Revisiting the common envelope evolution in binary stars: A new semianalytic model for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-body and population synthesis codes
Alessandro A. Trani, Steven Rieder, Ataru Tanikawa, Giuliano Iorio, Riccardo Martini, Georgii Karelin, Hila Glanz, Simon Portegies Zwart
Abstract
We present a novel way of modeling common envelope evolution in binary and few-body systems. We consider the common envelope inspiral as driven by a drag force with a power-law dependence in relative distance and velocity. The orbital motion is resolved either by direct $N$-body integration or by solving the set of differential equations for the orbital elements as derived using perturbation theory. Our formalism can model the eccentricity during the common envelope inspiral, and it gives results consistent with smoothed particles hydrodynamical simulations. We apply our formalism to common envelope events from binary population synthesis models and find that the final eccentricity distribution resembles the observed distribution of post-common-envelope binaries. Our model can be used for time-resolved common-envelope evolution in population synthesis calculations or as part of binary interactions in direct $N$-body simulations of star clusters.