Neutrino luminosities and heat capacities of neutron stars in analytic form

Abstract

We derive analytic approximations for the neutrino luminosities and the heat capacities of neutron stars with isothernal nucleon cores as functions of the mass and radius of stars. The neutrino luminosities are approximated for the three basic neutrino emission mechanisms, and the heat capacities for the five basic combinations of the partial heat capacities. The approximations are valid for for a wide class of equations of state of dense nucleonmatter. The results significantly simplify the theoretical interpretation of observations of cooling neutron stars as well as of quasistationary thermal states of neutron stars in X-ray transients. For illustration, we present an analysis of the neutrino cooling functions of nine isolated neutron stars taking into account the effects of their magnetic fields and of the presence of light elements in their heat blanketing envelopes. These results allow one to investigate the superfluid properties of neutron star cores.

Thermal Spectrum and Neutrino Cooling Rate of the Vela Pulsar

“…In the frame of the minimal cooling paradigm, the Vela's heat blanket cannot contain a large fraction of accreted matter. These conclusions are consistent with the earlier results [20] obtained from a more simplified analysis.…”

“…This special status of the Vela pulsar has been noticed previously (e.g., [20]). The Vela's spectrum has been analyzed assuming M = 1.4 M and R = 10 km (e.g., [7]).…”

“…In this standard case, the cooling function = stand can be well approximated by analytic expressions valid in a wide range of M and R for many different EOSs in nucleon cores (e.g., [20]). The cooling curves of such stars, T ∞ s (t), are almost independent of M and EOS.…”

“…We will employ the method similar to that discussed in [17,20,34] and in references therein. It is well described in the literature; we just outline the main points.…”

Occurrence of a Mott-like gap in single-particle spectra of electron systems possessing flat bands

“…In the scenario, discussed in the present article, opening the Mott's gap results in the profound suppression of neutrino cooling of hybrid compact stars with a sharp hadron-quark interface. In connection with this idea, it is not improbable that this suppression is relevant to recent observations of a central compact object in the supernova remnant HESSJ1731-347, being the hottest isolated neutron star, in spite of its venerable age [29,30]. I thank A. Chubukov, V. Shaginyan, G. Volovik and M. Zverev for valuable discussions.…”