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 [202359]. 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 m1 and m2, in an orbit of eccentricity e and period Pb, the period decay is given by the generalization of Equation (32View Equation[291]:

( ) ( ) 192π 2πℳ 5∕3 73 2 37 4 ( 2)− 7∕2 P˙b = − ----- ------ 1 + --e + ---e 1 − e , (109 ) 5 Pb 24 96
where we recall that
ℳ = (m1m2 )3∕5(m1 + m2 )− 1∕5 = μ3∕5M 2∕5 (110 )
is the chirpmass of the binary that we defined in Equation (31View Equation). (In the third expression here, μ is the reduced mass of the binary and M 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: m1 = 1.4414M ⊙, m2 = 1.3867M ⊙, e = 0.6171338, Pb = 2.790698 × 104 s. The predicted value ˙ GR − 12 Pb = − (2.40242 ± 0.00002) × 10, 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 Obs P˙b = − (2.4056 ± 0.0051) × 10−12 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 [103249]. 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.

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