Observations of radio pulsar- white dwarf binaries are also very promising. Both companions of such a system, a neutron star and a white dwarf, are compact stars, i.e., the approximation of point masses is valid. A pulsar timing easily gives at least all Keplerian parameters of the orbit (particularly, Pb, e, and x1 = a1 sin i). In order to measure the masses, one needs however two additional independent relations (§§ 9.1.1 a and 9.1.2a). In a compact enough binary, the relativistic effects in pulsar motion can be detected as described in § 9.1.2 a. With some luck, two relativistic parameters can be determined and the stellar masses M1 = MPSR and M2 = MWD can be obtained. However, in wide binary systems, the relativistic effects are weak. One may reliably determine only one relativistic parameter or no parameters at all.
The great advantage of the pulsar - white dwarf binaries is that the additional relations for a mass measurement can be taken from optical observations of white dwarf companions, as described, for instance, by Thorsett & Chakrabarty (1999). For example, because a white dwarf mass and radius are theoretically related, an estimate of the radius (from measurements of the optical flux, effective surface temperature, and distance) can give the white dwarf mass. Another possibility is to measure the surface gravity by fitting an observed white dwarf spectrum with spectra given by theoretical atmosphere models.
However, the most powerful tool is provided by the so-called Pb — M2 relation (e.g, Rappaport et al. 1995, Podsiadlowski et al. 2002, and references therein). It is expected that this relation holds for wide binaries containing millisecond pulsars in almost circular orbits. It assumes that in the past a binary contained a neutron star and a low-mass giant evolved later to a white dwarf. The evolution was accompanied by a mass transfer from the giant envelope to the pulsar. The mass exchange circularizes the orbit and recycles the pulsar to millisecond periods. The stellar evolution theory gives a strict relation between the mass of the giant core and the radius of its envelope. It is expected that the envelope fills its Roche lobe until the end of the mass transfer. The orbital separation at this phase is then a known function of the envelope radius and the giant-core mass (equal to the mass M2 of the future white dwarf), which allows one to estimate M2.
The parameters of some selected pulsar - white dwarf binaries are presented in Table 9.5; the inferred masses are given in Table 9.6. All the orbits, except for J1141-6545, B1802-07 and B2303+46, are nearly circular, which is probably a result of preceding evolution. PSR B1802-07 belongs to the globular cluster NGC 6539 - its orbit can be eccentric as a result of recent close encounter with one of the cluster stars. The two other eccentric binaries (J1141-6545 and B2303+46) are compact and contain rather young neutron stars born after white dwarfs - they had not enough time to circularize their orbits. Only two systems, B2320+46 and J1141-6545, contain slowly rotating pulsars; the spin periods of pulsars in other systems are short, from 3 ms to 30 ms. Only four systems, J0751+1807, J1012+5307, J1141-6545, and J1909-3744, are really compact (Pb < 1 day), i.e., the pulsars can show strong relativistic effects. The orbits of three of them (J0751+1807, J1012+5307, and J1909-3744) are nearly circular, which hampers the measurement of the periastron advance oj and the parameter 7. In Table 9.5 we list the measured relativistic parameters. Let us mention that for some systems (particularly, for PSR J1713+0747 and PSR J2019+2425) kinematic variations of x 1/x1 induced by pulsar proper motion have been extracted from pulsar timing (Nice et al. 2003) to impose constraints
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