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Repeated mergers, mass-gap black holes, and formation of intermediate-mass black holes in nuclear star clusters

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 Added by Giacomo Fragione
 Publication date 2021
  fields Physics
and research's language is English




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Current theoretical models predict a mass gap with a dearth of stellar black holes (BHs) between roughly $50,M_odot$ and $100,M_odot$, while, above the range accessible through massive star evolution, intermediate-mass BHs (IMBHs) still remain elusive. Repeated mergers of binary BHs, detectable via gravitational wave emission with the current LIGO/Virgo/Kagra interferometers and future detectors such as LISA or the Einstein Telescope, can form both mass-gap BHs and IMBHs. Here we explore the possibility that mass-gap BHs and IMBHs are born as a result of successive BH mergers in dense star clusters. In particular, nuclear star clusters at the centers of galaxies have deep enough potential wells to retain most of the BH merger products after they receive significant recoil kicks due to anisotropic emission of gravitational radiation. We show that a massive stellar BH seed can easily grow to $sim 10^3 - 10^4,M_odot$ as a result of repeated mergers with other smaller BHs. We find that lowering the cluster metallicity leads to larger final BH masses. We also show that the growing BH spin tends to decrease in magnitude with the number of mergers, so that a negative correlation exists between final mass and spin of the resulting IMBHs. Assumptions about the birth spins of stellar BHs affect our results significantly, with low birth spins leading to the production of a larger population of massive BHs.



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Intermediate-mass black holes (IMBHs) have masses of about 100 to 100,000 solar masses. They remain elusive. Observing IMBHs in present-day globular clusters (GCs) would validate a formation channel for seed black holes in the early universe and inform event predictions for gravitational wave facilities. Reaching a large number of GCs per galaxy is key, as models predict that only a few percent will have retained their gravitational-wave fostering IMBHs. Related, many galaxies will need to be examined to establish a robust sample of IMBHs in GCs. These needs can be meet by using a next-generation Very Large Array (ngVLA) to search for IMBHs in the GCs of hundreds of galaxies out to a distance of 25 Mpc. These galaxies hold tens of thousands of GCs in total. We describe how to convert an ngVLA signal from a GC to an IMBH mass according to a semi-empirical accretion model. Simulations of gas flows in GCs would help to improve the robustness of the conversion. Also, self-consistent dynamical models of GCs, with stellar and binary evolution in the presence of IMBHs, would help to improve IMBH retention predictions for present-day GCs.
Collisions were suggested to potentially play a role in the formation of massive stars in present day clusters, and have likely been relevant during the formation of massive stars and intermediate mass black holes within the first star clusters. In the early Universe, the first stellar clusters were particularly dense, as fragmentation typically only occurred at densities above $10^9$cm$^{-3}$, and the radii of the protostars were enhanced due to the larger accretion rates, suggesting a potentially more relevant role of stellar collisions. We present here a detailed parameter study to assess how the number of collisions as well as the mass growth of the most massive object depends on the properties of the cluster, and we characterize the time evolution with three effective parameters, the time when most collisions occur, the duration of the collisions period, as well as the normalization required to obtain the total number of collisions. We apply our results to typical Population III (Pop.III) clusters of about $1000$M$_odot$, finding that a moderate enhancement of the mass of the most massive star by a factor of a few can be expected. For more massive Pop.III clusters as expected in the first atomic cooling halos, we expect a more significant enhancement by a factor of $15-32$. We therefore conclude that collisions in massive Pop.III clusters were likely relevant to form the first intermediate mass black holes.
For a sample of nine Galactic globular clusters we measured the inner kinematic profiles with integral-field spectroscopy that we combined with existing outer kinematic measurements and HST luminosity profiles. With this information we are able to detect the crucial rise in the velocity-dispersion profile which indicates the presence of a central black hole. In addition, N-body simulations compared to our data will give us a deeper insight in the properties of clusters with black holes and stronger selection criteria for further studies. For the first time, we obtain a homogeneous sample of globular cluster integral- field spectroscopy which allows a direct comparison between clusters with and without an intermediate-mass black hole.
We present post-Newtonian $N$-body simulations on mergers of accreting stellar-mass black holes (BHs), where such general relativistic effects as the pericenter shift and gravitational wave (GW) emission are taken into consideration. The attention is concentrated on the effects of the dynamical friction and the Hoyle-Lyttleton mass accretion by ambient gas. We consider a system composed of ten BHs with initial mass of $30~M_odot$. As a result, we show that mergers of accreting stellar-mass BHs are classified into four types: a gas drag-driven, an interplay-driven, a three body-driven, or an accretion-driven merger. We find that BH mergers proceed before significant mass accretion, even if the accretion rate is $sim10$ Eddington accretion rate, and then all BHs can merge into one heavy BH. Using the simulation results for a wide range of parameters, we derive a critical accretion rate ($dot{m}_{rm c}$), below which the BH growth is promoted faster by mergers. Also, it is found that the effect of the recoil by the GW emission can reduce $dot{m}_{rm c}$ especially in gas number density higher than $10^8~{rm cm}^{-3}$, and enhance the escape probability of merged BHs. Very recently, a gravitational wave event, GW150914, as a result of the merger of a $sim 30~M_odot$ BH binary has been detected (Abbott et al. 2016). Based on the present simulations, the BH merger in GW150914 is likely to be driven by three-body encounters accompanied by a few $M_odot$ of gas accretion, in high-density environments like dense interstellar clouds or galactic nuclei.
Intermediate-mass black holes (IMBHs) by definition have masses of $M_{rm IMBH} sim 10^{2-5}~M_odot$, a range with few observational constraints. Finding IMBHs in globular star clusters (GCs) would validate a formation channel for massive black-hole seeds in the early universe. Here, we simulate a 60-hour observation with the next-generation Very Large Array (ngVLA) of 728 GC candidates in the Virgo Cluster galaxy NGC,4472. Interpreting the radio detection thresholds as signatures of accretion onto IMBHs, we benchmark IMBH mass thresholds in three scenarios and find the following: (1) Radio analogs of ESO,243-49 HLX-1, a strong IMBH candidate with $M_{rm IMBH}^{rm HLX} sim 10^{4-5}~M_odot$ in a star cluster, are easy to access in all 728 GC candidates. (2) For the 30 GC candidates with extant X-ray detections, the empirical fundamental-plane relation involving black hole mass plus X-ray and radio luminosities suggests access to $M_{rm IMBH}^{rm FP} sim 10^{1.7-3.6}~M_odot$, with an uncertainty of 0.44 dex. (3) A fiducial Bondi accretion model was applied to all 728 GC candidates and to radio stacks of GC candidates. This model suggests access to IMBH masses, with a statistical uncertainty of 0.39 dex, of $M_{rm IMBH}^{rm B} sim 10^{4.9-5.1}~M_odot$ for individual GC candidates and $M_{rm IMBH}^{rm B,stack} sim 10^{4.5}~M_odot$ for radio stacks of about 100-200 GC candidates. The fiducial Bondi model offers initial guidance, but is subject to additional systematic uncertainties and should be superseded by hydrodynamical simulations of gas flows in GCs.
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