arXiv subjects

Elisa Bortolas

Publications and source records attributed to Elisa Bortolas.

35 records · Page 2Linked to original sources

arXiv2021

Revised event rates for extreme and extremely large mass-ratio inspirals

One of the main targets of the Laser Interferometer Space Antenna (LISA) is the detection of extreme mass-ratio inspirals (EMRIs) and extremely large mass-ratio inspirals (X-MRIs). Their orbits are expected to be highly eccentric and relativistic when entering the LISA band. Under these circumstances, the inspiral time-scale given by Peters' formula loses precision and the shift of the last-stable orbit (LSO) caused by the massive black hole spin could influence the event rates estimate. We re-derive EMRIs and X-MRIs event rates by implementing two different versions of a Kerr loss-cone angle that includes the shift in the LSO, and a corrected version of Peters' time-scale that accounts for eccentricity evolution, 1.5 post-Newtonian hereditary fluxes, and spin-orbit coupling. The main findings of our study are summarized as follows: (1) implementing a Kerr loss-cone changes the event rates by a factor ranging between 0.9 and 1.1; (2) the high-eccentricity limit of Peters' formula offers a reliable inspiral time-scale for EMRIs and X-MRIs, resulting in an event rate estimate that deviates by a factor of about 0.9 to 3 when compared to event rates computed with the corrected version of Peters' time-scale and the usual loss-cone definition. (3) Event rates estimates for systems with a wide range of eccentricities should be revised. Peters' formula overestimates the inspiral rates of highly eccentric systems by a factor of about 8 to 30 compared to the corrected values. Besides, for e$_0 \lesssim$0.8, implementing the corrected version of Peters' formula would be necessary to obtain accurate estimates.

astro-ph.GA↗

arXiv2021

Stellar hardening of massive black hole binaries: the impact of the host rotation

Massive black hole binaries (MBHBs) with masses of ~ 10^4 to ~ 10^10 of solar masses are one of the main targets for currently operating and forthcoming space-borne gravitational wave observatories. In this paper, we explore the effect of the stellar host rotation on the bound binary hardening efficiency, driven by three-body stellar interactions. As seen in previous studies, we find that the centre of mass (CoM) of a prograde MBHB embedded in a rotating environment starts moving on a nearly circular orbit about the centre of the system shortly after the MBHB binding. In our runs, the oscillation radius is approximately 0.25 ( approximately 0.1) times the binary influence radius for equal mass MBHBs (MBHBs with mass ratio 1:4). Conversely, retrograde binaries remain anchored about the centre of the host. The binary shrinking rate is twice as fast when the binary CoM exhibits a net orbital motion, owing to a more efficient loss cone repopulation even in our spherical stellar systems. We develop a model that captures the CoM oscillations of prograde binaries; we argue that the CoM angular momentum gain per time unit scales with the internal binary angular momentum, so that most of the displacement is induced by stellar interactions occurring around the time of MBHB binding, while the subsequent angular momentum enhancement gets eventually quashed by the effect of dynamical friction. The effect of the background rotation on the MBHB evolution may be relevant for LISA sources, that are expected to form in significantly rotating stellar systems.

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arXiv2021

The competing effect of gas and stars in massive black hole binaries evolution

Massive black hole binaries are predicted to form during the hierarchical assembly of cosmic structures and will represent the loudest sources of low-frequency gravitational waves (GWs) detectable by present and forthcoming GW experiments. Before entering the GW-driven regime, their evolution is driven by the interaction with the surrounding stars and gas. While stellar interactions are found to always shrink the binary, recent studies predict the possibility of binary outspiral mediated by the presence of a gaseous disk, which could endlessly delay the coalescence and impact the merger rates of massive binaries. Here we implement a semi-analytical treatment that follows the binary evolution under the combined effect of stars and gas. We find that binaries may outspiral only if they accrete near or above their Eddington limit and only until their separation reaches the gaseous disk self-gravitating radius. Even in case of an outspiral, the binary eventually reaches a large enough mass for GW to take over and drive it to coalescence. The combined action of stellar hardening, mass growth and GW-driven inspiral brings binaries to coalescence in few hundreds Myr at most, implying that gas-driven expansion will not severely affect the detection prospects of upcoming GW facilities.

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arXiv2021

Improved gravitational radiation time-scales II: spin-orbit contributions and environmental perturbations

Peters' formula is an analytical estimate of the time-scale of gravitational wave (GW)-induced coalescence of binary systems. It is used in countless applications, where the convenience of a simple formula outweighs the need for precision. However, many promising sources of the Laser Interferometer Space Antenna (LISA), such as supermassive black hole binaries and extreme mass-ratio inspirals (EMRIs), are expected to enter the LISA band with highly eccentric ($e \gtrsim$ 0.9) and highly relativistic orbits. These are exactly the two limits in which Peters' estimate performs the worst. In this work, we expand upon previous results and give simple analytical fits to quantify how the inspiral time-scale is affected by the relative 1.5 post-Newtonian (PN) hereditary fluxes and spin-orbit couplings. We discuss several cases that demand a more accurate GW time-scale. We show how this can have a major influence on quantities that are relevant for LISA event-rate estimates, such as the EMRI critical semi-major axis. We further discuss two types of environmental perturbations that can play a role in the inspiral phase: the gravitational interaction with a third massive body and the energy loss due to dynamical friction and torques from a surrounding gas medium ubiquitous in galactic nuclei. With the aid of PN corrections to the time-scale in vacuum, we find simple analytical expressions for the regions of phase space in which environmental perturbations are of comparable strength to the effects of any particular PN order, being able to qualitatively reproduce the results of much more sophisticated analyses.

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arXiv2021

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.

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arXiv2020

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 $z \sim$ 1-3, are amongst 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 ($10^8 \,{\rm M}_{\odot}$) 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 $10^{-6}$-$10^{-5}$ and $10^{-8}$-$10^{-7}$ yr$^{-1}$, respectively, depending on the assumptions for the initial inner density profile of the system ($ρ\propto r^{-2}$ or $\propto r^{-1}$) and the initial mass of the central IMBH ($10^5$ or $10^3\,{\rm M}_{\odot}$). By integrating the GW event rate over $z$ = 1-3, we expect that the Laser Interferometer Space Antenna will be able to detect $\sim$2 GW events per yr coming from these massive clumps; the intrinsic rate of TD events from these systems amounts instead to a few $10^3$ per yr, 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.

astro-ph.GA↗

arXiv2020

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.

astro-ph.GA↗

arXiv2020

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.

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arXiv2020

Dynamical friction-driven orbital circularisation in rotating discs: a semi-analytical description

We present and validate a novel semi-analytical approach to study the effect of dynamical friction on the orbits of massive perturbers in rotating stellar discs. We find that dynamical friction efficiently circularises the orbit of co-rotating perturbers, while it constantly increases the eccentricity of counter-rotating ones until their angular momenta reverse, then once again promoting circularisation. Such "drag toward circular corotation" could shape the distribution of orientations of kinematically decoupled cores in disc galaxies, naturally leading to the observed larger fraction of co-rotating cores.

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arXiv2020

The erratic path to coalescence of LISA massive black hole binaries in sub-pc resolution simulations of smooth circumnuclear gas disks

We report on high-resolution simulations that explore the orbital decay of massive black hole (MBH) pairs with masses between $10^5$ and $10^7 M_{\odot}$ embedded in a circumnuclear gas disk (CND). An adiabatic equation of state is adopted, with a range of adiabatic indices, which maintains a smooth flow. Mergers between MBHs in this mass range would be detectable by the upcoming Laser Inteferometer Space Antenna (LISA). The orbital evolution is followed from the CND scale ($100$~pc) down to separations of $0.1$--$0.01$~pc at which a circumbinary disk (CBD) could form. The decay is erratic and strongly dependent on the gas flow within the disk, that ultimately determines the net torques experienced by the sinking MBH. Overall, we can identify three different evolutionary stages: (i) an initially slow decay that leads to no significant change in the orbital angular momentum, resulting in some circularization; (ii) a fast migration phase in which the orbital angular momentum decreases rapidly; and (iii) a final, very slow decay phase, in which orbital angular momentum can even increase, and a CBD can form. The fast migration phase owes to disk-driven torques originating primarily from the co-orbital region of the secondary MBH, at a distance of 1--3 Hill radii. We find strong analogies with fast Type III migration for massive planets in protoplanetary disks. The CBD forms only when the decay rate becomes small enough to allow it enough time to carve a cavity around the primary MBH, at scales $\lesssim 1$~pc; when this happens, the MBH separation nearly stalls in our higher-resolution run. We suggest an empirically modified gap-opening criterion that takes into account such timescale effects as well as other deviations from standard assumptions made in the literature. [Abriged]

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arXiv2020

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.

astro-ph.GA↗

arXiv2019

Can supernova kicks trigger EMRIs in the Galactic Centre?

One of the most promising gravitational wave (GW) sources detectable by the forthcoming LISA observatory are the so-called extreme-mass ratio inspirals (EMRIs), i.e. GW-driven inspirals of stellar-mass compact objects onto supermassive black holes (SMBHs). In this paper, we suggest that supernova (SN) kicks may trigger EMRIs in galactic nuclei by scattering newborn stellar black holes and neutron stars on extremely eccentric orbits; as a consequence, the time-scale over which these compact objects are expected to inspiral onto the central SMBH via GW emission may become shorter than the time-scale for other orbital perturbations to occur. By applying this argument to the Galactic Centre, we show that the S-cluster and the clockwise disc are optimal regions for the generation of such events: one SN out of about 10 000 (100 000) occurring in the S-cluster (clockwise disc) is expected to induce an EMRI. If we assume that the natal kicks affecting stellar black holes are significantly slower than those experienced by neutron stars, we find that most SN-driven EMRIs involve neutron stars. We further estimate the time spanning from the SN to the final plunge onto the SMBH to be of the order of few Myr. Finally, we extrapolate the rate of SN-driven EMRIs per Milky Way to be up to 10^-8/yr, thus we expect that LISA will detect up to a few tens of SN-driven EMRIs every year.

astro-ph.GA↗

arXiv2018

Star Cluster Disruption by a Supermassive Black Hole Binary

Supermassive black hole binaries (BHBs) 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, BHBs evolving in gas-poor nuclei shrink primarily through the slingshot ejection of stars approaching the BHB from sufficiently close distances. Here we address the possibility that the BHB shrinking rate is enhanced through the infall of a star cluster (SC) onto the BHB. We present the results of direct summation N-body simulations exploring different orbits for the SC infall, and we show that SCs reaching the BHB on non-zero angular momentum orbits (with eccentricity 0.75) fail to enhance the BHB hardening, while SCs approaching the BHB on radial orbits reduce the BHB separation by ~10% in less than 10 Myr, effectively shortening the BHB path towards GWs.

astro-ph.GA↗

arXiv2018

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.

astro-ph.GA↗

arXiv2017

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 80,000 solar masses 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 semi-major axis of the BHB shrinks by more than 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 a 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.

astro-ph.GA↗

arXiv2016

Collisionless loss-cone refilling: there is no final parsec problem

Coalescing massive black hole binaries, formed during galaxy mergers, are expected to be a primary source of low frequency gravitational waves. Yet in isolated gas-free spherical stellar systems, the hardening of the binary stalls at parsec-scale separations owing to the inefficiency of relaxation-driven loss-cone refilling. Repopulation via collisionless orbit diffusion in triaxial systems is more efficient, but published simulation results are contradictory. While sustained hardening has been reported in simulations of galaxy mergers with $N \sim 10^6$ stars and in early simulations of rotating models, in isolated non-rotating triaxial models the hardening rate continues to fall with increasing N, a signature of spurious two-body relaxation. We present a novel approach for studying loss cone repopulation in galactic nuclei. Since loss cone repopulation in triaxial systems owes to orbit diffusion, it is a purely collisionless phenomenon and can be studied with an approximated force calculation technique, provided the force errors are well behaved and sufficiently small. We achieve this using an accurate fast multipole method and define a proxy for the hardening rate that depends only on stellar angular momenta. We find that the loss cone is efficiently replenished even in very mildly triaxial models (with axis ratios 1 : 0.9 : 0.8). Such triaxiality is unavoidable following galactic mergers and can drive binaries into the gravitational wave regime. We conclude that there is no final parsec problem.

astro-ph.GA↗

arXiv2016

Dynamics of supernova remnants in the Galactic Centre

The Galactic centre (GC) is a unique place to study the extreme dynamical processes occurring near a super-massive black hole (SMBH). Here we simulate a large set of binaries orbiting the SMBH while the primary member undergoes a supernova (SN) explosion, in order to study the impact of SN kicks on the orbits of stars and dark remnants in the GC. We find that SN explosions are efficient in scattering neutron stars and other light stars on new (mostly eccentric) orbits, while black holes (BHs) tend to retain memory of the orbit of their progenitor star. SN kicks are thus unable to eject BHs from the GC: a cusp of dark remnants may be lurking in the central parsec of our Galaxy.

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