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Register a new userSecular Stellar Dynamics near a Massive Black Hole
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The angular momentum evolution of stars close to massive black holes (MBHs) is driven by secular torques. In contrast to two-body relaxation, where interactions between stars are incoherent, the resulting resonant relaxation (RR) process is characterized by coherence times of hundreds of orbital periods. In this paper, we show that all the statistical properties of RR can be reproduced in an autoregressive moving average (ARMA) model. We use the ARMA model, calibrated with extensive N-body simulations, to analyze the long-term evolution of stellar systems around MBHs with Monte Carlo simulations. We show that for a single-mass system in steady-state, a depression is carved out near an MBH as a result of tidal disruptions. Using Galactic center parameters, the extent of the depression is about 0.1 pc, of similar order to but less than the size of the observed hole in the distribution of bright late-type stars. We also find that the velocity vectors of stars around an MBH are locally not isotropic. In a second application, we evolve the highly eccentric orbits that result from the tidal disruption of binary stars, which are considered to be plausible precursors of the S-stars in the Galactic center. We find that RR predicts more highly eccentric (e > 0.9) S-star orbits than have been observed to date.
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In galactic nuclei, the gravitational potential is dominated by the central supermassive black hole, so stars follow quasi-Keplerian orbits. These orbits are distorted by gravitational forces from other stars, leading to long-term orbital relaxation. The direct numerical study of these processes is challenging because the fast orbital motion imposed by the central black hole requires very small timesteps. Within the secular approximation of smearing out stars along their underlying Keplerian orbits, a multipole expansion of the pairwise interaction between the stars yields an efficient numerical code to investigate the long-term evolution of their orbital parameters. These new simulations precisely recover the diffusion coefficients of stellar eccentricities obtained through analytical calculations of the secular dynamics. The computational complexity of the present method scales linearly with the total number of stars, so it should prove useful to study the long-term evolution of self-gravitating systems dominated by a central mass.
We derive the kinetic equation that describes the secular evolution of a large set of particles orbiting a dominant massive object, such as stars bound to a supermassive black hole or a proto-planetary debris disc encircling a star. Because the particles move in a quasi-Keplerian potential, their orbits can be approximated by ellipses whose orientations remain fixed over many dynamical times. The kinetic equation is obtained by simply averaging the BBGKY equations over the fast angle that describes motion along these ellipses. This so-called Balescu-Lenard equation describes self-consistently the long-term evolution of the distribution of quasi-Keplerian orbits around the central object: it models the diffusion and drift of their actions, induced through their mutual resonant interaction. Hence, it is the master equation that describes the secular effects of resonant relaxation. We show how it captures the phenonema of mass segregation and of the relativistic Schwarzschild barrier recently discovered in $N$-body simulations.
Among the astrophysical systems targeted by LISA, stars on relativistic orbits around massive black holes (MBHs) are particularly promising sources. Unfortunately, the prediction for the number and characteristics of such sources suffers from many uncertainties. Stellar dynamical Monte Carlo simulations of the evolution of galactic nucleus models allow more realistic estimates of these quantities. The computations presented here strongly suggest that the closest such extreme mass-ratio binary to be detected by LISA could be a low-mass MS star (MSS) orbiting the MBH at the center of our Milky Way. Only compact stars contribute to the expected detections from other galaxies because MSSs are disrupted by tidal forces too early.
We study the dynamical evolution of eccentric massive black hole binaries (MBHBs) interacting with unbound stars by means of an extensive set of three body scattering experiments. Compared to previous studies, we extend the investigation down to a MBHB mass ratio of $q=m_2/m_1=10^{-4}$, where $m_1$ and $m_2$ are the masses of the primary and secondary hole respectively. Contrary to a simple extrapolation from higher mass ratios, we find that for $qlesssim 10^{-3}$ the eccentricity growth rate becomes negative, i.e., the binary {it circularises} as it shrinks. This behaviour is due to the subset of interacting stars captured in metastable counter-rotating orbits; those stars tend to extract angular momentum from the binary, promoting eccentricity growth for $q>10^{-3}$, but tend to inject angular momentum into the binary driving it towards circularisation for $q<10^{-3}$. The physical origin of this behaviour requires a detailed study of the orbits of this subset of stars and is currently under investigation. Our findings might have important consequences for intermediate MBHs (IMBHs) inspiralling onto MBHs (e.g. a putative $10^3rm M_{odot}$ black hole inspiralling onto SgrA$^*$).
We study the effects of black hole dark matter on the dynamical evolution of stars in dwarf galaxies. We find that mass segregation leads to a depletion of stars in the center of dwarf galaxies and the appearance of a ring in the projected stellar surface density profile. Using Segue 1 as an example we show that current observations of the projected surface stellar density rule out at the 99.9% confidence level the possibility that more than 6% of the dark matter is composed of black holes with a mass of few tens of solar masses.
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