neutrino luminosities lower and higher than the modified Urca level.

![Very schematic view of (a) neutrino emissivity profile in a neutron star core and (b) neutrino luminosity versus star’s mass at a fixed core temperature $T$. Units are arbitrary.[]{data-label="concept"}](yakfig3.ps){width="7.8cm"}

Now consider a set of nonsuperfluid neutron star models of masses from 1.1 to $1.97\,{\mbox{$M_\odot$}}$, with the mass step of $0.01\, {\mbox{$M_\odot$}}$ (Fig. \[cool4\]b). The first 26 models ($M \leq 1.35\, {\mbox{$M_\odot$}}< M_{\rm D}$) belong to the class of low-mass stars and show the universal slow cooling behavior. The next $1.36 \, {\mbox{$M_\odot$}}$ star has a small central kernel with the enhanced neutrino emission and shows much faster cooling (is much colder than all observed sources). All other more massive stars cool even faster via the direct Urca process and belong to the family of cold massive rapidly cooling stars. Evidently, these cooling curves cannot explain the data.

Basic concept
=============

A majority of realistic cooling scenarios, constructed up to now, satisfy the following basic phenomenological concept:

\(1) Low-mass stars undergo slow neutrino cooling.

\(2) Massive stars cool much faster via neutrino emission from their inner cores.

\(3) There is a family of medium-mass stars whose cooling is intermediate between the 