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Register a new userStellar Dynamics and Black Holes
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David Merritt
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Chandrasekhars most important contribution to stellar dynamics was the concept of dynamical friction. I briefly review that work, then discuss some implications of Chandrasekhars theory of gravitational encounters for motion in galactic nuclei.
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The center of our Galaxy is known to host a massive compact object, Sgr A$^*$, which is commonly considered as a super-massive black hole of $sim 4times 10^6$ M$_odot$. It is surrounded by a dense and massive nuclear star cluster, with a half mass radius about $5$~pc and a mass larger than $10^{7}$ M$_odot$. In this paper we studied the evolutionary fate of a very dense cluster of intermediate mass black holes, possible remnants of the dissipative orbital evolution of massive globular cluster hosts. We performed a set of high precision $N$-body simulations taking into account deviations from pure Newtonian gravitational interaction via a Post Newtonian development up to $2.5$ order, which is the one accounting for energy release by gravitational wave emission. The violent dynamics of the system leads to various successive merger events such to grow a single object containing $sim 25$ per cent of the total cluster mass before partial dispersal of the cluster, and such to generate, in different bursts, a significant quantity of gravitational waves emission. If generalized, the present results suggest a mechanism of mass growth up to the scale of a super massive black hole.
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 clusters 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.
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.
We study the formation of intermediate-mass ratio inspirals (IMRIs) triggered by the interactions between two stellar black holes (BHs) and an intermediate-mass BH (IMBH) inhabiting the centre of a dense star cluster. We exploit $N$-body models varying the IMBH mass, the stellar BH mass spectrum, and the star cluster properties. These simulations are coupled with a semi-analytic procedure to characterise the evolution of the remnant IMBH. The IMRIs formation probability attains values $sim 5-50%$, with larger values corresponding to larger IMBH masses. IMRIs map out the stellar BH mass spectrum, thus they might be used to unravel BH populations in star clusters harboring an IMBH. After the IMRI phase, an IMBH initially nearly maximal(almost non-rotating) tends to decrease(increase) its spin. If IMBHs grow mostly via repeated IMRIs, we show that only IMBH seeds sufficiently massive ($M_{rm seed} > 300$ M$_odot$) can grow up to $M_{rm imbh} >10^3$ M$_odot$ in dense globular clusters. Assuming that these seeds form at a redshift $zsim 2-6$, we find that around $1-5%$ of them would reach masses $sim 500-1500$ M$_odot$ at redshift $z=0$ and would exhibit low-spins, $S_{rm imbh} < 0.2$. Measuring the mass and spin of IMBHs involved in IMRIs could help unravelling their formation mechanisms. We show that LISA can detect IMBHs in Milky Way globular clusters with a signal-to-noise ratio SNR$=10-100$, or in the Large Magellanic Cloud with an SNR$=8-40$. We provide the IMRIs merger rate for LIGO ($Gamma_{rm LIG} = 0.003-1.6$ yr$^{-1}$), LISA ($Gamma_{rm LIS} = 0.02-60$ yr$^{-1}$), ET ($Gamma_{rm ET} = 1-600$ yr$^{-1}$), and DECIGO ($Gamma_{rm DEC} = 6-3000$ yr$^{-1}$). Our simulations show that IMRIs mass and spin encode crucial insights on the mechanisms that regulate IMBH formation and that the synergy among different detectors would enable us to fully unveil them. (Abridged)
Gravitational microlensing is a powerful tool to search for a population of invisible black holes (BHs) in the Milky Way (MW), including isolated BHs and binary BHs at wide orbits that are complementary to gravitational wave observations. By monitoring highly populated regions of source stars like the MW bulge region, one can pursue microlensing events due to these BHs. We find that if BHs have a Salpeter-like mass function extended beyond $30M_odot$ and a similar velocity and spatial structure to stars in the Galactic bulge and disk regions, the BH population is a dominant source of the microlensing events at long timescales of the microlensing light curve $gtrsim 100~$days. This is due to a boosted sensitivity of the microlensing event rate to lens mass, given as $M^2$, for such long-timescale events. A monitoring observation of $2 times 10^{10}$ stars in the bulge region over 10 years with the Rubin Observatory Legacy Survey of Space and Time (LSST) would enable one to find about $6times 10^5$ BH microlensing events. We evaluate the efficiency of potential LSST cadences for characterizing the light curves of BH microlensing and find that nearly all events of long timescales can be detected.
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