is the neutrinospheric temperature in units of $4$ MeV.

The numerical models are evolved in FLASH3.2 [@dubey2009], with the modifications introduced in @F12. The computational domain covers the radial range $r\in [0.4,7]r_{\rm s0}$, and the full range of polar angles. The radial grid spacing is logarithmic, with 408 cells in radius ($\Delta r/r \simeq 0.7\%$). We use 300 angular cells equispaced in $\cos\theta$, yielding constant volume elements at fixed radius ($\Delta \theta \simeq \Delta r/r$ on the equator). The boundary conditions are reflecting at the polar axis and at the surface of the neutron star, and set to the upstream solution at the outer radial boundary. Accreted material accumulates in the innermost $\sim $ two cells next to the inner boundary.

  ----------- ------------------------- ---------------------------------- -------------- --------------------------------- ----------- ----------- ------------------------------- --------------------- ------------------------- -------------------------------- ------------------------------- -------------------
  [Model]{}       [$\varepsilon$]{}                  [$B$]{}                [$\chi_0$]{}   [$(\Delta\rho/\rho)_{\rm c}$]{}   [$r_g$]{}   [$r_s$]{}             [Pert.]{}                  [Ampl.]{}        [$\bar{t}_{\rm adv}$]{}          [$\bar{\chi}$]{}          [$E_{\rm kin,g}/M_{\rm g}$]{}   [$t_{\rm exp}$]{}
  [ ]{}        [($v_{\rm ff0}^2/2$)]{}   [($r_{\rm s0} v_{\rm ff0}^3$)]{}                                                                                                            [($t_{\rm ff0}$)]{}                             [($10^{-2}\,v_{\rm ff0}^2$)]{}        [($t_{\rm ff0}$)]{}       
  e0B00                   0                             0                        0                       ...                    ...          1       rand. $\delta \mathbf{v}/v_r$        $10^{-3}$                  8.9                           0                               ...                       ...
  e0B02                                               0.002                     0.06                    0.14                   0.90        1.04                                                                      9.5                          0.69                             3.7                       ...
  e0B04                                               0.004                     0.3                     0.07                   0.78        1.09                                                                     10.2                          0.64                             2.9                       