 AGB envelope-loss and core-growth timescales

The fate of an Asymptotic giant branch star depends on whether its envelope is removed before its core reaches the next ignition or instability threshold. The approximate envelope-loss time is $t_{\mathrm{env}}=M_{\mathrm{env}}/|\dot{M}|$, while the time to add a required core mass $\Delta M_c$ is $t_{\mathrm{grow}}=\Delta M_c/{\dot{M}}_c$. Shell stellar nuclear fusion grows the core; third dredge-up can reduce the net growth. If $t_{\mathrm{env}}\ll t_{\mathrm{grow}}$, shell fuel disappears first and a white dwarf remnant is favored. The opposite ordering permits further core growth but does not by itself specify whether carbon burning is stable, explosive, or followed by further evolution. Both rates change with time, so the estimates guide rather than replace a stellar model.