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Added by
Jean-Baptiste Fouvry
Publication date
2018
fields
Physics
and research's language is
English
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In the vicinity of a massive black hole, stars move on precessing Keplerian orbits. The mutual stochastic gravitational torques between the stellar orbits drive a rapid reorientation of their orbital planes, through a process called vector resonant relaxation. We derive, from first principles, the correlation of the potential fluctuations in such a system, and the statistical properties of random walks undergone by the stellar orbital orientations. We compare this new analytical approach with effective $N$-body simulations. We also provide a simple scheme to generate the random walk of a test stars orbital orientation using a stochastic equation of motion. We finally present quantitative estimations of this process for a nuclear stellar cluster such as the one of the Milky Way.
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We investigate the rate of orbital orientation dilution of young stellar clusters in the vicinity of supermassive black holes. Within the framework of vector resonant relaxation, we predict the time evolution of the two-point correlation function of the stellar orbital plane orientations as a function of their initial angular separation and diversity in orbital parameters (semi-major axis, eccentricity). As expected, the larger the spread in initial orientations and orbital parameters, the more efficient the dilution of a given set of co-eval stars, with a characteristic timescale set up by the coherence time of the background potential fluctuations. A Markovian prescription which matches numerical simulations allows us to efficiently probe the underlying kinematic properties of the unresolved nucleus when requesting consistency with a given dilution efficiency, imposed by the observed stellar disc within the one arcsecond of Sgr A*. As a proof of concept, we compute maps of constant dilution times as a function of the semi major axis cusp index and fraction of intermediate mass black holes in the old background stellar cluster. This computation suggests that vector resonant relaxation should prove useful in this context since it impacts orientations on timescales comparable to the stars age.
Based on the secular theory, we discuss the orbital evolution of stars in a nuclear star cluster to which a secondary massive black hole is infalling with vanishing eccentricity. We find that the eccentricities of the stars could show sharp transitions, depending strongly on their initial conditions. By examining the phase-space structure of an associated Hamiltonian, we show that these characteristic behaviors are partly due to a probabilistic bifurcation at a separatrix crossing, resulting from the retrograde apsidal precession by the cluster potential. We also show that separatrix crossings are closely related to realization of a large eccentricity and could be important for astrophysical phenomena such as tidal disruption events or gravitational wave emissions.
The orbits of stars close to a massive black hole are nearly Keplerian ellipses. Such orbits exert long term torques on each other, which lead to an enhanced angular momentum relaxation known as resonant relaxation. Under certain conditions, this process can modify the angular momentum distribution and affect the interaction rates of the stars with the massive black hole more efficiently than non-resonant relaxation. The torque on an orbit exerted by the cluster depends on the eccentricity of the orbit. In this paper, we calculate this dependence and determine the resonant relaxation timescale as a function of eccentricity. In particular, we show that the component of the torque that changes the magnitude of the angular momentum is linearly proportional to eccentricity, so resonant relaxation is much more efficient on eccentric orbits than on circular orbits.
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