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General Relativity

Tests of General Relativity with Binary Pulsars

Tests of general relativity are difficult to come by. The curvature of space time that is central to the theory is only strong around black holes and neutron stars. Around the Sun, the effects of space-time curvature are of order GM/Rc2 = 2 × 10−6 or less, where G is the gravitational constant, M is the mass of the binary system, R is the radius of the Sun, and c is the speed of light. Farther out from the Sun, such as at the orbit of Mercury, the effects are weaker by the ratio of the distance from the Sun to the radius of the Sun. Tests based on the drift in the perihelion of Mercury's orbit are measuring a value of only 43 arc seconds per century. Tests based on the time delay of light passing by the Sun are measuring a value of order 0.2 milliseconds.

Testing general relativity outside of our own Solar System is difficult. While neutron stars and black hole candidates have strong gravitational fields that should produce strong general relativistic effects, these effects are generally mixed in with the physics of energy generation and light production. Especially in x-ray binaries, where gas is flowing to the compact object from a companion star, the environment is much too complex to definitively test general relativity.

Nature does, however, provide us with several very nice systems for testing general relativity. These are the binary pulsars that contain two neutron stars. These double-neutron-star systems, which now number 8, contain a radio pulsar in orbit with another neutron star. The stars in most of these systems are in close orbit. For instance, the original Binary Pulsar, PSR B1913+16, has an orbit with a 7×105 km projected semimajor axis (the length of the semimajor axis projected on the sky), making the system about the size of the Sun. The binary period for this system is 7 hours 45 minutes. A more compact binary system, PSR J0737−3039, has a projected semimajor axis of 4.2×105 km and a binary period of only 2 hours 27 minutes. The neutron stars in these systems are generally around 1.4 solar masses, and the environment surrounding these stars is clean of gas that would affect the propagation of radio waves from the pulsar to the observer. These properties ensure that the observable effects of general relativity are stronger within these systems without the complicating factor of a solar wind or accretion disk that can alter the propagation of light.

But the crucial feature that makes these systems valuable for testing general relativity is that the radio pulsar is a superb clock. In accurately measuring time over years, pulsars surpass atomic clocks in accuracy. This feature allows astronomers to measure precisely the changes in light travel time from Earth to the pulsar as it orbits its companion.

Tests of Space-Time Curvature

Two of the basic tests of general relativity within our Solar System—the modification of the propagation time of light by the gravitational field and the perihelion drift of Mercury—can be performed with the double-neutron-star double pulsars. These effects, along with the Gravitational redshift and the Doppler shift of radio waves from the pulsar and the propagation time across the binary system, appear to observers as changes in the arrival times of radio pulses from the pulsar.

The modification of the pulse arrival time is quite small, of order (GM/ac2)3/2 (a is the semimajor axis), which is of order 10−9 for PSR B1913+16. Despite being 3 orders of magnitude smaller than the shift in arrival time caused by the Gravitational redshift and the Doppler shift, which are of order GM/ac2, the effect is seen by observers.

The other test, the periastron drift of a binary pulsar's orbit, is a rather large effect, because while the shift per orbit is only of order GM/ac2 = 10−6, the binary pulsar completes of order 1,000 orbits per year. The periastron of PSR B1913+16 drifts by 4 degrees per year. The periastron drift of a binary pulsar's orbit is much more impressive than that of Mercury's orbit.

Test of Gravitational Radiation

Beyond providing better tests of general relativistic effects seen in our own Solar System, binary pulsars provide us with our only unambiguous confirmation of gravitational radiation.

All orbiting systems, whether galaxies, planetary systems, or binary stars, radiate gravitational waves. The gravitational waves carry energy and angular momentum from a system, causing the orbits within the system to decay. In most instances, this effect effect is too small to observe. The exception is in compact binary stars. Gravitational radiation drives the orbital decay of x-ray binary stars, causing the mass transfer that enables us to see them as brilliant x-ray sources. But this is an indirect and somewhat theoretical way of seeing the effect of gravitational radiation, because binary systems can lose energy and angular momentum through mechanisms other than gravitational radiation. In the close double-neutron-star binary pulsars, we can see the effect of gravitational waves on the system directly, because these binary pulsars can only lose orbital and angular momentum by radiating gravitational waves.

When a binary pulsar emits gravitational radiation, it loses orbital energy and angular momentum, which causes the orbit to shrink and the period to decrease. This is a tiny effect, but the precision of the pulsar as a clock allows us to see it. In the case of the original binary pulsar, PSR B1913+16, the period decreases by 2.3×10−12 seconds every second, or 1 second every 14,000 years. This decrease is what is predicted by general relativity. So we know that gravitational radiation is being emitted; the question remains whether we can detect it.

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