Dynamical friction
Dynamical friction (DF), defined as the momentum loss experienced by a massive moving body due to its interaction with its gravitationally induced wake, is very important in theoretical studies of several astronomical systems. The analytic theory of DF for a collisionless system was first formulated by Subrahmanyan Chandrasekhar in his seminal paper on the subject, the result of which has since been verified in observed astronomical systems, and applied on numerical simulations over the past several years. Its consequences have been instrumental in theoretically describing the sinking of orbiting satellites towards their parent galaxy, planet migration, the growth of planetisimals, and the dynamical evolution of star clusters near the galactic center, among many. It was computed in the Post-Newtonian approximation by Lee for the same uniform and isotropic system, and was later extended to a fully relativistic treatment by Petrich et al for a moving Schwarzschild black hole of mass \(M\).
Although less well-known, DF also operates in a gaseous environment. For supersonic cases, the drag force approaches the same expression for the collisionless case. However, it was found that the drag is absent in the subsonic case because of the upwind-downwind symmetry, in both relativistic and non-relativistic cases. It was not until the finite-time analysis of Ostriker for the straight-line case, and Kim & Kim for circular orbits, that dynamical friction was characterized for both subsonic and supersonic motion in collisional systems.
In most cases, a Newtonian treatment is enough to describe the behavior of an astronomical system. However, at the limit wherein orbital velocities reach the speed of light, such as the case for extreme-mass ratio inspirals (EMRIs), a relativistic extension is necessary to accurately describe the evolution of the system. Enrico Barausse laid the framework for the relativistic extension of DF in collisional systems by using tools from general relativity, while closely following the methods used by Ostriker, and Kim & Kim, that is by analyzing DF effects for straight-line motion and circular orbits on flat spacetime.
In this project, we derived expressions for the density perturbations induced by a point perturber in a slightly-eccentric orbit. As an extension of the problem for finite gaseous disks, we also derived expressions for a point perturber moving along a circular orbit immersed in a finite background.
Related publications / presentations
- Ugalino, Mark Ivan, and Vega, Michael Francis Ian, “Density perturbations in a collisional fluid induced by a particle on a slightly-eccentric orbit.” Proceedings of the Samahang Pisika ng Pilipinas, Jun 2018
- Ugalino, Mark Ivan, and Vega, Michael Francis Ian, “Steady-state density perturbations induced by a point mass in a finite cylinder.” Proceedings of the Samahang Pisika ng Pilipinas, Jun 2020