  Chandra or XMM-Newton observations of quiescent low-mass X-ray binaries can
provide important constraints on the equation of state of neutron stars. The
mass and radius of the neutron star can potentially be determined from fitting
a neutron star atmosphere model to the observed X-ray spectrum. For a radius
measurement it is of critical importance that the distance to the source is
well constrained since the fractional uncertainty in the radius is at least as
large as the fractional uncertainty in the distance. Uncertainties in modelling
the neutron star atmosphere remain. At this stage it is not yet clear if the
soft thermal component in the spectra of many quiescent X-ray binaries is
variable on timescales too short to be accommodated by the cooling neutron star
scenario. This can be tested with a long XMM-Newton observation of the neutron
star X-ray transient CenX-4 in quiescence. With such an observation one can use
the Reflection Grating Spectrometer spectrum to constrain the interstellar
extinction to the source. This removes this parameter from the X-ray spectral
fitting of the EPIC pn and MOS spectra and allows one to investigate whether
the variability observed in the quiescent X-ray spectrum of this source is due
to variations in the soft thermal spectral component or variations in the power
law spectral component coupled with variations in N_H. This will test whether
the soft thermal component can indeed be due to the hot thermal glow of the
neutron star. Irrespective of the outcome of such a study, the observed cooling
in quiescence in sources for which the crust is significantly out of thermal
equilibrium with the core due to a prolonged outburst, such as KS 1731-260,
seem excellent candidates for mass and radius determinations through modelling
the observed X-rays with a neutron star atmosphere model.
