Net reaction rate and neutrino emissivity for the Urca process in departure from chemical equilibrium

We discuss the effect of compression on Urca shells in the ocean and crust of accreting neutron stars, especially in superbursting sources. We find that Urca shells may be deviated from chemical equilibrium in neutron stars which accrete at several tenths of the local Eddington accretion rate. The deviation depends on the energy threshold of the parent and daughter nuclei, the transition strength, the temperature, and the local accretion rate. In a typical crust model of accreting neutron stars, the chemical departures range from a few tenths of $k_{B}T$ to tens of $k_{B}T$ for various Urca pairs. If the Urca shell can exist in crusts of accreting neutron stars, compression may enhance the net neutrino cooling rate by a factor of about $1\sim 2$ relative to the neutrino emissivity in chemical equilibrium. For some cases, such as Urca pairs with small energy thresholds and/or weak transition strength, the large chemical departure may result in net heating rather than cooling, although the released heat can be small. Strong Urca pairs in the deep crust are hard to be deviated even in neutron stars accreting at the local Eddington accretion rate.

Figure 1

Net cooling rate ${\epsilon }_{\mathrm{net}}(T,\eta )$ in units of ${\epsilon }_{\nu }(T,0)$. According to the $\chi$ values in Table 1, we choose $\chi =40,60,80,100,200,300$ for illustrations. These lines have shown much in common, the dependence of net cooling rate on $\chi$ values (thus Urca pairs) is relatively weak, the net cooling rate will be enhanced if $0<\eta \lesssim 4.5$, when $\eta >5.5$, there will be no net cooling but net heating.