The circularization time-scales of late–type binary stars

Abstract

ABSTRACT We examine the consequences of, and apply, the formalism developed in Terquem (2021) for calculating the rate DR at which energy is exchanged between fast tides and convection. In this previous work, DR (which is proportional to the gradient of the convective velocity) was assumed to be positive in order to dissipate the tidal energy. Here we argue that, even if energy is intermittently transferred from convection to the tides, it must ultimately return to the convective flow and transported efficiently to the stellar surface on the convective time-scale. This is consistent with, but much less restrictive than, enforcing DR > 0. Our principle result is a calculation of the circularization time-scale of late–type binaries, taking into account the full time evolution of the stellar structure. We find that circularization is very efficient during the PMS phase, inefficient during the MS, and once again efficient when the star approaches the RGB. These results are in much better agreement with observations than earlier theories. We also apply our formalism to hot Jupiters, and find that tidal dissipation in a Jupiter mass planet yields a circularization time-scale of 1 Gyr for an orbital period of 3 d, also in good overall agreement with observations. The approach here is novel, and the apparent success of the theory in resolving longstanding time-scale puzzles is compelling.