After core collapse in a supernova, a neutron star forms with a temperature of ~10^12 K. It cools off rapidly by the emission of neutrinos from the core, primarily generated by the direct URCA reactions n -> p + e- + nu-bar_e and e- + p -> n + nu_e. These processes dominate the cooling at least down to a core temperature of 10^9 K. Depending on the equation of state, at this temperature the direct URCA reactions may not conserve momentum, and are therefore strongly suppressed. If the core contains only neutrons, protons, and electrons then the most important process for core neutrino emission below 10^9 K is the modified URCA process, which adds a bystander nucleus to each side to absorb momentum. If, however, there are other significant particles in the core (e.g pions, kaons, or quarks), neutrino production - and therefore cooling - can proceed more efficiently than via the modified URCA process.
To determine a lower limit to the sensitivity of current observations to measurements of NS surface temperatures, we have used data from the Einstein Slew Survey (Elvis et al. 1990) to establish temperature limits for 275 pulsars which received nonzero exposure during the survey. The analysis procedure consisted of determining a count rate (or upper limit) for each pulsar position, and then converting this into a temperature assuming blackbody emission from the surface of a 10 km NS by folding the spectrum through the Einstein IPC response matrix. Values for the distance, age, and dispersion measure for each pulsar were taken from the Princeton pulsar database (Taylor, Manchester, and Lyne 1993). The dispersion measures were used to calculate values of N_H assuming ionization fractions identical to that derived from Crab pulsar data. The data are illustrated in the Figure below where we have plotted T_surf vs. age. Filled squares correspond to pulsars actually detected in the survey data; the smaller symbols correspond to upper limits to the count rates. For comparison, we have plotted cooling curves for a number of cooling models.
Click here for plot of x-ray data vs. cooling curves.
The vertical lines in the Figure correspond to the increase in sensitivity, for several particular samples, in going from the several second slew survey exposures to the existing ~10 ks ROSAT PSPC exposures, for which we have repeated the analysis (Slane and Lloyd 1995). It is clear that one of the data points already provides an interesting constraint on several cooling models. We note that similar survey results, using the ~500 s exposures obtained in the ROSAT all-sky survey, were reported by Becker et al. (1992).
Significant modifications to the x-ray spectrum can be introduced by the presence of a neutron star atmosphere. Models for such effects have been compiled by a number of authors (in partcular, see work by Pavlov, Shibanov & Zavlin and Rajagopal, Romani, & Miller).