Electron capture (solid lines) and beta decay (dashed lines) rates of the ﹩{}^{23}\mathrm{Na}﹩–﹩{}^{23}\mathrm{Ne}﹩ Urca pair as calculated by MESA, using the on-the-fly methods described in this section. The value of ﹩\mathrm{log}(T/{\rm{K}})﹩ is shown next to each electron capture line; the beta decay line of matching color is at the same temperature. The rates vary rapidly, with both temperature and density, near the threshold density, which is roughly in the center of the plot.