A New Fokker–Planck Approach for the Relaxation-driven Evolution of Galactic Nuclei

Abstract

We present an approach for simulating the collisional evolution of spherical isotropic stellar systems based on the one-dimensional Fokker-Planck equation. A novel aspect is that we use the phase volume as the argument of the distribution function, instead of the traditionally used energy, which facilitates the solution. The publicly available code, PhaseFlow, implements a high-accuracy finite-element method for the Fokker-Planck equation, and can handle multiple-component systems, optionally with the central black hole and taking into account loss-cone effects and star formation. We discuss the energy balance in the general setting, and in application to the Bahcall-Wolf cusp around a central black hole, for which we derive a perturbative solution. We stress that the cusp is not a steady-state structure, but rather evolves in amplitude while retaining an approximately ρ ∝ r −7/4 density profile. Finally, we apply the method to the nuclear star cluster of the Milky Way, and illustrate a possible evolutionary scenario in which a two-component system of lighter main-sequence stars and stellarmass black holes develops a Bahcall-Wolf cusp in the heavier component and a weaker ρ ∝ r −3/2 cusp in the lighter, visible component, over the period of several Gyr. The present-day density profile is consistent with the recently detected mild cusp inside the central parsec, and is weakly sensitive to initial conditions.

Rates of Stellar Tidal Disruption

“…If additional kinematic information is available, a two-integral DF f (E, L z ) may be computed instead (Magorrian and Tremaine 1999), which will selfconsistently account for the impact of flattening and orbital anisotropy on TDE rates. The simple procedure outlined above has repeatedly been used to compute TDE rates in large galaxy samples, and at this point can be performed with the publicly available Fokker-Planck code PhaseFlow (Vasiliev 2017), as was done in, e.g. Pfister et al (2019).…”

Mass Segregation in Eccentric Nuclear Disks: Enhanced Tidal Disruption Event Rates for High-mass Stars

“…Time averages are taken between t = 100P and the end of the simulation. This is done to allow the disk a secular time to relax, as the TDEs do not begin to happen until after one secular time.5 The disruption and capture rates are ∼ 6 × 10 −5 and 5 × 10 −7 per year Vasiliev (2017). gives 5 × 10 −6 for the latter, but this is actually the mass of black holes (in solar units) that are consumed per year(Vasiliev, personal communication).…”

Improved constraints from ultra-faint dwarf galaxies on primordial black holes as dark matter

“…To perform the simulations of the UFDGs, we use Phase-Flow (Vasiliev 2017), which is part of the publicly available software library Agama (Vasiliev 2019). PhaseFlow dynamically evolves a given spherically symmetric system consisting of one or more collisional components (e.g.…”

“…Its low computational cost allows us to perform the large sets of simulations required for the exploration of the input parameters using MCMC. Additionally, PhaseFlow is well tested in the context of nuclear star clusters (Generozov et al 2018;Emami & Loeb 2019a,b), Bahcall-Wolf cusps (Bahcall & Wolf 1976;Vasiliev 2017), and monochromatic PBH mass functions (Zhu et al 2018).…”