The imprint of massive black hole formation models on the LISA data stream

The formation, merging and accretion history of massive black holes (MBHs) along the hierarchical build-up of cosmic structures leaves a unique imprint on the background of gravitational waves (GWs) at mHz frequencies. We study here, by means of dedicated simulations of black hole build-up, the possibility of constraining different models of black hole cosmic evolution using future GW space-borne missions, such as LISA . We consider two main scenarios for black hole formation, namely, one where seeds are light (  ≃10² M_⊙  , remnant of Population III stars) and one where seeds are heavy (  ≳10⁴ M_⊙  , direct collapse). In all the models we have investigated, MBH binary coalescences do not produce a stochastic GW background, but rather, a set of individual resolved events. Detection of several hundreds merging events in a 3-yr LISA mission will be the sign of a heavy seed scenario with efficient formation of black hole seeds in a large fraction of high-redshift haloes. At the other extreme, a low event rate, about a few tens in 3 yr, is peculiar of scenarios where either the seeds are light, and many coalescences do not fall into the LISA band, or seeds are massive, but rare. In this case a decisive diagnostic is provided by the shape of the mass distribution of detected events. Light binaries  ( m < 10⁴ M_⊙)  are predicted in a fairly large number in Population III remnant models, but are totally absent in direct collapse models. Finally, a further, helpful diagnostic of black hole formation models lies in the distribution of the mass ratios in binary coalescences. While heavy seed models predict that most of the detected events involve equal-mass binaries, in the case of light seeds, mass ratios are equally distributed in the range 0.1–1.     

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.     

Gravitational waves from resolvable massive black hole binary systems and observations with Pulsar Timing Arrays

Massive black holes are key components of the assembly and evolution of cosmic structures, and a number of surveys are currently on going or planned to probe the demographics of these objects and to gain insight into the relevant physical processes. Pulsar Timing Arrays (PTAs) currently provide the only means to observe gravitational radiation from massive black hole binary systems with masses  ≳10⁷ M_⊙  . The whole cosmic population produces a stochastic background that could be detectable with upcoming PTAs. Sources sufficiently close and/or massive generate gravitational radiation that significantly exceeds the level of the background and could be individually resolved. We consider a wide range of massive black hole binary assembly scenarios, investigate the distribution of the main physical parameters of the sources, such as masses and redshift, and explore the consequences for PTAs observations. Depending on the specific massive black hole population model, we estimate that on average at least one resolvable source produces timing residuals in the range  ∼5–50 ns  . PTAs, and in particular the future Square Kilometre Array, can plausibly detect these unique systems, although the events are likely to be rare. These observations would naturally complement on the high-mass end of the massive black hole distribution function future surveys carried out by the Laser Interferometer Space Antenna .     

Gravitational wave background from Population III black hole formation

We study the generation of a stochastic gravitational wave (GW) background produced from a population of core-collapse supernovae, which form black holes in scenarios of structure formation. We obtain, for example, that the formation of a population (Population III) of black holes, in cold dark matter scenarios, could generate a stochastic GW background with a maximum amplitude of   h _BG≃10⁻²⁴  and corresponding closure energy density of  Ω_GW∼10⁻⁷  , in the frequency band   ν _obs≃30–470 Hz  (assuming a maximum efficiency of generation of GWs, namely,   ɛ _GWmax=7×10⁻⁴)  for stars forming at redshifts   z ≃30–10  . We show that it will be possible in the future to detect this isotropic GW background by correlating the signals of a pair of 'advanced' LIGO observatories (LIGO III) at a signal-to-noise ratio of ≃40. We discuss what astrophysical information could be obtained from a positive (or even a negative) detection of such a GW background generated in scenarios such as those studied here. One of them is the possibility of obtaining the initial and final redshifts of the emission period from the observed spectrum of GWs.     

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 gravitational wave background from star–massive black hole fly-bys

Stars on eccentric orbits around a massive black hole (MBH) emit bursts of gravitational waves (GWs) at periapse. Such events may be directly resolvable in the Galactic Centre. However, if the star does not spiral in, the emitted GWs are not resolvable for extragalactic MBHs, but constitute a source of background noise. We estimate the power spectrum of this extreme mass ratio burst background (EMBB) and compare it to the anticipated instrumental noise of the Laser Interferometer Space Antenna (LISA). To this end, we model the regions close to an MBH, accounting for mass segregation, and for processes that limit the presence of stars close to the MBH, such as GW inspiral and hydrodynamical collisions between stars. We find that the EMBB is dominated by GW bursts from stellar mass black holes, and the magnitude of the noise spectrum  ( fS _GW)^1/2  is at least a factor of ∼10 smaller than the instrumental noise. As an additional result of our analysis, we show that LISA is unlikely to detect relativistic bursts in the Galactic Centre.     

Gravitational wave emission from a companion black hole in the presence of an accretion disc around a super-massive Kerr black hole

Gravitational wave signal characteristics from a binary black hole system in which the companion moves through the accretion disc of the primary are studied. We chose the primary to be a super-massive  ( M = 10⁸ M_⊙)  Kerr black hole and the companion to be a massive black hole  ( M = 10⁵ M_⊙)  to clearly demonstrate the effects. We show that the drag exerted on the companion by the disc is sufficient to reduce the coalescence time of the binary. The drag is primarily due to the fact that the accretion disc on a black hole deviates from a Keplerian disc and becomes sub-Keplerian due to inner boundary condition on the black hole horizon. We consider two types of accretion rates on to the companion. The companion is deeply immersed inside the disc and it can accrete at the Bondi rate which depends on the instantaneous density of the disc. However, an accretion disc can also form around the smaller black hole and it can accrete at its Eddington rate. Thus, this case is also studied and the results are compared. We find that the effect of the disc will be significant in reducing the coalescence time and one needs to incorporate this while interpreting gravitational wave signals emitted from such a binary system.     

The evolution of massive black hole seeds

We investigate the evolution of high-redshift seed black hole masses at late times and their observational signatures. The massive black hole seeds studied here form at extremely high redshifts from the direct collapse of pre-galactic gas discs. Populating dark matter haloes with seeds formed in this way, we follow the mass assembly of these black holes to the present time using a Monte Carlo merger tree. Using this machinery, we predict the black hole mass function at high redshifts and at the present time, the integrated mass density of black holes and the luminosity function of accreting black holes as a function of redshift. These predictions are made for a set of three seed models with varying black hole formation efficiency. Given the accuracy of present observational constraints, all three models can be adequately fitted. Discrimination between the models appears predominantly at the low-mass end of the present-day black hole mass function which is not observationally well constrained. However, all our models predict that low surface brightness, bulgeless galaxies with large discs are least likely to be sites for the formation of massive seed black holes at high redshifts. The efficiency of seed formation at high redshifts has a direct influence on the black hole occupation fraction in galaxies at   z = 0  . This effect is more pronounced for low-mass galaxies. This is the key discriminant between the models studied here and the Population III remnant seed model. We find that there exist a population of low-mass galaxies that do not host nuclear black holes. Our prediction of the shape of the M _BH–σ relation at the low-mass end is in agreement with the recent observational determination from the census of low-mass galaxies in the Virgo cluster.     

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.     

Optical Gravitational Lensing Experiment OGLE-1999-BUL-32: the longest ever microlensing event – evidence for a stellar mass black hole?

We describe the discovery of the longest microlensing event ever observed, OGLE-1999-BUL-32, also independently identified by the MACHO collaboration as MACHO-99-BLG-22. This unique event has an Einstein radius crossing time of 640 d. The high-quality data obtained with difference image analysis shows a small but significant parallax signature. This parallax effect allows one to determine the Einstein radius projected on to the observer plane as     . The transverse velocity projected on to the observer plane is about 79 km s⁻¹. We argue that the lens is likely to have a mass of at least a few solar masses, i.e. it could be a stellar black hole. The black hole hypothesis can be tested using the astrometric microlensing signature with the soon-to-be installed Advanced Camera for Surveys on board the Hubble Space Telescope . Deep X-ray and radio images may also be useful for revealing the nature of the object.     

Formation of intermediate-mass black holes as primordial black holes in the inflationary cosmology with running spectral index

Formation of primordial black holes (PBHs) on astrophysical mass scales is a natural consequence of inflationary cosmology, if the primordial perturbation spectrum has a large and negative running of the spectral index as observationally suggested today because double inflation is required to explain it and fluctuations on some astrophysical scales are enhanced in the field-oscillation regime in between. It is argued that PBHs thus produced can serve as intermediate-mass black holes (IMBHs), which act as the observed ultraluminous X-ray sources (ULXs) by choosing appropriate values of the model parameters in their natural ranges. Our scenario can be observationally tested in near future because the mass of PBHs is uniquely determined once we specify the values of the amplitude of the curvature perturbation, spectral index and its running on large scales.