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We use direct $N$-body simulations to explore some possible scenarios for the future evolution of two massive clusters observed toward the center of NGC\,4654, a spiral galaxy with mass similar to that of the Milky Way. Using archival HST data, we obtain the photometric masses of the two clusters, $M=3\times 10^5$ M$_\odot$ and $M=1.7\times 10^6$ M$_\odot$, their half-light radii, $R_{\rm eff}\sim4$ pc and $R_{\rm eff} \sim 6$ pc, and their projected distances from the photometric center of the galaxy (both $, 10 Pages, 11 Figures, 2 Tables. Published in MNRAS

GW190521 is the most massive binary black hole (BBH) merger observed to date. This catastrophic event, which happened ~4.53 Gpc away from us, gave birth to a ~140 Msun black hole (BH) falling in the still unexplored intermediate-mass black hole (IMBH) regime. Nevertheless, the origin of GW190521 is still a matter of debate: several hints may favor a dense stellar environment as a birthplace. In this poster, I present the impact of three-body encounters on the formation of GW190521-like systems in young (0.3 in LISA band. Finally, I present the role of three-body interactions on the merger rate density of GW190521-like binaries, which in our simulations result as ~0.03 Gpc^-3 yr^-1., {"references":["Abbott R. et al., 2020, Phys. Rev. Lett.125, 101102","Abbott R. et al., 2020, ApJ, 900, L13","Chassonnery P. et al., 2019, arXiv:1910.05202","Dall'Amico M. et al., 2021, arXiv:2105.12757","Di Carlo U. N. et al., 2019, MNRAS, 487, 2947, arXiv:1901.00863","Healy J. & Lousto C. O., 2018, Phys. Rev. D, 97, 084002","Memmesheimer R-M. et al., 2004, Phys. Rev. D 70, 104011","Nitz A. H. & Capano C. D., 2021, ApJ, 907, L9"]}

We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to $\mu$-Hz frequency range. By the 2040s', the $\mu$-Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a $\mu$-Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe., Comment: 28 pages, 8 figures; White Paper submitted to ESA's Voyage 2050 call for papers on behalf of the LISA Consortium 2050 Task Force

We present some results from the DRAGON simulations, a set of four direct N-body simulations of globular clusters (GCs) with a million stars and five percent initial (primordial) binaries. These simulations were undertaken with the NBODY6++GPU code, which allowed us to follow dynamical and stellar evolution of individual stars and binaries, formation and evolution of white dwarfs, neutron stars, and black holes, and the effect of a galactic tidal field. The simulations are the largest existing models of a realistic globular cluster over its full lifetime of 12 billion years. In particular we will show here an investigation of the population of binaries including compact objects (such as white dwarfs - cataclysmic variables and merging black hole binaries in the model as counterparts of LIGO/Virgo sources); their distribution in the cluster and evolution with time.

A vast number of observed galactic nuclei are known to harbour a central supermassive black hole (SMBH). In their early lifetime, these systems might have witnessed the strong interaction between the SMBH and massive star clusters formed in the inner galactic regions. Due to the strong tidal field exerted from the SMBH, clusters are likely to undergo tidal disruption, releasing their stars all around the SMBH, and possibly driving the formation of a nuclear cluster (NC). This mechanism can contribute to populate galactic nuclei with intermediate-mass black holes (IMBH). Interactions with the central SMBH can lead to the formation of tight massive BH binaries (MBBH) that undergo coalescence via gravitational waves (GW) emission. We discuss this mechanism in the context of the Milky Way centre, exploring the possibility that SgrA*, the Galactic SMBH, has an IMBH companion.

Our Galaxy and the nearby Andromeda Galaxy (M31) form a bound system, even though the relative velocity vector of M31 is currently not well constrained. Their orbital motion is highly dependent on the initial conditions, but all the reliable scenarios imply a first close approach in the next 3-5 Gyrs. In our study, we simulate this interaction via direct N-body integration, using the HiGPUs code. Our aim is to investigate the dependence of the time of the merger on the physical and dynamical properties of the system. Finally, we study the dynamical evolution of the two Supermassive Black Holes placed in the two galactic centers, with the future aim to achieve a proper resolution to follow their motion until they form a tight binary system., Proceedings of IAU Symposium No. 351, 2019A, (MODEST-19), "Star Clusters: From the Milky Way to the Early Universe". Bragaglia, M.B. Davies, A. Sills & E. Vesperini, eds. 4 pages, 3 figures

We investigate the possible dynamical origin of GW190814, a gravitational wave (GW) source discovered by the LIGO-Virgo-Kagra collaboration (LVC) associated with a merger between a stellar black hole (BH) with mass $23.2$ M$_\odot$ and a compact object, either a BH or a neutron star (NS), with mass $2.59$ M$_\odot$. Using a database of 240,000 $N$-body simulations modelling the formation of NS-BH mergers via dynamical encounters in dense clusters, we find that systems like GW190814 are likely to form in young, metal-rich clusters. Our model suggests that a little excess ($\sim 2-4\%$) of objects with masses in the range $2.3-3$ M$_\odot$ in the compact remnants mass spectrum leads to a detection rate for dynamically formed "GW190814 -like" mergers of $\Gamma_{\rm GW190814} \simeq 1-6$ yr Gpc$^{-3}$, i.e. within the observational constraints set by the GW190814 discovery, $\Gamma_{\rm LVC} \sim 1-23$ yr Gpc$^{-3}$. Additionally, our model suggests that $\sim 1.8-4.8\%$ of dynamical NS-BH mergers are compatible with GW190426\_152155, the only confirmed NS-BH merger detected by the LVC. We show that the relative amount of light and heavy NS-BH mergers can provide clues about the environments in which they developed., Comment: main paper 7 pages, appendix 11 pages, 7 figures, 5 tables. Accepted for publication in ApJL

Our Galaxy and the nearby Andromeda galaxy (M31) are the most massive members of the Local Group, and they seem to be a bound pair, despite the uncertainties on the relative motion of the two galaxies. A number of studies have shown that the two galaxies will likely undergo a close approach in the next 4$-$5 Gyr. We used direct $N$-body simulations to model this interaction to shed light on the future of the Milky Way - Andromeda system and for the first time explore the fate of the two supermassive black holes (SMBHs) that are located at their centers. We investigated how the uncertainties on the relative motion of the two galaxies, linked with the initial velocities and the density of the diffuse environment in which they move, affect the estimate of the time they need to merge and form ``Milkomeda''. After the galaxy merger, we follow the evolution of their two SMBHs up to their close pairing and fusion. Upon the fiducial set of parameters, we find that Milky Way and Andromeda will have their closest approach in the next 4.3 Gyr and merge over a span of 10 Gyr. Although the time of the first encounter is consistent with other predictions, we find that the merger occurs later than previously estimated. We also show that the two SMBHs will spiral in the inner region of Milkomeda and coalesce in less than 16.6 Myr after the merger of the two galaxies. Finally, we evaluate the gravitational-wave emission caused by the inspiral of the SMBHs, and we discuss the detectability of similar SMBH mergers in the nearby Universe ($z\leq 2$) through next-generation gravitational-wave detectors., Comment: 8 Pages, 11 Figures, 1 Table. Published in A&A

Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the $\sim 10$-$10^3~\mathrm{Hz}$ band of ground-based observatories and the $\sim10^{-4}$-$10^{-1}~\mathrm{Hz}$ band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass ($\sim10^2$-$10^4 M_\odot$) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology., Comment: 13 pages, 1 figure. Published in Experimental Astronomy. Summarising white paper arXiv:1908.11375

The LIGO-Virgo-Kagra collaboration (LVC) discovered recently GW190521, a gravitational wave (GW) source associated with the merger between two black holes (BHs) with mass $66$ M$_\odot$ and $>85$ M$_\odot$. GW190521 represents the first BH binary (BBH) merger with a primary mass falling in the "upper mass-gap" and the first leaving behind a $\sim 150$ M$_\odot$ remnant. So far, the LVC reported the discovery of four further mergers having a total mass $>100$ M$_\odot$, i.e. in the intermediate-mass black holes (IMBH) mass range. Here, we discuss results from a series of 80 $N$-body simulations of young massive clusters (YMCs) that implement relativistic corrections to follow compact object mergers. We discover the development of a GW190521-like system as the result of a 3rd-generation merger, and four IMBH-BH mergers with total mass $~(300-350)$ M$_\odot$. We show that these IMBH-BH mergers are low-frequency GW sources detectable with LISA and DECIGO out to redshift $z=0.01-0.1$ and $z>100$, and we discuss how their detection could help unravelling IMBH natal spins. For the GW190521 test case, we show that the 3rd-generation merger remnant has a spin and effective spin parameter that matches the $90\%$ credible interval measured for GW190521 better than a simpler double merger and comparably to a single merger. Due to GW recoil kicks, we show that retaining the products of these mergers require birth-sites with escape velocities $\gtrsim 50-100$ km s$^{-1}$, values typically attained in galactic nuclei and massive clusters with steep density profiles., 23 pages, 11 figures, 2 tables, 2 Appendix. ApJ accepted

We explore hierarchical black hole (BH) mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs), accounting for both original and dynamically assembled binary BHs (BBHs). We find that the median mass of both first- and nth-generation dynamical mergers is larger in GCs and YSCs with respect to NSCs, because the lighter BHs are ejected by supernova kicks from the lower-mass clusters. Also, first- and nth-generation BH masses are strongly affected by the metallicity of the progenitor stars: the median mass of the primary BH of a nth-generation merger is $\sim{}24-38$ M$_\odot$ ($\sim{}9-15$ M$_\odot$) in metal-poor (metal-rich) NSCs. The maximum BH mass mainly depends on the escape velocity: BHs with mass up to several thousand M$_\odot$ form in NSCs, while YSCs and GCs host BHs with mass up to several hundred M$_\odot$. Furthermore, we calculate the fraction of mergers with at least one component in the pair-instability mass gap ($f_{\rm PI}$) and in the intermediate-mass BH regime ($f_{\rm IMBH}$). In the fiducial model for dynamical BBHs with metallicity $Z=0.002$, we find $f_{\rm PI}\approx{}0.05$, $0.02$ and $0.007$ ($f_{\rm IMBH}\approx{}0.01$, $0.002$ and $0.001$) in NSCs, GCs and YSCs, respectively. Both $f_{\rm PI}$ and $f_{\rm IMBH}$ drop by at least one order of magnitude at solar metallicity. Finally, we investigate the formation of GW190521 by assuming that it is either a nearly equal-mass BBH or an intermediate-mass ratio inspiral., 20 pages, 13 figures, accepted for publication in MNRAS

We present a comprehensive investigation of main-sequence (MS) binaries in the DRAGON simulations, which are the first one-million particles direct $N$-body simulations of globular clusters. We analyse the orbital parameters of the binary samples in two of the DRAGON simulations, D1-R7- IMF93 and D2-R7-IMF01, focusing on their secular evolution and correlations up to 12 Gyr. These two models have different initial stellar mass functions: Kroupa 1993 (D1-R7-IMF93) and Kroupa 2001 (D2-R7-IMF01); and different initial mass ratio distributions: random paring (D1-R7-IMF93) and a power-law (D1-R7-IMF93). In general, the mass ratio of a population of binaries increases over time due to stellar evolution, which is less significant in D2-R7-IMF01. In D1-R7-IMF93, primordial binaries with mass ratio $q \approx$ 0.2 are most common, and the frequency linearly declines with increasing $q$ at all times. Dynamical binaries of both models have higher eccentricities and larger semi-major axes than primordial binaries. They are preferentially located in the inner part of the star cluster. Secular evolution of binary orbital parameters does not depend on the initial mass-ratio distribution, but is sensitive to the initial binary distribution of the system. At t = 12 Gyr, the binary fraction decreases radially outwards, and mass segregation is present. A color difference of 0.1 mag in $F330W-F814W$ and 0.2 mag in $NUV-y$ between the core and the outskirts of both clusters is seen, which is a reflection of the binary radial distribution and the mass segregation in the cluster. The complete set of data for primordial and dynamical binary systems at all snapshot intervals is made publicly available., 40 pages, 22 figures, accepted for publication in ApJS on date 29 November 2020

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 a massive stellar system 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 3-5 Gyr ago. A comparison between our models and characteristic Galactocentric distance and metallicity distributions of Milky Way satellites and globular clusters favours the Galactic scenario. A comparison with clusters associated with the Enceladus-Sausage, Sequoia, Sagittarius and Canis Major structures suggests that the progenitor of the observed metal-poor substructure formed in-situ rather than being accreted., Comment: 16 pages, 9 figures, 1 table, 2 online data files available upon publication. published in ApJL

Hierarchical mergers are one of the distinctive signatures of binary black hole (BBH) formation through dynamical evolution. Here, we present a fast semi-analytic approach to simulate hierarchical mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs). Hierarchical mergers are more common in NSCs than they are in both GCs and YSCs because of the different escape velocity. The mass distribution of hierarchical BBHs strongly depends on the properties of first-generation BBHs, such as their progenitor’s metallicity. In our fiducial model, we form black holes (BHs) with masses up to ∼103 M⊙ in NSCs and up to ∼102 M⊙ in both GCs and YSCs. When escape velocities in excess of 100 km s−1 are considered, BHs with mass &gt, 103 M⊙ are allowed to form in NSCs. Hierarchical mergers lead to the formation of BHs in the pair instability mass gap and intermediate-mass BHs, but only in metal-poor environments. The local BBH merger rate in our models ranges from ∼10 to ∼60 Gpc−3 yr−1, hierarchical BBHs in NSCs account for ∼10−2–0.2 Gpc−3 yr−1, with a strong upper limit of ∼10 Gpc−3 yr−1. When comparing our models with the second gravitational-wave transient catalog, we find that multiple formation channels are favored to reproduce the observed BBH population.

We study the dynamics and evolution of the Milky Way nuclear star cluster performing a high resolution direct one-million-body simulation. Focusing on the interactions between such stellar system and the central supermassive black hole, we find that different stellar components adapt their overall distribution differently. After 5 Gyr, stellar mass black holes are characterized by a spatial distribution with power-slope $-1.75$, fully consistent with the prediction of Bahcall-Wolf pioneering work. Using the vast amount of data available, we infer the rate for tidal disruption events, being $4 \times 10^{-6}$ per yr, and estimate the number of objects that emit gravitational waves during the phases preceding the accretion onto the super-massive black hole, $\sim 270$ per Gyr. We show that some of these sources could form extreme mass-ratio inspirals. We follow the evolution of binary stars population, showing that the initial binary fraction of $5\%$ drops down to $2.5\%$ inside the inner parsec. Also, we explored the possible formation of binary systems containing a compact object, discussing the implications for millisecond pulsars formation and the development of Ia Supernovae., Comment: Accepted by MNRAS after a major revision

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

The detection of gravitational waves emitted during a neutron star - black hole merger and the associated electromagnetic counterpart will provide a wealth of information about stellar evolution nuclear matter, and General Relativity. While the theoretical framework about neutron star - black hole binaries formed in isolation is well established, the picture is loosely constrained for those forming via dynamical interactions. Here, we use N-body simulations to show that mergers forming in globular and nuclear clusters could display distinctive marks compared to isolated mergers, namely larger masses, heavier black holes, and the tendency to have no associated electromagnetic counterpart. These features could represent a useful tool to interpreting forthcoming observations. In the Local Universe, gravitational waves emitted from dynamical mergers could be unravelled by detectors sensitive in the decihertz frequency band, while those occurring at the distance range of Andromeda and the Virgo Cluster could be accessible to lower-frequency detectors like LISA., 18 Pages, 10 Figures, 1 Table. Published in Communication Physics

We study the dynamical evolution of eccentric massive black hole binaries (MBHBs) interacting with unbound stars by means of an extensive set of three body scattering experiments. Compared to previous studies, we extend the investigation down to a MBHB mass ratio of $q=m_2/m_1=10^{-4}$, where $m_1$ and $m_2$ are the masses of the primary and secondary hole respectively. Contrary to a simple extrapolation from higher mass ratios, we find that for $q\lesssim 10^{-3}$ the eccentricity growth rate becomes negative, i.e., the binary {\it circularises} as it shrinks. This behaviour is due to the subset of interacting stars captured in metastable counter-rotating orbits; those stars tend to extract angular momentum from the binary, promoting eccentricity growth for $q>10^{-3}$, but tend to inject angular momentum into the binary driving it towards circularisation for $q, 6 pages, 5 figures; accepted for publication in MNRAS

There have been increasing theoretical speculations and observational indications that certain globular clusters (GCs) could contain a sizeable population of stellar mass black holes (BHs). In this paper, we shortlist at least 29 Galactic GCs that could be hosting a subsystem of BHs (BHS). In a companion paper, we analysed results from a wide array of GC models (simulated with the MOCCA code for cluster simulations) that retained few tens to several hundreds of BHs at 12 Gyr and showed that the properties of the BHS in those GCs correlate with the GC's observable properties. Building on those results, we use available observational properties of 140 Galactic GCs to identify 29 GCs that could potentially be harbouring up to a few hundreds of BHs. Utilizing observational properties and theoretical scaling relations, we estimate the density, size and mass of the BHS in these GCs. We also calculate the total number of BHs and the fraction of BHs contained in a binary system for our shortlisted Galactic GCs. Additionally, we mention other Galactic GCs that could also contain significant number of single BHs or BHs in binary systems., 13 pages, 5 figures, 3 tables, accepted for publication in MNRAS. Revised manuscript includes minor corrections and a new subsection (2.5)

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 $\Gamma_{\rm IMBH-SMBH} = 2.8\times 10^{-3}$ 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 $\Gamma_{\rm EMRI} = 0.25$ 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 $\Gamma_{\rm BHB} = 0.4-4$ yr$^{-1}$ Gpc$^{-3}$., Comment: 21 pages, 29 figures, 6 tables. Accepted for publication in MNRAS

We study the formation of intermediate-mass ratio inspirals (IMRIs) triggered by the interactions between two stellar black holes (BHs) and an intermediate-mass BH (IMBH) inhabiting the centre of a dense star cluster. We exploit $N$-body models varying the IMBH mass, the stellar BH mass spectrum, and the star cluster properties. These simulations are coupled with a semi-analytic procedure to characterise the evolution of the remnant IMBH. The IMRIs formation probability attains values $\sim 5-50\%$, with larger values corresponding to larger IMBH masses. IMRIs map out the stellar BH mass spectrum, thus they might be used to unravel BH populations in star clusters harboring an IMBH. After the IMRI phase, an IMBH initially nearly maximal(almost non-rotating) tends to decrease(increase) its spin. If IMBHs grow mostly via repeated IMRIs, we show that only IMBH seeds sufficiently massive ($M_{\rm seed} > 300$ M$_\odot$) can grow up to $M_{\rm imbh} >10^3$ M$_\odot$ in dense globular clusters. Assuming that these seeds form at a redshift $z\sim 2-6$, we find that around $1-5\%$ of them would reach masses $\sim 500-1500$ M$_\odot$ at redshift $z=0$ and would exhibit low-spins, $S_{\rm imbh} < 0.2$. Measuring the mass and spin of IMBHs involved in IMRIs could help unravelling their formation mechanisms. We show that LISA can detect IMBHs in Milky Way globular clusters with a signal-to-noise ratio SNR$=10-100$, or in the Large Magellanic Cloud with an SNR$=8-40$. We provide the IMRIs merger rate for LIGO ($\Gamma_{\rm LIG} = 0.003-1.6$ yr$^{-1}$), LISA ($\Gamma_{\rm LIS} = 0.02-60$ yr$^{-1}$), ET ($\Gamma_{\rm ET} = 1-600$ yr$^{-1}$), and DECIGO ($\Gamma_{\rm DEC} = 6-3000$ yr$^{-1}$). Our simulations show that IMRIs' mass and spin encode crucial insights on the mechanisms that regulate IMBH formation and that the synergy among different detectors would enable us to fully unveil them. (Abridged), Comment: 18 pages, 20 figures, 3 tables. Accepted for publication in A&A

Binary black holes (BBHs) are thought to form in different environments, including the galactic field and (globular, nuclear, young and open) star clusters. Here, we propose a method to estimate the fingerprints of the main BBH formation channels associated with these different environments. We show that the metallicity distribution of galaxies in the local Universe along with the relative amount of mergers forming in the field or in star clusters determine the main properties of the BBH population. Our fiducial model predicts that the heaviest merger to date, GW170729, originated from a progenitor that underwent 2--3 merger events in a dense star cluster, possibly a galactic nucleus. The model predicts that at least one merger remnant out of 100 BBH mergers in the local Universe has mass $90 < M_{\rm rem}/ {\rm ~M}_\odot \leq{} 110$, and one in a thousand can reach a mass as large as $M_{\rm rem} \gtrsim 250$ M$_\odot$. Such massive black holes would bridge the gap between stellar-mass and intermediate-mass black holes. The relative number of low- and high-mass BBHs can help us unravelling the fingerprints of different formation channels. Based on the assumptions of our model, we expect that isolated binaries are the main channel of BBH merger formation if $\sim 70\%$ of the whole BBH population has remnants masses $75$ M$_\odot$ point to a significant sub-population of dynamically formed BBH binaries., 25 pages, 13 figures, 2 tables. Accepted for publication in the ApJ

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 find 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., Comment: 6 pages, 5 figures, accepted to ApJ Letters

The gravitational-wave astronomical revolution began in 2015 with LIGO's observation of the coalescence of two stellar-mass black holes. Over the coming decades, ground-based detectors like LIGO will extend their reach, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will enable gravitational-wave observations of the massive black holes in galactic centres. Between LISA and ground-based observatories lies the unexplored decihertz gravitational-wave frequency band. Here, we propose a Decihertz Observatory to cover this band, and complement observations made by other gravitational-wave observatories. The decihertz band is uniquely suited to observation of intermediate-mass ($\sim 10^2$-$10^4 M_\odot$) black holes, which may form the missing link between stellar-mass and massive black holes, offering a unique opportunity to measure their properties. Decihertz observations will be able to detect stellar-mass binaries days to years before they merge and are observed by ground-based detectors, providing early warning of nearby binary neutron star mergers, and enabling measurements of the eccentricity of binary black holes, providing revealing insights into their formation. Observing decihertz gravitational-waves also opens the possibility of testing fundamental physics in a new laboratory, permitting unique tests of general relativity and the Standard Model of particle physics. Overall, a Decihertz Observatory will answer key questions about how black holes form and evolve across cosmic time, open new avenues for multimessenger astronomy, and advance our understanding of gravitation, particle physics and cosmology., 52 pages, 5 figures, 4 tables. Submitted to Classical & Quantum Gravity. Based upon a white paper for ESA's Voyage 2050 on behalf of the LISA Consortium 2050 Task Force

This study presents a comprehensive chemo-dynamical analysis of LAMOST J1109+0754, a bright (V = 12.8), extremely metal-poor (\abund{Fe}{H} = $-3.17$) star, with a strong \textit{r}-process enhancement (\abund{Eu}{Fe} = +0.94 $\pm$ 0.12). Our results are based on the 7-D measurements supplied by $Gaia$ and the chemical composition derived from a high-resolution ($R\sim 110,000$), high signal-to-noise ratio ($S/N \sim 60)$ optical spectrum obtained by the 2.4\,m Automated Planet Finder Telescope at Lick Observatory. We obtain chemical abundances of 31 elements (from lithium to thorium). The abundance ratios (\abund{X}{Fe}) of the light-elements (Z $\leqslant 30$) suggest a massive Population\,III progenitor in the 13.4-29.5\,M$_\odot$ mass range. The heavy-element ($30

Sizeable number of stellar-mass black holes (BHs) in globular clusters (GCs) can strongly influence the dynamical evolution and observational properties of their host cluster. Using results from a large set of numerical simulations, we identify the key ingredients needed to sustain a sizeable population of BHs in GCs up to a Hubble time. We find that while BH natal kick prescriptions are essential in determining the initial retention fraction of BHs in GCs, the long-term survival of BHs is determined by the size, initial central density and half-mass relaxation time of the GC. Simulated GC models that contain many BHs are characterized by relatively low central surface brightness, large half-light and core radii values. We also discuss novel ways to compare simulated results with available observational data to identify GCs that are most likely to contain many BHs., Comment: 4 pages, 2 figures, 1 table. Contribution to the proceedings of the IAU Symposium No. 351: "Star Clusters: from the Milky Way to the Early Universe"

A large fraction of galactic nuclei is expected to host supermassive black hole binaries (BHB), likely formed during the early phase of galaxies assembly and merging. In this paper, we use a large set of state-of-art numerical models to investigate the interplay between a BHB and a massive star cluster (GCs) driven toward the galactic centre by dynamical friction. Varying the BHB mass and mass ratio and the GC orbit, we show that the reciprocal feedback exerted between GCs and the BHB shapes their global properties. We show that, at GC-to-BHB mass ratios above 0.1, the GC affects notably the BHB orbital evolution, possibly boosting its coalescence. This effect is maximized if the GC moves on a retrograde orbit, and for a non-equal mass BHB. We show that the GC debris dispersed around the galactic nucleus can lead to the formation of a nuclear cluster, depending on the BHB tidal field, and that the distribution of compact remnants resulting from the GC disruption can carry information about the BHB orbital properties. We find that red giant stars delivered by the spiralling GC can be disrupted at a rate of $\simeq (0.7-7)\times 10^{-7}$ yr$^{-1}$ for BHB masses $\sim 10^7{\rm M}_\odot$, while tens to hundreds of stars can be possibly observed in the galactic halo as high-velocity stars, with velocities up to $\sim 2000$ km s$^{-1}$, depending on the BHB orbital properties., Comment: 26 pages, 27 figures, 2 tables. Resubmitted to MNRAS after minor revision

In this paper, we explore the mechanisms that regulate the formation and evolution of stellar black hole binaries (BHBs) around supermassive black holes (SMBHs). We show that dynamical interactions can efficiently drive "in-situ" BHB formation if the SMBH is surrounded by a massive nuclear cluster (NC), while orbitally segregated star clusters can replenish the BHB reservoir in SMBH-dominated nuclei. We discuss how the combined action of stellar hardening and mass segregation sculpts the BHB orbital properties. We use direct N-body simulations including post-Newtonian corrections up to 2.5 order to study the BHB-SMBH interplay, showing that the Kozai-Lidov mechanism plays a crucial role in shortening binaries lifetime. We find that the merging probability weakly depends on the SMBH mass in the $10^6-10^9{\rm ~M}_\odot$ mass range, leading to a merger rate $��\simeq 3-8$ yr$^{-1}$ Gpc$^{-3}$ at redshift zero. Nearly $40\%$ of the mergers have masses in the "BH mass gap", $50-140{\rm ~M}_\odot$, thus indicating that galactic nuclei are ideal places to form BHs in this mass range. We argue that gravitational wave (GW) sources with components mass $m_1>40{\rm ~M}_\odot$ and $m_2, 29 pages, 24 figures, 4 Tables, and 1 Appendix. Accepted for publication in the Astrophysical Journal

Black hole (BH) triples represent one of the astrophysical pathways for BH mergers in the Universe detectable by LIGO and VIRGO. We study the formation of BH triples via binary-binary encounters in dense clusters, showing that one-third of triples formed through this channel are in a non-hierarchical, unstable configuration. We build a database of $32,000$ $N$-body simulations to investigate the evolution of these BH triples. Varying the mutual orbital inclination, the three BH masses and the inner and outer eccentricities, we show that retrograde, nearly planar configurations lead to a significant shrinkage of the inner binary. We find an universal trend of triple systems, namely that they tend to evolve toward prograde configurations and that the orbital flip, driven by the torque exerted on the inner BH binary (BHB) by the outer BH, leads in general to tighter inner orbits that, in some cases, merge within a Hubble time. We find that the mergers' mass distribution maps the original BH binary spectrum. A large fraction of merging BHBs with initial separation $1$ AU enter the $10^{-3}-10^{-1}$ Hz frequency band with large eccentricities, thus representing potential eccentric LISA sources. Mergers originating from initially tighter BHB ($a\sim 0.01$ AU), instead, often have eccentricities above 0.7 in the $1$ Hz band. This might imply that eccentric sources detected in high-frequency detectors are most likely connected with a high-velocity dispersion stellar environment, whereas eccentric sources detected in low-frequency detectors are likely to develop in low-density clusters. (Abridged), 27 pages, 26 figures, 6 tables, 2 appendixes

We investigate the interaction of a massive globular cluster (GC) with a super massive black hole (SMBH), located at the centre of its host galaxy, by means of direct N-body simulations. The results show that tidal distortions induced by the stellar background and the SMBH act on a time shorter than that of dynamical friction decay for a $10^6$ M$_\odot$ GC whenever the SMBH mass exceeds $\sim 10^8$ M$_\odot$ . This implies an almost complete dissolution of the infalling GC before it reaches the inner region ($\lesssim 5$ pc) of the parent galaxy. The generalization of this result to a larger sample of infalling GCs shows that such destructive process may prevent the formation and growth of a bright galactic nucleus. Another interesting, serendipitous, result we obtained is that the close interaction between the SMBH and the GC produces a "wave" of stars that escape from the cluster and, in a fraction, even from the whole galaxy., 11 pages, 11 figures, 3 tables

In this paper, we discuss how globular clusters (GCs) structural and observational properties can be used to infer the presence of a black hole system (BHS) inhabiting their inner regions. We propose a novel way to identify the BHS size, defined as the GC radius containing a mass contributed equally from stars and stellar BHs. Using this definition, similar to the well-known concept of "influence radius", we found a "fundamental plane" connecting the BHS typical density with the GC central surface density profile, total luminosity and observational half-mass radius. Our approach allows us to define a unique way to connect the observational GCs parameters with their dark content. Comparing our results with observed Milky Way GCs, we found that many of them likely host, at the present time, as many as several hundreds of BHs. These BHS are characterized by a relatively low typical density, $\rho_\bhs \sim 10-10^5\Ms$ pc$^{-3}$ and composed of relatively massive BHs, with average masses in the range $m_\bhs = 14-22\Ms$. We also show that a similar approach can be used to find Milky Way GCs potentially hosting an intermediate-mass black hole., Comment: 14 pages, 12 figures, resubmitted to MNRAS after requested revision

The first neutron star-neutron star (NS-NS) merger was discovered on August 17, 2017 through gravitational waves (GW170817) and followed with electromagnetic observations. This merger was detected in an old elliptical galaxy with no recent star formation. We perform a suite of numerical calculations to understand the formation mechanism of this merger. We probe three leading formation mechanisms of double compact objects: classical isolated binary star evolution, dynamical evolution in globular clusters and nuclear cluster formation to test whether they are likely to produce NS-NS mergers in old host galaxies. Our simulations with optimistic assumptions show current NS-NS merger rates at the level of 10^-2 yr^-1 from binary stars, 5 x 10^-5 yr^-1 from globular clusters and 10^-5 yr^-1 from nuclear clusters for all local elliptical galaxies (within 100 Mpc^3). These models are thus in tension with the detection of GW170817 with an observed rate 1.5 yr^-1 (per 100 Mpc^3; LIGO/Virgo estimate). Our results imply that either (i) the detection of GW170817 by LIGO/Virgo at their current sensitivity in an elliptical galaxy is a statistical coincidence; or that (ii) physics in at least one of our three models is incomplete in the context of the evolution of stars that can form NS-NS mergers; or that (iii) another very efficient (unknown) formation channel with a long delay time between star formation and merger is at play., A&A: accepted

Recently, observational data and high precision mapping of the local velocity field of Local Group and Virgo cluster have revealed a linear velocity-distance relation of the outermost galaxies, properly referred to as Local Hubble Flow. By means of direct N-body method, we performed several simulations in which a galaxy cluster undergoes the action of the Dark Energy force and of the gravitational one induced by the gas. We reproduced the so-called Hubble diagrams, to highlight the outflow of the galaxies lying in the external region of the cluster. Our preliminary results suggest that the observed outflow of galaxies is likely due to the local effect of Dark Energy. Furthermore, the accuracy of the N-body method used, allows us to follow the merging process among some galaxies with the aim to reproduce the formation of a single compact object in the centre of the cluster., 6 pages, 3 figures, to be published in the proceeding of the 14th Marcel Grossmann meeting

We investigated the evolution of a massive galactic nucleus hosting a super-massive black hole (SMBH) with mass $M_\mathrm{SMBH}=10^8 \mathrm{M}_\odot$ surrounded by a population of 42 heavy star clusters (GCs). Using direct $N$-body modelling, we show here that the assembly of an NSC through GCs orbital decay and merger is efficiently inhibited by the tidal forces exerted from the SMBH. The GCs mass loss induced by tidal forces causes a significant modification of their mass function, leading to a population of low-mass ($, 15 pages, 10 figures, 4 tables. Accepted for publication in MNRAS

We investigate the evolution of intermediate-mass (IMBHs), stellar (BHs) and binary black holes (BHBs), deposited near a supermassive black hole (SMBH) by a population of massive star clusters. Stellar BHs rapidly segregate around the SMBH, driving the formation of extreme mass-ratio inspirals that coalesce at a rate $\Gamma= 0.02-0.2$ yr$^{-1}$ Gpc$^{-3}$ at redshift $z=0$. A few IMBHs orbiting the SMBH favour the formation of massive pairs that coalescence within a Hubble time, being the merger rate for this channel $\Gamma =0.03$ yr$^{-1}$ Gpc$^{-3}$. Recoiling kicks post-merger can eject the remnant from the galaxy centre, especially in dwarf galaxies. Our results suggest that this mechanism can lead to up to $10^5$ ejected SMBH within 1 Gpc. An IMBH co-existing with a few single and binary BHs in the same cluster can affect significantly their evolution, either driving binary disruption, yielding to intermediate-mass ratio inspirals (merger rate $\Gamma =9.5$ yr$^{-1}$ Gpc$^{-3}$), or boosting BHBs coalescence ($\Gamma =2-8$ yr$^{-1}$ Gpc$^{-3}$). In a few simulations, the SMBH boosts BHBs coalescence, leading this process to a merger rate $\Gamma =1$ yr$^{-1}$ Gpc$^{-3}$. We note that BHBs experiencing a merger in a galactic nucleus can be erroneously estimated $\sim 30\%$ heavier than it really is because of the Doppler shift of the wave frequency as caused by the rapid motion around the SMBH. All our simulations are carried out using an $N$-body code tailored to treat close encounters and post-Newtonian dynamics, that includes also the galaxy field and dynamical friction in the particles' equation of motion., Comment: 23 pages, 13 Figures, 5 tables. Accepted for publication in MNRAS. This version matches the accepted one

During their evolution, star clusters undergo mass segregation, by which the orbits of the most massive stars shrink, while the lighter stars move outwards from the cluster centre. In this context, recent observations and dynamical modelling of several galactic and extra-galactic globular clusters (GCs) suggest that most of them show, close to their centre, an overabundance of mass whose nature is still matter of debate. For instance, many works show that orbitally segregated stars may collide with each other in a runaway fashion, leading to the formation of a very massive star or an intermediate mass black hole (IMBH) with a mass comparable to the observed mass excess. On the other hand, segregated stars can form a dense system if the IMBH formation fails. In this paper we study the early formation phase of a dense, massive sub-system (MSS) in several GCs models using a recently developed semi-analytical treatment of the mass segregation process. In order to investigate how the MSS properties depend on the host cluster properties, we varied initial mass function (IMF), total mass, spatial distribution and metallicity of our models. Our results show how the IMF contributes to determine the final mass of the MSS, while the metallicity and the spatial distribution play a minor role. The method presented in this paper allowed us to provide scaling relations that connect the MSS mass and the host cluster mass in agreement with the observed correlation. In order to follow the early formation stage of the MSSs and improve our statistical results, we performed several $N$-body simulations of stellar clusters with masses between $10^3$ and $2\times 10^5$ solar masses., Comment: 17 pages, 13 figures, 6 tables

We present results of a set of $N$-body simulations to model the future evolution of the 11 young massive clusters hosted in the central region of the dwarf starburst galaxy Henize 2-10, which contains at its center a massive black hole with a mass $M_{\rm BH} \simeq 2\times 10^6$ M$_\odot$. Nuclear star clusters are present in a great quantity of galaxies of mass similar to Henize 2-10. Our results \citep{ASCD15} show that the orbital decay and merging of the Henize 2-10 clusters will likely lead to the formation of a nuclear star cluster with mass $M_{\rm NSC} \simeq 4-6 \times 10^6$ M$_\odot$ and effective radius $r_{\rm NSC} \simeq 4.1$ pc. Additionally, we found that this mechanism can lead to the formation of disky structures with global properties similar to those of nuclear stellar disks, which reside in many "middle-weight" galaxies. This work confirms and enlarge recent results \citep{ASCDS15} that indicate how nuclear star clusters and super massive black holes are only partially correlated, since the formation process of nuclear star clusters is poorly affected by a black hole of the size of that in Henize 2-10. A new result is that nuclear star clusters and nuclear stellar disks may share the same formation path., Comment: 6 pages, 2 figures, 1 table, to be published in the proceedings of the 14th Marcel Grossmann meeting

One of the leading scenarios for the formation of nuclear star clusters in galaxies is related to the orbital decay of globular clusters (GCs) and their subsequent merging, though alternative theories are currently debated. The availability of high-quality data for GCs structural and orbital parameters allow to test different nuclear star cluster formation scenarios. The Fornax dwarf spheroidal (dSph) galaxy is the heaviest satellite of the Milky Way and it is the only known dwarf spheroidal hosting 5 GCs, whereas there are no clear signatures for the presence of a central massive black hole. For this reason, it represents a suited place to study the orbital decay process in dwarf galaxies. In this paper we model the future evolution of the Fornax GCs simulating them and the host galaxy by means of direct $N$-body simulations. Our simulations take in account also the gravitational field generated by the Milky Way. We found that if the Fornax galaxy is embedded in a standard Cold Dark Matter Halo, the nuclear cluster formation would be significantly hampered by the high central galactic mass density. In this context, we discuss the possibility that infalling GCs drive the flattening of the galactic density profile, giving a possible alternative explanation to the so-called cusp/core problem. Moreover, we briefly discuss the link between GC infall process and the absence of massive black holes in the centre of dSphs., Comment: 12 pages, 14 figures, 4 tables, in press in the MNRAS

The Fornax dwarf spheroidal galaxy is the most massive satellites of the Milky Way, claimed to be embedded in a huge dark matter halo, and the only among the Milky Way satellites hosting five globular clusters. Interestingly, their estimated masses, ages and positions seem hardly compatible with the presence of a significant dark matter component, as expected in the $\Lambda$ CDM scheme. Indeed, if Fornax would have a CDM halo with a standard density profile, all its globular clusters should have sunk to the galactic centre many Gyr ago due to dynamical friction. Due to this, some authors proposed that the most massive clusters may have formed out of Fornax and later tidally captured. In this paper we investigate the past evolution of the Fornax GC system by using both a recently developed, semi-analytical treatment of dynamical friction and direct $N$-body simulations of the orbital evolution of the globular clusters within Fornax and of Fornax galaxy around the Milky Way. Our results suggest that an "in-situ" origin for all the clusters is likely if their observed positions are close to their spatial ones and their orbits are almost circular. Moreover, the Milky Way seems to accelerate the GC decay reducing the decay time of $15\%$. Nevertheless, our results indicate that the GCs survival probability exceeds $50\%$, even in the case of cuspy density profiles. We conclude that more detailed data are required to shed light on the Fornax dark matter content, to distinguish between a cuspy or a cored profile., Comment: 9 pages, 8 tables, 5 figures in Monthly Notices of the Royal Astronomical Society 2016

Almost all galaxies along the Hubble sequence host a compact massive object (CMO) in their center. The CMO can be either a supermassive black hole (SMBH) or a very dense stellar cluster, also known as nuclear star cluster (NSC). Generally, heavier galaxies (mass $\gtrsim 10^{11}\mathrm{M}_{\odot}$ ) host a central SMBH while lighter show a central NSC. Intermediate mass hosts, instead, contain both a NSC and a SMBH. One possible formation mechanisms of a NSC relies on the dry-merger (migratory) scenario, in which globular clusters (GCs) decay toward the center of the host galaxy and merge. In this framework, the absence of NSCs in high-mass galaxies can be imputed to destruction of the infalling GCs by the intense tidal field of the central SMBH. In this work, we report preliminary results of N-body simulations performed using our high-resolution, direct, code HiGPUs, to investigate the effects of a central SMBH on a single GC orbiting around it. By varying either the mass of the SMBH and the mass of the host galaxy, we derived an upper limit to the mass of the central SMBH, and thus to the mass of the host, above which the formation of a NSC is suppressed., 4 pages, 1 figure, 1 table. To be published in the Proceedings IAU Symposium No. 312, Star Clusters and Black Holes in Galaxies and Across Cosmic Time

The central region of the galaxy Henize 2-10 has a central black hole (BH) with a mass of about $2\times 10^6$ M$_\odot$. While this black hole does not appear to coincide with any central stellar over density, it is surrounded by 11 young massive clusters with masses above $10^5$ M$_\odot$. The availability of high quality data on the structure of the galaxy and the age and mass of the clusters provides excellent initial conditions for studying the dynamical evolution of Henize 2-10's nucleus. Here we present a set of $N$-body simulations of the central clusters and black hole to understand whether and how they will merge to form a nuclear star cluster. Nuclear star clusters (NSCs) are present in a majority of galaxies with stellar mass similar to Henize 2-10. Despite the results depend on the choice of initial conditions, we find that a NSC with mass $M_{NSC}\simeq 4-6\times 10^6$ M$_\odot$ and effective radius $r_{NSC}\simeq 2.6-4.1$ pc will form within $0.2$ Gyr. This work is the first showing, in a realistic realization of the host galaxy and its star cluster system, that the formation of a bright nucleus is a process that can happen after the formation of a central massive BH leading to a composite NSC+BH central system. The merging process of the clusters does not affect significantly the kinematics of the BH, whose motion, after the globular cluster merger, is limited to a $\sim 1$ pc oscillation at less than $2$ kms$^{-1}$ speed., 14 pages, 17 figures, 5 tables. Accepted for publication in the Astrophysical Journal

Nuclear Star Clusters (NSCs) are often present in spiral galaxies as well as resolved Stellar Nuclei (SNi) in elliptical galaxies centres. Ever growing observational data indicate the existence of correlations between the properties of these very dense central star aggregates and those of host galaxies, which constitute a significant constraint for the validity of theoretical models of their origin and formation. In the framework of the well known 'migratory and merger' model for NSC and SN formation, in this paper we obtain, first, by a simple argument the expected scaling of the NSC/SN mass with both time and parent galaxy velocity dispersion in the case of dynamical friction as dominant effect on the globular cluster system evolution. This generalizes previous results by \cite{TrOsSp} and is in good agreement with available observational data showing a shallow correlation between NSC/SN mass and galactic bulge velocity dispersion. Moreover, we give statistical relevance to predictions of this formation model, obtaining a set of parameters to correlate with the galactic host parameters. We find that the correlations between the masses of NSCs in the migratory model and the global properties of the hosts reproduce quite well the observed correlations, supporting the validity of the migratory-merger model. In particular, one important result is the flattening or even decrease of the value of the NSC/SN mass obtained by the merger model as function of the galaxy mass for high values of the galactic mass, i.e. $\gtrsim 3\times 10^{11}$M$_\odot$, in agreement with some growing observational evidence., Comment: 19 pages, 20 figures, submitted to MNRAS

The Milky Way centre exhibits an intense flux in the gamma and X-ray bands, whose origin is partly ascribed to the possible presence of a large population of millisecond pulsars (MSPs) and cataclysmic variables (CVs), respectively. However, the number of sources required to generate such an excess is much larger than what is expected from in situ star formation and evolution, opening a series of questions about the formation history of the Galactic nucleus. In this paper we make use of direct $N$-body simulations to investigate whether these sources could have been brought to the Galactic centre by a population of star clusters that underwent orbital decay and formed the Galactic nuclear star cluster (NSC). Our results suggest that the gamma ray emission is compatible with a population of MSPs that were mass segregated in their parent clusters, while the X-ray emission is consistent with a population of CVs born via dynamical interactions in dense star clusters. Combining observations with our modelling, we explore how the observed $\gamma$ ray flux can be related to different NSC formation scenarios. Finally, we show that the high-energy emission coming from the galactic central regions can be used to detect black holes heavier than $10^5\Ms$ in nearby dwarf galaxies., Comment: 19 pages, 14 figures and 7 tables. Accepted for publication to MNRAS

The grand challenges of contemporary fundamental physics-dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem-all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'., SCOPUS: re.j, info:eu-repo/semantics/published