4.5 Post-Keplerian parameters4 Pulsar Timing4.3 Timing stability

4.4 Binary pulsars and Kepler's laws 

For binary pulsars, the simple timing model introduced in §  4.2 needs to be extended to incorporate the additional radial acceleration of the pulsar as it orbits the common centre-of-mass of the binary system. Treating the binary orbit using Kepler's laws to refer the TOAs to the binary barycentre requires five additional model parameters: the orbital period (tex2html_wrap_inline9007), projected semi-major orbital axis (tex2html_wrap_inline9555, see below), orbital eccentricity (e), longitude of periastron (tex2html_wrap_inline9559) and the epoch of periastron passage (tex2html_wrap_inline9561). This description, using five ``Keplerian parameters'', is identical to that used for spectroscopic binary stars.

For spectroscopic binaries the orbital velocity curve shows the radial component of the star's velocity as a function of time. The analogous plot for pulsars is the apparent pulse period against time. Two examples are given in Fig.  22 .


Click on thumbnail to view imageClick on thumbnail to view image

Figure 22: Orbital velocity curves for two binary pulsars. Left: PSR J1012+5307, a 5.25-ms pulsar in a 14.5-hour circular orbit around a low-mass white dwarf companion [177Jump To The Next Citation Point In The Article, 256Jump To The Next Citation Point In The Article, 125Jump To The Next Citation Point In The Article]. Right: PSR J1811-1736, a 104-ms pulsar in a highly eccentric 18.8-day orbit around a massive companion (probably another neutron star) [147Jump To The Next Citation Point In The Article].

Constraints on the mass of the orbiting companion can be placed by combining the projected semi-major axis tex2html_wrap_inline9555 and the orbital period to obtain the mass function:


where G is the universal gravitational constant. Assuming a pulsar mass tex2html_wrap_inline9569 of tex2html_wrap_inline9571 (see below), the mass of the orbiting companion tex2html_wrap_inline9573 can be estimated as a function of the (initially unknown) angle i between the orbital plane and the plane of the sky. The minimum companion mass tex2html_wrap_inline9577 occurs when the orbit is assumed edge-on (tex2html_wrap_inline9579). For a random distribution of orbital inclination angles, the probability of observing a binary system at an angle less than some value tex2html_wrap_inline9581 is tex2html_wrap_inline9583 . This implies that the chances of observing a binary system inclined at an angle tex2html_wrap_inline9585 is only 10%; evaluating the companion mass for this inclination angle tex2html_wrap_inline9587 constrains the mass range between tex2html_wrap_inline9577 and tex2html_wrap_inline9587 at the 90% confidence level.

4.5 Post-Keplerian parameters4 Pulsar Timing4.3 Timing stability

image Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
© Max-Planck-Gesellschaft. ISSN 1433-8351
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