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 . For PSR B1913+16 this amounts to about 4.2 degrees per year , 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  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  and B2127+11C . 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  and B1913+16 .
|Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
© Max-Planck-Gesellschaft. ISSN 1433-8351
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