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The system consists of a pulsar of nominal period in a close binary orbit with an as yet
unseen companion. The orbital period is about 7.75 hours, and the eccentricity is 0.617. From
detailed analyses of the arrival times of pulses (which amounts to an integrated version of the
Doppler-shift methods used in spectroscopic binary systems), extremely accurate orbital and physical
parameters for the system have been obtained (see Table 6). Because the orbit is so close (
)
and because there is no evidence of an eclipse of the pulsar signal or of mass transfer from
the companion, it is generally agreed that the companion is compact. Evolutionary arguments
suggest that it is most likely a dead pulsar, while B1913+16 is a “recycled” pulsar. Thus the
orbital motion is very clean, free from tidal or other complicating effects. Furthermore, the data
acquisition is “clean” in the sense that by exploiting the intrinsic stability of the pulsar clock
combined with the ability to maintain and transfer atomic time accurately using GPS, the
observers can keep track of pulse time-of-arrival with an accuracy of
, despite extended gaps
between observing sessions (including a several-year gap in the middle 1990s for an upgrade
of the Arecibo radio telescope). The pulsar has shown no evidence of “glitches” in its pulse
period.
Three factors make this system an arena where relativistic celestial mechanics must be used: the
relatively large size of relativistic effects [], a factor of 10 larger than the
corresponding values for solar-system orbits; the short orbital period, allowing secular effects to build up
rapidly; and the cleanliness of the system, allowing accurate determinations of small effects. Because the
orbital separation is large compared to the neutron stars’ compact size, tidal effects can be ignored.
Just as Newtonian gravity is used as a tool for measuring astrophysical parameters of ordinary
binary systems, so GR is used as a tool for measuring astrophysical parameters in the binary
pulsar.
The observational parameters that are obtained from a least-squares solution of the arrival-time data fall into three groups:
The five post-Keplerian parameters are: , the average rate of periastron advance;
, the amplitude of
delays in arrival of pulses caused by the varying effects of the gravitational redshift and time dilation as the
pulsar moves in its elliptical orbit at varying distances from the companion and with varying speeds;
,
the rate of change of orbital period, caused predominantly by gravitational radiation damping; and
and
, respectively the “range” and “shape” of the Shapiro time delay of the pulsar signal as it
propagates through the curved spacetime region near the companion, where
is the angle of inclination of
the orbit relative to the plane of the sky. An additional 14 relativistic parameters are measurable in
principle [88].
In GR, the five post-Keplerian parameters can be related to the masses of the two bodies and to
measured Keplerian parameters by the equations (TEGP 12.1, 14.6 (a) [281])
Because and
are separately measured parameters, the measurement of the three post-Keplerian
parameters provide three constraints on the two unknown masses. The periastron shift measures the total
mass of the system,
measures the chirp mass, and
measures a complicated function of the masses.
GR passes the test if it provides a consistent solution to these constraints, within the measurement
errors.
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The consistency among the constraints provides a test of the assumption that the two bodies behave as “point” masses, without complicated tidal effects, obeying the general relativistic equations of motion including gravitational radiation. It is also a test of strong gravity, in that the highly relativistic internal structure of the neutron stars does not influence their orbital motion, as predicted by the SEP of GR.
Recent observations [157, 271] indicate variations in the pulse profile, which suggests that the pulsar is undergoing geodetic precession on a 300-year timescale as it moves through the curved spacetime generated by its companion (see Section 3.7.2). The amount is consistent with GR, assuming that the pulsar’s spin is suitably misaligned with the orbital angular momentum. Unfortunately, the evidence suggests that the pulsar beam may precess out of our line of sight by 2025.
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