Pulsar timing and neutron star masses

4.6 Pulsar timing and neutron star masses

Multiple PK parameters have now been measured for a number of binary pulsars which provide very precise measurements of the neutron star masses [378 , 339

]. Figure 28

shows the distribution of masses following updates to a recent compilation [339 ]. While the young pulsars and the double neutron star binaries are consistent with, or just below, the canonical $1.4 M ⊙$ , we note that the millisecond pulsars in binary systems have, on average, significantly larger masses. This provides strong support for their formation through an extended period of accretion in the past, as discussed in Section 2.6.

Figure 28: Distribution of neutron star masses as inferred from timing observations of binary pulsars and X-ray binary systems. Figure adapted from an original version provided by Ingrid Stairs. Additional information on globular cluster pulsar mass constraints provided by Paulo Freire. Error bars show one-sigma uncertainties on each mass determination.

Also shown on this diagram are several eccentric binary systems in globular clusters which have their masses constrained from measurements of the relativistic advance of periastron and the Keplerian mass function. In these cases, the condition $sin i < 1$ sets a lower limit on the companion mass $mc > (fmassM 2)1∕3$ and a corresponding upper limit on the pulsar mass. Probability density functions for both $mp$ and $mc$ can also be estimated in a statistical sense by assuming a random distribution of orbital inclination angles. An example of this is shown in Figure 29 for the eccentric binary millisecond pulsar in M5 [120 ] where the nominal pulsar mass is $2.08 ± 0.19M ⊙$ ! This is a potentially outstanding result. If confirmed by the measurement of other relativistic parameters, these supermassive neutron stars will have important constraints on the equation of state of superdense matter.

Figure 29: Pulsar mass versus companion mass diagram showing mass constraints for the eccentric binary millisecond pulsar B1516+02B [120 ]. The allowed parameter space is bounded by the dashed lines which show the uncertainty on the total mass from the measurement of the relativistic advance of periastron. Masses within the hatched region are disallowed by the Keplerian mass function and the constraint that $sini < 1$ . Assuming a random distribution of orbital inclination angles allows the probability density functions of the pulsar and companion mass to be derived, as shown by the top and right hand panels. Figure provided by Paulo Freire.

Currently the largest measurement of a radio pulsar mass through multiple PK parameters is the eccentric millisecond pulsar binary system J1903+0327 [72 ] (see also Section 2.9). Thus, in addition to challenging models of millisecond pulsar formation, this new discovery has important implications for fundamental physics. When placed on the mass–radius diagram for neutron stars [209 ], this $1.74 M ⊙$ pulsar appears to be incompatible with at least four equations of state for superdense matter. Future timing measurements are required to consolidate and verify this potentially very exciting result.