A Monte Carlo Approach to Modeling Dynamical Friction in Realistic Galactic Environments

Mid galaxy merger, a process called dynamical friction allows collided galaxies' central massive black holes (MBHs) to spiral into the center of the system. Dynamical friction (DF) is a result of interactions between background material of small masses and one larger mass, such as a MBH. This creates a wake of particles behind the MBH, causing a gravitational pull opposite to its velocity, slowing it down. This process controls the orbit of non-central black holes in a galaxy and drives the creation of massive black hole binaries, prospective gravitational wave sources for current and future low-frequency detectors. The standard equation used to estimate DF, the Chandrasekhar DF formula, assumes that a galaxy has a uniform density profile, and all small particles have the same mass with Maxwellian velocity distribution. With this formula, many scenarios such as density fluctuations, large mass interactions, and perpendicular force are ignored. These conditions are not representative of realistic galactic environments and thus provide an incomplete look at dynamical friction. Taking a Monte-Carlo approach, we developed a numerical formula, to create an accurate and computationally efficient method to calculate the dynamical friction. Our method allows for density fluctuations and a range of particle masses and velocities to be accounted for.