10.1 Binaries in star clusters
X-ray sources are good tracers of compact binaries, especially low mass X-ray binaries (LMXBs), that are systems in which a compact object, i.e., a white dwarf (WD), a neutron star (NS) or a BH, accretes matter from a low-mass companion star. Accretion occurs through Roche-lobe overflow and disk formation around a compact object, or, in the case of red giants, wind-fed accretion partially captured by the compact object. NS binaries are mainly millisecond pulsars (MSPs), which form in dense clusters and are subsequently ejected as a consequence of tidal disruption and evaporation of the cluster (see e.g. Fragione et al.
2018). WD binaries (WD-WD or WD-MS stars) can be found in nearby GCs.
In particular, WD-MS binaries are known as cataclysmic variables (CVs). The optimal way to identify possible CVs in GCs is by combining different techniques, to measure their optical variability, blue colour, H
α excess, and X-ray emission (Knigge et al.
2011). Belloni et al. (
2016) analysed the population of CVs in a sample of 12 GCs evolved with MOCCA, by considering two initial binary populations. They found that a population of CVs is mainly found in later stages of the evolution of GCs, and that selection effects can drastically limit the number of observable CVs. They also found that the probability of observing CVs during the outburst is extremely small, and they concluded that the best way of detecting such objects is by searching for variabilities during the quiescent phase. In addition, magnetic fields might be needed to explain the rare frequency of outbursts amongst bright CVs (
\(\sim 10 \%\)).
10.2 Stellar-mass black holes
A relevant aspect of the dynamics of stellar-mass BHs in dense stellar environments is related to the retention of massive objects in star clusters. Indeed, the retention of BHs (and NSs) can have a strong influence on the global evolution of globular clusters (e.g., see Breen and Heggie
2013a; Contenta et al.
2015; Pavlík et al.
2018). Initial mass function and BH formation mechanisms (especially kicks) play a major role in determining the subsequent evolution of the BH population in a GC (Chatterjee
2016; Mandel and de Mink
2016), and a clear distinction is seen between the mass loss due to stellar evolution (connected with metallicity, Spera et al.
2016) and relaxation. BH subsystems can be formed and preserved in dense environments, provided the cluster has a sufficiently long relaxation time (Breen and Heggie
2013a,
2013b).
Massive binary black holes (BBHs) are preferentially formed in low-metallicity and dynamically active stellar environment (e.g., see Mapelli
2016). Recent works carried out with Monte Carlo simulations pointed out that more massive clusters are more likely to trigger BBH mergers (Rodriguez et al.
2016a,
2016b) although these events may also take place in stellar systems with a lower density (such as open clusters, see Sect.
11). The recent detections of gravitational waves from merging BBH have the potential to revolutionize our understanding of compact object astrophysics, but to fully utilize this new window into the universe, these observations must be compared to detailed theoretical models of BBH formation throughout cosmic time. Tanikawa (
2013) and, more recently, Fujii et al. (
2017) calculated the detection rates of gravitational waves emitted from merging BBHs in star clusters modelled as direct N-body systems. Hurley et al. (
2016) have also reported quantitative confirmation of the merging of two stellar-mass BHs in a binary system which was dynamically formed in a moderately-sized direct N-body model. Merger rates determined on the basis of Monte Carlo modelling approaches have also been intensively explored (e.g., see Rodriguez et al.
2016b; Askar et al.
2017; Hong et al.
2018). More details are discussed in Sect.
11.
Intermediate-mass black holes (IMBHs) are defined as covering a mass range of
\(10^{2}\text{--}10^{5}~\mathrm{M}_{\odot}\) and have become a promising field of research. With their existence it could be possible to explain the rapid growth of SMBHs, which are observed at high redshifts (Fan
2006), by assuming that IMBHs act as SMBH seeds (e.g., Ebisuzaki et al.
2001; Tanaka and Haiman
2009). Recent discoveries of black holes in the centres of dwarf galaxies (Reines and Volonteri
2015) have shown that the mass range between supermassive and stellar-mass black holes is by far not empty. However, whether or not IMBHs exist in ordinary GCs is still under debate.
Several formation scenarios have been proposed for these objects, but conclusive evidence on which one is preferred is still missing. Madau and Rees (
2001) proposed that IMBHs could be the remnants of Population III stars, obtained after an evolution of a few Myr. However, if this is indeed the route to build up IMBHs, we should not expect them to be found in clusters of Population I stars. Portegies Zwart et al. (
2004) suggested that an IMBH could be the end product of a runaway collision in the centre of star clusters. This process needs specific initial conditions, and requires the time scale of the mass segregation of the most massive stars to be shorter than the evolution time-scale for those stars, to avoid them to evolve before they start to collide. Recently, another scenario has been proposed, also indicating that these objects form in star clusters. Giersz et al. (
2015) proposed that an IMBH is formed as a consequence of the build-up of BH mass due to mergers in dynamical interactions and mass transfers in binaries; in spite of the ones described before, this scenario does not require the onset of particular initial conditions, but the process of IMBH formation is highly stochastic. A larger formation probability is obtained for clusters with larger concentration, and for earlier and faster BH mass build-up. A great effort has been devoted to numerical simulations, not only to test these formation scenarios, but also to understand which properties of the host system are mainly determining the presence and the mass of an IMBH in their centre.
Direct detection of an IMBH is extremely challenging because GCs are almost gas free. Radio observations (Strader et al.
2012) of the cores of three Galactic GCs (M15, M19 and M22) do not unveil any compact source: this non-detection sets the upper limit of the masses of IMBHs in these systems to
\(\sim 3\text{--}9 \times 10^{2}~\mathrm{M}_{\odot}\). Such a result has been recently confirmed by a more extensive radio continuum survey conducted on Galactic GCs (Tremou et al.
2018). These limits suggest that either IMBHs more massive than
\(10^{3}~\mathrm{M}_{\odot}\) are rare in GCs, or that if they are present, they accrete in a very inefficient manner. On the other hand, an X-ray outburst has been detected in a star cluster located off-center of a large lenticular galaxy; such an event has been interpreted as providing strong evidence that the source contains an IMBH of
\(10^{4}~\mathrm{M}_{\odot}\). Kains et al. (
2016) proposed a different method to look for IMBHs in GCs, by means of gravitational microlensing. From a suite of simulations, they estimate the probabilities of detecting such an event for Galactic GCs: as an example, they consider M22, and conclude that if it hosts an IMBH with mass
\(10^{5}~\mathrm{M}_{\odot}\), there is a probability of 86% of detecting an astrometric microlensing event over a baseline of 20 yr.
Nevertheless, even though direct detections of IMBHs are challenging, signatures of the presence of an IMBH are imprinted in the phase-space distribution of stars in its immediate surrounding (Bahcall and Wolf
1976). The effects of the presence of an IMBH on the structural and kinematic properties of the host star clusters have subsequently been explored in detail by means of direct N-body simulations (Baumgardt et al.
2004a,
2004b,
2005). In particular, two signatures are at the basis of the observational claims for the detection of IMBHs in Galactic GCs: the detection of a shallow cusp in the surface brightness profile (e.g., see Noyola et al.
2008) and the presence of a rise in the projected velocity dispersion profile towards the centre (e.g., see Anderson and van der Marel
2010; Lützgendorf et al.
2013b). However, these signatures can also be due to other processes: core collapse, mass segregation, or a population of binaries in the centre also produce a shallow cusp in the brightness profile, as shown with dedicated
N-body simulations (Vesperini and Trenti
2010), and the central rise in the velocity dispersion profile is also not unique (Zocchi et al.
2017,
2018). The controversial case of
ω Cen is an example of this degeneracy: isotropic spherical models only reproduce the observed rise in the projected velocity dispersion when a central IMBH of mass
\(\sim 4\times 10^{4}~\mathrm{M}_{\odot}\) is included (Noyola et al.
2008), while by comparing anisotropic models (with radial anisotropy in the core and tangential anisotropy in the outer parts) to proper motion measurements an upper limit to the IMBH mass of only
\(\sim 7 \times 10^{3}~\mathrm{M}_{\odot}\) is obtained (van der Marel and Anderson
2010).
This degeneracy in the signatures of the presence of an IMBH has also been explored by means of numerical simulations. Lützgendorf et al. (
2013a) presented a set of direct N-body simulations of GCs in an external tidal field, considering several values for IMBH masses, BHs retention fractions, and binary fractions. Their results show that the presence of an IMBH, or of a central population of binaries or stellar-mass BHs increases the escape rate of high-mass stars; these simulations show a good agreement with observational mass functions and structural parameters of GCs. A similar result has been found by Arca-Sedda (
2016), who proposed an analysis of numerical simulations showing that the excess of mass in the centre of a cluster could be due to the presence of a subsystem of heavy remnants orbitally segregated, instead of being due to an IMBH (see also Zocchi et al.
2018). Finally, the coexistence of an IMBH and of a population of stellar-mass BHs has been explored by Leigh et al. (
2014), by means of direct N-body simulations.
In addition, some controversy has recently arisen when comparing data obtained by means of integrated light spectroscopy to measurements of line-of-sight velocities of single stars (see for example the emblematic case of NGC 6388, Lützgendorf et al.
2011,
2015; Lanzoni et al.
2013). Studies of mock observations of numerical simulations of star clusters with and without a central IMBH have been carried out to determine the magnitude of this effect. Bianchini et al. (
2015) showed that luminosity-weighted IFU observations can be strongly biased by a few bright stars introducing a scatter in the measurement of the velocity dispersion up to ∼40% around the expected value: this prevents any sound assessment of the central kinematics, and does not allow for an interpretation of the data in terms of the presence of a central IMBH. de Vita et al. (
2017) estimated that in 20% of the cases the analysis of data did not allow for a statistically significant detection of IMBHs having mass equal to 3% of the mass of their host, because of shot noise due to bright stars close to the IMBH, and that when considering a smaller fractional mass for the IMBH (∼0.1) the rate of non-detections corresponds to 75% of the cases. The combination of data from new-generation facilities (such as Gaia proper motions and MUSE spectroscopic data of the central regions of clusters) will provide further constraints to the GC dynamics, allowing us to determine if IMBHs are hiding in the cores of GCs, and how massive they are.
Leaving the uncertainties and difficulties of detecting IMBHs in GCs aside, other systems have proven to host IMBHs at their centre. In the last decade, detections of AGN in nearby dwarf galaxies have provided great evidence of the existence of SMBHs in the lower mass regime (e.g. Baldassare et al.
2015; Reines et al.
2011; Filippenko and Ho
2003; Barth et al.
2004; den Brok et al.
2015). Inspired by those recent discoveries, researchers have branched out to search for BHs in smaller stellar systems such as ultra compact dwarf galaxies (Seth et al.
2014) and even our closest neighbour, the Large Magellanic Cloud (Boyce et al.
2017).
In addition, there have been recent suggestions of the presence of candidate IMBHs embedded in gas clouds in the region of our Galactic Centre, as based on emissions in the millimetre (Oka et al.
2016,
2017) and infra-red bands (Tsuboi et al.
2017). More generally in this context, a powerful diagnostic tool is offered by the phenomenology of tidal disruption events. Indeed, there have been recent reports of events that may involve IMBHs (Lin et al.
2018; Kuin et al.
2018), with fresh developments also on the theoretical side (e.g., see Rosswog et al.
2009; Tanikawa
2018; Anninos et al.
2018).
Over the next years, this spectrum of studies will greatly contribute in filling the lower mass range of the BH mass/host galaxy property relations and enhance our understanding of BH evolution and occupation fractions.