Rapidly rotating pulsars and the equation of state

It has recently been claimed that a submillisecond pulsar has been observed in the remnant of SN 1987A. If the pulsations are due to rotation of a neutron star at this frequency, the equation of state (EOS) must be severely limited. In general, soft equations of state allow rapid enough rotational frequencies, but the softness is limited by the observed neutron star mass of 1.44 M_⊙ in the binary pulsar PSR 1913+16. In order to simultaneously satisfy these two constraints, we show that in the vicinity of ordinary nuclear density, the pressure must vary relatively slowly with density, but at higher densities, the EOS must become relatively stiff and approach the causality limit. Specifically, in the absence of phase transitions above nuclear density and for cases in which the nuclear symmetry energy is an increasing function of density, the compression modulus of symmetric nuclear matter at the saturation density 0.16 fm^-3 must be less than about 160 MeV. If either of these situations occurs, higher values for the compression modulus may be possible, but in any case the EOS must still stiffen to the causal limit at high density. Examples of phase transitions that might permit rapid enough rotation are those due to pion or kaon condensates or to parity-doublet matter occurring around a few times the nuclear matter density. On the other hand, phase transitions to ordinary or strange quark matter well above nuclear densities soften the EOS to well below the causal limit and make rapid rotation much more difficult. Self-bound stars composed entirely of perturbative strange quark matter are not quite able to satisfy the requirements of rapid enough rotation and sufficient mass even in the optimum case where strange quarks are assumed to be massless. Other schematic self-bound stars can satisfy these constraints, but physical motivations for such equations of state are presently lacking.