M/R estimates for two neutron stars in LMXBs with possible r-mode frequencies detected

The puzzling existence of a number of neutron stars that appear to be in the r-mode instability window supports further investigations of the r-mode frequencies, damping times and saturation amplitudes, especially now in light of the much anticipated and exciting results from LIGO and NICER. It has been suggested by Mahmoodifar and Strohmayer that coherent frequencies found in the RXTE data of the accreting millisecond pulsar XTE J1751-305 and during the 2001 superburst of 4U 1636-536 (one of the accreting sources to be observed by NICER) could, in fact, be r-modes. Based on these observations, we expand here the results of a previous work on relativistic, rotational, and differential rotation corrections to the r-mode frequency in order to provide more accurate estimates of the M-R relation for these neutron stars. Finally, we compare our results with predictions from a few realistic tabulated equations of state, providing further constraints that favour more compact models. We find that, if the observed frequencies indeed correspond to r-modes, then the masses of XTE J1751-305 and 4U 1636-536 should lie in the approximate ranges 1.48-1.56 and 1.60-1.68M(circle dot), respectively.