We carry out a general-relativistic global linear stability analysis of the amassed carbon fuel on the surface of an accreting neutron star to determine the conditions under which superbursts occur .
We reproduce the general observational characteristics of superbursts , including burst fluences , recurrence times , and the absence of superbursts on stars with accretion rates \dot { M } < 0.1 \dot { M } _ { \mathrm { Edd } } , where \dot { M } _ { \mathrm { Edd } } denotes the Eddington limit .
By comparing our results with observations , we are able to set constraints on neutron star parameters such as the stellar radius and neutrino cooling mechanism in the core .
Specifically , we find that accreting neutron stars with ordered crusts and highly efficient neutrino emission in their cores ( due to direct URCA or pionic reactions , for example ) produce extremely energetic ( > 10 ^ { 44 } ergs ) superbursts which are inconsistent with observations , in agreement with previous investigations .
Also , because of pycnonuclear burning of carbon , they do not have superbursts in the range of accretion rates at which superbursts are actually observed unless the crust is very impure .
Stars with less efficient neutrino emission ( due to modified URCA reactions , for example ) produce bursts that agree better with observations .
Stars with highly inefficient neutrino emission in their cores produce bursts that agree best with observations .
Furthermore , we find that neutron stars with large radii ( R \sim 16 km ) produce very energetic superbursts that conflict with observations , even if the core neutrino emission mechanism is highly inefficient .
Superburst characteristics are quite sensitive to several other parameters as well , most notably the composition of the accreted gas , concentration of carbon in the ignition region , and degree of crystallization of the crust .
All systems that accrete primarily hydrogen and in which superbursts are observed show evidence of H- and He-burning delayed mixed bursts .
We speculate that delayed mixed bursts provide sufficient amounts of carbon fuel for superbursts and are thus a prerequisite for having superbursts .
We compare our global stability analysis to approximate one-zone criteria used by other authors and identify a particular set of approximations that give accurate results for most choices of parameters .