Observations of cooling neutron stars allow to measure photospheric radii and to constrain the equation of state of nuclear matter at high densities .
In this paper we concentrate on neutron stars , which show thermal ( photospheric ) X-ray emission and have measured distances .
After a short summary of the radio pulsars falling into this category we review the observational data of the 7 radio quiet isolated neutron stars discovered by ROSAT which have been studied in detail by Chandra , XMM-Newton and optical observations .
Their spectra show blackbody temperatures between 0.5 and 1 million Kelvin and an optical excess of a factor of 5-10 over the extrapolation of the X-ray spectrum .
Four of these sources show periodicities between 3.45 and 11.37 sec indicating slow rotation .
The pulsed fractions are small , between 6 and 18 % .
The magnetic fields derived from spin down and/or possible proton cyclotron lines are of the order 10 ^ { 13 } -10 ^ { 14 } G. We then discuss RX J1856.5–3754 in detail and suggest that the remarkable absence of any line features in its X-ray spectrum is due to effects of strong magnetic fields ( \sim 10 ^ { 13 } G ) .
Assuming blackbody emission to fit the optical and X-ray spectrum we derive a conservative lower limit of the ‘ ‘ apparent ’ ’ neutron star radius of 16.5 km \times ( d/117 pc ) .
This corresponds to the radius for the ‘ ‘ true ’ ’ radius of 14 km for a 1.4 M _ { \odot } neutron star , indicating a stiff equation of state at high densities .
A comparison of the result with mass-radius relations shows that in this case a quark star or a neutron star with a quark matter core can be ruled out with high confidence .