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 sets a lower limit on the companion mass and a corresponding upper limit on the pulsar mass. Probability density functions for both and 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  where the nominal pulsar mass is ! 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.
Currently the largest measurement of a radio pulsar mass through multiple PK parameters is the eccentric millisecond pulsar binary system J1903+0327  (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 , this 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.
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