Extended Data Figure 2: Temperature as a function of depth in the accreted neutron star crust for different Urca shell cooling strengths.

Here we use as a proxy for depth, where P is the pressure, g the local gravitational acceleration, ρ the mass density and z the spatial depth coordinate. As a baseline model, we fix the temperature to be T = 0.42 GK at P/g = 10⁹ g cm⁻² and T = 0.35 GK at the crust–core transition. In the absence of Urca shell cooling, the peak local temperature reaches 0.73 GK (solid curve) with the temperature at the superburst ignition depth (P/g ≈ 10¹² g cm⁻²) being 0.66 GK. With the addition of cooling using the HFB-21 mass model and a superburst ash composition (blue dotted line), a local temperature minimum, T = 0.33 GK, appears at the location of the Urca shell. Indeed, for these conditions the temperature at the Urca shell is lower than that at the upper boundary, so that a temperature inversion develops. Even for the much lower Urca shell emissivity of the FRDM mass model (blue dashed line), the temperature at the depth of the superburst ignition is ≲, which is inconsistent with typical superburst ignition conditions¹⁰. For both mass models, the temperature has a local minimum at the location of the Urca shell. The steady-state cooling luminosity from the shell is 2 × 10³⁵ erg s⁻¹ for the HFB-21 mass model and 1.4 × 10³⁵ erg s⁻¹ for the FRDM mass model. As a result, the Urca shell thermally decouples the envelope of light elements from the heating in the deeper crust.