M. Coleman Miller
Intermediate-mass black holes (IMBHs), with masses of hundreds to thousands of solar masses, will be unique sources of gravitational waves for LISA. Here we discuss their context as well as specific characteristics of IMBH-IMBH and IMBH-supermassive black hole mergers and how these would allow sensitive tests of the predictions of general relativity in strong gravity.
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Based on a high resolution cosmological n-body simulation, we track the hierarchical growth of black holes in galaxy clusters from z=20 to z=0. We present a census of black holes as function of redshift and will determine their mass assembly history under a variety of assumptions regarding the importance of gas accretion in black hole growth, from early supercritical Eddington accretion to gas-poor hierarchical assembly. Following a galaxy merger, black holes are expected to form, inspiral and merge after strongly radiating energy via gravitational waves. For each binary black hole inspiral an…
All the physical processes involved in the formation, merging, and accretion history of massive black holes along the hierarchical build--up of cosmic structures are likely to leave an imprint on the gravitational waves detectable by future space--borne missions, such as LISA. We report here the results of recent studies, carried out by means of dedicated simulations of black hole build--up, aiming at understanding the impact on LISA observations of two ingredients that are crucial in every massive black hole formation scenario, namely: (i) the nature and abundance of the first black hole seed…
Some issues relevant for the formation of supermassive black holes are discused and estimates of the event rates for the emission of gravitational waves by coalescing supermassive black hole binaries are given. The models take into account recent improvements in our knowledge of galaxy and star formation in the high-redshift universe. Estimated event rates range from a few to a hundred per year. Typical events will occur at redshift three or larger in galaxies lying at the (very) faint end of the luminosity function at these redshifts.
The gravitational waves generated during supermassive black hole (SMBH) coalescence are prime candidates for detection by the satellite LISA. We use the extended Press-Schechter formalism combined with empirically motivated estimates for the SMBH--dark matter halo mass relation and SMBH occupation fraction to estimate the maximum coalescence rate for major SMBH mergers. Assuming efficient binary coalescence, and guided by the lowest nuclear black hole mass inferred in local galactic bulges and nearby low-luminosity active galactic nuclei (10^5 Msun) we predict approximately 15 detections per y…
Massive black hole binaries, with masses in the range 1E3-1E8 Msun, are expected to be the most powerful sources of gravitational radiation at mHz frequencies, and hence are among the primary targets for the planned Laser Interferometer Space Antenna (LISA). We extend and refine our previous analysis (Sesana et al. 2004), detailing the gravitational wave signal expected from a cosmological population of massive black hole binaries. As done in our previous paper, we follow the merger history of dark matter halos, the dynamics of the massive black holes they host, and their growth via gas accret…
Binary black hole coalescences emit gravitational waves that will be measurable by the space-based detector it 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 wil…
The formation, merging, and accretion history of massive black holes along the hierarchical build--up of cosmic structures leaves a unique imprint on the background of gravitational waves 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 gravitational wave space--borne missions, such as LISA. We consider two main scenarios for black hole formation, namely, one where seeds are light (~10^2 \msun, remnant of Population III stars), and one where seeds are heavy …
LISA will be able to detect gravitational waves from inspiralling massive black hole (MBH) binaries out to redshifts z > 10. If the binary masses and luminosity distances can be extracted from the LISA data stream, this information can be used to reveal the merger history of MBH binaries and their host galaxies in the evolving universe. Since this parameter extraction generally requires that LISA observe the inspiral for a significant fraction of its yearly orbit, carrying out this program requires adequate sensitivity at low frequencies, f < 10^{-4} Hz. Using several candidate low frequency s…
Idealized models are used to illustrate the potential of the Laser Interferometer Space Antenna (LISA) as a probe of the largely unknown population of cosmologically-distant Massive Black Holes (MBHs) and as a tool to measure their masses with unprecedented accuracy. The models suggest that LISA will most efficiently probe a MBH population of lower mass than the one found in bright quasars and nearby galactic nuclei. The mass spectrum of these MBHs could constrain formation scenarios for high-redshift, low-mass galaxies.
We estimate the rate at which the proposed space gravitational-wave interferometer LISA could detect intermediate-mass black-hole binaries, that is, binaries containing a black hole in the mass range 10 -- 100 Msun orbiting a black hole in the mass range 100 -- 1000 Msun. For one-year integrations leading up to the innermost stable orbit, and a signal-to-noise ratio of 10, we estimate a detection rate of only 1 per million years for 10 Msun/100 Msun binaries. The estimate uses the method of parameter estimation via matched filtering, incorporates a noise curve for LISA established by the LISA …
The signal-to-noise ratio (SNR) for black hole quasinormal mode sources of low-frequency gravitational waves is estimated using a Monte Carlo approach that replaces the all-sky average approximation. We consider an eleven dimensional parameter space that includes both source and detector parameters. We find that in the black-hole mass range $M\sim 4$-$7\times 10^6M_{\odot}$ the SNR is significantly higher than the SNR for the all-sky average case, as a result of the variation of the spin parameter of the sources. This increased SNR may translate to a higher event rate for the Laser Interferome…
We study how the angular resolution of LISA for merging massive black-hole binaries would be improved if we observe multiple gravitational wave ``images'' due to strong gravitational lensing. The correlation between fitting parameters is reduced by the additional information of the second image which significantly reduces the error box on the sky. This improvement would be very helpful for identifying the host galaxy of a binary. The angular resolution expected with multiple detectors is also discussed.
Current expectations on the signal to noise ratios and masses of supermassive black holes which the Laser Interferometer Space Antenna (LISA) can observe are based on using in matched filtering only the dominant harmonic of the inspiral waveform at twice the orbital frequency. Other harmonics will affect the signal-to-noise ratio of systems currently believed to be observable by LISA. More significantly, inclusion of other harmonics in our matched filters would mean that more massive systems that were previously thought to be {\it not} visible in LISA should be detectable with reasonable SNRs.…
We study the angular resolution of the gravitational wave detector LISA and show that numerical relativity can drastically improve the accuracy of position location for coalescing Super Massive Black Hole (SMBH) binaries. For systems with total redshifted mass above $10^7 M_{\odot}$, LISA will mainly see the merger and ring-down of the gravitational wave (GW) signal, which can now be computed numerically using the full Einstein equations. Using numerical waveforms that also include about ten GW cycles of inspiral, we improve inspiral-only position estimates by an order of magnitude. We show th…
The merger of two supermassive black holes is expected to produce a gravitational-wave signal detectable by the satellite LISA. The rate of supermassive-black-hole mergers is intimately connected to the halo merger rate, and the extended Press-Schechter formalism is often employed when calculating the rate at which these events will be observed by LISA. This merger theory is flawed and provides two rates for the merging of the same pair of haloes. We show that the two predictions for the LISA supermassive-black-hole-merger event rate from extended Press-Schechter merger theory are nearly equal…
In this review article I attempt to summarise past and present-ongoing-work on the problem of the inspiral of a small body in the gravitational field of a much more massive Kerr black hole. Such extreme mass ratio systems, expected to occur in galactic nuclei, will constitute prime sources of gravitational radiation for the future LISA gravitational radiation detector. The article's main goal is to provide a survey of basic celestial mechanics in Kerr spacetime and calculations of gravitational waveforms and backreaction on the small body's orbital motion, based on the traditional `flux-balanc…
The observability of gravitational waves from supermassive and intermediate-mass black holes by the forecoming Laser Interferometer Space Antenna (LISA), and the physics we can learn from the observations, will depend on two basic factors: the event rates for massive black hole mergers occurring in the LISA best sensitivity window, and our theoretical knowledge of the gravitational waveforms. We first provide a concise review of the literature on LISA event rates for massive black hole mergers, as predicted by different formation scenarios. Then we discuss what (in our view) are the most urgen…
We study the inspiral of double black holes, with masses in the LISA window of detectability, orbiting inside a massive circum-nuclear disc. Using high-resolution SPH 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 co-rotate with the gaseous disc, forming a binary with a low eccentricity, consistent with zero within our numerical resolution limit…
By being the first observatory to survey the source rich low frequency region of the gravitational wave spectrum, the Laser Interferometer Space Antenna (LISA) will revolutionize our understanding of the Cosmos. For the first time we will be able to detect the gravitational radiation from millions of galactic binaries, the coalescence of two massive black holes, and the inspirals of compact objects into massive black holes. The signals from multiple sources in each class, and possibly others as well, will be simultaneously present in the data. To achieve the enormous scientific return possible…
Current simulations of the rate at which stellar-mass compact objects merge with supermassive black holes (called extreme mass ratio inspirals, or EMRIs) focus on two-body capture by emission of gravitational radiation. The gravitational wave signal of such events will likely involve a significant eccentricity in the sensitivity range of the Laser Interferometer Space Antenna (LISA). We show that tidal separation of stellar-mass compact object binaries by supermassive black holes will instead produce events whose eccentricity is nearly zero in the LISA band. Compared to two-body capture events…
We propose a scenario in which massive stars form in a self-gravitating gaseous disc around a supermassive black hole. We find that once the surface density of the disc exceeds a critical value, the disc fragments into dense clumps. The clumps accrete material from the remaining disc and merge into larger clumps; the upper mass of a merged clump is a few tens to a few hundreds of solar mass. This picture fits well with the observed young stellar discs near the SgrA* black hole in the Galactic Center. In particular, we show how the masses and spatial distribution of the young stars, and the tot…
Newly formed black holes are expected to emit characteristic radiation in the form of quasi-normal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multi-mode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected …
Laser Interferometer Space Antenna (LISA) will routinely observe coalescences of supermassive black hole (BH) binaries up to very high redshifts. LISA can measure mass parameters of such coalescences to a relative accuracy of $10^{-4}-10^{-6}$, for sources at a distance of 3 Gpc. The problem of parameter estimation of massive nonspinning binary black holes using post-Newtonian (PN) phasing formula is studied in the context of LISA. Specifically, the performance of the 3.5PN templates is contrasted against its 2PN counterpart using a waveform which is averaged over the LISA pattern functions. T…
Black hole binaries with extreme ($\gtrsim 10^4:1$) or intermediate ($\sim 10^2-10^4:1$) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed Laser Interferometer Space Antenna. These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis, and applications to testing general relativity, providing both a description of the c…
Binary systems of massive black holes will be detectable by the Laser Interferometer Space Antenna (LISA) throughout the entire Universe. Observations of gravitational waves from this class of sources will have important repercussions on our understanding of the behaviour of gravity in the highly non-linear relativistic regime, the distribution and interaction of massive black holes at high redshift and the formation and evolution of cosmic structures. It is therefore important to address how accurately LISA can measure the source parameters and explore the implications for astronomy and cosmo…
LISA is a planned space-based gravitational-wave (GW) detector that would be sensitive to waves from low-frequency sources, in the band of roughly $(0.03 - 0.1) {\rm mHz} \lesssim f \lesssim 0.1 {\rm Hz}$. This is expected to be an extremely rich chunk of the GW spectrum -- observing these waves will provide a unique view of dynamical processes in astrophysics. Here we give a quick survey of some key LISA sources and what GWs can uniquely teach us about these sources. Particularly noteworthy science which is highlighted here is the potential for LISA to track the moderate to high redshift evol…
The Laser Interferometer Space Antenna (LISA) will produce a data stream containing a vast number of overlapping sources: from strong signals generated by the coalescence of massive black hole binary systems to much weaker radiation form sub-stellar mass compact binaries and extreme-mass ratio inspirals. It has been argued that the observation of weak signals could be hampered by the presence of loud ones and that they first need to be removed to allow such observations. Here we consider a different approach in which sources are studied simultaneously within the framework of Bayesian inference…
LISA is a planned space-based gravitational-wave (GW) detector that would be sensitive to waves from low-frequency sources, in the band of roughly (0.03 - 0.1) mHz < f < 0.1 Hz. This is expected to be an extremely rich chunk of the GW spectrum -- observing these waves will provide a unique view of dynamical processes in astrophysics. Here we give a quick survey of some key LISA sources and what GWs can uniquely teach us about these sources. Particularly noteworthy science which is highlighted here is the potential for LISA to track the moderate to high redshift evolution of black hole masses a…
The coalescence of massive black hole (BH) binaries due to galaxy mergers provides a primary source of low-frequency gravitational radiation detectable by pulsar timing measurements and by the proposed LISA (Laser Interferometry Space Antenna) observatory. We compute the expected gravitational radiation signal from sources at all redshifts by combining the predicted merger rate of galactic halos with recent measurements of the relation between BH mass, M_bh, and the velocity dispersion of its host galaxy, sigma. Our main findings are as follows: (i) the nHz frequency background is dominated by…
The LISA Parameter Estimation (LISAPE) Taskforce was formed in September 2007 to provide the LISA Project with vetted codes, source distribution models, and results related to parameter estimation. The Taskforce's goal is to be able to quickly calculate the impact of any mission design changes on LISA's science capabilities, based on reasonable estimates of the distribution of astrophysical sources in the universe. This paper describes our Taskforce's work on massive black-hole binaries (MBHBs). Given present uncertainties in the formation history of MBHBs, we adopt four different population m…
Observations of binary inspirals with LISA will allow us to place bounds on alternative theories of gravity and to study the merger history of massive black holes (MBH). These possibilities rely on LISA's parameter estimation accuracy. We update previous studies of parameter estimation including non-precessional spin effects. We work both in Einstein's theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. Inclusion of non-precessional spin terms in MBH binaries has little effect on the angular resolution or on distance determination accuracy, but it deg…
We propose a scenario in which massive stars form at the outer edges of an AGN accretion disc. We analyze the dynamics of a disc forming around a supermassive black hole, in which the angular momentum is transported by turbulence induced by the disc's self-gravity. We find that once the surface density of the disc exceeds a critical value, the disc fragments into dense clumps. The biggest clumps collapse and form massive stars, which produce few-tens-solar-mass black holes at the end of their evolution. The embedded black holes will interact gravitationally with the massive accretion disc and …
We open the discussion into how the Laser Interferometer Space Antenna (LISA) observations of supermassive black-hole (SMBH) mergers (in the mass range ~10^6-10^8 Msun) may be complementary to pulsar timing-based gravitational wave searches. We consider the toy model of determining pulsar distances by exploiting the fact that LISA SMBH inspiral observations can place tight parameter constraints on the signal present in pulsar timing observations. We also suggest, as a future path of research, the use of LISA ring-down observations from the most massive (>~ a few 10^7 Msun) black-hole mergers, …
Inspirals of stellar-mass compact objects into $\sim 10^6 M_{\odot}$ black holes are especially interesting sources of gravitational waves for LISA. We investigate whether the emitted waveforms can be used to strongly constrain the geometry of the central massive object, and in essence check that it corresponds to a Kerr black hole (BH). For a Kerr BH, all multipole moments of the spacetime have a simple, unique relation to $M$ and $S$, the BH's mass and spin; in particular, the spacetime's mass quadrupole moment is given by $Q=- S^2/M$. Here we treat $Q$ as an additional parameter, independen…
The intensity of low frequency gravitational waves from black hole MACHO binaries is studied. First we estimate the gravitational wave background produced by black hole MACHO binaries in the Milky Way halo as well as the cosmological gravitational wave background produced by the extragalactic black hole MACHO binaries. It is found that the cosmological gravitational wave background due to black hole MACHO binaries is larger than the halo background unless an extreme model of the halo is assumed, while it is smaller than the background due to close white dwarf binaries at $ν_{gw} \siml 10^{-2.5…
The coalescence of massive black holes is one of the primary sources of gravitational waves (GWs) for LISA. Measurements of the GWs can localize the source on the sky to an ellipse with a major axis of a few tens of arcminutes to a few degrees, depending on source redshift, and a minor axis which is 2--4 times smaller. The distance (and thus an approximate redshift) can be determined to better than a per cent for the closest sources we consider, although weak lensing degrades this performance. It will be of great interest to search this three-dimensional `pixel' for an electromagnetic counterp…
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