The Binary Pulsar (2) ...

The Binary Pulsar is a superb laboratory for precision tests of the theory of general relativity. Because of the precise repetition frequency of the pulsar, it is basically a very high quality clock orbiting in a binary system. Furthermore, because the orbit is highly elliptical, the pulsar velocity and the strength of the gravitational field that it feels changes periodically by significant amounts.
Tests of General Relativity
Since the general theory of relativity makes definite predictions about the effect of velocity and gravitational field strength on observable quantities, the Binary Pulsar is a ready-made laboratory to apply stringent tests to the theory. Some of these tests are summarized below.

1. Because spacetime is warped by the gravitational field in the vicinity of the pulsar, the orbit will precess with time, as illustrated in the bottom right figure on the preceding page. This is the same effect as the precession of the perihelion of Mercury (see this animation), but it is much larger for the present case. The position of the Binary Pulsar's periastron is observed to advance by 4.2 degrees per year, in accord with the predictions of general relativity. In a single day, the orbit of the Binary Pulsar advances by as much as the orbit of Mercury advances in a century.
2. When the binary pulsar is close to its companion near periastron, the gravitational field that it feels is stronger and its velocity is higher and time should run slower according to relativity theory. Near apastron the field is weaker and the velocity lower, so it should run faster. It does both, in the amount predicted by the theory.
3. The revolving pair of masses is predicted by general relativity to radiate gravitational waves. Since this takes energy away from the orbital motion, the radius of the orbit must shrink with time if general relativity is correct. The time of periastron can be measured very precisely and is found to be shifting. This shift corresponds to a decrease in the orbital period by 76 millionths of a second per year (implying a corresponding decrease in the size of the orbit). The decrease in periastron time is illustrated by the data points in the above right figure (with the vertical bars indicating the estimated uncertainty in the measurement for each point). Because the orbital period is short, the shift in periastron arrival time accumulates to more than a second (earlier) every 10 years. This decay of the size of the orbit is in agreement with the amount of energy that general relativity predicts should be leaving the system in the form of gravitational waves. The prediction of the theory is denoted by the solid line in the above right figure of the shift in periastron time.

Shrinkage of the Orbit
Because of the gravitational wave radiation and the corresponding shrinkage of the orbit (about 3.3 millimeters for each revolution), the two stars are predicted to merge in about 300 million years. The shrinkage of the orbit is illustrated in the adjacent right figure.

As we shall discuss in the following module on black holes, the sum of the masses of the two neutron stars is likely above the critical mass to form a black hole. Therefore, we may expect that the probable fate of the Binary Pulsar in about 300 million years is for the two neutron stars to merge and collapse to a black hole. As the two neutron stars approach each other they will revolve faster and faster (Kepler's third law). This will cause them to emit gravitational radiation more rapidly, which will in turn cause the orbit to shrink even faster. Thus, near the end the merger of two neutron stars will proceed rapidly and will emit very strong gravitational waves. These considerations are valid for any neutron star binary, not just the Binary Pulsar; see the box below.

Merging Neutron Stars

The gravitational waves from merging neutron stars are expected to be strong enough that their characteristic signature will be detectable in new Earth-based gravitational wave detectors that are just beginning to operate. Such observations would provide direct confirmation of the existence of gravitational waves that we presently can infer only indirectly from the Binary Pulsar. The merger of two neutron stars is also a prime candidate for producing the gamma ray bursts that we shall discuss in Chapter 26.

The possibility of two neutron stars merging might seem a remote one. A critical point is that once a neutron star binary is formed its orbital motion radiates energy as gravitational waves, the orbits must shrink, and eventually the two neutron stars must merge. Formation of the neutron star binary is not easy, however. Either a binary (or multiple star system with more than two stars) must form with two stars massive enough to become supernovae and the neutron stars thus formed must remain bound to each other through the two supernova explosions, or the neutron star binary must result from gravitational capture. Although these are improbable events, calculations indicate that they are not impossible. Some theoretical estimates indicate that formation of a neutron star binary can happen often enough to produce about one neutron star merger each day in some direction in the observable Universe. The probablility of forming a neutron star binary in any one region of space is very small, but the Universe is a very big place.