Laser Interferometer Space Antenna double black holes: dynamics in gaseous nuclear discs

We study the inspiral of double black holes, with masses in the Laser Interferometer Space Antenna ( LISA ) window of detectability, orbiting inside a massive circumnuclear, rotationally supported gaseous disc. Using high-resolution smoothed particle hydrodynamics simulations, we follow the black hole dynamics in the early phase when gas-dynamical friction acts on the black holes individually, and continue our simulation until they form a close binary. We find that in the early sinking the black holes lose memory of their initial orbital eccentricity if they corotate with the gaseous disc. As a consequence, the massive black holes bind forming a binary with a low eccentricity, consistent with zero within our numerical resolution limit. The cause of circularization resides in the rotation present in the gaseous background where dynamical friction operates. Circularization may hinder gravitational waves from taking over and leading the binary to coalescence. In the case of counter-rotating orbits, the initial eccentricity (if present) does not decrease, and the black holes may bind forming an eccentric binary. When dynamical friction has subsided, for equal mass black holes and regardless their initial eccentricity, angular momentum loss, driven by the gravitational torque exerted on the binary by surrounding gas, is nevertheless observable down to the smallest scale probed (≃1 pc). In the case of unequal masses, dynamical friction remains efficient down to our resolution limit, and there is no sign of formation of any ellipsoidal gas distribution that may further harden the binary. During inspiral, gravitational capture of gas by the black holes occurs mainly along circular orbits; eccentric orbits imply high relative velocities and weak gravitational focusing. Thus, the active galactic nucleus activity may be excited during the black hole pairing process and double active nuclei may form when circularization is completed, on distance scales of tens of parsecs.     

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.     

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.     

Gravitational waves from scattering of stellar-mass black holes in galactic nuclei

Stellar-mass black holes (BHs) are expected to segregate and form a steep density cusp around supermassive black holes (SMBHs) in galactic nuclei. We follow the evolution of a multimass system of BHs and stars by numerically integrating the Fokker–Planck energy diffusion equations for a variety of BH mass distributions. We find that the BHs 'self-segregate', and that the rarest, most massive BHs dominate the scattering rate closest to the SMBH  (≲10⁻¹ pc)  . BH–BH binaries form out of gravitational wave emission during BH encounters. We find that the expected rate of BH coalescence events detectable by Advanced LIGO is  ∼1–10² yr⁻¹  , depending on the initial mass function of stars in galactic nuclei and the mass of the most massive BHs. We find that the actual merger rate is likely ∼10 times larger than this due to the intrinsic scatter of stellar densities in many different galaxies. The BH binaries that form this way in galactic nuclei have significant eccentricities as they enter the LIGO band (90 per cent with   e > 0.9  ), and are therefore distinguishable from other binaries, which circularize before becoming detectable. We also show that eccentric mergers can be detected to larger distances and greater BH masses than circular mergers, up to  ∼700 M_⊙  . Future ground-based gravitational wave observatories will be able to constrain both the mass function of BHs and stars in galactic nuclei.     

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.     

The distribution of supermassive black holes in the nuclei of nearby galaxies

The growth of supermassive black holes by merging and accretion in hierarchical models of galaxy formation is studied by means of Monte Carlo simulations. A tight linear relation between masses of black holes and masses of bulges arises if the mass accreted by supermassive black holes scales linearly with the mass-forming stars and if the redshift evolution of mass accretion tracks closely that of star formation. Differences in redshift evolution between black hole accretion and star formation introduce a considerable scatter in this relation. A non-linear relation between black hole accretion and star formation results in a non-linear relation between masses of remnant black holes and masses of bulges. The relation of black hole mass to bulge luminosity observed in nearby galaxies and its scatter are reproduced reasonably well by models in which black hole accretion and star formation are linearly related but do not track each other in redshift. This suggests that a common mechanism determines the efficiency for black hole accretion and the efficiency for star formation, especially for bright bulges.     

High-redshift galaxies, their active nuclei and central black holes

We demonstrate that the luminosity function of the recently detected population of actively star-forming galaxies at redshift z  = 3 and the B -band luminosity function of quasi-stellar objects (QSOs) at the same redshift can both be matched with the mass function of dark matter haloes predicted by standard variants of hierarchical cosmogonies for lifetimes of optically bright QSOs anywhere in the range 10⁶ to 10⁸ yr. There is a strong correlation between the lifetime and the required degree of non-linearity in the relation between black hole and halo mass. We suggest that the mass of supermassive black holes may be limited by the back-reaction of the emitted energy on the accretion flow in a self-gravitating disc. This would imply a relation of black hole to halo mass of the form M _bh ∝  v ⁵_halo ∝  M ^5/3_halo and a typical duration of the optically bright QSO phase of a few times 10⁷ yr. The high integrated mass density of black holes inferred from recent black hole mass estimates in nearby galaxies may indicate that the overall efficiency of supermassive black holes for producing blue light is smaller than previously assumed. We discuss three possible accretion modes with low optical emission efficiency: (i) accretion at far above the Eddington rate, (ii) accretion obscured by dust, and (iii) accretion below the critical rate leading to an advection-dominated accretion flow lasting for a Hubble time. We further argue that accretion with low optical efficiency might be closely related to the origin of the hard X-ray background and that the ionizing background might be progressively dominated by stars rather than QSOs at higher redshift.     

Untangling the merger history of massive black holes with LISA

Binary black hole coalescences emit gravitational waves that will be measurable by the space-based detector LISA to large redshifts. This suggests that LISA may be able to observe black holes grow and evolve as the Universe evolves, mapping the distribution of black hole masses as a function of redshift. An immediate difficulty with this idea is that LISA measures certain redshifted combinations of masses with good accuracy: if a system has some mass parameter m , then LISA measures  (1+ z ) m   . This mass–redshift degeneracy makes it difficult to follow the mass evolution. In many cases, LISA will also measure the luminosity distance D of a coalescence accurately. Since cosmological parameters (particularly the mean density, the cosmological constant and the Hubble constant) are now known with moderate precision, we can obtain z from D and break the degeneracy. This makes it possible to untangle the mass and redshift and to study the mass and merger history of black holes. Mapping the black hole mass distribution could open a window on to an early epoch of structure formation.     

Can gas dynamics in centres of galaxies reveal orbiting massive black holes?

If supermassive black holes in centres of galaxies form by merging of black hole remnants of massive Population III stars, then there should be a few black holes of mass one or two orders of magnitude smaller than that of the central ones, orbiting around the centre of a typical galaxy. These black holes constitute a weak perturbation in the gravitational potential, which can generate wave phenomena in gas within a disc close to the centre of the galaxy. Here, we show that a single orbiting black hole generates a three-arm spiral pattern in the central gaseous disc. The density excess in the spiral arms in the disc reaches values of 3–12 per cent when the orbiting black hole is about 10 times less massive than the central black hole. Therefore, the observed density pattern in gas can be used as a signature in detecting the most massive orbiting black holes.     

Compact massive objects in Virgo galaxies: the black hole population

We investigate the distribution of massive black holes (MBHs) in the Virgo cluster. Observations suggest that active galactic nuclei activity is widespread in massive galaxies ( M _*≳ 10¹⁰ M_⊙), while at lower galaxy masses star clusters are more abundant, which might imply a limited presence of central black holes in these galaxy-mass regimes. We explore if this possible threshold in MBH hosting is linked to nature , nurture or a mixture of both. The nature scenario arises naturally in hierarchical cosmologies, as MBH formation mechanisms typically are efficient in biased systems, which would later evolve into massive galaxies. Nurture , in the guise of MBH ejections following MBH mergers, provides an additional mechanism that is more effective for low mass, satellite galaxies. The combination of inefficient formation, and lower retention of MBHs, leads to the natural explanation of the distribution of compact massive objects in Virgo galaxies. If MBHs arrive to the correlation with the host mass and velocity dispersion during merger-triggered accretion episodes, sustained tidal stripping of the host galaxies creates a population of MBHs which lie above the expected scaling between the holes and their host mass, suggesting a possible environmental dependence.     

Quasi-stars: accreting black holes inside massive envelopes

We study the structure and evolution of 'quasi-stars', accreting black holes embedded within massive hydrostatic gaseous envelopes. These configurations may model the early growth of supermassive black hole seeds. The accretion rate on to the black hole adjusts so that the luminosity carried by the convective envelope equals the Eddington limit for the total mass,   M _*+ M _BH≈ M _*  . This greatly exceeds the Eddington limit for the black hole mass alone, leading to rapid growth of the black hole. We use analytic models and numerical stellar structure calculations to study the structure and evolution of quasi-stars. We show that the photospheric temperature of the envelope scales as   T _ph∝ M ^−2/5_BH M ^7/20_*  , and decreases with time while the black hole mass increases. Once   T _ph < 10⁴ K  , the photospheric opacity drops precipitously and T _ph hits a limiting value, analogous to the Hayashi track for red giants and protostars, below which no hydrostatic solution for the convective envelope exists. For metal-free (Population III) opacities, this limiting temperature is approximately 4000 K. After a quasi-star reaches this limiting temperature, it is rapidly dispersed by radiation pressure. We find that black hole seeds with masses between 10³ and  10⁴ M_⊙  could form via this mechanism in less than a few Myr.     

Dual black holes in merger remnants – I. Linking accretion to dynamics

We study the orbital evolution and accretion history of massive black hole (MBH) pairs in rotationally supported circumnuclear discs up to the point where MBHs form binary systems. Our simulations have high resolution in mass and space which, for the first time, makes it feasible to follow the orbital decay of a MBH either counter- or corotating with respect to the circumnuclear disc. We show that a moving MBH on an initially counter-rotating orbit experiences an 'orbital angular momentum flip' due to the gas-dynamical friction, i.e. it starts to corotate with the disc before a MBH binary forms. We stress that this effect can only be captured in very high resolution simulations. Given the extremely large number of gas particles used, the dynamical range is sufficiently large to resolve the Bondi–Hoyle–Lyttleton radii of individual MBHs. As a consequence, we are able to link the accretion processes to the orbital evolution of the MBH pairs. We predict that the accretion rate is significantly suppressed and extremely variable when the MBH is moving on a retrograde orbit. It is only after the orbital angular momentum flip has taken place that the secondary rapidly 'lights up' at which point both MBHs can accrete near the Eddington rate for a few Myr. The separation of the double nucleus is expected to be around ≲10 pc at this stage. We show that the accretion rate can be highly variable also when the MBH is corotating with the disc (albeit to a lesser extent) provided that its orbit is eccentric. Our results have significant consequences for the expected number of observable double active galactic nuclei at separations of ≲100 pc.     

Computation of mass outflow rate from relativistic quasi-spherical accretion on to black holes

We compute the mass outflow rate R _m˙ from relativistic matter that is accreting quasi-spherically on to the Schwarzschild black holes. Taking the pair-plasma pressure-mediated shock surface as the effective boundary layer (of the black hole) from where the bulk of the outflow is assumed to be generated, computation of this rate is done using combinations of exact transonic inflow and outflow solutions. We find that R _m˙ depends on the initial parameters of the flow, the polytropic index of matter, the degree of compression of matter near the shock surface and the location of the shock surface itself. We thus not only study the variation of the mass outflow rate as a function of various physical parameters governing the problem, but also provide a sufficiently plausible estimation of this rate.