White Dwarf Heating and Subsequent Cooling in Dwarf Nova Outbursts

We follow the time dependent thermal evolution of a white dwarf (WD)undergoing sudden accretion in a dwarf nova outburst, using both simulationsand analytic estimates. The post-outburst lightcurve clearly separates intoearly times when the WD flux is high, and late times when the flux is near thequiescent level. The break between these two regimes, occurring at a time oforder the outburst duration, corresponds to a thermal diffusion wave reachingthe base of the freshly accreted layer. Our principal result is that long afterthe outburst, the fractional flux perturbation about the quiescent flux decaysas a power law with time (and {\it not} as an exponential). We use this resultto construct a simple fitting formula that yields estimates for both thequiescent flux and the accreted column, i.e. the total accreted mass divided byWD surface area. The WD mass is not well constrained by the late timelightcurve alone, but it can be inferred if the accreted mass is known fromobservations. We compare our work with the well-studied outburst of WZ Sge,finding that the cooling is well described by our model, giving an effectivetemperature $T_{\rm eff}=14,500 {\rm K}$ and accreted column $\Deltay\approx10^6 {\rm g cm^{-2}}$, in agreement with the modeling of Godon et al.To reconcile this accreted column with the accreted mass inferred from thebolometric accretion luminosity, a large WD mass $\gtrsim1.1M_\odot$ is needed.Our power law result is a valuable tool for making quick estimates of theoutburst properties. We show that fitting the late time lightcurve with thisformula yields a predicted column within 20% of that estimated from our fullnumerical calculations.Comment: Accepted for publication in The Astrophysical Journal, 10 pages, 8 figure