Constraining accreted neutron star crust shallow heating with the inferred depth of carbon ignition in X-ray superbursts

Evidence has accumulated for an as-yet unaccounted for source of heat located at shallow depths within the accreted neutron star crust. However, the nature of this heat source is unknown. I demonstrate that the inferred depth of carbon ignition in X-ray superbursts can be used as an additional constraint for the magnitude and depth of shallow heating. The inferred shallow heating properties are relatively insensitive to the assumed crust composition and carbon fusion reaction rate. For low-accretion rates, the results are weakly dependent on the duration of the accretion outburst, so long as accretion has ensued for enough time to replace the ocean down to the superburst ignition depth. For accretion rates at the Eddington rate, results show a stronger dependence on the outburst duration. Consistent with earlier work, it is shown that urca cooling does not impact the calculated superburst ignition depth unless there is some proximity in depth between the heating and cooling sources.