Dr Alessia Gualandris

The coalescence of the most massive black hole (MBH) binaries releases gravitational waves (GWs) within the detectable frequency range of pulsar timing arrays (PTAs; 10(-9) to 10(-6) Hz). The incoherent superposition of GWs from MBH mergers, the stochastic gravitational wave background (GWB), can provide unique information on MBH parameters and the large-scale structure of the Universe. The recent evidence for a GWB reported by the PTAs opens an exciting new window on to MBHs and their host galaxies. However, the astrophysical interpretation of the GWB requires accurate estimations of MBH merger time-scales for a statistically representative sample of galaxy mergers. This is numerically challenging; a high numerical resolution is required to avoid spurious relaxation and stochastic effects, while a large number of simulations are needed to sample a cosmologically representative volume. Here, we present a new multimass modelling method to increase the central resolution of a galaxy model at a fixed particle number. We follow mergers of galaxies hosting central MBHs with the fast multiple method code griffin at two reference resolutions and with two refinement schemes. We show that both refinement schemes are effective at increasing central resolution, reducing spurious relaxation and stochastic effects. A particle number of N >= 10(6) within a radius of five times the sphere of influence of the MBHs is required to reduce numerical scatter in the binary eccentricity and the coalescence time-scale to

We have performed N-body simulations of the formation of hyper-velocity stars (HVS) in the centre of the Milky Way due to inspiralling intermediate-mass black holes (IMBHs). We considered IMBHs of different masses, all starting from circular orbits at an initial distance of 0.1 pc. We find that the IMBHs sink to the centre of the Galaxy due to dynamical friction, where they deplete the central cusp of stars. Some of these stars become HVS and are ejected with velocities sufficiently high to escape the Galaxy. Since the HVS carry with them information about their origin, in particular in the moment of ejection, the velocity distribution and the direction in which they escape the Galaxy, detecting a population of HVS will provide insight in the ejection processes and could therefore provide indirect evidence for the existence of IMBHs. Our simulations show that HVS are generated in short bursts which last only a few Myrs until the IMBH is swallowed by the supermassive black hole (SMBH). HVS are ejected almost isotropically, which makes IMBH induced ejections hard to distinguish from ejections due to encounters of stellar binaries with a SMBH. After the HVS have reached the galactic halo, their escape velocities correlate with the distance from the Galactic centre in the sense that the fastest HVS can be found furthest away from the centre. The velocity distribution of HVS generated by inspiralling IMBHs is also nearly independent of the mass of the IMBH and can be quite distinct from one generated by binary encounters. Finally, our simulations show that the presence of an IMBH in the Galactic centre changes the stellar density distribution inside r

We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's "algorithmic" chain regularization scheme including post-Newtonian terms up to PN2.5 order. Stars moving beyond the chain are advanced using a fourth-order integrator with forces computed on a GRAPE board. Performance tests confirm that the hybrid code achieves better energy conservation, in less elapsed time, than the standard scheme and that it reproduces the orbits of stars tightly bound to the black hole with high precision. The hybrid code is applied to two sample problems: the effect of finite-N gravitational fluctuations on the orbits of the S-stars; and inspiral of an intermediate-mass black hole into the galactic centre. © 2008 WILEY-VCH Verlag GmbH & Co. KGaA.

Regular star formation is thought to be inhibited close to the massive black hole (MBH) in the Galactic center. Nevertheless, tens of young main-sequence B-stars have been observed in an isotropic distribution close to it. These stars are observed to have an apparently continuous distribution from very close to the MBH (

We describe source code level parallelization for the {____tt kira} direct gravitational $N$-body integrator, the workhorse of the {____tt starlab} production environment for simulating dense stellar systems. The parallelization strategy, called ``j-parallelization'', involves the partition of the computational domain by distributing all particles in the system among the available processors. Partial forces on the particles to be advanced are calculated in parallel by their parent processors, and are then summed in a final global operation. Once total forces are obtained, the computing elements proceed to the computation of their particle trajectories. We report the results of timing measurements on four different parallel computers, and compare them with theoretical predictions. The computers employ either a high-speed interconnect, a NUMA architecture to minimize the communication overhead or are distributed in a grid. The code scales well in the domain tested, which ranges from 1024 - 65536 stars on 1 - 128 processors, providing satisfactory speedup. Running the production environment on a grid becomes inefficient for more than 60 processors distributed across three sites.

Galaxies and the dark matter haloes that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealized calculations and analysis of observational data. The assumption leads to an exact conservation of angular momentum for every particle, making the dynamics unrealistic. But how much does that inaccuracy matter in practice for analyses of stellar distribution functions, collisionless relaxation, or dark matter core-creation? We provide a general answer to this question for a wide class of aspherical systems; specifically, we consider distribution functions that are `maximally stable', i.e. that do not evolve at first order when external potentials (which arise from baryons, large-scale tidal fields or infalling substructure) are applied. We show that a spherically symmetric analysis of such systems gives rise to the false conclusion that the density of particles in phase space is ergodic (a function of energy alone). Using this idea we are able to demonstrate that: (a) observational analyses that falsely assume spherical symmetry are made more accurate by imposing a strong prior preference for near-isotropic velocity dispersions in the centre of spheroids; (b) numerical simulations that use an idealized spherically symmetric setup can yield misleading results and should be avoided where possible; and (c) triaxial dark matter haloes (formed in collisionless cosmological simulations) nearly attain our maximally stable limit, but their evolution freezes out before reaching it.

The European Pulsar Timing Array (EPTA) and Indian Pulsar Timing Array (InPTA) collaborations have measured a low-frequency common signal in the combination of their second and first data releases respectively, with the correlation properties of a gravitational wave background (GWB). Such signal may have its origin in a number of physical processes including a cosmic population of inspiralling supermassive black hole binaries (SMBHBs); inflation, phase transitions, cosmic strings and tensor mode generation by non-linear evolution of scalar perturbations in the early Universe; oscillations of the Galactic potential in the presence of ultra-light dark matter (ULDM). At the current stage of emerging evidence, it is impossible to discriminate among the different origins. Therefore, in this paper, we consider each process separately, and investigate the implications of the signal under the hypothesis that it is generated by that specific process. We find that the signal is consistent with a cosmic population of inspiralling SMBHBs, and its relatively high amplitude can be used to place constraints on binary merger timescales and the SMBH-host galaxy scaling relations. If this origin is confirmed, this is the first direct evidence that SMBHBs merge in nature, adding an important observational piece to the puzzle of structure formation and galaxy evolution. As for early Universe processes, the measurement would place tight constraints on the cosmic string tension and on the level of turbulence developed by first-order phase transitions. Other processes would require non-standard scenarios, such as a blue-tilted inflationary spectrum or an excess in the primordial spectrum of scalar perturbations at large wavenumbers. Finally, a ULDM origin of the detected signal is disfavoured, which leads to direct constraints on the abundance of ULDM in our Galaxy.

Very massive stars preferentially reside in the cores of their parent clusters and form binary or multiple systems. We study the role of tight very massive binaries in the origin of the field population of very massive stars. We performed numerical simulations of dynamical encounters between single (massive) stars and a very massive binary with parameters similar to those of the most massive known Galactic binaries, WR 20a and NGC 3603-A1. We found that these three-body encounters could be responsible for the origin of high peculiar velocities (>= 70 km s-1) observed for some very massive (>= 60-70 M-circle dot) runaway stars in the Milky Way and the Large Magellanic Cloud (e.g. lambda Cep, BD+43 degrees 3654, Sk -67 degrees 22, BI 237, 30 Dor 016), which can hardly be explained within the framework of the binary-supernova scenario. The production of high-velocity massive stars via three-body encounters is accompanied by the recoil of the binary in the opposite direction to the ejected star. We show that the relative position of the very massive binary R145 and the runaway early B-type star Sk-69 degrees 206 on the sky is consistent with the possibility that both objects were ejected from the central cluster, R136, of the star-forming region 30 Doradus via the same dynamical event - a three-body encounter.

Recent observations of the Galactic center revealed a nuclear disk of young OB stars near the massive black hole (MBH), in addition to many similar outlying stars with higher eccentricities and/or high inclinations relative to the disk (some of them possibly belonging to a second disk). In addition, observations show the existence of young B stars (the 'S-cluster') in an isotropic distribution in the close vicinity of the MBH ($

Dalessandro et al. observed a similar distribution for blue straggler stars and main-sequence turn-off stars in the Galactic globular cluster NGC 6101, and interpreted this feature as an indication that this cluster is not mass-segregated. Using direct N-body simulations, we find that a significant amount of mass segregation is expected for a cluster with the mass, radius and age of NGC 6101. Therefore, the absence of mass segregation cannot be explained by the argument that the cluster is not yet dynamically evolved. By varying the retention fraction of stellar-mass black holes, we show that segregation is not observable in clusters with a high black hole retention fraction (>50 per cent after supernova kicks and >50 per cent after dynamical evolution). Yet all model clusters have the same amount of mass segregation in terms of the decline of the mean mass of stars and remnants with distance to the centre. We also discuss how kinematics can be used to further constrain the presence of a stellar-mass black hole population and distinguish it from the effect of an intermediate-mass black hole. Our results imply that the kick velocities of black holes are lower than those of neutron stars. The large retention fraction during its dynamical evolution can be explained if NGC 6101 formed with a large initial radius in a Milky Way satellite.

The last decade has seen the detection of fast moving stars in the Galactic halo, the so-called hypervelocity stars (HVSs). While the bulk of this population is likely the result of a close encounter between a stellar binary and the supermassive black hole (MBH) in the Galactic Centre (GC), other mechanims may contribute fast stars to the sample. Few observed HVSs show apparent ages which are shorter than the flight time from the GC, thereby making the binary disruption scenario unlikely. These stars may be the result of the breakup of a stellar triple in the GC which led to the ejection of a hypervelocity binary (HVB). If such binary evolves into a blue straggler star due to internal processes after ejection, a rejuvenation is possible that make the star appear younger once detected in the halo. A triple disruption may also be responsible for the presence of HVBs, of which one candidate has now been observed. We present a numerical study of triple disruptions by the MBH in the GC and find that the most likely outcomes are the production of single HVSs and single/binary stars bound to the MBH, while the production of HVBs has a probability ≲1% regardless of the initial parameters. Assuming a triple fraction of ≈10% results in an ejection rate of ≲1 Gyr−1, insufficient to explain the sample of HVSs with lifetimes shorter than their flight time. We conclude that alternative mechanisms are responsible for the origin of such objects and HVBs in general.

We study the acceleration of the star HE0437-5439, to hypervelocity and discuss its possible origin in the Large Magellanic Cloud (LMC). The star has a radial velocity of 723 km/s and is located at a distance of 61 kpc from the Sun. With a mass of about 8 Msun, the travel time from the Galactic centre is of about 100 Myr, much longer than its main sequence lifetime. Given the relatively small distance to the LMC (18 kpc), we consider it likely that HE0437-5439 originated in the cloud rather than in the Galactic centre, like the other hypervelocity stars. The minimum ejection velocity required to travel from the LMC to its current location within its lifetime is of about 500 km/s. Such a high velocity can only be obtained in a dynamical encounter with a massive black hole. We perform 3-body scattering simulations in which a stellar binary encounters a massive black hole and find that a black hole more massive than 1000 Msun is necessary to explain the high velocity of HE0437-5439. We look for possible parent clusters for HE0437-5439 and find that NGC 2100 and NGC 2004 are young enough to host stars coeval to HE0437-5439 and dense enough to produce an intermediate mass black hole able to eject an 8 Msun star with hypervelocity.

The Milky Way nuclear star cluster (MW NSC) has been used as a template to understand the origin and evolution of galactic nuclei and the interaction of nuclear star clusters with supermassive black holes. It is the only nuclear star cluster with a supermassive black hole where we can resolve individual stars to measure their kinematics and metal abundance to reconstruct its formation history. Here, we present results of the first chemo-dynamical model of the inner 1 pc of the MW NSC using metallicity and radial velocity data from the KMOS spectrograph on the Very Large Telescope. We found evidence for two kinematically and chemically distinct components in this region. The majority of the stars belong to a previously-known super-solar metallicity component with a rotation axis perpendicular to the Galactic plane. However, we identify a new kinematically distinct sub-solar metallicity component which contains about 7% of the stars and appears to be rotating faster than the main component with a rotation axis that may be misaligned. This second component may be evidence for an infalling star cluster or remnants of a dwarf galaxy, merging with the MW NSC. These measurements show that the combination of chemical abundances with kinematics is a promising method to directly study the MW NSC's origin and evolution.

The tidal breakup of binary star systems by the supermassive black hole (SMBH) in the center of the galaxy has been suggested as the source of both the observed sample of hypervelocity stars (HVSs) in the halo of the Galaxy and the S stars that remain in tight orbits around Sgr A*. Here, we use a post-Newtonian N-body code to study the dynamics of main-sequence binaries on highly elliptical bound orbits whose periapsides lie close to the SMBH, determining the properties of ejected and bound stars as well as collision products. Unlike previous studies, we follow binaries that remain bound for several revolutions around the SMBH, finding that in the case of relatively large periapsides and highly inclined binaries the Kozai resonance can lead to large periodic oscillations in the internal binary eccentricity and inclination. Collisions and mergers of the binary elements are found to increase significantly for multiple orbits around the SMBH, while HVSs are primarily produced during a binary's first passage. This process can lead to stellar coalescence and eventually serve as an important source of young stars at the Galactic center.

There is increasing evidence that many galaxies host both a nuclear star cluster (NC) and a super-massive black hole (SMBH). Their coexistence is particularly prevalent in spheroids with stellar mass 10(8)-10(10) M-circle dot. We study the possibility that a stellar-mass black hole (BH) hosted by a NC inspirals and merges with the central SMBH. Due to the high stellar density in NCs, extreme mass-ratio inspirals (EMRIs) of BHs onto SMBHs in NCs may be important sources of gravitational waves (GWs). We consider sensitivity curves for three different space-based GW laser interferometric mission concepts: the Laser Interferometer Space Antenna (LISA), the New Gravitational wave Observatory (NGO) and the DECi-hertz Interferometer Gravitational wave Observatory (DECIGO). We predict that, under the most optimistic assumptions, LISA and DECIGO will detect up to thousands of EMRIs in NCs per year, while NGO will observe up to tens of EMRIs per year. We explore how a number of factors may affect the predicted rates. In particular, if we assume that the mass of the SMBH scales with the square of the host spheroid mass in galaxies with NCs, rather than a linear scaling, then the event rates are more than a factor of 10 lower for both LISA and NGO, while they are almost unaffected in the case of DECIGO.

Stars slingshotted by the supermassive black hole at the Galactic centre will escape the Milky Way so quickly that their trajectories will be almost straight lines. Previous works have shown how these `hypervelocity stars' are subsequently deflected by the gravitational field of the Milky Way and the Large Magellanic Cloud (LMC), but have neglected to account for the reflex motion of the Milky Way in response to the fly by of the LMC. A consequence of this motion is that the hypervelocity stars we see on the outskirts of the Milky Way today were ejected from where the Milky Way centre was hundreds of millions of years ago. This change in perspective causes large apparent deflections in the trajectories of the hypervelocity stars, which are of the same order as the deflections caused by the gravitational force of the Milky Way and LMC. We quantify these deflections by simulating the production of hypervelocity stars in an isolated Milky Way (with a spherical or flattened dark matter halo), in a fixed-in-place Milky Way with a passing LMC, and in a Milky Way which responds to the passage of the LMC. The proper motion precision necessary to measure these deflections will be possible with the combination of Gaia with the proposed GaiaNIR successor mission, and these measurements will unlock the hypervelocity stars as probes of the shape of the Milky Way, the mass of the LMC, and of the dance of these two galaxies.

We study the short- and long-term effects of an intermediate mass black hole (IMBH) on the orbits of stars bound to the supermassive black hole (SMBH) at the center of the Milky Way. A regularized N-body code including post-Newtonian terms is used to carry out direct integrations of 19 stars in the S-star cluster for 10 Myr. The mass of the IMBH is assigned one of four values from 400 Msun to 4000 Msun, and its initial semi-major axis with respect to the SMBH is varied from 0.3-30 mpc, bracketing the radii at which inspiral of the IMBH is expected to stall. We consider two values for the eccentricity of the IMBH/SMBH binary, e=(0,0.7), and 12 values for the orientation of the binary's plane. Changes at the level of 1% in the orbital elements of the S-stars could occur in just a few years if the IMBH is sufficiently massive. On time scales of 1 Myr or longer, the IMBH efficiently randomizes the eccentricities and orbital inclinations of the S-stars. Kozai oscillations are observed when the IMBH lies well outside the orbits of the stars. Perturbations from the IMBH can eject stars from the cluster, producing hypervelocity stars, and can also scatter stars into the SMBH; stars with high initial eccentricities are most likely to be affected in both cases. The distribution of S-star orbital elements is significantly altered from its currently-observed form by IMBHs with masses greater than 1000 Msun if the IMBH/SMBH semi-major axis lies in the range 3-10 mpc. We use these results to further constrain the allowed parameters of an IMBH/SMBH binary at the Galactic center.

We present a dynamical friction model based on Chandrasekhar’s formula that reproduces the fast inspiral and stalling experienced by satellites orbiting galaxies with a large constant density core. We show that the fast inspiral phase does not owe to resonance. Rather, it owes to the background velocity distribution function for the constant density core being dissimilar from the usually-assumed Maxwellian distribution. Using the correct background velocity distribution function and the semi-analytic model from Petts, Gualandris & Read (2015), we are able to correctly reproduce the infall rate in both cored and cusped potentials. However, in the case of large cores, our model is no longer able to correctly capture core-stalling. We show that this stalling owes to the tidal radius of the satellite approaching the size of the core. By switching off dynamical friction when rt(r) = r (where rt is the tidal radius at the satellite’s position) we arrive at a model which reproduces the N-body results remarkably well. Since the tidal radius can be very large for constant density background distributions, our model recovers the result that stalling can occur for Ms/Menc 1, where Ms and Menc are the mass of the satellite and the enclosed galaxy mass, respectively. Finally, we include the contribution to dynamical friction that comes from stars moving faster than the satellite. This next-to-leading order effect becomes the dominant driver of inspiral near the core region, prior to stalling.

Massive elliptical galaxies are typically observed to have central cores in their projected radial light profiles. Such cores have long been thought to form through ‘binary scouring’ as supermassive black holes (SMBHs), brought in through mergers, form a hard binary and eject stars from the galactic centre. However, the most massive cores, like the $\sim 3{\, \mathrm{kpc}}$ core in A2261-BCG, remain challenging to explain in this way. In this paper, we run a suite of dry galaxy merger simulations to explore three different scenarios for central core formation in massive elliptical galaxies: ‘binary scouring’, ‘tidal deposition’, and ‘gravitational wave (GW) induced recoil’. Using the griffin code, we self-consistently model the stars, dark matter, and SMBHs in our merging galaxies, following the SMBH dynamics through to the formation of a hard binary. We find that we can only explain the large surface brightness core of A2261-BCG with a combination of a major merger that produces a small $\sim 1{\, \mathrm{kpc}}$ core through binary scouring, followed by the subsequent GW recoil of its SMBH that acts to grow the core size. Key predictions of this scenario are an offset SMBH surrounded by a compact cluster of bound stars and a non-divergent central density profile. We show that the bright ‘knots’ observed in the core region of A2261-BCG are best explained as stalled perturbers resulting from minor mergers, though the brightest may also represent ejected SMBHs surrounded by a stellar cloak of bound stars.

[Abridged] Recent numerical relativity simulations have shown that the emission of gravitational waves during the merger of two supermassive black holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as 4000 km/s. We study the motion of SMBHs ejected from galaxy cores by such kicks and the effects on the stellar distribution using high-accuracy direct N-body simulations. Following the kick, the motion of the SMBH exhibits three distinct phases. (1) The SMBH oscillates with decreasing amplitude, losing energy via dynamical friction each time it passes through the core. Chandrasekhar's theory accurately reproduces the motion of the SMBH in this regime if 2 < ln Lambda < 3 and if the changing core density is taken into account. (2) When the amplitude of the motion has fallen to roughly the core radius, the SMBH and core begin to exhibit oscillations about their common center of mass. These oscillations decay with a time constant that is at least 10 times longer than would be predicted by naive application of the dynamical friction formula. (3) Eventually, the SMBH reaches thermal equilibrium with the stars. We estimate the time for the SMBH's oscillations to damp to the Brownian level in real galaxies and infer times as long as 1 Gyr in the brightest galaxies. Ejection of SMBHs also results in a lowered density of stars near the galaxy center; mass deficits as large as five times the SMBH mass are produced for kick velocities near the escape velocity. We compare the N-body density profiles with luminosity profiles of early-type galaxies in Virgo and show that even the largest observed cores can be reproduced by the kicks, without the need to postulate hypermassive binary SMBHs. Implications for displaced AGNs and helical radio structures are discussed.

We report the detection of five high-velocity stars in the core of the globular cluster NGC 2808. The stars lie on the the red giant branch and show total velocities between 40 and 45 km/s. For a core velocity dispersion sigma_c = 13.4 km/s, this corresponds to up to 3.4 sigma_c. These velocities are close to the estimated escape velocity (~ 50 km/s) and suggest an ejection from the core. Two of these stars have been confirmed in our recent integral field spectroscopy data and we will discuss them in more detail here. These two red giants are located at a projected distance of ~ 0.3 pc from the center. According to their positions on the color magnitude diagram, both stars are cluster members. We investigate several possible origins for the high velocities of the stars and conceivable ejection mechanisms. Since the velocities are close to the escape velocity, it is not obvious whether the stars are bound or unbound to the cluster. We therefore consider both cases in our analysis. We perform numerical simulations of three-body dynamical encounters between binaries and single stars and compare the resulting velocity distributions of escapers with the velocities of our stars. We compare the predictions for a single dynamical encounter with a compact object with those of a sequence of two-body encounters due to relaxation. If the stars are unbound, the encounter must have taken place recently, when the stars were already in the giant phase. After including binary fractions and black-hole retention fractions, projection effects, and detection probabilities from Monte-Carlo simulations, we estimate the expected numbers of detections for all the different scenarios. Based on these numbers, we conclude that the most likely scenario is that the stars are bound and were accelerated by a single encounter between a binary of main-sequence stars and a ~ 10 M_sun black hole.

The inspiral of a turbulent molecular cloud in the Galactic Centre may result in the formation of a small, dense and moderately eccentric gas disc around the supermassive black hole (SMBH). Such a disc is unstable to fragmentation and may lead to the formation of young massive stars in the central parsec of the Galaxy. Here we perform high-accuracy direct summation N-body simulations of a ring of massive stars (with initial semimajor axes 0.1

We explore the origin of the Galactic high latitude black hole X-ray binary XTE J1118+480, and in particular its birth location and the magnitude of the kick received by the black hole upon formation in the supernova explosion. We constrain the age of the companion to the black hole using stellar evolution calculations between 2 Gyr and 5 Gyr, making an origin in a globular cluster unlikely. We therefore argue that the system was born in the Galactic disk and the supernova propelled it in its current high latitude orbit. Given the current estimates on its distance, proper motion and radial velocity, we back-trace the orbit of XTE J1118+480 in the Galactic potential to infer the peculiar velocity of the system at different disk crossings over the last 5 Gyr. Taking into account the uncertainties on the velocity components, we infer an average peculiar velocity of 183 ____pm 31 km/s. The maximum velocity which the binary can acquire by symmetric supernova mass loss is about 100 km/s, which is 2.7 sigma away from the mean of the peculiar velocity distribution. We therefore argue that an additional asymmetric kick velocity is required. By considering the orientation of the system relative to the plane of the sky, we derive a 95% probability for a non null component of the kick perpendicular to the orbital plane of the binary. The distribution of perpendicular velocities is skewed to lower velocities with an average of 93^{+55}_{-60} km/s.

Hills (1988) predicted that runaway stars could be accelerated to velocities larger than 1000 km/s by dynamical encounters with the supermassive black hole (SMBH) in the Galactic center. The recently discovered hypervelocity star SDSS J090745.0+024507 (hereafter HVS) is escaping the Galaxy at high speed and could be the first object in this class. With the measured radial velocity and the estimated distance to the HVS, we trace back its trajectory in the Galactic potential. Assuming it was ejected from the center, we find that a $____sim$ 2 mas/yr proper motion is necessary for the star to have come within a few parsecs of the SMBH. We perform three-body scattering experiments to constrain the progenitor encounter which accelerated the HVS. As proposed by Yu & Tremaine (2003), we consider the tidal disruption of binary systems by the SMBH and the encounter between a star and a binary black hole, as well as an alternative scenario involving intermediate mass black holes. We find that the tidal disruption of a stellar binary ejects stars with a larger velocity compared to the encounter between a single star and a binary black hole, but has a somewhat smaller ejection rate due to the greater availability of single stars.

We model the inspiral of globular clusters (GCs) towards a galactic nucleus harboring a supermassive black hole (SMBH), a leading scenario for the formation of nuclear star clusters.We consider the case of GCs containing either an intermediate-mass black hole (IMBH) or a population of stellar mass black holes (BHs), and study the formation of gravitational wave (GW) sources. We perform direct summation N-body simulations of the infall of GCs with different orbital eccentricities in the live background of a galaxy with either a shallow or steep density profile. We find that the GC acts as an efficient carrier for the IMBH, facilitating the formation of a bound pair. The hardening and evolution of the binary depends sensitively on the galaxy’s density profile. If the host galaxy has a shallow profile the hardening is too slow to allow for coalescence within a Hubble time, unless the initial cluster orbit is highly eccentric. If the galaxy hosts a nuclear star cluster, the hardening leads to coalescence by emission of GWs within 3−4 Gyr. In this case, we find a IMBH-SMBH merger rate of IIMBH−SMBH = 2.8×10−3 yr−1 Gpc−3. If the GC hosts a population of stellar BHs, these are deposited close enough to the SMBH to form extreme-mass-ratio-inspirals with a merger rate of IEMRI = 0.25 yr−1 Gpc−3. Finally, the SMBH tidal field can boost the coalescence of stellar black hole binaries delivered from the infalling GCs. The merger rate for this merging channel is IBHB = 0.4 − 4 yr−1 Gpc−3.

Was the black hole in XTE J1118+480 ejected from a globular cluster or kicked away from the galactic disk?

The coalescence of massive black hole binaries (BHBs) in galactic mergers is the primary source of gravitational waves (GWs) at low frequencies. Current estimates of GW detection rates for the Laser Interferometer Space Antenna and the Pulsar Timing Array vary by three orders of magnitude. To understand this variation, we simulate the merger of equal-mass, eccentric, galaxy pairs with central massive black holes and shallow inner density cusps. We model the formation and hardening of a central BHB using the fast multiple method as a force solver, which features a O(N) scaling with the number N of particles and obtains results equivalent to direct-summation simulations. At N similar to 5 x 10(5), typical for contemporary studies, the eccentricity of the BHBs can vary significantly for different random realizations of the same initial condition, resulting in a substantial variation of the merger time-scale. This scatter owes to the stochasticity of stellar encounters with the BHB and decreases with increasing N. We estimate that N similar to 10(7) within the stellar half-light radius suffices to reduce the scatter in the merger time-scale to similar to 10 per cent. Our results suggest that at least some of the uncertainty in low-frequency GW rates owes to insufficient numerical resolution.

We study the dynamical interaction in which the two single runaway stars AE Aurigae and mu Columbae and the binary iota Orionis acquired their unusually high space velocity. The two single runaways move in almost opposite directions with a velocity greater than 100 km/s away from the Trapezium cluster. The star iota Ori is an eccentric (e=0.8) binary moving with a velocity of about 10 km/s at almost right angles with respect to the two single stars. The kinematic properties of the system suggest that a strong dynamical encounter occurred in the Trapezium cluster about 2.5 Myr ago. Curiously enough, the two binary components have similar spectral type but very different masses, indicating that their ages must be quite different. This observation leads to the hypothesis that an exchange interaction occurred in which an older star was swapped into the original iota Orionis binary. We test this hypothesis by a combination of numerical and theoretical techniques, using N-body simulations to constrain the dynamical encounter, binary evolution calculations to constrain the high orbital eccentricity of iota Orionis and stellar evolution calculations to constrain the age discrepancy of the two binary components. We find that an encounter between two low eccentricity (0.4

The centre of our Galaxy is one of the most studied and yet enigmatic places in the Universe. At a distance of about 8 kpc from our Sun, the Galactic centre (GC) is the ideal environment to study the extreme processes that take place in the vicinity of a supermassive black hole (SMBH). Despite the hostile environment, several tens of early-type stars populate the central parsec of our Galaxy. A fraction of them lie in a thin ring with mild eccentricity and inner radius ~0.04 pc, while the S-stars, i.e. the ~30 stars closest to the SMBH (

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 ∼ 106 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’.

We explore the hypothesis that some high-velocity runaway stars attain their peculiar velocities in the course of exchange encounters between hard massive binaries and a very massive star (either an ordinary 50–100 M⊙ star or a more massive one, formed through runaway mergers of ordinary stars in the core of a young massive star cluster). In this process, one of the binary components becomes gravitationally bound to the very massive star, while the second one is ejected, sometimes with a high speed. We performed three-body scattering experiments and found that early B-type stars (the progenitors of the majority of neutron stars) can be ejected with velocities of ≳200–400 km s−1 (typical of pulsars), while 3–4 M⊙ stars can attain velocities of ≳300–400 km s−1 (typical of the bound population of halo late B-type stars). We also found that the ejected stars can occasionally attain velocities exceeding the Milky Ways's escape velocity.

The inner hundred parsecs of the Milky Way hosts the nearest supermassive black hole, largest reservoir of dense gas, greatest stellar density, hundreds of massive main and post main sequence stars, and the highest volume density of supernovae in the Galaxy. As the nearest environment in which it is possible to simultaneously observe many of the extreme processes shaping the Universe, it is one of the most well-studied regions in astrophysics. Due to its proximity, we can study the center of our Galaxy on scales down to a few hundred AU, a hundred times better than in similar Local Group galaxies and thousands of times better than in the nearest active galaxies. The Galactic Center (GC) is therefore of outstanding astrophysical interest. However, in spite of intense observational work over the past decades, there are still fundamental things unknown about the GC. JWST has the unique capability to provide us with the necessary, game-changing data. In this White Paper, we advocate for a JWST NIRCam survey that aims at solving central questions, that we have identified as a community: i) the 3D structure and kinematics of gas and stars; ii) ancient star formation and its relation with the overall history of the Milky Way, as well as recent star formation and its implications for the overall energetics of our galaxy's nucleus; and iii) the (non-)universality of star formation and the stellar initial mass function. We advocate for a large-area, multi-epoch, multi-wavelength NIRCam survey of the inner 100\,pc of the Galaxy in the form of a Treasury GO JWST Large Program that is open to the community. We describe how this survey will derive the physical and kinematic properties of ~10,000,000 stars, how this will solve the key unknowns and provide a valuable resource for the community with long-lasting legacy value.

Using proper motion measurements from Gaia DR2, we probe the origin of 26 previously known hypervelocity stars (HVSs) around the Milky Way. We find that a significant fraction of these stars have a high probability of originating close to the Milky Way centre, but there is one obvious outlier. HVS3 is highly likely to be coming almost from the centre of the Large Magellanic Cloud (LMC). During its closest approach, 21.1 +6.1 −4.6 Myr ago, it had a relative velocity of 870 +69 −66 kms −1 with respect to the LMC. This large kick velocity is only consistent with the Hills mechanism, requiring a massive black hole at the centre of the LMC. This provides strong direct evidence that the LMC itself harbours a massive black hole of at least 4×10 3 −10 4 M ⊙ .

Direct-summation N-body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N^2). Performance can be greatly enhanced via the use of special-purpose accelerator boards like the GRAPE-6A. However the memory of the GRAPE boards is limited. Here, we present a performance analysis of direct N-body codes on two parallel supercomputers that incorporate special-purpose boards, allowing as many as four million particles to be integrated. Both computers employ high-speed, Infiniband interconnects to minimize communication overhead, which can otherwise become significant due to the small number of "active" particles at each time step. We find that the computation time scales well with processor number; for 2*10^6 particles, efficiencies greater than 50% and speeds in excess of 2 TFlops are reached.

Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion. Here we study the significance of Brownian motion of BHBs in merger remnants in the context of the final parsec problem. We simulate mergers with various particle numbers (from 8k to 1M) and with several density profiles. Moreover, we compare simulations where the BHB is fixed at the centre of the merger remnant with simulations where the BHB is free to random walk. We find that Brownian motion does not significantly affect the evolution of BHBs in simulations with particle numbers in excess of one million, and that the hardening measured in merger simulations is due to collisionless loss cone refilling.

Recent results from pulsar timing arrays (PTAs) show evidence for a gravitational wave background (GWB) consistent with a population of unresolved supermassive black hole (SMBH) binaries (BHBs). While the data do not yet constrain the slope of the spectrum, this appears to flatten at the lowest frequencies, deviating from the power-law shape expected for circular binaries evolving solely due to gravitational wave (GW) emission. Interestingly, such flattening can be explained with a population of eccentric rather than circular binaries. The eccentricity of BHBs is notoriously difficult to predict based simply on the parameters of the host galaxies and the initial galactic orbit, as it is subject to stochastic effects. We study the evolution of the eccentricity of BHBs formed in galactic mergers with cosmological initial conditions from pairing to coalescence, with a focus on potential PTA sources. We select galactic mergers from the IllustrisTNG100-1 simulation and re-simulate them at high resolution with the í µí±-body code Griffin down to binary separations of the order of a parsec. We then estimate coalescence timescales with a semi-analytical model of the evolution under the effects of GW emission and stellar hardening. We find that most mergers in IllustrisTNG100-1 occur on highly eccentric orbits, and that the eccentricity of BHBs at binary formation correlates with the initial eccentricity of the merger, if this is no larger than approximately 0.9. For extremely eccentric mergers, the binaries tend to form with modest eccentricities. We discuss the implications of these results on the interpretation of the observed GWB.

NGC6752 hosts in its halo PSR J1911-5958A, a newly discovered binary millisecond pulsar which is the most distant pulsar ever known from the core of a globular cluster. Interestingly, its recycling history seems in conflict with a scenario of ejection resulting from ordinary stellar dynamical encounters. A scattering event off a binary system of two black holes with masses in the range of 3-50 solar masses that propelled PSR J1911-5958A into its current peripheral orbit seems more likely. It is still an observational challenge to unveil the imprint(s) left from such a dark massive binary on cluster's stars: PSR J1911-5958A may be the first case.

In a star cluster with a sufficiently large escape velocity, black holes (BHs) that are produced by BH mergers can be retained, dynamically form new BH binaries, and merge again. This process can repeat several times and lead to significant mass growth. In this paper, we calculate the mass of the largest BH that can form through repeated BH mergers and determine how its value depends on the physical properties of the host cluster. We adopt an analytical model in which the energy generated by the black hole binaries in the cluster core is assumed to be regulated by the process of two-body relaxation in the bulk of the system. This principle is used to compute the hardening rate of the binaries and to relate this to the time-dependent global properties of the parent cluster. We demonstrate that in clusters with initial escape velocity ≳300kms−1 in the core and density ≳105M⊙⁠pc−3⁠, repeated mergers lead to the formation of BHs in the mass range 100−105M⊙⁠, populating any upper mass gap created by pair-instability supernovae. This result is independent of cluster metallicity and the initial BH spin distribution. We show that about 10 per cent of the present-day nuclear star clusters meet these extreme conditions, and estimate that BH binary mergers with total mass ≳100M⊙⁠ should be produced in these systems at a maximum rate ≈0.05Gpc−3yr−1⁠, corresponding to one detectable event every few years with Advanced LIGO/Virgo at design sensitivity.

We simulate mergers between galaxies containing collisionally relaxed nuclei around massive black holes (MBHs). Our galaxies contain four mass groups, representative of old stellar populations; a primary goal is to understand the distribution of stellar-mass black holes (BHs) after the merger. Mergers are followed using direct-summation N-body simulations, assuming a mass ratio of 1: 3 and two different orbits. Evolution of the binary MBH is followed until its separation has shrunk by a factor of 20 below the hard-binary separation. During the galaxy merger, large cores are carved out in the stellar distribution, with radii several times the influence radius of the massive binary. Much of the pre-existing mass segregation is erased during this phase. We follow the evolution of the merged galaxies for approximately three central relaxation times after coalescence of the massive binary; both standard and top-heavy mass functions are considered. The cores that were formed in the stellar distribution persist, and the distribution of the stellar-mass BHs evolves against this essentially fixed background. Even after one central relaxation time, these models look very different from the relaxed, multi-mass models that are often assumed to describe the distribution of stars and stellar remnants near a massive BH. While the stellar BHs do form a cusp on roughly a relaxation timescale, the BH density can be much smaller than in those models. We discuss the implications of our results for the extreme-mass-ratio inspiral problem and for the existence of Bahcall-Wolf cusps.

For understanding the process of star formation it is essential to know how many stars are formed as singles or in multiple systems, as a function of environment and binary parameters. This requires a characterization of the primordial binary population, which we define as the population of binaries that is present just after star formation has ceased, but before dynamical and stellar evolution have significantly altered its characteristics. In this article we present the first results of our adaptive optics survey of 200 (mainly) A-type stars in the nearby OB association Sco OB2. We report the discovery of 47 new candidate companions of Sco OB2 members. The next step will be to combine these observations with detailed simulations of young star clusters, in order to find the primordial binary population.

We have investigated different scenarios for the origin of the binary millisecond pulsar PSR J1911-5958A in NGC 6752, the most distant pulsar discovered from the core of a globular cluster to date. The hypothesis that it results from a truly primordial binary born in the halo calls for accretion-induced collapse and negligible recoil speed at the moment of neutron star formation. Scattering or exchange interactions off cluster stars are not consistent with both the observed orbital period and its offset position. We show that a binary system of two black holes with (unequal) masses in the range of 3-100 solar masses can live in NGC 6752 until present time and can have propelled PSR J1911-5958A into an eccentric peripheral orbit during the last ~1 Gyr.

We use N-body simulations to study the evolution of the orbital eccentricities of stars deposited near (

Recent proper motion and parallax measurements for the pulsar PSR B1508+55 indicate a transverse velocity of ~1100 km/s, which exceeds earlier measurements for any neutron star. The spin-down characteristics of PSR B1508+55 are typical for a non-recycled pulsar, which implies that the velocity of the pulsar cannot have originated from the second supernova disruption of a massive binary system. The high velocity of PSR B1508+55 can be accounted for by assuming that it received a kick at birth or that the neutron star was accelerated after its formation in the supernova explosion. We propose an explanation for the origin of hyperfast neutron stars based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star which attained its peculiar velocity (similar to that of the pulsar) in the course of a strong dynamical three- or four-body encounter in the core of dense young star cluster. To check this hypothesis we investigated three dynamical processes involving close encounters between: (i) two hard massive binaries, (ii) a hard binary and an intermediate-mass black hole, and (iii) a single star and a hard binary intermediate-mass black hole. We find that main-sequence O-type stars cannot be ejected from young massive star clusters with peculiar velocities high enough to explain the origin of hyperfast neutron stars, but lower mass main-sequence stars or the stripped helium cores of massive stars could be accelerated to hypervelocities. Our explanation for the origin of hyperfast pulsars requires a very dense stellar environment of the order of 10^6 -10^7 stars pc^{-3}. Although such high densities may exist during the core collapse of young massive star clusters, we caution that they have never been observed.

The central parsec of the Milky Way hosts two puzzlingly young stellar populations, a tight isotropic distribution of B stars around SgrA* (the S-stars) and a disk of OB stars extending to 0.5 pc. Using a modified version of Sverre Aarseth’s direct summation code NBODY6 we explore the scenario in which a young star cluster migrates to the Galactic Centre within the lifetime of the OB disk population via dynamical friction. We find that star clusters massive and dense enough to reach the central parsec form a very massive star via physical collisions on a mass segregation timescale. We follow the evolution of the merger product using the most up to date, yet conservative, mass loss recipes for very massive stars. Over a large range of initial conditions, we find that the very massive star expels most of its mass via a strong stellar wind, eventually collapsing to form a black hole of mass 20−400M , incapable of bringing massive stars to the Galactic Centre. No massive intermediate mass black hole can form in this scenario. The presence of a star cluster in the central 10 pc within the last 15 Myr would also leave a 2 pc ring of massive stars, which is not currently observed. Thus, we conclude that the star cluster migration model is highly unlikely to be the origin of either young population, and in-situ formation models or binary disruptions are favoured.

Very massive stars preferentially reside in the cores of their parent clusters and form binary or multiple systems. We study the role of tight very massive binaries in the origin of the field population of very massive stars. We performed numerical simulations of dynamical encounters between single (massive) stars and a very massive binary with parameters similar to those of the most massive known Galactic binaries, WR 20a and NGC 3603-A1. We found that these three-body encounters could be responsible for the origin of high peculiar velocities ($____geq$ 70 km/s) observed for some very massive ($____geq$ 60-70 Msun) runaway stars in the Milky Way and the Large Magellanic Cloud (e.g., $____lambda$ Cep, BD+43 3654, Sk-67 22, BI 237, 30 Dor 016), which can hardly be explained within the framework of the binary-supernova scenario. The production of high-velocity massive stars via three-body encounters is accompanied by the recoil of the binary in the opposite direction to the ejected star. We show that the relative position of the very massive binary R145 and the runaway early B-type star Sk-69 206 on the sky is consistent with the possibility that both objects were ejected from the central cluster, R136, of the star-forming region 30 Doradus via the same dynamical event -- a three-body encounter.

We explore the origin of a population of stars recently detected in the inner parsec of the Milky Way Nuclear Cluster (NC), which exhibit sub-solar metallicity and a higher rotation compared to the dominant population. Using state-of-the-art N-body simulations, we model the infall of massive stellar systems into the Galactic center, both of Galactic and extra-galactic origin. We show that the newly discovered population can either be the remnant of a massive star cluster formed a few kpc away from the Galactic center (Galactic scenario) or be accreted from a dwarf galaxy originally located at 10-100 kpc (extragalactic scenario) and that reached the Galactic center 3

The coalescence of massive black hole binaries (BHBs) in galactic mergers is the primary source of gravitational waves (GWs) at low frequencies. Current estimates of GW detection rates for the Laser Interferometer Space Antenna and the Pulsar Timing Array vary by three orders of magnitude. To understand this variation, we simulate the merger of equal-mass, eccentric, galaxy pairs with central massive black holes and shallow inner density cusps. We model the formation and hardening of a central BHB using the Fast Multiple Method as a force solver, which features a $O(N)$ scaling with the number $N$ of particles and obtains results equivalent to direct-summation simulations. At $N \sim 5\times 10^5$, typical for contemporary studies, the eccentricity of the BHBs can vary significantly for different random realisations of the same initial condition, resulting in a substantial variation of the merger timescale. This scatter owes to the stochasticity of stellar encounters with the BHB and decreases with increasing $N$. We estimate that $N \sim 10^7$ within the stellar half-light radius suffices to reduce the scatter in the merger timescale to $\sim 10$\%. Our results suggest that at least some of the uncertainty in low-frequency GW rates owes to insufficient numerical resolution.

Stars slingshotted by the supermassive black hole at the Galactic centre escape from the Milky Way so quickly that their trajectories are almost straight lines. Previous works have shown how these `hypervelocity stars' (stars moving faster than the local Galactic escape speed) are subsequently de ected by the gravitational field of the Milky Way and the Large Magellanic Cloud (LMC), but have neglected to account for the reflex motion of the Milky Way in response to the y-by of the LMC. A consequence of this motion is that the hypervelocity stars we see in the outskirts of the Milky Way today were ejected from where the Milky Way centre was hundreds of millions of years ago. This change in perspective causes large apparent de ections of several degrees in the trajectories of the hypervelocity stars. We quantify these deflections by simulating the ejection of hypervelocity stars from an isolated Milky Way (with a spherical or flattened dark matter halo), from a fixed-in-place Milky Way with a passing LMC, and from a Milky Way which responds to the passage of the LMC, finding that LMC passage causes larger de ections than can be caused by a attened Galactic dark matter halo in CDM. The 10 as yr

We discuss the performance of direct summation codes used in the simulation of astrophysical stellar systems on highly distributed architectures. These codes compute the gravitational interaction among stars in an exact way and have an O(N^2) scaling with the number of particles. They can be applied to a variety of astrophysical problems, like the evolution of star clusters, the dynamics of black holes, the formation of planetary systems, and cosmological simulations. The simulation of realistic star clusters with sufficiently high accuracy cannot be performed on a single workstation but may be possible on parallel computers or grids. We have implemented two parallel schemes for a direct N-body code and we study their performance on general purpose parallel computers and large computational grids. We present the results of timing analyzes conducted on the different architectures and compare them with the predictions from theoretical models. We conclude that the simulation of star clusters with up to a million particles will be possible on large distributed computers in the next decade. Simulating entire galaxies however will in addition require new hybrid methods to speedup the calculation.

We present a model for the concurrent formation of globular clusters (GCs) and supermassive stars (SMSs, >103M⊙) to address the origin of the HeCNONaMgAl abundance anomalies in GCs. GCs form in converging gas flows and accumulate low-angular momentum gas, which accretes onto protostars. This leads to an adiabatic contraction of the cluster and an increase of the stellar collision rate. A SMS can form via runaway collisions if the cluster reaches sufficiently high density before two-body relaxation halts the contraction. This condition is met if the number of stars ≳106 and the gas accretion rate ≳105M⊙/Myr, reminiscent of GC formation in high gas-density environments, such as -- but not restricted to -- the early Universe. The strong SMS wind mixes with the inflowing pristine gas, such that the protostars accrete diluted hot-hydrogen burning yields of the SMS. Because of continuous rejuvenation, the amount of processed material liberated by the SMS can be an order of magnitude higher than its maximum mass. This `conveyor-belt' production of hot-hydrogen burning products provides a solution to the mass budget problem that plagues other scenarios. Additionally, the liberated material is mildly enriched in helium and relatively rich in other hot-hydrogen burning products, in agreement with abundances of GCs today. Finally, we find a super-linear scaling between the amount of processed material and cluster mass, providing an explanation for the observed increase of the fraction of processed material with GC mass. We discuss open questions of this new GC enrichment scenario and propose observational tests.

Using adaptive optics we study the binary population in the nearby OB association Scorpius OB2. We present the first results of our near-infrared adaptive optics survey among 199 (mainly) A- and B-type stars in Sco OB2. In total 151 components other than the target stars are found, out of which 77 are probably background stars. Our findings are compared with data collected from literature. Out of the remaining 74 candidate physical companions 42 are new, demonstrating that many stars A/B stars have faint, close companions.

We study the evolution of the orientation of the orbital plane of massive black hole binaries (BHBs) in rotating stellar systems in which the total angular momentum of the stellar cusp is misaligned with respect to that of the binary. We compare results from direct summation N-body simulations with predictions from a simple theoretical model. We find that the same encounters between cusp stars and the BHBs that are responsible for the hardening and eccentricity evolution of the binary lead to a reorientation of the binary orbital plane. In particular, binaries whose angular momentum is initially misaligned with respect to that of the stellar cusp tend to realign their orbital planes with the angular momentum of the cusp on a time-scale of a few hardening times. This is due to angular momentum exchange between stars and the BHBs during close encounters, and may have important implications for the relative orientation of host galaxies and radio jets.

The dynamics of galactic nuclei reflects the presence of supermassive black holes (SBHs) in many ways. Single SBHs act as sinks, destroying a mass in stars equal to their own mass in roughly one relaxation time and forcing nuclei to expand. Formation of binary SBHs displaces a mass in stars roughly equal to the binary mass, creating low-density cores and ejecting hyper-velocity stars. Gravitational radiation recoil can eject coalescing binary SBHs from nuclei, resulting in offset SBHs and lopsided cores. We review recent work on these mechanisms and discuss the observable consequences.

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.

We study the short-term effects of an intermediate mass black hole (IBH) on the orbit of star S2 (S02), the shortest-period star known to orbit the supermassive black hole (MBH) in the centre of the Milky Way. Near-infrared imaging and spectroscopic observations allow an accurate determination of the orbit of the star. Given S2's short orbital period and large eccentricity, general relativity (GR) needs to be taken into account, and its effects are potentially measurable with current technology. We show that perturbations due to an IBH in orbit around the MBH can produce a shift in the apoapsis of S2 that is as large or even larger than the GR shift. An IBH will also induce changes in the plane of S2's orbit at a level as large as one degree per period. We apply observational orbital fitting techniques to simulations of the S-cluster in the presence of an IBH and find that an IBH more massive than about 1000 solar masses at the distance of the S-stars will be detectable at the next periapse passage of S2, which will occur in 2018.

Studies of the Galactic Centre suggest that in-situ star formation may have given rise to the observed stellar population near the central supermassive black hole (SMBH). Direct evidence for a recent starburst is provided by the currently observed young stellar disc (2-7Myr) in the central 0:5 pc of the Galaxy. This result suggests that star formation in galactic nuclei may occur close to the SMBH and produce initially attened stellar discs. Here we explore the possible build-up and evolution of nuclear stellar clusters near SMBHs through in-situ star formation producing stellar discs similar to those observed in the Galactic Centre and other nuclei. We make use of N-body simulations to model the evolution of multiple young stellar discs, and explore the potential observable signatures imprinted by such processes. Each of the five simulated discs is evolved for 100Myr before the next one is introduced in the system. We find that populations born at different epochs show different morphologies and kinematics. Older and presumably more metal poor populations are more relaxed and extended, while younger populations show a larger amount of rotation and attening. We conclude that star formation in central discs can reproduce the observed properties of multiple stellar populations in galactic nuclei differing in age, metallicity and kinematic properties.

We study the circumstances under which first collisions occur in young and dense star clusters. The initial conditions for our direct $N$-body simulations are chosen such that the clusters experience core collapse within a few million years, before the most massive stars have left the main-sequence. It turns out that the first collision is typically driven by the most massive stars in the cluster. Upon arrival in the cluster core, by dynamical friction, massive stars tend to form binaries. The enhanced cross section of the binary compared to a single star causes other stars to engage the binary. A collision between one of the binary components and the incoming third star is then mediated by the encounters between the binary and other cluster members. Due to the geometry of the binary-single star engagement the relative velocity at the moment of impact is substantially different than in a two-body encounter. This may have profound consequences for the further evolution of the collision product.

In this letter we study the eccentricity evolution of a massive black hole (MBH) binary (MBHB) embedded in a rotating stellar cusp. Following the observation that stars on counter-rotating (with respect to the MBHB) orbits extract angular momentum from the binary more efficiently then their co-rotating counterparts, the eccentricity evolution of the MBHB must depend on the degree of co-rotation (counter-rotation) of the surrounding stellar distribution. Using an hybrid scheme that couples numerical three-body scatterings to an analytical formalism for the cusp-binary interaction, we verify this hypothesis by evolving the MBHB in spherically symmetric cusps with different fractions F of co-rotating stars. Consistently with previous works, binaries in isotropic cusps (F=0.5) tend to increase their eccentricity, and when F approaches zero (counter-rotating cusps) the eccentricity rapidly increases to almost unity. Conversely, binaries in cusps with a significant degree of co-rotation (F>0.7) tend to become less and less eccentric, circularising quite quickly for F approaching unity. Direct N-body integrations performed to test the theory, corroborate the results of the hybrid scheme, at least at a qualitative level. We discuss quantitative differences, ascribing their origin to the oversimplified nature of the hybrid approach.

Regular star formation is thought to be inhibited close to the massive black hole (MBH) in the Galactic center. Nevertheless, tens of young main sequence B stars have been observed in an isotropic distribution close to it. Various models have been suggested for the formation of the B-stars closest to the MBH (

We explore the hypothesis that some high-velocity runaway stars attain their peculiar velocities in the course of exchange encounters between hard massive binaries and a very massive star (either an ordinary 50-100 Msun star or a more massive one, formed through runaway mergers of ordinary stars in the core of a young massive star cluster). In this process, one of the binary components becomes gravitationally bound to the very massive star, while the second one is ejected, sometimes with a high speed. We performed three-body scattering experiments and found that early B-type stars (the progenitors of the majority of neutron stars) can be ejected with velocities of $____ga$ 200-400 km/s (typical of pulsars), while 3-4 Msun stars can attain velocities of $____ga$ 300-400 km/s (typical of the bound population of halo late B-type stars). We also found that the ejected stars can occasionally attain velocities exceeding the Milky Ways's escape velocity.

We present a new technique to probe the central dark matter (DM) density profile of galaxies that harnesses both the survival and observed properties of star clusters. As a first application, we apply our method to the `ultra-faint' dwarf Eridanus II (Eri II) that has a lone star cluster ~45 pc from its centre. Using a grid of collisional N-body simulations, incorporating the effects of stellar evolution, external tides and dynamical friction, we show that a DM core for Eri II naturally reproduces the size and the projected position of its star cluster. By contrast, a dense cusped galaxy requires the cluster to lie implausibly far from the centre of Eri II (>1 kpc), with a high inclination orbit that must be observed at a particular orbital phase. Our results imply that either a cold DM cusp was `heated up' at the centre of Eri II by bursty star formation, or we are seeing an evidence for physics beyond cold DM.

Hypervelocity stars (HVSs) represent a unique population of stars in the Galaxy reflecting properties of the whole Galactic potential. Determining their origin is of fundamental importance to constrain the shape and mass of the dark halo. The leading scenario for the ejection of HVSs is an encounter with the supermassive black hole in the Galactic Centre. However, new proper motions from the Gaia mission indicate that only the fastest HVSs can be traced back to the Galactic centre and the remaining stars originate in the disc or halo. In this paper, we study HVSs generated by encounters of stellar binaries with an intermediate-mass black hole (IMBH) in the core of a star cluster. For the first time, we model the effect of the cluster orbit in the Galactic potential on the observable properties of the ejected population. HVSs generated by this mechanism do not travel on radial orbits consistent with a Galactic centre origin, but rather point back to their parent cluster, thus providing observational evidence for the presence of an IMBH. We also model the ejection of high-velocity stars from the Galactic population of globular clusters, assuming that they all contain an IMBH, including the effects of the cluster’s orbit and propagation of the star in the Galactic potential up to detection. We find that high-velocity stars ejected by IMBHs have distinctive distributions in velocity, Galactocentric distance and Galactic latitude, which can be used to distinguish them from runaway stars and stars ejected from the Galactic Centre.

The tidal breakup of binary star systems by the supermassive black hole (SMBH) in the center of the galaxy has been suggested as the source of both the observed sample of hypervelocity stars (HVSs) in the halo of the Galaxy and the S-stars that remain in tight orbits around Sgr A*. Here, we use a post-Newtonian N-body code to study the dynamics of main-sequence binaries on highly elliptical bound orbits whose periapses lie close to the SMBH, determining the properties of ejected and bound stars as well as collision products. Unlike previous studies, we follow binaries that remain bound for several revolutions around the SMBH, finding that in the case of relatively large periapses and highly inclined binaries the Kozai resonance can lead to large periodic oscillations in the internal binary eccentricity and inclination. Collisions and mergers of the binary elements are found to increase significantly for multiple orbits around the SMBH, while HVSs are primarily produced during a binary's first passage. This process can lead to stellar coalescence and eventually serve as an important source of young stars at the galactic center.

We performed numerical simulations of dynamical encounters between hard massive binaries and a very massive star (VMS; formed through runaway mergers of ordinary stars in the dense core of a young massive star cluster), in order to explore the hypothesis that this dynamical process could be responsible for the origin of high-velocity (____geq 200-400 km/s) early or late B-type stars. We estimated the typical velocities produced in encounters between very tight massive binaries and VMSs (of mass of ____geq 200 Msun) and found that about 3-4 per cent of all encounters produce velocities of ____geq 400 km/s, while in about 2 per cent of encounters the escapers attain velocities exceeding the Milky Ways's escape velocity. We therefore argue that the origin of high-velocity (____geq 200-400 km/s) runaway stars and at least some so-called hypervelocity stars could be associated with dynamical encounters between the tightest massive binaries and VMSs formed in the cores of star clusters. We also simulated dynamical encounters between tight massive binaries and single ordinary 50-100 Msun stars. We found that from 1 to ____simeq 4 per cent of these encounters can produce runaway stars with velocities of ____geq 300-400 km/s (typical of the bound population of high-velocity halo B-type stars) and occasionally (in less than 1 per cent of encounters) produce hypervelocity (____geq 700 km/s) late B-type escapers.

We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's 'algorithmic' chain regularization scheme including post-Newtonian terms up to PN2.5 order. Stars moving beyond the chain are advanced using a fourth-order integrator with forces computed on a GRAPE board. Performance tests confirm that the hybrid code achieves better energy conservation, in less elapsed time, than the standard scheme and that it reproduces the orbits of stars tightly bound to the black hole with high precision. The hybrid code is applied to two sample problems: the effect of finite-N gravitational fluctuations on the orbits of the S-stars; and inspiral of an intermediate-mass black hole into the galactic center.

Coalescing supermassive black hole binaries (BHBs) are expected to be the loudest sources of gravitational waves (GWs) in the Universe. Detection rates for ground or space-based detectors based on cosmological simulations and semi-analytic models are highly uncertain. A major difficulty stems from the necessity to model the BHB from the scale of the merger to that of inspiral. Of particular relevance to the GW merger timescale is the binary eccentricity. Here we present a self-consistent numerical study of the eccentricity of BHBs formed in massive gas-free mergers from the early stages of the merger to the hardening phase, followed by a semi-analytical model down to coalescence. We find that the early eccentricity of the unbound black hole pair is largely determined by the initial orbit. It systematically decreases during the dynamical friction phase. The eccentricity at binary formation is affected by stochasticity and noise owing to encounters with stars, but preserves a strong correlation with the initial orbital eccentricity. Binding of the black holes is a phase characterised by strong perturbations, and we present a quantitative definition of the time of binary formation. During hardening the eccentricity increases in minor mergers, unless the binary is approximately circular, but remains largely unchanged in major mergers, in agreement with predictions from semi-analytical models based on isotropic scattering experiments. Coalescence times due to hardening and GW emission in gas-poor non-rotating ellipticals are 0.5 Gyr for the large initial eccentricities (0.5 ≤ e ≤ 0.9) typical of galaxy mergers in cosmological simulations.

We propose an explanation for the origin of hyperfast neutron stars (e.g. PSR B1508+55, PSR B2224+65, RX J0822-4300) based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star (or its helium core) which attained its peculiar velocity (similar to that of the neutron star) in the course of a strong three- or four-body dynamical encounter in the core of a young massive star cluster. This hypothesis implies that the dense cores of star clusters (located either in the Galactic disk or near the Galactic centre) could also produce the so-called hypervelocity stars -- the ordinary stars moving with a speed of ~1000 km/s.

The young stars near the supermassive black hole at the galactic center follow orbits that are nearly random in orientation and that have an approximately thermal distribution of eccentricities, N(e) ~ e. We show that both of these properties are a natural consequence of a few million years' interaction with an intermediate-mass black hole (IBH), if the latter's orbit is mildly eccentric and if its mass exceeds approximately 1500 solar masses. Producing the most tightly-bound S-stars requires an IBH orbit with periastron distance less than about 10 mpc. Our results provide support for a model in which the young stars are carried to the galactic center while bound to an IBH, and are consistent with the hypothesis that an IBH may still be orbiting within the nuclear star cluster.