Clovis Hopman

Massive Perturber-driven Interactions between Stars and a Massive Black Hole

We study the role of massive perturbers (MPs) in deflecting stars and binaries to almost radial (loss cone) orbits, where they pass near the central massive black hole (MBH), interact with it at periapse, and are ultimately destroyed. MPs dominate dynamical relaxation when the ratio of the second moments of the MP and star mass distributions, ?2 ? NpM/NM, satisfies ?2 1. We compile the MP mass function from published observations and show that MPs in the nucleus of the Galaxy (mainly giant molecular clouds), and plausibly in late-type galaxies generally, have 102 ?2 108. MPs thus shorten the relaxation timescale by 101-107 relative to two-body relaxation by stars alone. We show that this increases by 101-103 the rate of large-periapse interactions with the MBH, where loss cone refilling by stellar two-body relaxation is inefficient. We extend the Fokker-Planck loss cone formalism to approximately account for relaxation by rare encounters with MPs. We show that binary star-MBH exchanges driven by MPs can explain the origin of the young main-sequence B stars that are observed very near the Galactic MBH and can increase by orders of magnitude the ejection rate of hypervelocity stars. In contrast, the rate of small-periapse interactions of single stars with the MBH, such as tidal disruption, is only increased by a factor of a few. We suggest that MP-driven relaxation plays an important role in the three-body exchange capture of stars on very tight orbits around the MBH. These captured stars may later be disrupted by the MBH via tidal orbital decay or direct scattering into the loss cone; captured compact objects may inspiral into the MBH by the emission of gravitational waves from zero-eccentricity orbits.

Resonant relaxation near a massive black hole: the stellar distribution and gravitational wave sources

Resonant relaxation (RR) of orbital angular momenta occurs near massive black holes (MBHs) where the potential is spherical and stellar orbits are nearly Keplerian and so do not precess significantly. The resulting coherent torques efficiently change the magnitude of the angular momenta and rotate the orbital inclination in all directions. As a result, many of the tightly bound stars very near the MBH are rapidly destroyed by falling into the MBH on low angular momentum orbits, while the orbits of the remaining stars are efficiently randomized. We solve numerically the Fokker-Planck equation in energy for the steady state distribution of a single-mass population with an RR sink term. We find that the steady state current of stars, which sustains the accelerated drainage close to the MBH, can be 10 larger than that due to noncoherent two-body relaxation alone. RR mostly affects tightly bound stars, and so it increases only moderately the total tidal disruption rate, which is dominated by stars originating from less bound orbits farther away. We show that the event rate of gravitational wave (GW) emission from inspiraling stars, originating much closer to the MBH, is dominated by RR dynamics. The GW event rate depends on the uncertain efficiency of RR. The efficiency indicated by the few available simulations implies rates 10 times higher than those predicted by two-body relaxation, which would improve the prospects of detecting such events by future GW detectors, such as LISA. However, a higher, but still plausible, RR efficiency can lead to the drainage of all tightly bound stars and strong suppression of GW events from inspiraling stars. We apply our results to the Galactic MBH and show that the observed dynamical properties of stars there are consistent with RR.

The effect of mass-segregation on gravitational wave sources near massive black holes

Gravitational waves (GWs) from the inspiral of compact remnants (CRs) into massive black holes (MBHs) will be observable to cosmological distances. While a CR spirals in, two-body scattering by field stars may cause it to fall into the central MBH before reaching a short-period orbit that would give an observable signal. As a result, only CRs very near (~0.01 pc) the MBH can spiral in successfully. In a multimass stellar population, the heaviest objects sink to the center, where they are more likely to slowly spiral into the MBH without being swallowed prematurely. We study how mass segregation modifies the stellar distribution and the rate of GW events. We find that the inspiral rate per galaxy is 30 Gyr-1 for white dwarfs, 6 Gyr-1 for neutron stars, and 250 Gyr-1 for 10 M? stellar black holes (SBHs). The high rate for SBHs is due to their extremely steep density profile, nBH(r) r-2. The GW detection rate will be dominated by SBHs.

STRONG MASS SEGREGATION AROUND A MASSIVE BLACK HOLE

We show that the mass-segregation solution for the steady-state distribution of stars around a massive black hole (MBH) has two branches: the well known weak-segregation solution and a strong segregation solution, which is analyzed here for the first time. The nature of the solution depends on the heavy-to-light stellar mass ratio MH /ML and on the unbound population number ratio NH /NL , through the relaxational coupling parameter Δ = 4NHM 2 H /[NLM 2 L (3 + MH /ML )]. When the heavy stars are relatively common (Δ 1), they scatter frequently on each other. This efficient self-coupling leads to weak mass segregation, where the stars form mass-dependent cusps near the MBH, with indices α H = 7/4 for the heavy stars and 3/2 < α L < 7/4 for the light stars (i.e. max(α H – α L ) 1/4). However, when the heavy stars are relatively rare (Δ 1), they scatter mostly on light stars, sink to the center by dynamical friction and settle into a much steeper cusp with 2 α H 11/4, while the light stars form a 3/2 < α L < 7/4 cusp, resulting in strong segregation (i.e., max(α H – α L ) 1). We show that the present-day mass function of evolved stellar populations with a universal initial mass function (coeval or continuously star forming) separates into two distinct mass scales, ~1 M ☉ of main sequence and compact dwarfs, and ~10 M ☉ of stellar black holes (SBHs), and have Δ < 0.1. We conclude that it is likely that many relaxed galactic nuclei are strongly segregated. We review indications of strong segregation in observations of the Galactic center and in results of numeric simulations, and briefly list possible implications of a very high central concentration of SBHs around an MBH.

The Orbital Statistics of Stellar Inspiral and Relaxation near a Massive Black Hole: Characterizing Gravitational Wave Sources

We study the orbital parameter distribution of stars that are scattered into nearly radial orbits and then spiral into a massive black hole (MBH) due to dissipation, in particular by emission of gravitational waves (GWs). This is important for GW detection, e.g., by the Laser Interferometer Space Antenna (LISA). Signal identification requires knowledge of the waveforms, which depend on the orbital parameters. We use analytical and Monte Carlo methods to analyze the interplay between GW dissipation and scattering in the presence of a mass sink during the transition from the initial scattering-dominated phase to the final dissipation-dominated phase of the inspiral. Our main results are as follows. (1) Stars typically enter the GW-emitting phase with high eccentricities. (2) The GW event rate per galaxy is a few × 10-9 yr-1 for typical central stellar cusps, almost independently of the relaxation time or the MBH mass. (3) For intermediate-mass black holes of ~103 M☉ such as may exist in dense stellar clusters, the orbits are very eccentric and the inspiral is rapid, so the sources are very short-lived.

Ultraluminous X-ray sources as intermediate-mass black holes fed by tidally captured stars

The nature of ultraluminous X-ray (ULX) sources is presently unknown. A possible explanation is that they are accreting intermediate-mass black holes (IBHs) that are fed by Roche lobe overflow from a tidally captured stellar companion. We show that a star can circularize around an IBH without being destroyed by tidal heating (in contrast to the case of massive black holes in galactic centers, where survival is unlikely). 6 M 1 10 M BH , We find that the capture and circularization rate is ∼ yr 1 , almost independently of the cluster’s relaxation 8 5 # 10 time. We follow the luminosity evolution of the binary system during the main-sequence Roche lobe overflow phase and show it can maintain ULX source–like luminosities for greater than 10 7 yr. In particular, we show that the ULX source in the young cluster MGG-11 in starburst galaxy M82, which possibly harbors an IBH, is well explained by this mechanism, and we predict that 10% of similar clusters with IBHs have a tidally captured circularized star. The cluster can evaporate on a timescale shorter than the lifetime of the binary. This raises the possibility of a ULX source that outlives its host cluster, or even lights up only after the cluster has evaporated, in agreement with observations of hostless ULX sources. Subject headings: black hole physics — galaxies: star clusters — stellar dynamics — X-rays: binaries

A NEW SECULAR INSTABILITY OF ECCENTRIC STELLAR DISKS AROUND SUPERMASSIVE BLACK HOLES, WITH APPLICATION TO THE GALACTIC CENTER

We identify a new secular instability of eccentric stellar disks around supermassive black holes. We show that retrograde precession of the stellar orbits, due to the presence of a stellar cusp, induces coherent torques that amplify deviations of individual orbital eccentricities from the average, and thus drive all eccentricities away from their initial value. We investigate the instability using N-body simulations, and show that it can propel individual orbital eccentricities to significantly higher or lower values on the order of a precession timescale. This physics is relevant for the Galactic center, where massive stars are likely to form in eccentric disks around the SgrA* black hole. We show that the observed bimodal eccentricity distribution of disk stars in the Galactic center is in good agreement with the distribution resulting from the eccentricity instability and demonstrate how the dynamical evolution of such a disk results in several of its stars acquiring high (1 ? e 0.1) orbital eccentricity. Binary stars on such highly eccentric orbits would get tidally disrupted by the SgrA* black hole, possibly producing both S-stars near the black hole and high-velocity stars in the Galactic halo.

Resonant relaxation near a massive black hole: the dependence on eccentricity

The orbits of stars close to a massive black hole (MBH) 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 MBH 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 time-scale 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.

Tidal capture of stars by intermediate-mass black holes

Recent X-ray observations and theoretical modelling have made it plausible that some ultraluminous X-ray sources (ULX) are powered by intermediate-mass black holes (IMBHs). N-body simulations have also shown that for certain initial conditions runaway merging of stars happens in dense star clusters, which could lead to the formation of IMBHs. In the present paper we have performed N-body simulations of young clusters such as MGG-11 of M82 in which IMBHs form through runaway merging. We took into account the effect of tidal energy dissipation of stars passing close to the IMBH to study the tidal capture and disruption of stars by IMBHs. In our simulations, IMBHs have a high chance of capturing stars through tidal energy dissipation within a few core relaxation times. For similar to 30 per cent of our runs a ULX is formed through tidal capture within 7-12 Myr, consistent with the age limits of MGG-11. Our results strengthen the case for some ULX being powered by IMBHs.

ORBITAL IN-SPIRAL INTO A MASSIVE BLACK HOLE IN A GALACTIC CENTER

A massive black hole (MBH) in a galactic center drives a flow of stars into nearly radial orbits to replace those it destroyed. Stars whose orbits cross the event horizon or the tidal disruption radius are promptly rr St destroyed in an orbital period P. Stars with orbital periapse slightly larger than the sink radius rq { p may slowly spiral in as a result of dissipative interactions with the MBH, e.g., gravitational wave max (r , r ) St emission, tidal heating, or accretion disk drag, with observable consequences and implications for the MBH growth rate. Unlike prompt destruction, the in-spiral time is typically kP. This time is limited by the same scattering process that initially deflected the star into its eccentric orbit, since it can deflect it again to a wider orbit where dissipation is inefficient. The ratio between slow and prompt event rates is therefore much smaller than that implied by the ratio of cross sections, ∼ , and so only prompt disruption contributes significantly to r /q p the mass of the MBH. Conversely, most stars that scatter off the MBH survive the extreme tidal interaction (“tidal scattering”). We derive general expressions for the in-spiral event rate and the mean number of in-spiraling stars, and we show that the survival probability of tidally scattered stars is ∼1 and that the number of tidally heated stars (“squeezars”) and gravity-wave–emitting stars in the galactic center is ∼0.1–1. Subject headings: black hole physics — Galaxy: center — gravitational waves — stellar dynamics