A binary black hole (BBH) is a system consisting of two black holes in close orbit around each other. Like black holes themselves, binary black holes are often divided into stellar binary black holes, formed either as remnants of high-mass binary star systems or by dynamic processes and mutual capture, and binary supermassive black holes believed to be a result of galactic mergers.
For many years, proving the existence of binary black holes was
made difficult because of the nature of black holes themselves, and the
limited means of detection available. However, in the event that a pair
of black holes were to merge, an immense amount of energy should be
given off as gravitational waves, with distinctive waveforms that can be calculated using general relativity.
Therefore, during the late 20th and early 21st century, binary black
holes became of great interest scientifically as a potential source of
such waves, and a means by which gravitational waves could be proven to
exist. Binary black hole mergers would be one of the strongest known
sources of gravitational waves in the Universe, and thus offer a good
chance of directly detecting such waves.
As the orbiting black holes give off these waves, the orbit decays, and
the orbital period decreases. This stage is called binary black hole
inspiral. The black holes will merge once they are close enough. Once
merged, the single hole settles down to a stable form, via a stage
called ringdown, where any distortion in the shape is dissipated as more
gravitational waves.
In the final fraction of a second the black holes can reach extremely
high velocity, and the gravitational wave amplitude reaches its peak.
The existence of stellar-mass binary black holes (and gravitational waves themselves) were finally confirmed when LIGO detected GW150914
(detected September 2015, announced February 2016), a distinctive
gravitational wave signature of two merging stellar-mass black holes of
around 30 solar masses each, occurring about 1.3 billion light years
away. In its final 20 ms of spiraling inward and merging, GW150914
released around 3 solar masses as gravitational energy, peaking at a
rate of 3.6×1049 watts — more than the combined power of all light radiated by all the stars in the observable universe put together. Supermassive binary black hole candidates have been found, but not yet categorically proven.
Occurrence
Supermassive black-hole binaries are believed to form during galaxy mergers. Some likely candidates for binary black holes are galaxies with double cores still far apart. An example double nucleus is NGC 6240. Much closer black-hole binaries are likely in single core galaxies with double emission lines. Examples include SDSS J104807.74+005543.5 and EGSD2 J142033.66 525917.5. Other galactic nuclei have periodic emissions suggesting large objects orbiting a central black hole, for example in OJ287.
The quasar PG 1302-102 appears to have a binary black hole with an orbital period of 1900 days.
Stellar mass binary black holes have been demonstrated to exist, by the first detection of a black hole merger event GW150914 by LIGO.
Final parsec problem
When two galaxies collide, the supermassive black holes at their centers do not hit head-on, but would shoot past each other on hyperbolic trajectories if some mechanism did not bring them together. The most important mechanism is dynamical friction, which transfers kinetic energy from the black holes to nearby matter. As a black hole passes a star, the gravitational slingshot accelerates the star while decelerating the black hole.
This slows the black holes enough that they form a bound, binary, system, and further dynamical friction steals orbital energy from the pair until they are orbiting within a few parsecs
of each other. However, this process also ejects matter from the
orbital path, and as the orbits shrink, the volume of space the black
holes pass through reduces, until there is so little matter remaining
that it could not cause merger within the age of the universe.
Gravitational waves can be a significant contributor, but not
until the separation shrinks to a much smaller value, roughly
0.01–0.001 parsec.
Nonetheless, supermassive black holes appear to have merged, and
what appears to be a pair in this intermediate range has been observed,
in PKS 1302-102. The question of how this happens is the "final parsec problem".
A number of solutions to the final parsec problem have been
proposed. Most involve mechanisms to bring additional matter, either
stars or gas, close enough to the binary pair to extract energy from the
binary and cause it to shrink. If enough stars pass close by to the
orbiting pair, their gravitational ejection can bring the two black
holes together in an astronomically plausible time.
One mechanism that is known to work, although infrequently, is a third supermassive black hole from a second galactic collision. With three black holes in close proximity, the orbits are chaotic and allow three additional energy loss mechanisms:
- The black holes orbit through a substantially larger volume of the galaxy, interacting with (and losing energy to) a much greater amount of matter,
- The orbits can become highly eccentric, allowing energy loss by gravitational radiation at the point of closest approach, and
- Two of the black holes can transfer energy to the third, possibly ejecting it.
Lifecycle
Inspiral
The first stage of the life of a binary black hole is the inspiral,
a gradually shrinking orbit. The first stages of the inspiral take a
very long time, as the gravitation waves emitted are very weak when the
black holes are distant from each other. In addition to the orbit
shrinking due to the emission of gravitational waves, extra angular
momentum may be lost due to interactions with other matter present, such
as other stars.
As the black holes’ orbit shrinks, the speed increases, and
gravitational wave emission increases. When the black holes are close
the gravitational waves cause the orbit to shrink rapidly.
The last stable orbit or innermost stable circular orbit (ISCO) is the innermost complete orbit before the transition from inspiral to merger.
Merger
This is
followed by a plunging orbit in which the two black holes meet, followed
by the merger. Gravitational wave emission peaks at this time.
Ringdown
Immediately
following the merger, the now single black hole will “ring” –
oscillating in shape between a distorted, elongated spheroid and a
flattened spheroid. This ringing is damped in the next stage, called the
ringdown, by the emission of gravitational waves. The
distortions from the spherical shape rapidly reduce until the final
stable sphere is present, with a possible slight distortion due to
remaining spin.
Observation
The first observation of stellar mass binary black holes merging was performed by the LIGO detector.
As observed from Earth, a pair of black holes with estimated masses
around 36 and 29 times that of the Sun spun into each other and merged
to form a 62 solar mass black hole (approximate) on 14 September 2015,
at 09:50 UTC. Three solar masses were converted to gravitational radiation in the final fraction of a second, with a peak power 3.6×1056 ergs/second (200 solar masses per second), which is 50 times the total output power of all the stars in the observable universe. The merger took place at 1.3 billion light years from Earth, and therefore 1.3 billion years ago. The observed signal is consistent with the predictions of numerical relativity.
Dynamics modelling
Some simplified algebraic models can be used for the case where the black holes are far apart, during the inspiral stage, and also to solve for the final ringdown.
Post-Newtonian approximations
can be used for the inspiral. These approximate the general relativity
field equations adding extra terms to equations in Newtonian gravity.
Orders used in these calculations may be termed 2PN (second order post
Newtonian) 2.5PN or 3PN (third order post Newtonian). Effective-one-body
(EOB) solves the dynamics of the binary black hole system by
transforming the equations to those of a single object. This is
especially useful where mass ratios are large, such as a stellar mass
black hole merging with a galactic core black hole, but can also be used for equal mass systems.
For the ringdown, black hole perturbation theory can be used. The final Kerr black hole is distorted, and the spectrum of frequencies it produces can be calculated.
To solve for the entire evolution, including merger, requires
solving the full equations of general relativity. This can be done in numerical relativity
simulations. Numerical relativity models space-time and simulates its
change over time. In these calculations it is important to have enough
fine detail close into the black holes, and yet have enough volume to
determine the gravitation radiation that propagates to infinity. In
order to make this have few enough points to be tractable to calculation
in a reasonable time, special coordinate systems can be used such as Boyer-Lindquist coordinates or fish-eye coordinates.
Numerical relativity techniques steadily improved from the initial attempts in
the 1960s and 1970s.
Long-term simulations of orbiting black holes,
however, were not possible until three groups independently developed
groundbreaking new methods to model the inspiral, merger, and ringdown of
binary black holes in 2005.
In the full calculations of an entire merger, several of the
above methods can be used together. It is then important to fit the
different pieces of the model that were worked out using different
algorithms. The Lazarus Project linked the parts on a spacelike
hypersurface at the time of the merger.
Results from the calculations can include the binding energy. In a
stable orbit the binding energy is a local minimum relative to
parameter perturbation. At the innermost stable circular orbit the local
minimum becomes an inflection point.
The gravitational waveform produced is important for observation
prediction and confirmation. When inspiralling reaches the strong zone
of the gravitational field, the waves scatter within the zone producing
what is called the post Newtonian tail (PN tail).
In the ringdown phase of a Kerr black hole, frame-dragging
produces a gravitation wave with the horizon frequency. In contrast the
Schwarzschild black-hole ringdown looks like the scattered wave from
the late inspiral, but with no direct wave.
The radiation reaction force can be calculated by Padé resummation
of gravitational wave flux. A technique to establish the radiation is
the Cauchy characteristic extraction technique CCE which gives a close
estimate of the flux at infinity, without having to calculate at larger
and larger finite distances.
The final mass of the resultant black hole depends on the definition of mass in general relativity. The Bondi mass MB is calculated from the Bondi-Sach mass loss formula. . With f(U) the gravitational wave flux at retarded time U. f is a surface integral of the News function at null infinity varied by solid angle. The Arnowitt-Deser-Misner (ADM) energy or ADM mass is the mass as measured at infinite distance and includes all the gravitational radiation emitted. .
Angular momentum
is also lost in the gravitational radiation. This is primarily in the z
axis of the initial orbit. It is calculated by integrating the product
of the multipolar metric waveform with the news function complement over
retarded time.
Shape
One of the problems to solve is the shape or topology of the event horizon during a black-hole merger.
In numerical models, test geodesics are inserted to see if they
encounter an event horizon. As two black holes approach each other, a
‘duckbill’ shape protrudes from each of the two event horizons towards
the other one. This protrusion extends longer and narrower until it
meets the protrusion from the other black hole. At this point in time
the event horizon has a very narrow X-shape at the meeting point. The
protrusions are drawn out into a thin thread. The meeting point expands to a roughly cylindrical connection called a bridge.
Simulations as of 2011 had not produced any event horizons with toroidal
topology (ring-shaped). Some researchers suggested that it would be
possible if, for example, several black holes in the same
nearly-circular orbit coalesce.
Black-hole merger recoil
An
unexpected result can occur with binary black holes that merge, in that
the gravitational waves carry momentum and the merging black-hole pair
accelerates seemingly violating Newton's third law. The center of gravity can add over 1000 km/s of kick velocity.
The greatest kick velocities (approaching 5000 km/s) occur for
equal-mass and equal-spin-magnitude black-hole binaries, when the spins
directions are optimally oriented to be counter-aligned, parallel to the
orbital plane or nearly aligned with the orbital angular momentum.
This is enough to escape large galaxies. With more likely orientations a
smaller effect takes place, perhaps only a few hundred kilometers per
second. This sort of speed will eject merging binary black holes from
globular clusters, thus preventing the formation of massive black holes
in globular cluster cores. In turn this reduces the chances of
subsequent mergers, and thus the chance of detecting gravitational
waves. For non spinning black holes a maximum recoil velocity of
175 km/s occurs for masses in the ratio of five to one. When spins are
aligned in the orbital plane a recoil of 5000 km/s is possible with two
identical black holes.
Parameters that may be of interest include the point at which the black
holes merge, the mass ratio which produces maximum kick, and how much
mass/energy is radiated via gravitational waves. In a head-on collision
this fraction is calculated at 0.002 or 0.2%. One of the best candidates of the recoiled supermassive black holes is CXO J101527.2+625911.
Halo drive for space travel
It has been hypothesized that binary black holes could transfer energy and momentum to a spacecraft using a "halo drive", exploiting the holographic reflection
created by a set of null geodesics looping behind and then around one
of the black holes before returning to the spacecraft. The reflection
passing through these null geodesics would form one end of a laser
cavity, with a mirror on the spacecraft forming the other end of the
laser cavity. Even a planet-sized spacecraft would thereby accelerate to
speeds exceeding the approaching black hole's relative speed. If true, a
network of these binary black holes might permit travel across the
galaxy.
