### 6.3 Gravitational radiation reaction

In 1974, Hulse and Taylor discovered the first double neutron star binary PSR B1913+16, a
system in which the emission of gravitational radiation has an observable effect [202, 359].
General relativity predicts that the loss of energy and angular momentum due to the emission of
gravitational waves should cause the period of the system to decrease and, by carefully monitoring the
orbital period of the binary, that it would be possible to measure the rate at which the period
changes. The rate at which the period decays can be computed using the quadrupole formula for
the luminosity of the emitted radiation combined with the energy-balance equation; namely
that the energy carried away by the waves comes at the expense of the binding energy of the
system.
For a binary consisting of stars of masses and , in an orbit of eccentricity and period
, the period decay is given by the generalization of Equation (32) [291]:

where we recall that
is the chirpmass of the binary that we defined in Equation (31). (In the third expression here, is the
reduced mass of the binary and its total mass.) Since the masses of the binary and the eccentricity of
the orbit can be measured by other means, one can use these parameters in the above equation to infer the
rate at which the period is predicted to decrease according to general relativity. For the Hulse–Taylor binary
the relevant values are: , , , .
The predicted value , while the observed period decay (after
subtracting the apparent decay due to the acceleration of the pulsar in the gravitational field of our galaxy,
as described in Section 3.4.3) is and the two are in agreement to
better than a tenth of a percent [394].
Observation of the decay of the orbital period in PSR B1913+16 is an unambiguous direct observation
of the effect of gravitational radiation backreaction on the dynamics of the system. PSR B1913+16 was the
first system in which the effect of gravitational radiation reaction force was measured. In 2004, a new binary
pulsar PSR J0737-3039 was discovered [103, 249]. J0737 is in a tighter orbit than PSR B1913+16;
with an orbital period of only 2.4 hrs, the orbit is shrinking by about 7 mm each day in good
agreement with the general relativistic prediction. Several other systems are also known [244]. In
Sections 6.5, 6.5.2 and 6.5.3 we will discuss in some detail the dynamics of relativistic binaries
and the radiation reaction as predicted by post-Newtonian theory and numerical relativity
simulations.