The influence of Massive Black Hole Binaries on the Morphology of Merger Remnants

Massive black hole (MBH) binaries, formed as a result of galaxy mergers, are expected to harden by dynamical friction and three-body stellar scatterings, until emission of gravitational waves (GWs) leads to their final coalescence. According to recent simulations, MBH binaries can efficiently harden via stellar encounters only when the host geometry is triaxial, even if only modestly, as angular momentum diffusion allows an efficient repopulation of the binary loss cone. In this paper, we carry out a suite of N-body simulations of equal-mass galaxy collisions, varying the initial orbits and density profiles for the merging galaxies and running simulations both with and without central MBHs. We find that the presence of an MBH binary in the remnant makes the system nearly oblate, aligned with the galaxy merger plane, within a radius enclosing 100 MBH masses. We never find binary hosts to be prolate on any scale. The decaying MBHs slightly enhance the tangential anisotropy in the centre of the remnant due to angular momentum injection and the slingshot ejection of stars on nearly radial orbits. This latter effect results in about 1% of the remnant stars being expelled from the galactic nucleus. Finally, we do not find any strong connection between the remnant morphology and the binary hardening rate, which depends only on the inner density slope of the remnant galaxy. Our results suggest that MBH binaries are able to coalesce within a few Gyr, even if the binary is found to partially erase the merger-induced triaxiality from the remnant.Comment: 16 pages, 13 figures, 4 tables; accepted for publication in MNRA

Star cluster disruption by a massive black hole binary

Massive black hole binaries (BHBs) are expected to form as the result of galaxy mergers; they shrink via dynamical friction and stellar scatterings, until gravitational waves (GWs) bring them to the final coalescence. It has been argued that BHBs may stall at a parsec scale and never enter the GW stage if stars are not continuously supplied to the BHB loss cone. Here, we perform several N-body experiments to study the effect of an 8 7 104M 99 stellar cluster (SC) infalling on a parsec-scale BHB. We explore different orbital elements for the SC, and we perform runs both with and without accounting for the influence of a rigid stellar cusp (modelled as a rigid Dehnen potential). We find that the semimajor axis of the BHB shrinks by 73 10 per cent if the SC is on a nearly radial orbit; the shrinking is more efficient when a Dehnen potential is included and the orbital plane of the SC coincides with that of the BHB. In contrast, if the SC orbit has non-zero angular momentum, only few stars enter the BHB loss cone and the resulting BHB shrinking is negligible. Our results indicate that SC disruption might significantly contribute to the shrinking of a parsec-scale BHB only if the SC approaches the BHB on a nearly radial orbit

Star cluster disruption by a supermassive black hole binary

Binary supermassive black holes (BBHs) are expected to be one of the most powerful sources of low-frequency gravitational waves (GWs) for future space-borne detectors. Prior to the GW emission stage, BBHs evolving in gas-poor nuclei shrink primarily through the slingshot ejection of stars approaching the BBH from sufficiently close distances. Here we address the possibility that the BBH shrinking rate is enhanced through the infall of a star cluster (SC) onto the BBH. We present the results of direct summation N-body simulations exploring different orbits for the SC infall, and we show that SCs reaching the BBH on non-zero angular momentum orbits (with eccentricity 0.75) fail to enhance the BBH hardening, while SCs approaching the BBH on radial orbits reduce the BBH separation by 3c 10% in less than 10 Myr, effectively shortening the BBH path towards GWs

Generation of gravitational waves and tidal disruptions in clumpy galaxies

Obtaining a better understanding of intermediate-mass black holes (IMBHs) is crucial, as their properties could shed light on the origin and growth of their supermassive counterparts. Massive star-forming clumps, which are present in a large fraction of massive galaxies at z ∼ 1–3, are among the venues wherein IMBHs could reside. We perform a series of Fokker–Planck simulations to explore the occurrence of tidal disruption (TD) and gravitational wave (GW) events about an IMBH in a massive star-forming clump, modelling the latter so that its mass (⁠108M⊙⁠) and effective radius (100 pc) are consistent with the properties of both observed and simulated clumps. We find that the TD and GW event rates are in the ranges of 10−6 to 10−5 and 10−8 to 10−7 yr−1, respectively, depending on the assumptions for the initial inner density profile of the system (ρ ∝ r−2 or ∝ r−1) and the initial mass of the central IMBH (105 or 103M⊙⁠). By integrating the GW event rate over z = 1–3, we expect that the Laser Interferometer Space Antenna will be able to detect ∼2 GW events per year coming from these massive clumps; the intrinsic rate of TD events from these systems amounts instead to a few 103 per year, a fraction of which will be observable by e.g. the Square Kilometre Array and the Advanced Telescope for High Energy Astrophysics. In conclusion, our results support the idea that the forthcoming GW and electromagnetic facilities may have the unprecedented opportunity of unveiling the lurking population of IMBHs

Global torques and stochasticity as the drivers of massive black hole pairing in the young Universe

The forthcoming Laser Interferometer Space Antenna (LISA) will probe the population of coalescing massive black hole (MBH) binaries up to the onset of structure formation. Here we simulate the galactic-scale pairing of $\sim10^6 M_\odot$ MBHs in a typical, non-clumpy main-sequence galaxy embedded in a cosmological environment at $z = 7-6$. In order to increase our statistical sample, we adopt a strategy that allows us to follow the evolution of six secondary MBHs concomitantly. We find that the magnitude of the dynamical-friction induced torques is significantly smaller than that of the large-scale, stochastic gravitational torques arising from the perturbed and morphologically evolving galactic disc, suggesting that the standard dynamical friction treatment is inadequate for realistic galaxies at high redshift. The dynamical evolution of MBHs is very stochastic, and a variation in the initial orbital phase can lead to a drastically different time-scale for the inspiral. Most remarkably, the development of a galactic bar in the host system either significantly accelerates the inspiral by dragging a secondary MBH into the centre, or ultimately hinders the orbital decay by scattering the MBH in the galaxy outskirts. The latter occurs more rarely, suggesting that galactic bars overall promote MBH inspiral and binary coalescence. The orbital decay time can be an order of magnitude shorter than what would be predicted relying on dynamical friction alone. The stochasticity, and the important role of global torques, have crucial implications for the rates of MBH coalescences in the early Universe: both have to be accounted for when making predictions for the upcoming LISA observatory.Comment: Accepted for publication in MNRAS; 15 pages, 10 Figures, 2 Table

Partial stellar tidal disruption events and their rates

Tidal disruption events (TDEs) of stars operated by massive black holes (MBHs) will be detected in thousands by upcoming facilities such as the Vera Rubin Observatory. In this work, we assess the rates of standard total TDEs, destroying the entire star, and partial TDEs, in which a stellar remnant survives the interaction, by solving 1-D Fokker-Planck equations. Our rate estimates are based on a novel definition of the loss cone whose size is commensurate to the largest radius at which partial disruptions can occur, as motivated by relativistic hydrodynamical simulations. Our novel approach unveils two important results. First, partial TDEs can be more abundant than total disruptions by a factor of a few to a few tens. Second, the rates of complete stellar disruptions can be overestimated by a factor of a few to a few tens if one neglects partial TDEs, as we find that many of the events classified at total disruptions in the standard framework are in fact partial TDEs. Accounting for partial TDEs is particularly relevant for galaxies harbouring a nuclear stellar cluster featuring many events coming from the empty loss cone. Based on these findings, we stress that partial disruptions should be considered when constraining the luminosity function of TDE flares; accounting for this may reconcile the theoretically estimated TDE rates with the observed ones.Comment: 12 pages + Appendix, MNRAS, accepte

Dynamics of Single and Binary Black Holes in Galactic Nuclei

Galactic nuclei represent one of the most fascinating and dynamically richest regions of our Universe. They are often found to host at least one supermassive black hole (MBH) at their centre; in addition, observations suggest that MBHs frequently coexist with massive and extremely dense nuclear star clusters, making galactic nuclei ideal laboratories for the study of a broad range of exotic dynamical phenomena. This thesis aims at providing new insights on the interplay between MBHs and their host environments by means of advanced numerical techniques. In particular, my work is relevant in the landscape of gravitational waves (GWs), as it explores the dynamical evolution of stellar compact objects and MBHs: these objects are expected to be promising GW sources detectable by present and future interferometers, as the forthcoming space-borne LISA observatory. In this framework, Bortolas et al. (2017) investigates the impact of natal kicks on the distribution of compact objects in the Milky Way Galactic Centre (GC). My results show that supernova (SN) kicks typically either unbind neutron stars from the MBH, or set them on very eccentric orbits. In contrast, stellar black holes are not significantly affected by the kick: this, combined with mass segregation, would suggest a cusp of stellar relics to inhabit the GC innermost region, as supported by the recent detection of a cusp of accreting X-ray binaries near the MBH. In addition, this thesis is the first to provide evidence that SN kicks may trigger extreme mass ratio inspirals (EMRIs), i.e. GW driven decays of stellar mass compact objects onto MBHs. In Bortolas & Mapelli (2019) I show that SN kicks effectively funnel infant black holes and neutron stars on low angular momentum orbits, promoting their GW decay onto the MBH. By applying this argument to the young stars in the GC, I predict up to 0.01% of SN kicks to induce an EMRI, meaning that LISA will detect up to a few SN-driven EMRIs from Milky-Way like galaxies every year. A further relevant GW source for the LISA observatory is constituted by the coalescence of MBH binaries (BHBs). BHBs are expected to form in large numbers along the cosmic history, being a natural outcome of galaxy collisions. Their coupling in gas-poor galaxies can be described as a three-step process: a dynamical friction dominated phase, a migration phase induced by slingshot ejections of stars, and a GW driven inspiral leading to rapid coalescence. It has been pointed out that the slingshot-driven pairing may be ineffective if too few stars are scattered in the BHB vicinity, and the shrinking may come to a halt at roughly pc separation. However, there is circumstantial evidence that MBH pairs are rare and BHBs are likely to merge: this motivated a series of works aimed to solve the 'final pc problem'. This thesis contributes to the forge of possible solutions in multiple ways. In Bortolas et al. (2018a), I explore the infall of a young massive star cluster onto a BHB. I show that a cluster approaching the BHB along a non-zero angular momentum orbit fails to enhance the BHB shrinking; in contrast, the same cluster free-falling onto the BHB considerably contributes to the BHB pairing, as the BHB separation shrinks by more than 10%. This suggests that several cluster infalls may effectively bring the BHB close to the regime at which GWs lead to a prompt coalescence. A more general solution to the final pc problem is currently believed to reside in the non-sphericity (triaxiality) of the host galaxy. If the host galaxy is triaxial (e.g. as a result of a merger), large scale gravitational torques ensure that stars are continually scattered in the BHB vicinity. This assumption was initially validated via direct summation N-body simulations. However, the reliability of such simulations has been questioned due to the modest achievable number of particles (~1M). In fact, resolution limits enhance the amplitude of the BHB random walk, artificially boosting the BHB shrinking rate. In Bortolas et al. (2016), I numerically explore the significance of such spurious effect: I show that Brownian motion does not affect the evolution of BHBs in simulations including 1M particles or more, providing more reliability to the conclusion that BHBs effectively find their way to coalescence in non-spherical systems. Finally, in Bortolas et al. (2018b) I explore the interplay between the BHB dynamics and the shape of its host system. My study suggests that no strong connection exists between the galaxy morphology and the BHB shrinking rate, which seems to depend only on the inner density slope of the host galaxy. Such result is particularly relevant for GW science, as the time needed for a BHB to reach its GW-emission stage can be assumed to scale only with the central density of the nucleus. In conclusion, this thesis adds several pieces of information to our knowledge of GW sources in galactic nuclei, in preparation for the future of GW observations

Dynamical evolution of massive perturbers in realistic multi-component galaxy models I: implementation and validation

Galaxies are self-gravitating structures composed by several components encompassing spherical, axial and triaxial symmetry. Although real systems feature heterogeneous components whose properties are intimately connected, semi-analytical approaches often exploit the linearity of the Poisson's equation to represent the potential and mass distribution of a multi-component galaxy as the sum of the individual components. In this work, we expand the semi-analytical framework developed in Bonetti et al. (2020) by including both a detailed implementation of the gravitational potential of exponential disc (modelled with a ${\rm sech}^2$ and an exponential vertical profile) and an accurate prescription for the dynamical friction experienced by massive perturbers in composite galaxy models featuring rotating disc structures. Such improvements allow us to evolve arbitrary orbits either within or outside the galactic disc plane. We validate the results obtained by our numerical model against public semi-analytical codes as well as full N-body simulations, finding that our model is in excellent agreement to the codes it is compared with. The ability to reproduce the relevant physical processes responsible for the evolution of massive perturber orbits and its computational efficiency make our framework perfectly suited for large parameter-space exploration studies.Comment: 17 pages, 9 figures; accepted for publication in MNRA

Improved constraints from ultra-faint dwarf galaxies on primordial black holes as dark matter

Soon after the recent first ever detection of gravitational waves from merging black holes it has been suggested that their origin is primordial. Appealingly, a sufficient number of primordial black holes (PBHs) could also partially or entirely constitute the dark matter (DM) in the Universe. However, recent studies on PBHs in ultra-faint dwarf galaxies (UFDGs) suggest that they would dynamically heat up the stellar component due to two-body relaxation processes. From the comparison with the observed stellar velocity dispersions and the stellar half-light radii it was claimed that only PBHs with masses $\lesssim10\,M_\odot$ can significantly contribute to the DM. In this work, we improve the latter constraints by considering the largest observational sample of UFDGs and by allowing the PBH masses to follow an extended (log-normal) distribution. By means of collisional Fokker-Planck simulations, we explore a wide parameter space of UFDGs containing PBHs. The analysis of the half-light radii and velocity dispersions resulting from the simulations leads to three general findings that exclude PBHs with masses $\sim\mathcal{O}(1$-$100)\,M_\odot$ from constituting all of the DM: (i) We identify a critical sub-sample of UFDGs that only allows for $\sim\mathcal{O}(1)\,M_\odot$ PBH masses; (ii) for any PBH mass, there is an UFDG in our sample that disfavours it; (iii) the spatial extensions of a majority of simulated UFDGs containing PBHs are too large to match the observed

Improved gravitational radiation time-scales: significance for LISA and LIGO-Virgo sources

We present a revised version of Peters' (1964) time-scale for the gravitational-wave (GW) induced decay of two point masses. The new formula includes the effects of the first-order post-Newtonian perturbation and additionally provides a simple fit to account for the Newtonian self-consistent evolution of the eccentricity. The revised time-scale is found by multiplying Peters' estimate by two factors, $R(e_0)= 8^{1-\sqrt{1-e_0}}$ and $Q_{\rm f}(p_0) = \exp \left(2.5 (r_{\rm S}/p_0) \right)$, where $e_0$ and $p_0$ are the initial eccentricity and periapsis, respectively, and $r_{\rm S}$ the Schwarzschild radius of the system. Their use can correct errors of a factor of 1-10 that arise from using the original Peters' formula. We apply the revised time-scales to a set of typical sources for existing ground-based laser interferometers and for the future Laser Interferometer Space Antenna (LISA), at the onset of their GW driven decay. We argue that our more accurate model for the orbital evolution will affect current event- and detection-rate estimates for mergers of compact object binaries, with stronger deviations for eccentric LISA sources, such as extreme and intermediate mass-ratio inspirals. We propose the correction factors $R$ and $Q_{\rm f}$ as a simple prescription to quantify decay time-scales more accurately in future population synthesis models. We also suggest that the corrected time-scale may be used as a computationally efficient alternative to numerical integration in other applications that include the modelling of radiation reaction for eccentric sources.Comment: Accepted for publication in MNRA