arXiv subjects

Eugene Vasiliev

Publications and source records attributed to Eugene Vasiliev.

68 records · Page 4Linked to original sources

arXiv2016

Tidal disruption rates in non-spherical galactic nuclei formed by galaxy mergers

We explore the rates of tidal disruption events (TDEs) of stars by supermassive black holes (SBHs) in galactic nuclei formed in mergers followed by a formation and coalescence of a binary SBH. Such systems initially have a deficit of stars on low-angular-momentum orbits caused by the slingshot process during the binary SBH stage, which tends to reduce the flux of stars into the SBH compared to the steady-state value. On the other hand, a newly formed galactic nucleus has a non-spherical shape which enhances the mixing of stars in angular momentum and thus the TDE rate. In galaxies with relatively low SBH masses (<10^7 Msun), relaxation times are short enough to wash out the anisotropy in initial conditions, and for more massive SBH the enhancement of flux due to non-sphericity turns out to be more important than its suppression due to initial anisotropy. Therefore, the present-day TDE rates generally exceed conventional steady-state estimates based on a spherical isotropic approximation. We thus conjecture that the lower observationally inferred TDE rates compared to theoretical predictions cannot be attributed to the depletion of low-angular-momentum stars by SBH binaries.

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arXiv2015

The final-parsec problem in the collisionless limit

A binary supermassive black hole loses energy via ejection of stars in a galactic nucleus, until emission of gravitational waves becomes strong enough to induce rapid coalescence. Evolution via the gravitational slingshot requires that stars be continuously supplied to the binary, and it is known that in spherical galaxies the reservoir of such stars is quickly depleted, leading to stalling of the binary at parsec-scale separations. Recent N-body simulations of galaxy mergers and isolated nonspherical galaxies suggest that this stalling may not occur in less idealized systems. However, it remains unclear to what degree these conclusions are affected by collisional relaxation, which is much stronger in the numerical simulations than in real galaxies. In this study, we present a novel Monte Carlo method that can efficiently deal with both collisional and collisionless dynamics, and with galaxy models having arbitrary shapes. We show that without relaxation, the final-parsec problem may be overcome only in triaxial galaxies. Axisymmetry is not enough, but even a moderate departure from axisymmetry is sufficient to keep the binary shrinking. We find that the binary hardening rate is always substantially lower than the maximum possible, "full-loss-cone" rate, and that it decreases with time, but that stellar-dynamical interactions are nevertheless able to drive the binary to coalescence on a timescale <=1 Gyr in any triaxial galaxy.

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arXiv2015

Suppression of stellar tidal disruption rates by anisotropic initial conditions

We compute the rates of capture of stars by supermassive black holes, using time-dependent Fokker--Planck equation with initial conditions that have a deficit of stars on low-angular-momentum orbits. One class of initial conditions has a gap in phase space created by a binary black hole, and the other has a globally tangentially-anisotropic velocity distribution. We find that for galactic nuclei that are younger than ~0.1 relaxation times, the flux of stars into the black hole is suppressed with respect to the steady-state value. This effect may substantially reduce the number of observable tidal disruption flares in galaxies with black hole masses M>10^7 Msun.

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arXiv2015

Applying Schwarzschild's orbit superposition method to barred or non-barred disc galaxies

We present an implementation of the Schwarzschild orbit superposition method which can be used for constructing self-consistent equilibrium models of barred or non-barred disc galaxies, or of elliptical galaxies with figure rotation. This is a further development of the publicly available code SMILE; its main improvements include a new efficient representation of an arbitrary gravitational potential using two-dimensional spline interpolation of Fourier coefficients in the meridional plane, as well as the ability to deal with rotation of the density profile and with multicomponent mass models. We compare several published methods for constructing composite axisymmetric disc--bulge--halo models and demonstrate that our code produces the models that are closest to equilibrium. We also apply it to create models of triaxial elliptical galaxies with cuspy density profiles and figure rotation, and find that such models can be found and are stable over many dynamical times in a wide range of pattern speeds and angular momenta, covering both slow- and fast-rotator classes. We then attempt to create models of strongly barred disc galaxies, using an analytic three-component potential, and find that it is not possible to make a stable dynamically self-consistent model for this density profile. Finally, we take snapshots of two N-body simulations of barred disc galaxies embedded in nearly-spherical haloes, and construct equilibrium models using only information on the density profile of the snapshots. We demonstrate that such reconstructed models are in near-stationary state, in contrast with the original N-body simulations, one of which displayed significant secular evolution.

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arXiv2014

Evolution of binary supermassive black holes and the final-parsec problem

I review the evolution of binary supermassive black holes and focus on the stellar-dynamical mechanisms that may help to overcome the final-parsec problem - the possible stalling of the binary at a separation much larger than is required for an efficient gravitational wave emission. Recent N-body simulations have suggested that a departure from spherical symmetry in the nucleus of the galaxy may keep the rate of interaction of stars with the binary at a high enough level so that the binary continues to shrink rather rapidly. However, a major problem of all these simulations is that they do not probe the regime where collisionless effects are dominant - in other words, the number of particles in the simulation is still not sufficient to reach the asymptotic behaviour of the system. I present a novel Monte Carlo method for simulating both collisional and collisionless evolution of non-spherical stellar systems, and apply it for the problem of binary supermassive black hole evolution. I show that in triaxial galaxies the final-parsec problem is largely non-existent, while in the axisymmetric case it seems to still exist in the limit of purely collisionless regime relevant for real galaxies, but disappears in the N-body simulations where the feasible values of N are still too low to get rid of collisional effects.

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arXiv2014

Rates of capture of stars by supermassive black holes in non-spherical galactic nuclei

We consider the problem of star consumption by supermassive black holes in non-spherical (axisymmetric, triaxial) galactic nuclei. We review the previous studies of the loss-cone problem and present a novel simulation method which allows to separate out the collisional (relaxation-related) and collisionless (related to non-conservation of angular momentum) processes and determine their relative importance for the capture rates in different geometries. We show that for black holes more massive than 10^7 Msun, the enhancement of capture rate in non-spherical galaxies is substantial, with even modest triaxiality being capable of keeping the capture rate at the level of few percent of black hole mass per Hubble time.

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arXiv2014

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

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.

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arXiv2014

The final-parsec problem in non-spherical galaxies revisited

We consider the evolution of supermassive black hole binaries at the center of spherical, axisymmetric, and triaxial galaxies, using direct N-body integrations as well as analytic estimates. We find that the rates of binary hardening exhibit a significant N-dependence in all the models, at least for N in the investigated range of 10^5<=N<=10^6. Binary hardening rates are also substantially lower than would be expected if the binary loss cone remained full, as it would be if the orbits supplying stars to the binary were being efficiently replenished. The difference in binary hardening rates between the spherical and nonspherical models is less than a factor of two even in the simulations with the largest N. By studying the orbital populations of our models, we conclude that the rate of supply of stars to the binary via draining of centrophilic orbits is indeed expected to be much lower than the full-loss-cone rate, consistent with our simulations. We argue that the binary's evolution in the simulations is driven in roughly equal amounts by collisional and collisionless effects, even at the highest N-values currently accessible. While binary hardening rates would probably reach a limiting value for large N, our results suggest that we cannot approach that rate with currently available algorithms and computing hardware. The extrapolation of results from N-body simulations to real galaxies is therefore not straightforward, casting doubt on recent claims that triaxiality or axisymmetry alone are capable of solving the final-parsec problem in gas-free galaxies.

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arXiv2013

The loss cone problem in axisymmetric nuclei

We consider the problem of consumption of stars by a supermassive black hole (SBH) at the center of an axisymmetric galaxy. Inside the SBH sphere of influence, motion of stars in the mean field is regular and can be described analytically in terms of three integrals of motion: the energy E, the z-component of angular momentum L_z, and the secular Hamiltonian H. There exist two classes of orbits, tubes and saucers; saucers occupy the low-angular-momentum parts of phase space and their fraction is proportional to the degree of flattening of the nucleus. Perturbations due to gravitational encounters lead to diffusion of stars in integral space, which can be described using the Fokker-Planck equation. We calculate the diffusion coefficients and solve this equation in the two-dimensional phase space (L_z, H), for various values of the capture radius and the degree of flattening. Capture rates are found to be modestly higher than in the spherical case, up to a factor of a few, and most captures take place from saucer orbits. We also carry out a set of collisional N-body simulations to confirm the predictions of the Fokker-Planck models. We discuss the implications of our results for rates of tidal disruption and capture in the Milky Way and external galaxies.

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arXiv2013

A new code for orbit analysis and Schwarzschild modelling of triaxial stellar systems

We review the methods used to study the orbital structure and chaotic properties of various galactic models and to construct self-consistent equilibrium solutions by Schwarzschild's orbit superposition technique. These methods are implemented in a new publicly available software tool, SMILE, which is intended to be a convenient and interactive instrument for studying a variety of 2D and 3D models, including arbitrary potentials represented by a basis-set expansion, a spherical-harmonic expansion with coefficients being smooth functions of radius (splines), or a set of fixed point masses. We also propose two new variants of Schwarzschild modelling, in which the density of each orbit is represented by the coefficients of the basis-set or spline spherical-harmonic expansion, and the orbit weights are assigned in such a way as to reproduce the coefficients of the underlying density model. We explore the accuracy of these general-purpose potential expansions and show that they may be efficiently used to approximate a wide range of analytic density models and serve as smooth representations of discrete particle sets (e.g. snapshots from an N-body simulation), for instance, for the purpose of orbit analysis of the snapshot. For the variants of Schwarzschild modelling, we use two test cases - a triaxial Dehnen model containing a central black hole, and a model re-created from an N-body snapshot obtained by a cold collapse. These tests demonstrate that all modelling approaches are capable of creating equilibrium models.

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arXiv2012

Spin Evolution of Supermassive Black Holes and Galactic Nuclei

The spin angular momentum S of a supermassive black hole (SBH) precesses due to torques from orbiting stars, and the stellar orbits precess due to dragging of inertial frames by the spinning hole. We solve the coupled post-Newtonian equations describing the joint evolution of S and the stellar angular momenta Lj, j = 1...N in spherical, rotating nuclear star clusters. In the absence of gravitational interactions between the stars, two evolutionary modes are found: (1) nearly uniform precession of S about the total angular momentum vector of the system; (2) damped precession, leading, in less than one precessional period, to alignment of S with the angular momentum of the rotating cluster. Beyond a certain distance from the SBH, the time scale for angular momentum changes due to gravitational encounters between the stars is shorter than spin-orbit precession times. We present a model, based on the Ornstein-Uhlenbeck equation, for the stochastic evolution of star clusters due to gravitational encounters and use it to evaluate the evolution of S in nuclei where changes in the Lj are due to frame dragging close to the SBH and to encounters farther out. Long-term evolution in this case is well described as uniform precession of the SBH about the cluster's rotational axis, with an increasingly important stochastic contribution when SBH masses are small. Spin precessional periods are predicted to be strongly dependent on nuclear properties, but typical values are 10-100 Myr for low-mass SBHs in dense nuclei, 100 Myr - 10 Gyr for intermediate mass SBHs, and > 10 Gyr for the most massive SBHs. We compare the evolution of SBH spins in stellar nuclei to the case of torquing by an inclined, gaseous accretion disk.

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arXiv2010

Orbits Around Black Holes in Triaxial Nuclei

We discuss the properties of orbits within the influence sphere of a supermassive black hole (BH), in the case that the surrounding star cluster is nonaxisymmetric. There are four major orbit families; one of these, the pyramid orbits, have the interesting property that they can approach arbitrarily closely to the BH. We derive the orbit-averaged equations of motion and show that in the limit of weak triaxiality, the pyramid orbits are integrable: the motion consists of a two-dimensional libration of the major axis of the orbit about the short axis of the triaxial figure, with eccentricity varying as a function of the two orientation angles, and reaching unity at the corners. Because pyramid orbits occupy the lowest angular momentum regions of phase space, they compete with collisional loss cone repopulation and with resonant relaxation in supplying matter to BHs. General relativistic advance of the periapse dominates the precession for sufficiently eccentric orbits, and we show that relativity imposes an upper limit to the eccentricity: roughly the value at which the relativistic precession time is equal to the time for torques to change the angular momentum. We argue that this upper limit to the eccentricity should apply also to evolution driven by resonant relaxation, with potentially important consequences for the rate of extreme-mass-ratio inspirals in low-luminosity galaxies. In giant galaxies, we show that capture of stars on pyramid orbits can dominate the feeding of BHs, at least until such a time as the pyramid orbits are depleted; however this time can be of order a Hubble time.

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arXiv2008

Dark matter dynamics in Galactic center

The evolution of dark matter in central areas of galaxies is considered (the Milky Way is taken as an example). It is driven by scattering off of dark matter particles by bulge stars, their absorption by the supermassive black hole and self-annihilation. This process is described by diffusion equation in the phase space of energy and angular momentum. The equation was integrated for several different models of initial dark matter distribution and using various assumptions about the dynamical factors. It turns out that because the Milky Way center is rather dynamically old (~5 relaxation times t_r), the difference in initial conditions almost vanishes. The density attains a nearly universal profile, and the gamma-ray flux from dark matter annihilation lies in rather narrow range, which enables more robust determination of the dark matter parameters. By present time the mass of dark matter inside the black hole sphere of influence (r<2 pc) has been reduced approximately twice, mostly because of heating by stars. It is shown that the dynamics of dark matter for t>t_r is determined mainly by stars outside the sphere of influence.

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arXiv2007

Dark matter annihilation near a black hole: plateau vs. weak cusp

Dark matter annihilation in so-called ``spikes'' near black holes is believed to be an important method of indirect dark matter detection. In the case of circular particle orbits, the density profile of dark matter has a plateau at small radii, the maximal density being limited by the annihilation cross-section. However, in the general case of arbitrary velocity anisotropy the situation is different. Particulary, for isotropic velocity distribution the density profile cannot be shallower than r^{-1/2} in the very centre. Indeed, a detailed study reveals that in many cases the term ``annihilation plateau'' is misleading, as the density actually continues to rise towards small radii and forms a weak cusp, rho ~ r^{-(beta+1/2)}, where beta is the anisotropy coefficient. The annihilation flux, however, does not change much in the latter case, if averaged over an area larger than the annihilation radius.

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