Binaries Traveling Through a Gaseous Medium: Dynamical Drag Forces and Internal Torques

Abstract

Using time-dependent linear theory, we investigate the morphology of the gravitational wake induced by a binary, whose center of mass moves at velocity V cm against a uniform background of gas. For simplicity, we assume that the binary's components are on circular orbits about their common center of mass. The consequences of dynamical friction is twofold. First, gas dynamical friction may drag the binary's center of mass and cause the binary to migrate. Second, drag forces also induce a braking torque, which causes the orbits of the binary components to shrink. We compute the drag forces acting on one component of the binary due to the gravitational interaction with its own wake. We show that the dynamical friction force responsible to decelerate the binary's center of mass is smaller than it is in the point-mass case because of the loss of gravitational focusing. We show that the braking internal torque depends on the Mach numbers of each binary component about their center of mass, and also on the Mach number of the center of mass of the binary. In general, the internal torque decreases with increasing the velocity of the binary relative to the ambient gas cloud. However, this is not always the case. We also mention the relevance of our results on the period distribution of binaries. Subject headings: binaries: general -black hole physics -hydrodynamics -ISM: general -waves 1 The evolution of binaries in stellar clusters due to the dynamical interactions with other stars has received considerable attention (e.g.,

Binary black hole growth by gas accretion in stellar clusters

“…In addition, it has been argued that dynamical friction due to the gas generates torques which tend to harden the binary [61]. This will add up to the effect we put forward here.…”

The Evolution of Binaries in a Gaseous Medium: Three-dimensional Simulations of Binary Bondi–Hoyle–Lyttleton Accretion

“…Only a few values of R φ are given, but Kim et al (2008) showed that R φ is a function of M orb . Without an understanding of how R φ scales with M orb , we are unable to include results from Sánchez-Salcedo & Chametla (2014) in Figure 13, although such a comparison is highly desirable.…”

Application of Gas Dynamical Friction for Planetesimals. Ii. Evolution of Binary Planetesimals

“…We do not account for the companion's wake in our simulation. By doing that, we overestimate GDF force by at most 2 − 3 times, according to both Kim et al (2008) and Sánchez-Salcedo & Chametla (2014). Moreover, for typical planetesimal masses and for eccentric primary orbit, v out v bin .…”

“…If the outer binary moves with relative velocity v out with respect to the gas, the morphology of the wake is different. Sánchez-Salcedo & Chametla (2014) have shown that the braking torque that causes the binary to lose angular momentum, is Γ = αa bin F (1)…”