coriolis, centrifugal, gas pressure, and viscous forces. The stellar structure models are computed with MESA. We focus on the effects of injecting heat in pulses lasting 0.01 Gyr, a time frame consistent with the synchronization timescale in binary systems. We find that the location of the tidally perturbed stars in the M67 color–magnitude diagram is shifted to significantly higher luminosities and effective temperatures than predicted by the standard model isochrone and includes locations corresponding to some of the blue straggler stars. Because tidal heating takes energy from the orbit, causing it to shrink, blue straggler stars could be merger or mass transfer progenitors, as well as products of these processes.