The Binary Pulsar PSR 1913+16:

In 1993, the Nobel Prize in Physics was awarded to Russell Hulse and Joseph Taylor of Princeton University for their 1974 discovery of a pulsar, designated PSR1913+16, in a binary system, in orbit with another star around a common center of mass.

Using the Arecibo 305m antenna, Hulse and Taylor detected pulsed radio emission and thus identified the source as a pulsar, a rapidly rotating, highly magnetized neutron star. The neutron star rotates on its axis 17 times per second; thus the pulse period is 59 milliseconds.

After timing the radio pulses for some time, Hulse and Taylor noticed that there was a systematic variation in the arrival time of the pulses. Sometimes, the pulses were received a little sooner than expected; sometimes, later than expected. These variations changed in a smooth and repetitive manner, with a period of 7.75 hours. They realized that such behavior is predicted if the pulsar were in a binary orbit with another star.

The pulsar and its companion both follow elliptical orbits around their common center of mass. Each star moves in its orbit according to Kepler's Laws; at all times the two stars are found on opposite sides of a line passing through the center of mass. The period of the orbital motion is 7.75 hours, and the stars are believed to be nearly equal in mass, about 1.4 solar masses. As shown in the figure here, the orbits are quite eccentric. The minimum separation at periastron is about 1.1 solar radii; the maximum separation at apastron is 4.8 solar radii.

In the case of PSR 1913+16, the orbit is inclined at about 45 degrees with respect to the plane of the sky, and it is oriented such that periastron occurs nearly perpendicular to our line of sight.

(Figure from Weisberg et al. 1981)

Remember that a star in an elliptical orbit will move slower when it is at apastron than when it is a periastron. In an eccentric orbit such as that of PSR 1913+16, the radial velocity varies from a minimum of 75 km/sec to a maximum of 300 km/sec. Hulse and Taylor used their timing measurements of the pulses to infer the details of the orbital motion.

The pulse repetition frequency, that is, the number of pulses received each second, can be used to infer the radial velocity of the pulsar as it moves through its orbit. When the pulsar is moving towards us and is close to its periastron, the pulses should come closer together; therefore, more will be received per second and the pulse repetition rate will be highest. When it is moving away from us near its apastron, the pulses should be more spread out and fewer should be detected per second.

(Figure from Weisberg et al. 1981)

The fact that the negative velocities (blueshifts, approaching the Earth) are larger than the postitive one (redshifts, moving away from Earth) show that the orbit is highly eccentric.

The pulsar arrival times also vary as the pulsar moves through its orbit. When the pulsar is on the side of its orbit closest to the Earth, the pulses arrive more than 3 seconds earlier that they do when it is on the side furthest from the Earth. The difference is caused by the shorter distance from Earth to the pulsar when it is on the the close side of its orbit. The difference of 3 light seconds implies that the orbit is about 1 million kilometers across.

(Figure from Weisberg et al. 1981)

Since the pulsing of the radio emission from the pulsar can be likened to ticks on a clock, Hulse and Taylor realized that they could look for changes in the ticking caused by relativistic changes in the measurement of time. As seen above, the pulsar's orbital speed changes by a factor of four during its orbit. Likewise, since the orbit of the pulsar around its companion is elliptical, the two are closer together at some times than at others, so that the gravitational field alternately strengthens at periastron and weakens at apastron. Thus the binary pulsar PSR1913+16 provides a powerful test of the predictions of the behavior of time perceived by a distant observer according to Einstein's Theory of Relativity.

When they are closer together, near apastron, the gravitational field is stronger, so that the pasage of time is slowed down -- the time between pulses (ticks) lengthens just as Einstein predicted. The pulsar clock is slowed down when it is travelling fastest and in the strongest part of the gravitational field; it regains time when it is travelling more slowly and in the weakest part of the field.

(Figure from Weisberg et al. 1981)

The relativistic time delay is the difference between what is observed and what one would expect to see if the pulsar were moving in circular orbit, at constant distance and at a constant speed, around its companion.

Space-time in the vicinity of the pulsar is greatly warped. This curvature causes the pulsar orbit to advance.

The orbit of the pulsar appears to rotate with time; in the diagram, notice that the orbit is not a closed ellipse, but a continuous elliptical arc whose point of closest approach (periastron) rotates with each orbit. The rotation of the pulsar's periastron is analogous to the advance of the perihelion of Mercury in its orbit. The observed advance for PSR 1913+16 is about 4.2 degrees per year; the pulsar's periastron advances in a single day by the same amount as Mercury's perihelion advances in a century.

(Figure from Weisberg et al. 1981)

Relativity predicts that the binary system will lose energy with time as orbital energy is converted to gravitational radiation.

In 1983, Taylor and collaborators reported that there was a systematic shift in the observed time of periastron relative to that expected if the orbital separation remained constant. In the diagram shown here, data taken in the first decade after the discovery showed a decrease in the orbital period as reported by Taylor and his colleagues of about 76 millionths of a second per year. By 1982, the pulsar was arriving at its periastron more than a second earlier than would have been expected if the orbit had remained constant since 1974.

(Figure from Weisberg et al. 1981)

In the intervening decade, continued timing of the pulsar shows the continued decrease just as predicted by Einstein.

Because the binary system is losing energy, the orbits are shrinking, and someday the two stars should coalesce. Such a merger might produce strong enough gravitational radiation to be detected by instruments like the Laser Inteferometer Gravitational-Wave Observatory now under contruction.

The pulsar's orbit is shrinking with time as shown in this diagram; currently, the orbit shrinks by about 3.1 mm per orbit. The two stars should merge in about 300 million years from now.

(Figure from Weisberg et al. 1981)

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