Gravitational Drag on a Point Mass in Hypersonic Motion Within a Gaussian Disk

Abstract

We develop an analytical model for the accretion and gravitational drag on a point mass that moves hypersonically in the midplane of a gaseous disk with a Gaussian vertical density stratification. Such a model is of interest for studying the interaction between a planet and a protoplanetary disk, as well as the dynamical decay of massive black holes in galactic nuclei. The model considers that the flow is ballistic, and gives fully analytical expressions for both the accretion rate onto the point mass, and the gravitational drag it suffers. The expressions are further simplified by taking the limits of a thick, and of a thin disk. The results for the thick disk reduce correctly to those for a uniform density environment (Cantó et al. 2011). We find that for a thin disk (small vertical scaleheight compared to the gravitational radius) the accretion rate is proportional to the mass of the moving object and to the surface density of the disk, while the drag force is independent of the velocity of the object. The gravitational deceleration of the hypersonic perturber in a thin disk was found to be independent of its parameters (i.e. mass or velocity) and depends only on the surface mass density of the disk. The predictions of the model are compared to the results of three-dimensional hydrodynamical simulations, with a reasonable agreement.

Orbital Evolution of Eccentric Low-mass Companions Embedded in Gaseous Disks: Testing the Local Approximation

“…By imposing an upper limit on the amplitude of these torque fluctuations, we have established the threshold value ∼ R (2D) soft for the local approximation to be faithful. An extension of the formula for the drag force in the local approximation that incorporates the vertical structure of the disk was proposed by Cantó et al (2013). We have been able to determine the validity domain of the 3D local approximation.…”

“…For a point-like perfect accretor such as a black hole, the drag force including the aerodynamical drag due to accretion is, in the local approximation, (Cantó et al 2013). This formula is very similar to Equation (17) except the numerical value of the factor in the logarithm, which is larger in the case of a perfect ac- cretor, reflecting the fact that accretion contributes to the drag force.…”

“….-Time evolution of T 1 /Ta for models with α = 0.5 (top panel) and α = 1.5 (middle and bottom panels). The horizontal dotted lines show the predicted values adopting the local approximation Cantó et al (2013),. we have computed f…”

Gap formation by inclined massive planets in locally isothermal three-dimensional discs

“…We assume the disc to be pressure-less, so that it consists of test particles, and calculate the disc and planet exchange of angular momentum as a result of the gravitational interaction of the particles with the planet. Treating the disc particles as being pressure-less is adequate as long as the velocity of the planet relative to the disc particles is supersonic (e.g., Cantó et al 2013;Xiang-Gruess & Papaloizou 2013). This condition is valid for planetary inclinations larger than the disc's aspect ratio 1 .…”

Dynamical friction in slab geometries and accretion discs

“…Most of the rigorous treatments of dynamical friction in the literature -with a few exceptions such as Ref. [9][10][11] -consider as a setup an infinite threedimensional medium. Clearly, such idealization breaks down in thin accretion or protoplanetary disks, where the geometry of the problem is more "slab-like" [12,13].…”