In addition to the symbols defined above for Equation (10),
,
,
and
s. All masses are in solar units.
Measurements of post-Keplerian parameters for PSR B1913+16
have been carried out by Taylor and a number of collaborators
over the years with steadily improving precision. The first of
these parameters to be measured was the advance of the longitude
of periastron
. This measurement is analogous to the perihelion advance of
Mercury [169]. For PSR B1913+16 this amounts to about 4.2 degrees per
year [237], some 4.6 orders of magnitude larger than for Mercury. A
measurement of
alone yields the total mass for this system,
, assuming this advance is due to general relativity.
Measurement of a second post-Keplerian parameter for B1913+16,
(gravitational redshift and transverse Doppler shifts in the
orbit), permits an unambiguous determination of
,
and
i
when combined with
and the five Keplerian parameters. The original
measurements [236
] have since been substantially refined [239
,
240
] and the mass of the pulsar and its unseen companion have been
determined to be
and
respectively. Such phenomenal precision is a testament to the
timing stability of radio pulsars as clocks, and the diligence of
Taylor and collaborators in carrying out these long-term
measurements. Similar mass measurements now exist for the two
other double neutron star binary systems discussed in §
3.4.1
: B1534+12 [220
] and B2127+11C [66]. For a number of other systems,
measurements allow interesting constraints to be placed on the
component masses [246
,
179
,
248].
An important general relativistic prediction for eccentric
double neutron star systems is the orbital decay due to the
emission of gravitational radiation (
in Equation (13
)). Taylor et al. [236
,
239
,
240
] were able to measure this for B1913+16 and found it to be in
excellent agreement with the predicted value.
The orbital decay, which corresponds to a shrinkage of about 3.2 mm per orbit, is seen most dramatically as the gradually increasing shift in orbital phase for periastron passages with respect to a non-decaying orbit shown in Fig. 23 . This figure includes recent Arecibo data taken in 1998 and 1999 following the upgrade of the telescope in the mid 1990s. The observations of the orbital decay, now spanning a 25-year baseline, are in agreement with general relativity at the level of about 0.5% and provide the first (indirect) evidence for the existence of gravitational radiation. Hulse and Taylor were awarded the Nobel prize in Physics in 1993 [241, 101, 234] in recognition of their discovery of this remarkable laboratory for testing general relativity.
For those binary systems which are oriented nearly edge-on to
the line-of-sight, a significant delay is expected for orbital
phases around superior conjunction where the pulsar radiation is
bent in the gravitational potential well of the companion star.
The so-called ``range'' and ``shape'' of the Shapiro delay effect
are parameterized by the last two post-Keplerian parameters
r
and
that were introduced in Equations (14
) and (15
). This effect, analogous to the solar system Shapiro delay, has
so far been measured for two neutron star-white dwarf binary
systems, B1855+09 and J1713+0747 [206,
117
,
46
], and for the double neutron star binaries B1534+12 [220
] and B1913+16 [240
].
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Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer http://www.livingreviews.org/lrr-2001-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |