A new Monte Carlo method for dynamical evolution of non-spherical stellar systems

Abstract

We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after each timestep using local velocity diffusion coefficients from the standard two-body relaxation theory. The potential and diffusion coefficients are updated after an interval of time that is a small fraction of the relaxation time, but may be longer than the dynamical time. Thus our approach is a bridge between the Spitzer's formulation of the Monte Carlo method and the temporally smoothed self-consistent field method. The primary advantages are the ability to follow the secular evolution of shape of the stellar system, and the possibility of scaling the amount of two-body relaxation to the necessary value, unrelated to the actual number of particles in the simulation. Possible future applications of this approach in galaxy dynamics include the problem of consumption of stars by a massive black hole in a non-spherical galactic nucleus, evolution of binary supermassive black holes, and the influence of chaos on the shape of galaxies, while for globular clusters it may be used for studying the influence of rotation.

Evolution of supermassive black hole binaries and tidal disruption rates in non-spherical galactic nuclei

“…Nevertheless, the semimajor axis reaches the critical value aGW (5) in less than 1 Gyr and continues to shrink; additional simulations with GW emission turned on (shown in dot-dashed line) demonstrate that the actual lifetime of the binary after this moment is much shorter than the Hubble time. The time-dependent hardening rates in the present study are well described by Equation 21 and Table 1 in Vasiliev et al (2015). A simple and reasonably realistic estimate is to approximate the hardening rate as a constant and take S µS full , with the dimensionless coefficient µ ∼ 0.1 − 0.3 (smaller q values correspond to higher µ).…”

AGAMA: action-based galaxy modelling architecture

“…Thus the potential expansion approach is well suited for analyzing the properties of orbits in a 'frozen' potential of an N -body system, and could be easily extended to represent a time-dependent potential whose coefficients are interpolated in time, providing a more flexible alternative to parametrized analytic models (used, e.g., in Muzzio et al 2005;Machado & Manos 2016) or tree-code potentials (e.g., Valluri et al 2010). The computation of a smooth potential from discrete samples is at the core of the Monte Carlo simulation code Raga (Vasiliev 2015), which is also included in the framework.…”

Star clusters, self-interacting dark matter halos, and black hole cusps: The fluid conduction model and its extension to general relativity

“…Next, using the value of s(t, M ) = v 3 /ρ obtained at the new time, Eqs. (14) and (15) are iterated to obtain r(t, M ), ρ(t, M ) and v(t, M ) on that time. Solving Eq.…”

“…The resulting nondimensional equilibrium Eqs. (14) and (15) are unchanged but the entropy evolution Eq. (16) now becomes…”