Ideal-ion white-dwarf cooling timescale
= Ideal-ion white-dwarf cooling timescale
With carbon-ion <thermal energy> $U=Mk_BT_c/(8m_u)$ and <luminosity> $L=A(M/M_\odot)T_c^{7/2}$, the time between two core <Temperature>[temperatures] is $k_BM_\odot(T_f^{-5/2}-T_i^{-5/2})/(20m_uA)$. Late cooling is slow in this approximation. Extrapolating the formula does not prove a categorical observational absence of ultracool remnants, since atmosphere, crystallization and heat-capacity physics alter the simple model.