4.6 Geodetic precession4 Pulsar Timing4.4 Binary pulsars and Kepler's

4.5 Post-Keplerian parameters 

Although many of the presently known binary pulsar systems can be adequately described by a Keplerian orbit, there are several systems, including the original binary pulsar B1913+16, which exhibit relativistic effects that require an additional set of up to five ``post-Keplerian'' parameters. Within the framework of general relativity, these can be written [37] as:

  equation892

equation900

  equation910

  equation928

  equation932

In addition to the symbols defined above for Equation (10Popup Equation), tex2html_wrap_inline9593, tex2html_wrap_inline9595, tex2html_wrap_inline9597 and tex2html_wrap_inline9599 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 tex2html_wrap_inline9601 . 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 tex2html_wrap_inline9601 alone yields the total mass for this system, tex2html_wrap_inline9605, assuming this advance is due to general relativity.

Measurement of a second post-Keplerian parameter for B1913+16, tex2html_wrap_inline9607 (gravitational redshift and transverse Doppler shifts in the orbit), permits an unambiguous determination of tex2html_wrap_inline9569, tex2html_wrap_inline9573 and i when combined with tex2html_wrap_inline9601 and the five Keplerian parameters. The original measurements [236Jump To The Next Citation Point In The Article] have since been substantially refined [239Jump To The Next Citation Point In The Article, 240Jump To The Next Citation Point In The Article] and the mass of the pulsar and its unseen companion have been determined to be tex2html_wrap_inline9617 and tex2html_wrap_inline9619 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 [220Jump To The Next Citation Point In The Article] and B2127+11C [66]. For a number of other systems, tex2html_wrap_inline9601 measurements allow interesting constraints to be placed on the component masses [246Jump To The Next Citation Point In The Article, 179Jump To The Next Citation Point In The Article, 248].

An important general relativistic prediction for eccentric double neutron star systems is the orbital decay due to the emission of gravitational radiation (tex2html_wrap_inline9623 in Equation (13Popup Equation)). Taylor et al. [236Jump To The Next Citation Point In The Article, 239Jump To The Next Citation Point In The Article, 240Jump To The Next Citation Point In The Article] were able to measure this for B1913+16 and found it to be in excellent agreement with the predicted value.

  

Click on thumbnail to view image

Figure 23: Orbital decay in the binary pulsar B1913+16 system demonstrated as an increasing orbital phase shift for periastron passages with time. The general relativistic prediction due entirely to the emission of gravitational radiation is shown by the parabola.

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 tex2html_wrap_inline9597 that were introduced in Equations (14Popup Equation) and (15Popup Equation). 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, 117Jump To The Next Citation Point In The Article, 46Jump To The Next Citation Point In The Article], and for the double neutron star binaries B1534+12 [220Jump To The Next Citation Point In The Article] and B1913+16 [240Jump To The Next Citation Point In The Article].



4.6 Geodetic precession4 Pulsar Timing4.4 Binary pulsars and Kepler's

image 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