7.2 Black hole astrophysics

Black holes are the most relativistic systems possible. Observing gravitational waves from them, individually or in binaries, helps to test some of the predictions of general relativity in the strongly nonlinear regime, such as the tails of gravitational waves, spin-orbit coupling induced precession, nonlinear amplitude terms, hereditary effects, etc [3638685325]. They are also good test beds to constrain other theories of gravity. Gravitational waves – emitted either during the inspiral and merger of rotating SMBHs or when a stellar-mass compact object falls into a SMBH – can be used to map the structure of spacetime and test uniqueness theorems on rotating black holes [363]. LISA will be able to see the formation of massive black holes at cosmological distances by detecting the waves emitted in the process [363]. We give below a brief discussion of the physics that will follow from the observation of gravitational waves from black holes.

7.2.1 Gravitational waves from stellar-mass black holes

Astronomers now recognize that there is an abundance of black holes in the universe. Observations across the electromagnetic spectrum have located black holes in X-ray binary systems in our galaxy in the centers of star clusters, and in the centers of galaxies.

These three classes of black holes have very different masses. Stellar black holes typically have masses of around 10M ⊙, and are thought to have been formed by the gravitational collapse of the center of a large, evolved red giant star, perhaps in a supernova explosion. Black holes in clusters have been found in the range of 104M ⊙, and are called intermediate-mass black holes. Black holes in galactic centers have masses between 106 and 1010M ⊙, and are called SMBHs. The higher masses are found in the centers of active galaxies and quasars. The history and method of formation of intermediate-mass and supermassive black holes are not yet well understood.

All three kinds of black hole can radiate gravitational waves. According to Figure 2View Image, stellar black-hole radiation will be in the ground-based frequency range, while galactic holes are detectable only from space. Intermediate-mass black holes may lie at the upper end of the LISA band or between LISA and ground-based detectors. The radiation from an excited black hole itself is strongly damped, lasting only a few cycles at its natural frequency [see Equation (12View Equation) with R = 2M]:

( )− 1 fBH ∼ 1000 -M---- Hz 10M ⊙


7.2.2 Stellar-mass black-hole binaries

Radiation from stellar-mass black holes is expected mainly from coalescing binary systems, when one or both of the components is a black hole. Although black holes are formed more rarely than neutron stars, the spatial abundance of binary systems consisting of neutron stars with black holes, or of two black holes, is amplified relative to neutron-star binaries because binary systems are much more easily broken up when a neutron star forms than when a black hole forms. When a neutron star forms, most of the progenitor star’s mass (6M ⊙ or more) must be expelled from the system rapidly. This typically unbinds the binary: the companion star has the same speed as before but is held to the neutron star by only a fraction of the original gravitational attraction. Observed neutron-star binaries are thought to have survived because the neutron star was coincidentally given a kick against its orbital velocity when it formed. When a black hole forms, most of the original mass may simply go down into the hole, and the binary will have a higher survival probability. However, this argument may not lead to observable black hole binaries; there is a possibility that systems that would form black holes close enough to coalesce in a Hubble time do not become binaries, but rather the two progenitor stars are so close that they merge before forming black holes.

On the other hand, double black-hole binaries may in fact be formed abundantly by capture processes in globular clusters, which appear to be efficient factories for black-hole binaries [297]. Being more massive than the average star in a globular cluster, black holes sink towards the center, where three-body interactions can lead to the formation of binaries. The key point is that these binaries are not strongly bound to the cluster, so they can easily be expelled by later encounters. From that point on they evolve in isolation, and typically have a lifetime shorter than 1010 yrs.

The larger mass of stellar black-hole systems makes them visible from a greater distance than neutron-star binaries. If the abundance of binaries with black holes is comparable to that of neutron-star binaries, black hole events will be detected much more frequently than those involving neutron stars. They may even be seen by first-generation detectors in the S5 science run of the LSC (see Section 4.3.1), although that is still not very probable, even with optimistic estimates of the black-hole binary population. It seems very possible, however, that the first observations of binaries by interferometers will eventually be of black holes.

More speculatively, black hole binaries may even be part of the dark matter of the universe. Observations of Massive Compact Halo Objects (MACHOs) – microlensing of distant stars by compact objects in the halo of our galaxy – have indicated that up to half of the galactic halo could be made up of dark compact objects of 0.5M ⊙ [27354]. This is difficult to understand in terms of stellar evolution, as we understand it today: neutron stars and black holes should be more massive than this, and white dwarfs of this mass should be bright enough to have been identified as the lensing objects. One speculative possibility is that the objects were formed primordially, when conditions may have allowed black holes of this mass to form. If so, there should also be a population of binaries among them, and occasional coalescences should, therefore, be expected. In fact, the abundance would be so high that the coalescence rate might be as large as one every 20 years in each galaxy, which is higher than the supernova rate. Since binaries are maximally non-axisymmetric, these systems could be easily detected by first-generation interferometers out to the distance of the Virgo Cluster [267].

The estimates used here of detectability of black hole systems depend mainly on the radiation emitted as the orbit decays, during which the point-particle post-Newtonian approximation should be adequate. But the inspiral phase will, of course, be followed by a burst of gravitational radiation from the merger of the black holes that will depend in detail on the masses and spins of the objects. Numerical simulations of such events will be used to interpret this signal and to provide templates for the detection of black holes too massive for their inspiral signals to be seen. There is an abundance of information in these signals: population studies of the masses and spins of black holes, studies of typical kick velocities for realistic mergers, tests of general relativity.

7.2.3 Intermediate-mass black holes

Intermediate-mass black holes, with masses between 100M ⊙ and 104M ⊙, are expected on general evolutionary grounds, but have proved hard to identify because of their weaker effect on surrounding stellar motions. Very recently [275] strong evidence has been found for such a black hole in the star cluster Omega Centauri. If such black holes are reasonably abundant, then they may be LISA sources when they capture a stellar-mass black hole or a neutron star from the surrounding cluster. For these merger events the mass ratio is not as extreme as for EMRIs, and so these are accordingly called IMRIs: Intermediate Mass-Ratio Inspirals.

The problem of modelling the signals from these systems has not yet been fully studied. If these signals can be detected, they will tell us how important black holes were in the early stellar population, and whether these black holes have anything to do with the central black holes in the same galaxies.

7.2.4 Supermassive black holes

Gravitational radiation is expected from SMBHs in two ways. In one scenario, two massive black holes spiral together in a much more powerful version of the coalescence we have just discussed. The frequency is much lower, in inverse proportion to their masses, and the amplitude is higher. Equation (128View Equation) implies that the effective signal amplitude (which is what appears in the expression for the SNR) is almost linear in the masses of the black holes, so that a signal from two 6 10 M ⊙ black holes will have an amplitude 105 times bigger than the signal from two 10M ⊙ holes at the same distance. Even allowing for differences in technology, this indicates why space-based detectors will be able to study such events with a very high SNR, no matter where in the universe they occur. Observations of coalescing massive black-hole binaries will therefore provide unique insight into the behavior of strong gravitational fields in general relativity.

The event rate for such coalescences is not easy to predict, but is likely to be large. It seems that the central core of most galaxies may contain a black hole of at least 106M ⊙. This is known to be true for our galaxy [152] and for a very large proportion of other galaxies that are near enough to be studied in sufficient detail [314]. SMBHs (up to a few times 9 10 M ⊙) are believed to power quasars and active galaxies, and there is a good correlation between the mass of the central black hole and the velocity dispersion of stars in the core of the host galaxy [174].

If black holes are formed with their galaxies, in a single spherical gravitational collapse event, and if nothing happens to them after that, then coalescences will never be seen. But this is unlikely for two reasons. First, it is believed that galaxies may have formed through the merger of smaller units, sub-galaxies of masses upwards of 106M ⊙. If these units had their own black holes, then the mergers would have resulted in the coalescences of many of the black holes on a timescale shorter than the present age of the universe. This would give an event rate of several mergers per year in the universe, most of which would be observable by LISA, if the more massive black hole is not larger than about 7 10 M ⊙. If the 6 10 M ⊙ black holes were formed from smaller black holes in a hierarchical merger scenario, then the event rate could be hundreds or thousands per year. The second reason is that we see large galaxies merging frequently. Interacting galaxies are common, and if galaxies come together in such a way that their central black holes both remain in the central core, then dynamical friction with other stars will bring them close enough together to allow gravitational radiation to bring about a merger on a timescale of less than 1010 yrs. There is considerable evidence for black hole binaries in a number of external galaxies [257]. There is even a recent report of an SMBH having been ejected from a galaxy, possibly by the kick following a merger [223] and of an SMBH binary that will coalesce in about 10,000 yrs [373]!

Besides mergers of holes with comparable masses, the capture of a small compact object by a massive black hole can also result in observable radiation. The tidal disruption of main-sequence or giant stars that stray too close to the black hole is thought to provide the gas that powers the quasar phenomenon. These disruptions are not expected to produce observable radiation. But the clusters will also contain a good number of neutron stars and stellar-mass black holes. They are too compact to be disrupted by the black hole, even if they fall directly into it.

Such captures, therefore, emit a gravitational wave signal that will be well approximated as that from a point mass near the black hole. This will again be a chirp of radiation, but in this case the orbit may be highly eccentric. The details of the waveform encode information about the geometry of spacetime near the black hole. In particular, it may be possible to measure the mass and spin of the black hole and thereby to test the uniqueness theorem for black holes. The event rate is not very dependent on the details of galaxy formation, and is probably high enough for many detections per year from a space-based detector [35], provided that theoretical calculations give data analysts accurate predictions of the motion of these point particles over many hundreds of thousands of orbits. These Extreme Mass-Ratio Inspiral sources (EMRIs) are a primary goal of the LISA detector. By observing them, LISA will provide information about the stellar population near central black holes. When combined with modelling and spectroscopic observations, this will facilitate a deep view of the centers of galaxies and their evolution.

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