
2.3 A Model for the Black Hole Binary GW150914
the observed gravitational waves was a binary system
of two black holes with a total mass of about 70 Solar
masses. But the gravitational forces involved are very
strong and detailed modelling of the system requires
the use of the general theory of relativity. The analysis
involves mathematical calculations as well as the use
of numerical methods. Such analysis is used to predict
the shape of the signal which would be observed from
black hole binaries with a wide range of properties. By
comparing the predicted shape with the observed signal,
the parameters which lead to the best agreement can be
determined.
The result is that the binary system, which emitted
the gravitational wave signal, was at a distance of about
1.34 billion light years from us. The mass of the two
black holes was 36 Solar masses and 29 Solar masses
respectively, so that the combined mass before the
merger was 65 Solar masses (the estimate above from
Newtonian dynamics was
>
70 Solar masses). As
described above, the binary contracts in size as the two
black holes rapidly spiral in. The eventual merger leads
to the formation of a rapidly spinning black hole with a
mass of 62 Solar masses. The mass of the final black
hole is therefore less than the combined mass of the two
black holes in the binary by three Solar masses.
What happened to the difference of about 3 Solar
masses? According the special theory of relativity,
mass and energy are equivalent, so the missing mass
must have been emitted from the system as energy.
Since the components of the binary are black holes, no
electromagnetic energy can be emitted, and the only
form of emission possible is gravitational waves. It is
this emission which leads to the contraction of the binary.
It can be shown, from the theory of gravitational wave
emission from binary sources, that the total amount of
gravitational wave energy emitted by the system is equal
to the energy corresponding to three Solar masses. This
is exactly equal to the mass missing after the formation
of the single black hole. The gravitational energy was
emitted in a fraction of a second, and at its peak the rate
of emission was equivalent to converting 200 times the
mass of the Sun to energy in a second.
After the peak frequency is reached, the two black
holes merge together and the waveform enters what is
known as the ringdown phase through which the merged
object settles down to a black hole which has only two
properties. These are the mass, which for GW150914 is
62 Solar masses, and spin, which is equivalent to about
100 rotations per second. Such an object is known as a
Kerr black hole (see BHS-9). The irregularities present
in the object soon after the merger are all radiated away
as gravitational waves, leaving behind a pristine black
hole described by just the mass and spin.
The observed ringdown phase agrees perfectly with
the form predicted from a theoretical calculation by C.
V. Vishveshwara in 1970. The calculated waveform
emitted by the binary is shown in the upper panel of
Figure 2, along with a sketch of the merging binary. The
shape of the single black hole soon after the merger, and
after the ringdown, are also shown. These have been
obtained using numerical calculations. The decreasing
separation of the two components, and the increasing
velocity are shown in the lower panel of the figure. The
waveform shows the increasing frequency as the black
holes approach each other, the peak amplitude reached,
and the ringdown after the merger. At their closest
distance before merger, the black holes are moving
relative to each other with a very high velocity of 0.6
times the velocity of light.
The binary black hole emits absolutely no
electromagnetic waves, so it could not have been
observed by any means other than the gravitational
waves detected by aLIGO. The discovery established
the existence of black holes, binary black holes,
gravitational waves and the correctness of Einstein’s
theory in describing the system. It therefore ranks as
one of the great discoveries in the history of physics
and astronomy, which yet again demonstrates how the
building of novel, large telescopes and detectors always
leads to startling new discoveries. The discovery is
of such great importance that the 2017 Noble prize in
physics was awarded jointly to the American physicists
Reiner Weiss, Barry C. Barish and Kip S. Thorne for
their decisive contribution to the LIGO detector and the
observation of gravitational waves’’.
It is interesting that the detection was made a
century after the formulation of the general theory
of relativity by Albert Einstein in 1915, and the
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