Thus, all three scenarios are currently consistent with the observations, but predict different families of cold stars. Similar conclusions have been made by a number of authors (see, e.g., [@yp04; @pgw06] and references therein). Calculations show that the the neutrino luminosity in the inner core should be $\approx$30–100 times higher than the modified Urca luminosity to explain all the sources and leave no space for neutron stars colder than the observed ones. A discovery of very cold neutron stars would be crucial to firmly constrain the enhanced neutrino emission level.

Unfortunately, current observations give no reliable constraints on the position of the transition layer between slowly and fastly neutrino emitting regions in the core (on $\rho_1$ and $\rho_2$ or $M_1$ and $M_2$ in Fig. \[concept\]).

Other aspects
=============

We do not discuss in detail many aspects of the cooling theory but mention them here.

First, cooling can also be regulated by heat conduction in the neutron star crust. The thermal conductivity in the crust can be affected by composition of the matter (e.g., by the presence of light elements in accreted surface layers) and magnetic fields (in the outer and inner crust; see, e.g., [@yp04; @pgw06; @gkp06] and references therein). 