The PSR B0833-45 (the Vela pulsar) is the famous neutron star. Its age is about $11$ kyr and it cools mainly via neutrino emission from its superdense core. Its surface temperature of $\sim 0.7$ MK was obtained from the analysis of its X-ray spectrum assuming that the star's mass is $1.4$ $M_\odot$ and the radius is $10$ km (Pavlov et al. 2001, ApJ 552, L129). The Vela pulsar appears to be one of the coldest middle-aged neutron stars with measured surface temperature.
We have reanalyzed the Vela's X-ray spectrum inferred from archival Chandra observations (ObsID 127, 131 and 1852). We have employed a magnetic hydrogen (nsmax) atmosphere model from Sherpa package, considering a wide range of possible masses and radii. Our results show that, while the Vela's surface temperature is very close to that derived by Pavlov et al. (2001), the star has likely either large mass ($\ge 1.7$ $M_\odot$) or large radius ($\ge 13$ km).
Using the results of spectral analysis, we have considered the cooling of the Vela pulsar. We have assumed that the star has a nucleon core with strong triplet neutron superfluidity, prohibited (or suppressed) direct Urca process and a partially accreted outer envelope (the so-called minimal cooling paradigm, Page et al. 2004, ApJSS 155, 623). Neutron pairing produces a sufficient enhancement of neutrino emission from the core (compared to the standard neutrino cooling via modified Urca process) so that the neutrino cooling can be responsible for the Vela's low temperature. Employing nuclear physics restrictions on neutron triplet pairing models, we can constrain the mass of the accreted matter (containing light elements) in the Vela's outer envelope.
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