Is there an upper limit to black hole masses?

We make a case for the existence for ultra-massive black holes (UMBHs) in the Universe, but argue that there exists a likely upper limit to black hole (BH) masses of the order of   M ∼ 10¹⁰ M_⊙  . We show that there are three strong lines of argument that predicate the existence of UMBHs: (i) expected as a natural extension of the observed BH mass bulge luminosity relation, when extrapolated to the bulge luminosities of bright central galaxies in clusters; (ii) new predictions for the mass function of seed BHs at high redshifts predict that growth via accretion or merger-induced accretion inevitably leads to the existence of rare UMBHs at late times; (iii) the local mass function of BHs computed from the observed X-ray luminosity functions of active galactic nuclei predict the existence of a high-mass tail in the BH mass function at   z = 0  . Consistency between the optical and X-ray census of the local BH mass function requires an upper limit to BH masses. This consistent picture also predicts that the slope of the   M _bh–σ  relation will evolve with redshift at the high-mass end. Models of self-regulation that explain the co-evolution of the stellar component and nuclear BHs naturally provide such an upper limit. The combination of multiwavelength constraints predicts the existence of UMBHs and simultaneously provides an upper limit to their masses. The typical hosts for these local UMBHs are likely the bright, central cluster galaxies in the nearby Universe.     

Evolution of massive binary black holes

Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). In this paper we study the evolution of massive BBHs in realistic galaxy models, using a generalization of techniques used to study tidal disruption rates around massive BHs. The evolution of BBHs depends on BH mass ratio and host galaxy type. BBHs with very low mass ratios (say, ≲0.001) are hardly ever formed by mergers of galaxies, because the dynamical friction time-scale is too long for the smaller BH to sink into the galactic centre within a Hubble time. BBHs with moderate mass ratios are most likely to form and survive in spherical or nearly spherical galaxies and in high-luminosity or high-dispersion galaxies; they are most likely to have merged in low-dispersion galaxies (line-of-sight velocity dispersion ≲90 km s⁻¹) or in highly flattened or triaxial galaxies.
The semimajor axes and orbital periods of surviving BBHs are generally in the range  10^-3–10 pc  and  10–10⁵ yr;  they are also larger in high-dispersion galaxies than in low-dispersion galaxies, larger in nearly spherical galaxies than in highly flattened or triaxial galaxies, and larger for BBHs with equal masses than for BBHs with unequal masses. The orbital velocities of surviving BBHs are generally in the range  10²–10⁴ km s^-1  . The methods of detecting surviving BBHs are also discussed.
If no evidence of BBHs is found in AGNs, this may be either because gas plays a major role in BBH orbital decay or because nuclear activity switches on soon after a galaxy merger, and ends before the smaller BH has had time to spiral to the centre of the galaxy.     

Star clusters around recoiled black holes in the Milky Way halo

Gravitational wave emission by coalescing black holes (BHs) kicks the remnant BH with a typical velocity of hundreds of  km s⁻¹  . This velocity is sufficiently large to remove the remnant BH from a low-mass galaxy but is below the escape velocity from the Milky Way (MW) galaxy. If central BHs were common in the galactic building blocks that merged to make the MW, then numerous BHs that were kicked out of low-mass galaxies should be freely floating in the MW halo today. We use a large statistical sample of possible merger tree histories for the MW to estimate the expected number of recoiled BH remnants present in the MW halo today. We find that hundreds of BHs should remain bound to the MW halo after leaving their parent low-mass galaxies. Each BH carries a compact cluster of old stars that populated the core of its original host galaxy. Using the time-dependent Fokker–Planck equation, we find that the present-day clusters are  ≲1 pc  in size, and their central bright regions should be unresolved in most existing sky surveys. These compact systems are distinguishable from globular clusters by their internal (Keplerian) velocity dispersion greater than 100 km s⁻¹ and their high mass-to-light ratio owing to the central BH. An observational discovery of this relic population of star clusters in the MW halo would constrain the formation history of the MW and the dynamics of BH mergers in the early Universe. A similar population should exist around other galaxies and may potentially be detectable in M31 and M33.     

Stellar-mass black hole binaries as ultraluminous X-ray sources

Ultraluminous X-ray sources (ULXs) with   L _x > 10³⁹ erg s⁻¹  have been discovered in great numbers in external galaxies with ROSAT , Chandra and XMM-Newton . The central question regarding this important class of sources is whether they represent an extension in the luminosity function of binary X-ray sources containing neutron stars and stellar-mass black holes (BHs), or a new class of objects, e.g. systems containing intermediate-mass BHs  (100–1000 M_⊙)  . We have carried out a theoretical study to test whether a large fraction of the ULXs, especially those in galaxies with recent star formation activity, can be explained with binary systems containing stellar-mass BHs. To this end, we have applied a unique set of binary evolution models for BH X-ray binaries, coupled to a binary population synthesis code, to model the ULXs observed in external galaxies. We find that for donor stars with initial masses  ≳10 M_⊙  the mass transfer driven by the normal nuclear evolution of the donor star is sufficient to potentially power most ULXs. This is the case during core hydrogen burning and, to an even more pronounced degree, while the donor star ascends the giant branch, although the latter phases last only ∼5 per cent of the main-sequence phase. We show that with only a modest violation of the Eddington limit, e.g. a factor of ∼10, both the numbers and properties of the majority of the ULXs can be reproduced. One of our conclusions is that if stellar-mass BH binaries account for a significant fraction of ULXs in star-forming galaxies, then the rate of formation of such systems is  ∼3 × 10⁻⁷ yr⁻¹  normalized to a core-collapse supernova rate of 0.01 yr⁻¹.     

Rates of tidal disruption of stars by massive central black holes

There is strong evidence for some kind of massive dark object in the centres of many galaxy bulges. The detection of flares from tidally disrupted stars could confirm that these objects are black holes (BHs). Here we present calculations of the stellar disruption rates in detailed dynamical models of real galaxies, taking into account the refilling of the loss cone of stars on disruptable orbits by two-body relaxation and tidal forces in non-spherical galaxies. The highest disruption rates (one star per 10⁴ yr) occur in faint ( L ≲10¹⁰ L_⊙) galaxies, which have steep central density cusps. More luminous galaxies are less dense and have much longer relaxation times and more massive BHs. Dwarf stars in such galaxies are swallowed whole by the BH and hence do not emit flares; giant stars could produce flares as often as every 10⁵ yr, although the rate depends sensitively on the shape of the stellar distribution function. We discuss the possibility of detecting disruption flares in current supernova searches. The total mass of stars consumed over the lifetime of the galaxy is of the order of 10⁶ M_⊙, independent of galaxy luminosity; thus, disrupted stars may contribute significantly to the present BH mass in galaxies fainter than ∼10⁹ L_⊙.     

Dry mergers: a crucial test for galaxy formation

We investigate the role that dry mergers play in the build-up of massive galaxies within the cold dark matter paradigm. Implementing an empirical shut-off mass scale for star formation, we find a nearly constant dry merger rate of  ∼6 × 10⁻⁵ Mpc⁻³ Gyr⁻¹  at   z ≤ 1  and a steep decline at larger z . Less than half of these mergers are between two galaxies that are morphologically classified as early-types, and the other half is mostly between an early- and late-type galaxy. Latter are prime candidates for the origin of tidal features around red elliptical galaxies. The introduction of a transition mass scale for star formation has a strong impact on the evolution of galaxies, allowing them to grow above a characteristic mass scale of   M _{*, c} ∼ 6.3 × 10¹⁰ M_⊙  by mergers only. As a consequence of this transition, we find that around   M _{*, c}   , the fraction of 1:1 mergers is enhanced with respect to unequal mass major mergers. This suggests that it is possible to detect the existence of a transition mass scale by measuring the relative contribution of equal mass mergers to unequal mass mergers as a function of galaxy mass. The evolution of the high-mass end of the luminosity function is mainly driven by dry mergers at low z . We however find that only 10–20 per cent of galaxies more massive than   M _{*, c}   experience dry major mergers within their last Gyr at any given redshift   z ≤ 1  .     

The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power-law cusp. We show that the bulk of stars with a small angular-momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so-called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement.
Our results show that for a primary black hole mass of  ∼10⁶–10⁷ M_⊙  , the black hole mass-ratio   q > 10⁻²  , cusp size ∼1 pc, the tidal disruption rate can be as large as  ∼10⁻²–1 M_⊙ yr⁻¹  . This is at least 10²–10⁴ times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical-friction time-scale, and it is rather short: ∼10⁵ yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.     

The masses of black holes in the nuclei of spirals

We use the innermost kinematics of spirals to investigate whether these galaxies could host the massive black hole remnants that once powered the quasi-stellar object (QSO) phenomenon. Hundreds of rotation curves of early- and late-type spirals are used to place upper limits on the central black hole (BH) masses. We find that (i) in late-type spirals, the central massive dark objects (MDOs) are about 10–100 times smaller than the MDOs detected in ellipticals, and (ii) in early-type spirals, the central bodies are likely to be in the same mass range as the elliptical MDOs. As a consequence, the contribution to the QSO/active galactic nuclei (AGN) phenomenon by the BH remnants eventually hosted in spirals is negligible: ρ _BH(Sb–Im)<6×10⁴ M_⊙ Mpc⁻³ . We find several hints that the MDO mass versus bulge mass relationship is significantly steeper in spirals than in ellipticals, although the very issue of the existence of such a relation for late Hubble type objects remains open. The upper limits on the masses of the BHs resident in late-type spirals are stringent: M _BH10⁶–10⁷ M_⊙, indicating that only low-luminosity activity could possibly have occurred in these objects .     

Imprints of recoiling massive black holes on the hot gas of early-type galaxies

Anisotropic gravitational radiation from a coalescing black hole (BH) binary is known to impart recoil velocities of up to  ∼1000 km s⁻¹  to the remnant BH. In this context, we study the motion of a recoiling BH inside a galaxy modelled as a Hernquist sphere, and the signature that the hole imprints on the hot gas, using N -body/smoothed particle hydrodynamics simulations. Ejection of the BH results in a sudden expansion of the gas ending with the formation of a gaseous core, similarly to what is seen for the stars. A cometary tail of particles bound to the BH is initially released along its trail. As the BH moves on a return orbit, a nearly spherical swarm of hot gaseous particles forms at every apocentre: this feature can live up to ≈10⁸ years. If the recoil velocity exceeds the sound speed initially, the BH shocks the gas in the form of a Mach cone in density near each supersonic pericentric passage. We find that the X-ray fingerprint of a recoiling BH can be detected in Chandra X-ray maps out to a distance of Virgo. For exceptionally massive BHs, the Mach cone and the wakes can be observed out to a few hundred of milliparsec. The detection of the Mach cone is of twofold importance as it can be a probe of high-velocity recoils, and an assessment of the scatter of the   M _BH− M _bulge  relation at large BH masses.     

Unresolved emission and ionized gas in the bulge of M31

We study the origin of unresolved X-ray emission from the bulge of M31 based on archival Chandra and XMM–Newton observations. We demonstrate that three different components are present. (i) Broad-band emission from a large number of faint sources – mainly accreting white dwarfs and active binaries, associated with the old stellar population, similar to the Galactic ridge X-ray emission of the Milky Way. The X-ray to K -band luminosity ratios are compatible with those for the Milky Way and for M32; in the 2–10 keV band, the ratio is  (3.6 ± 0.2) × 10²⁷ erg s⁻¹ L⁻¹_⊙  . (ii) Soft emission from ionized gas with a temperature of about ∼300 eV and a mass of  ∼2 × 10⁶ M_⊙  . The gas distribution is significantly extended along the minor axis of the galaxy, suggesting that it may be outflowing in the direction perpendicular to the galactic disc. The mass and energy supply from evolved stars and Type Ia supernovae is sufficient to sustain the outflow. We also detect a shadow cast on the gas emission by spiral arms and the 10-kpc star-forming ring, confirming significant extent of the gas in the 'vertical' direction. (iii) Hard extended emission from spiral arms, most likely associated with young stellar objects and young stars located in the star-forming regions. The   L _X/SFR  (star formation rate) ratio equals  ∼9 × 10³⁸ (erg s⁻¹)(M_⊙ yr⁻¹)⁻¹  , which is about ∼1/3 of the high-mass X-ray binary contribution, determined earlier from Chandra observations of other nearby galaxies.     

Merging of a massive binary due to ejection of bound stars – II

In this paper, the second in a series of two, we justify two important assumptions on which the result is based that in the course of a galaxy merger, the slingshot ejection of bound stars is sufficiently efficient to allow a supermassive black hole binary (BHB) to merge. A steep cusp with a power-law index of 2.5–3 is required which is as massive as the binary and surrounds the BHs when the binary becomes hard. This cusp is probably formed when both clusters, surrounding each BH, merge and combine with the matter funnelled into the centre. We find this profile to be in agreement with observed post-merger distributions after the cusp has been destroyed. The time dependency we derive for the merger predicts that stalled BHs, if they exist at all, will preferentially be found at less than  ∼0.2 pc  distance. To test this prediction we compute the current semimajor axis of 12 candidates of ongoing mergers. We find all binaries unambiguously to be already in the last phase when they decay due to the emission of gravitational waves. Therefore, in striking contradiction with predictions of a depleted loss-cone, the absence of even a single source in the slingshot phase strongly supports our previous and current results: binaries merge due to the slingshot ejection of stars which have been funnelled into the central regions in the course of a galaxy collision.     

Explaining the energetic AGN outburst of MS 0735+7421 with massive slow jets

By conducting axisymmetrical hydrodynamical numerical simulations (2.5 dimensional code) we show that slow, massive, wide jets can reproduce the morphology of the huge X-ray deficient bubble pair in the cluster of galaxies MS 0735+7421. The total energy of the jets, composed of the energy in the bubble pair and in the shock wave, is constrained by observations conducted by McNamara et al. to be  ∼10⁶² erg  . We show that two opposite jets that are active for ∼100 Myr, each with a launching half opening angle of  α≃ 70°  , an initial velocity of   v _j∼ 0.1 c   and a total mass loss rate of the two jets of     , can account for the observed morphology. Rapidly precessing narrow jets can be used instead of wide jets. In our model the cluster suffered from a cooling catastrophe ∼100 Myr ago. Most of the mass that cooled,  ∼10¹⁰ M_⊙  , was expelled back to the intracluster medium by the active galactic nuclei activity and is inside the bubbles now, ∼10 per cent formed stars and ∼10 per cent of the cold gas was accreted by the central black hole and was the source of the outburst energy. This type of activity is similar to that expected to occur in galaxy formation.     

Galaxy cores as relics of black hole mergers

We investigate the hypothesis that the cores of elliptical galaxies and bulges are created from the binding energy liberated by the coalescence of supermassive binary black holes during galaxy mergers. Assuming that the central density profiles of galaxies were initially steep power laws,   ρ ∼ r ^-2  , we define the 'mass deficit' as the mass in stars that had to be removed from the nucleus in order to produce the observed core. We use non-parametric deprojection to compute the mass deficit in a sample of 35 early-type galaxies with high-resolution imaging data. We find that the mass deficit correlates well with the mass of the nuclear black hole, consistent with the predictions of merger models. We argue that cores in haloes of non-interacting dark matter particles should be comparable in size to those observed in the stars.     

Implications of primordial black holes on the first stars and the origin of the super-massive black holes

If the cosmological dark matter has a component made of small primordial black holes (BHs), they may have a significant impact on the physics of the first stars and on the subsequent formation of massive BHs. Primordial BHs would be adiabatically contracted into these stars and then would sink to the stellar centre by dynamical friction, creating a larger BH which may quickly swallow the whole star. If these primordial BHs are heavier than  ∼10²² g  , the first stars would likely live only for a very short time and would not contribute much to the reionization of the Universe. They would instead become  10–10³ M_⊙  BHs which (depending on subsequent accretion) could serve as seeds for the super-massive BHs seen at high redshifts as well as those inside galaxies today.     

Numerical simulations of hot halo gas in galaxy mergers

Galaxy merger simulations have explored the behaviour of gas within the galactic disc, yet the dynamics of hot gas within the galaxy halo have been neglected. We report on the results of high-resolution hydrodynamic simulations of colliding galaxies with metal-free hot halo gas. To isolate the effect of the halo gas, we simulate only the dark matter halo and the hot halo gas over a range of mass ratios, gas fractions and orbital configurations to constrain the shocks and gas dynamics within the progenitor haloes. We find that (i) a strong shock is produced in the galaxy haloes before the first passage, increasing the temperature of the gas by almost an order of magnitude to   T ∼ 10^6.3 K  . (ii) The X-ray luminosity of the shock is strongly dependent on the gas fraction; it is  ≳10³⁹ erg s⁻¹  for halo gas fractions larger than 10 per cent. (iii) The hot diffuse gas in the simulation produces X-ray luminosities as large as  10⁴² erg s⁻¹  . This contributes to the total X-ray background in the Universe. (iv) We find an analytic fit to the maximum X-ray luminosity of the shock as a function of merger parameters. This fit can be used in semi-analytic recipes of galaxy formation to estimate the total X-ray emission from shocks in merging galaxies. (v) ∼10–20 per cent of the initial gas mass is unbound from the galaxies for equal-mass mergers, while 3–5 per cent of the gas mass is released for the 3:1 and 10:1 mergers. This unbound gas ends up far from the galaxy and can be a feasible mechanism to enrich the intergalactic medium with metals.     

Vertical distribution of Galactic disc stars and gas constrained by a molecular cloud complex

We investigate the dynamical effects of a molecular cloud complex with a mass ∼ 10⁷ M_⊙ and a size ∼ a few 100 pc on the vertical distribution of stars and atomic hydrogen gas in a spiral galactic disc. Such massive complexes have now been observed in a number of spiral galaxies. The extended mass distribution in a complex, with an average mass density 6 times higher than the Oort limit, is shown to dominate the local gravitational field. This results in a significant redistribution or clustering of the surrounding disc components towards the mid-plane, with a resulting decrease in their vertical scaleheights.
The modified, self-consistent stellar density distribution is obtained by solving the combined Poisson equation and the force equation along the z -direction for an isothermal stellar disc on which the complex is imposed. The effect of the complex is strongest at its centre, where the stellar mid-plane density increases by a factor of 2.6 and the vertical scaleheight decreases by a factor of 3.4 compared with the undisturbed stellar disc. A surprising result is the large radial distance of ∼ 500 pc from the complex centre over which the complex influences the disc; this is due to the extended mass distribution in a complex. The complex has a comparable effect on the vertical distribution of the atomic hydrogen gas in the galactic disc. This 'pinching' or constraining effect should be detectable in the nearby spiral galaxies, as for example has been done for NGC 2403 by Sicking. Thus the gravitational field of a complex results in local corrugations of the stellar and H  i vertical scaleheights, and the galactic disc potential is highly non-uniform on scales of the intercomplex separation of ∼ 1 kpc.     

Active galactic nuclei jet mass loading and truncation by stellar winds

Active galactic nuclei can produce extremely powerful jets. While tightly collimated, the scale of these jets and the stellar density at galactic centres implies that there will be many jet/star interactions, which can mass load the jet through stellar winds. Previous work employed modest wind mass outflow rates, but this does not apply when mass loading is provided by a small number of high mass-loss stars. We construct a framework for jet mass loading by stellar winds for a broader spectrum of wind mass-loss rates than has previously been considered. Given the observed stellar mass distributions in galactic centres, we find that even highly efficient (0.1 Eddington luminosity) jets from supermassive black holes of masses M _BH≲ 10⁴ M_⊙ are rapidly mass loaded and quenched by stellar winds. For  10⁴ M_⊙ < M _BH < 10⁸ M_⊙  , the quenching length of highly efficient jets is independent of the jet's mechanical luminosity. Stellar wind mass loading is unable to quench efficient jets from more massive engines, but can account for the observed truncation of the inefficient M87 jet, and implies a baryon-dominated composition on scales ≳2 kpc therein even if the jet is initially pair plasma dominated.     

Quantifying the coexistence of massive black holes and dense nuclear star clusters

In large spheroidal stellar systems, such as elliptical galaxies, one invariably finds a  10⁶–10⁹ M_⊙  supermassive black hole at their centre. In contrast, within dwarf elliptical galaxies one predominantly observes a  10⁵–10⁷ M_⊙  nuclear star cluster. To date, few galaxies have been found with both types of nuclei coexisting and even less have had the masses determined for both central components. Here, we identify one dozen galaxies housing nuclear star clusters and supermassive black holes whose masses have been measured. This doubles the known number of such hermaphrodite nuclei – which are expected to be fruitful sources of gravitational radiation. Over the host spheroid (stellar) mass range  10⁸–10¹¹ M_⊙  , we find that a galaxy's nucleus-to-spheroid (baryon) mass ratio is not a constant value but decreases from a few per cent to ∼0.3 per cent such that  log[( M _BH+ M _NC)/ M _sph]=−(0.39 ± 0.07) log[ M _sph/10¹⁰ M_⊙]− (2.18 ± 0.07)  . Once dry merging commences and the nuclear star clusters disappear, this ratio is expected to become a constant value.
As a byproduct of our investigation, we have found that the projected flux from resolved nuclear star clusters is well approximated with Sérsic functions having a range of indices from ∼0.5 to ∼3, the latter index describing the Milky Way's nuclear star cluster.     

Supermassive Black Holes in Early-Type Galaxies: Relationship with Radio Emission and Constraints on the Black Hole Mass Function

Using recently published estimates — based on high spatial resolution spectroscopy — of the mass M _BH of nuclear black holes for a sample of nearby galaxies, we explore the dependence of galaxy nucleus emissivity at various wavelengths on M _BH. We confirm an almost linear scaling of the black hole mass with the baryonic mass of the host spheroidal galaxy. A remarkably tight relationship is also found with both nuclear and total radio centimetric flux, with a very steep dependence of the radio flux on M _BH ( P  ∝  M ^2.5_BH). The high-frequency radio power is thus a very good tracer of a supermassive black hole, and a good estimator of its mass. This, together with the lack of significant correlations with the low-energy X-ray and far-IR flux, supports the view that advection-dominated accretion is ruling the energy output in the low accretion rate regime. Using the tight dependence of total radio power on M _BH and the rich statistics of radio emission of galaxies, we derive an estimate of the mass function of remnants in the nearby Universe. This is compared with current models of quasar and active galactic nucleus (AGN) activity and of the origin of the hard X-ray background (HXRB). As for the former, continuous long-lived AGN activity is excluded by the present data with high significance, whereas the assumption of a short-lived, possibly recurrent, activity pattern gives remarkable agreement. The presently estimated black hole mass function also implies that the HXRB has been produced by a numerous population (∼ 10⁻² Mpc⁻³) of moderately massive ( M _BH ∼ 10⁷ M⊙) black holes.     

Collisions and close encounters involving massive main-sequence stars

We study close encounters involving massive main-sequence stars and the evolution of the exotic products of these encounters as common-envelope systems or possible hypernova progenitors. We show that parabolic encounters between low- and high-mass stars and between two high-mass stars with small periastrons result in mergers on time-scales of a few tens of stellar free-fall times (a few tens of hours). We show that such mergers of unevolved low-mass stars with evolved high-mass stars result in little mass-loss  (∼0.01 M_⊙)  and can deliver sufficient fresh hydrogen to the core of the collision product to allow the collision product to burn for several million years. We find that grazing encounters enter a common-envelope phase which may expel the envelope of the merger product. The deposition of energy in the envelopes of our merger products causes them to swell by factors of ∼100. If these remnants exist in very densely populated environments  ( n ≳ 10⁷ pc⁻³)  , they will suffer further collisions which may drive off their envelopes, leaving behind hard binaries. We show that the products of collisions have cores rotating sufficiently rapidly to make them candidate hypernova/gamma-ray burst progenitors and that ∼0.1 per cent of massive stars may suffer collisions, sufficient for such events to contribute significantly to the observed rates of hypernovae and gamma-ray bursts.