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Tal Alexander

Publications and source records attributed to Tal Alexander.

At least 19 recordsLinked to original sources
arXiv2017

EMRIs and the relativistic loss-cone: The curious case of the fortunate coincidence

Extreme mass ratio inspiral (EMRI) events are vulnerable to perturbations by the stellar background, which can abort them prematurely by deflecting EMRI orbits to plunging ones that fall directly into the massive black hole (MBH), or to less eccentric ones that no longer interact strongly with the MBH. A coincidental hierarchy between the collective resonant Newtonian torques due to the stellar background, and the relative magnitudes of the leading-order post-Newtonian precessional and radiative terms of the general relativistic 2-body problem, allows EMRIs to decouple from the background and produce semi-periodic gravitational wave signals. I review the recent theoretical developments that confirm this conjectured fortunate coincidence, and briefly discuss the implications for EMRI rates, and show how these dynamical effects can be probed locally by stars near the Galactic MBH.

astro-ph.GA↗
arXiv2017

Stellar Dynamics and Stellar Phenomena Near A Massive Black Hole

Most galactic nuclei harbor a massive black hole (MBH), whose birth and evolution are closely linked to those of its host galaxy. The unique conditions near the MBH: high velocity and density in the steep potential of a massive singular relativistic object, lead to unusual modes of stellar birth, evolution, dynamics and death. A complex network of dynamical mechanisms, operating on multiple timescales, deflect stars to orbits that intercept the MBH. Such close encounters lead to energetic interactions with observable signatures and consequences for the evolution of the MBH and its stellar environment. Galactic nuclei are astrophysical laboratories that test and challenge our understanding of MBH formation, strong gravity, stellar dynamics, and stellar physics. I review from a theoretical perspective the wide range of stellar phenomena that occur near MBHs, focusing on the role of stellar dynamics near an isolated MBH in a relaxed stellar cusp.

astro-ph.GA↗
arXiv2017

A universal minimal mass scale for present-day central black holes

Intermediate-mass black holes (IMBHs) of mass $M_{\bullet} \approx 10^{2} - 10^{5}$ solar masses, $M_{\odot}$, are the long-sought missing link between stellar black holes, born of supernovae, and massive black holes, tied to galaxy evolution by the empirical $M_{\bullet}/\sigma_{\star}$ correlation. We show that low-mass black hole seeds that accrete stars from locally dense environments in galaxies following a universal $M_{\bullet}/\sigma_{\star}$ relation grow over the age of the Universe to be above ${\mathcal{M}}_{0}\approx3\times10^{5}M_{\odot}$ ($5\%$ lower limit), independent of the unknown seed masses and formation processes. The mass ${\mathcal{M}}_{0}$ depends weakly on the uncertain formation redshift, and sets a universal minimal mass scale for present-day black holes. This can explain why no IMBHs have yet been found, and it implies that present-day galaxies with ${\sigma_{\star}<{\mathcal{S}}_{0}\approx40\,\mathrm{km\,s}^{-1}}$ lack a central black hole, or formed it only recently. A dearth of IMBHs at low redshifts has observable implications for tidal disruptions and gravitational wave mergers.

astro-ph.GA↗
arXiv2015

Steady state relativistic stellar dynamics around a massive black hole

A massive black hole (MBH) consumes stars whose orbits evolve into the small phase-space volume of unstable orbits, the "loss-cone", which take them directly into the MBH, or close enough to interact strongly with it. The resulting phenomena: tidal heating and tidal disruption, binary capture and hyper-velocity star ejection, gravitational wave (GW) emission by inspiraling compact remnants, or hydrodynamical interactions with an accretion disk, are of interest as they can produce observable signatures and thereby reveal the existence of the MBH, affect its mass and spin evolution, probe strong gravity, and provide information on stars and gas near the MBH. The continuous loss of stars and the processes that resupply them shape the central stellar distribution. We investigate relativistic stellar dynamics near the loss-cone of a non-spinning MBH in steady-state analytically and by Monte Carlo simulations of the diffusion of the orbital parameters. These take into account Newtonian mass precession due to enclosed stellar mass, in-plane precession due to general relativity, dissipation by GW, uncorrelated two-body relaxation, correlated resonant relaxation (RR) and adiabatic invariance due to secular precession, using a rigorously derived description of correlated post-Newtonian dynamics in the diffusion limit. We argue that general maximal entropy considerations strongly constrain orbital diffusion in steady-state, irrespective of the relaxation mechanism. We identify the exact phase-space separatrix between plunges and inspirals, predict their steady-state rates, and verify they are robust under a wide range of assumptions. We derive the dependence of the rates on the mass of the MBH, show that the contribution of RR is small, and discuss special cases where unquenched RR in restricted volumes of phase-space may affect the steady-state substantially.

astro-ph.GA↗
arXiv2014

Rapid growth of seed black holes in the early universe by supra-exponential accretion

Mass accretion by black holes (BHs) is typically capped at the Eddington rate, when radiation's push balances gravity's pull. However, even exponential growth at the Eddington-limited e-folding time t_E ~ few x 0.01 billion years, is too slow to grow stellar-mass BH seeds into the supermassive luminous quasars that are observed when the universe is 1 billion years old. We propose a dynamical mechanism that can trigger supra-exponential accretion in the early universe, when a BH seed is trapped in a star cluster fed by the ubiquitous dense cold gas flows. The high gas opacity traps the accretion radiation, while the low-mass BH's random motions suppress the formation of a slowly-draining accretion disk. Supra-exponential growth can thus explain the puzzling emergence of supermassive BHs that power luminous quasars so soon after the Big Bang.

astro-ph.GA↗
arXiv2014

The statistical mechanics of relativistic orbits around a massive black hole

Stars around a massive black hole (MBH) move on nearly fixed Keplerian orbits, in a centrally-dominated potential. The random fluctuations of the discrete stellar background cause small potential perturbations, which accelerate the evolution of orbital angular momentum by resonant relaxation. This drives many phenomena near MBHs, such as extreme mass-ratio gravitational wave inspirals, the warping of accretion disks, and the formation of exotic stellar populations. We present here a formal statistical mechanics framework to analyze such systems, where the background potential is described as a correlated Gaussian noise. We derive the leading order, phase-averaged 3D stochastic Hamiltonian equations of motion, for evolving the orbital elements of a test star, and obtain the effective Fokker-Planck equation for a general correlated Gaussian noise, for evolving the stellar distribution function. We show that the evolution of angular momentum depends critically on the temporal smoothness of the background potential fluctuations. Smooth noise has a maximal variability frequency $\nu_{\max}$. We show that in the presence of such noise, the evolution of the normalized angular momentum $j=\sqrt{1-e^{2}}$ of a relativistic test star, undergoing Schwarzschild (in-plane) General Relativistic precession with frequency $\nu_{GR}/j^{2}$, is exponentially suppressed for $j<j_{b}$, where $\nu_{GR}/j_{b}^{2}\sim\nu_{\max}$, due to the adiabatic invariance of the precession against the slowly varying random background torques. This results in an effective Schwarzschild precession-induced barrier in angular momentum. When $j_{b}$ is large enough, this barrier can have significant dynamical implications for processes near the MBH.

astro-ph.GA↗
arXiv2013

Constraining the dark cusp in the Galactic Center by long-period binaries

Massive black holes (MBHs) in galactic nuclei are believed to be surrounded by a high density stellar cluster, whose mass is mostly in hard-to-detect faint stars and compact remnants. Such dark cusps dominate the dynamics near the MBH: a dark cusp in the Galactic center (GC) of the Milky Way would strongly affect orbital tests of General Relativity there; on cosmic scales, dark cusps set the rates of gravitational wave emission events from compact remnants that spiral into MBHs, and they modify the rates of tidal disruption events, to list only some implications. A recently discovered long-period massive young binary (P_12 <~ 1 yr, M_12 ~ O(100 M_sun), T_12 ~ 6x10^6 yr), only ~0.1 pc from the Galactic MBH (Pfuhl et al 2013), sets a lower bound on the 2-body relaxation timescale there, min t_rlx ~ (P_12/M_12)^(2/3)T_12 ~ 10^7 yr, and correspondingly, an upper bound on the stellar number density, max n ~ few x 10^8/ 1/pc^3, based on the binary's survival against evaporation by the dark cusp. However, a conservative dynamical estimate, the drain limit, implies t_rlx > O(10^8) yr. Such massive binaries are thus too short-lived and tightly bound to constrain a dense relaxed dark cusp. We explore here in detail the use of longer-period, less massive and longer-lived binaries (P_12 ~ few yr, M_12 ~ 2-4 M_sun, T_12 ~ 10^8-10^10 yr), presently just below the detection threshold, for probing the dark cusp, and develop the framework for translating their future detections among the giants in the GC into dynamical constraints.

astro-ph.GA↗
arXiv2013

Improved AGN light curve analysis with the z-transformed discrete correlation function

The cross-correlation function (CCF) is commonly employed in the study of AGN, where it is used to probe the structure of the broad line region by line reverberation, to study the continuum emission mechanism by correlating multi-waveband light curves and to seek correlations between the variability and other AGN properties. The z -transformed discrete correlation function (ZDCF) is a new method for estimating the CCF of sparse, unevenly sampled light curves. Unlike the commonly used interpolation method, it does not assume that the light curves are smooth and it does provide errors on its estimates. The ZDCF corrects several biases of the discrete correlation function method of Edelson & Krolik (1988) by using equal population binning and Fisher's z -transform. These lead to a more robust and powerful method of estimating the CCF of sparse light curves of as few as 12 points. Two examples of light curve analysis with the ZDCF are presented. 1) The ZDCF estimate of the auto-correlation function is used to uncover a correlation between AGN magnitude and variability time scale in a small simulated sample of very sparse and irregularly sampled light curves. 2) A maximum likelihood function for the ZDCF peak location is used to estimate the time-lag between two light curves. Fortran 77 and 95 code implementations of the ZDCF and the maximum likelihood peak location (PLIKE) algorithms are freely available (see http://www.weizmann.ac.il/weizsites/tal/research/software/).

astro-ph.IM↗
arXiv2012

Stellar dynamics and tidal disruption events in galactic nuclei

The disruption of a star by the tidal field of a massive black hole is the final outcome of a chain of complex dynamical processes in the host galaxy. I introduce the "loss cone problem", and describe the many theoretical and numerical challenges on the path of solving it. I review various dynamical channels by which stars can be supplied to a massive black hole, and the relevant dynamical relaxation / randomization mechanisms. I briefly mention some "exotic" tidal disruption scenarios, and conclude by discussing some new dynamical results that are changing our understanding of dynamics near a massive black hole, and may well be relevant for tidal disruption dynamics.

astro-ph.GA↗
arXiv2012

Stellar Energy Relaxation around A Massive Black Hole

[abridged] Energy relaxation around a massive black hole (MBH) is key to establishing the dynamical state of galactic nuclei, and the nature of close stellar interactions with the MBH. The standard description of relaxation as diffusion provides a perturbative 2nd-order solution in the weak two-body interaction limit. We run N-body simulations and find that this solution fails to describe the non-Gaussian relaxation on short timescale, which is strongly influenced by extreme events even in the weak limit, and is thus difficult to characterize and measure. We derive a non-perturbative solution for relaxation as an anomalous diffusion process, and develop a robust estimation technique to measure it in simulations. These enable us to analyze and model our numerical results, and validate in detail, for the first time, this model of energy relaxation around an MBH on all timescales. We derive the relation between the energy diffusion time, t_E, and the time for a small perturbation to return to steady state, t_r, in a relaxed, single mass cusp around a MBH. We constrain the contribution of strong encounters, measure that of the weakest encounters, determine the value of the Coulomb logarithm, and provide a robust analytical estimate for t_E in a finite nuclear stellar cusp. We find that t_r ~ 10t_E ~(5/32)Q^2P_h/N_h log Q, where Q=M_bh/M_* is the MBH to star mass ratio, the orbital period P_h and number of stars N_h are evaluated at the energy scale corresponding to the MBH's sphere of influence, E_h=sigma_inf^2, where sigma_inf is the velocity dispersion far from the MBH. We conclude, using the observed cosmic M_bh/sigma correlation, that cusps around lower-mass MBHs (M_bh<10^7 Mo), which evolved passively over a Hubble time, should be relaxed. We consider the effects of anomalous energy diffusion on orbital perturbations of stars observed near the Galactic MBH.

astro-ph.GA↗
arXiv2011

The torquing of circumnuclear accretion disks by stars and the evolution of massive black holes

An accreting massive black hole (MBH) in a galactic nucleus is surrounded by a dense stellar cluster. We analyze and simulate numerically the evolution of a thin accretion disk due to its internal viscous torques, due to the frame-dragging torques of a spinning MBH (the Bardeen-Petterson effect) and due to the orbit-averaged gravitational torques by the stars (Resonant Relaxation). We show that the evolution of the MBH mass accretion rate, the MBH spin growth rate, and the covering fraction of the disk relative to the central ionizing continuum source, are all strongly coupled to the stochastic fluctuations of the stellar potential via the warps that the stellar torques excite in the disk. These lead to fluctuations by factors of up to a few in these quantities over a wide range of timescales, with most of the power on timescales >~(M_bh/M_d)P(R_d), where M_bh and M_d are the masses of the MBH and disk, and P is the orbital period at the disk's mass-weighted mean radius R_d. The response of the disk is stronger the lighter it is and the more centrally concentrated the stellar cusp. As proof of concept, we simulate the evolution of the low-mass maser disk in NGC4258, and show that its observed O(10 deg) warp can be driven by the stellar torques. We also show that the frame-dragging of a massive AGN disk couples the stochastic stellar torques to the MBH spin and can excite a jitter of a few degrees in its direction relative to that of the disk's outer regions.

astro-ph.GA↗
arXiv2011

Stellar Dynamics of Extreme-Mass-Ratio Inspirals

Inspiral of compact stellar remnants into massive black holes (MBHs) is accompanied by the emission of gravitational waves at frequencies that are potentially detectable by space-based interferometers. Event rates computed from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due to uncertaintities about the rate coefficients. Here we present results from direct integration of the post-Newtonian N-body equations of motion descrbing dense clusters of compact stars around Schwarzschild MBHs. These simulations embody an essentially exact (at the post-Newtonian level) treatment of the interplay between stellar dynamical relaxation, relativistic precession, and gravitational-wave energy loss. The rate of capture of stars by the MBH is found to be greatly reduced by relativistic precession, which limits the ability of torques from the stellar potential to change orbital angular momenta. Penetration of this "Schwarzschild barrier" does occasionally occur, resulting in capture of stars onto orbits that gradually inspiral due to gravitational wave emission; we discuss two mechanisms for barrier penetration and find evidence for both in the simulations. We derive an approximate formula for the capture rate, which predicts that captures would be strongly disfavored from orbits with semi-major axes below a certain value; this prediction, as well as the predicted rate, are verified in the N-body integrations. We discuss the implications of our results for the detection of extreme-mass-ratio inspirals from galactic nuclei with a range of physical properties.

astro-ph.CO↗
arXiv2010

Key questions about Galactic Center dynamics

I discuss four key questions about Galactic Center dynamics, their implications for understanding both the environment of the Galactic MBH and galactic nuclei in general, and the progress made in addressing them. The questions are (1) Is the stellar system around the MBH relaxed? (2) Is there a "dark cusp" around the MBH? (3) What is the origin of the stellar disk(s)?, and (4) What is the origin of the S-stars?

astro-ph.GA↗
arXiv2009

Testing Properties of the Galactic Center Black Hole Using Stellar Orbits

The spin and quadrupole moment of the supermassive black hole at the Galactic center can in principle be measured via astrometric monitoring of stars orbiting at milliparsec (mpc) distances, allowing tests of general relativistic "no-hair" theorems (Will 2008). One complicating factor is the presence of perturbations from other stars, which may induce orbital precession of the same order of magnitude as that due to general relativistic effects. The expected number of stars in this region is small enough that full N-body simulations can be carried out. We present the results of a comprehensive set of such simulations, which include a post-Newtonian treatment of spin-orbit effects. A number of possible models for the distribution of stars and stellar remnants are considered. We find that stellar perturbations are likely to obscure the signal due to frame-dragging for stars beyond ~0.5 mpc from the black hole, while measurement of the quadrupole moment is likely to require observation of stars inside ~0.2 mpc. A high fraction of stellar remnants, e.g. 10-Solar-mass black holes, in this region would make tests of GR problematic at all radii. We discuss the possibility of separating the effects of stellar perturbations from those due to GR.

astro-ph.GA↗
arXiv2009

Accretion disk warping by resonant relaxation: The case of maser disk NGC4258

The maser disk around the massive black hole (MBH) in active galaxy NGC 4258 exhibits an O(10 deg) warp on the O(0.1 pc) scale. The physics driving the warp are still debated. Suggested mechanisms include torquing by relativistic frame dragging or by radiation pressure. We propose here a new warping mechanism: resonant torquing of the disk by stars in the dense cusp around the MBH. We show that resonant torquing can induce such a warp over a wide range of observed and deduced physical parameters of the maser disk.

astro-ph.GA↗
arXiv2009

Dynamical evolution of the young stars in the Galactic center: N-body simulations of the S-stars

We use N-body simulations to study the evolution of the orbital eccentricities of stars deposited near (<0.05 pc) the Milky Way massive black hole (MBH), starting from initial conditions motivated by two competing models for their origin: formation in a disk followed by inward migration; and exchange interactions involving a binary star. The first model predicts modest eccentricities, lower than those observed in the S-star cluster, while the second model predicts higher eccentricities than observed. The N-body simulations include a dense cluster of 10 M_sun stellar black holes (SBHs), expected to accumulate near the MBH by mass segregation. Perturbations from the SBHs tend to randomize the stellar orbits, partially erasing the dynamical signatures of their origin. The eccentricities of the initially highly eccentric stars evolve, in 20 Myr (the S-star lifespan), to a distribution that is consistent at the ~95 % level with the observed eccentricity distribution. In contrast, the eccentricities of the initially more circular orbits fail to evolve to the observed values in 20 Myr, arguing against the disk migration scenario. We find that 20 % - 30 % of the S-stars are tidally disrupted by the MBH over their lifetimes, and that the S-stars are not likely to be ejected as hypervelocity stars outside the central 0.05 pc by close encounters with stellar black holes.

astro-ph.GA↗
arXiv2009

Probing Stellar Dynamics in Galactic Nuclei

Electromagnetic observations over the last 15 years have yielded a growing appreciation for the importance of supermassive black holes (SMBH) to the evolution of galaxies, and for the intricacies of dynamical interactions in our own Galactic center. Here we show that future low-frequency gravitational wave observations, alone or in combination with electromagnetic data, will open up unique windows to these processes. In particular, gravitational wave detections in the 10^{-5}-10^{-1} Hz range will yield SMBH masses and spins to unprecedented precision and will provide clues to the properties of the otherwise undetectable stellar remnants expected to populate the centers of galaxies. Such observations are therefore keys to understanding the interplay between SMBHs and their environments.

astro-ph.GA↗