Thermal Evolution of the Central Star in Pa 30

Pa 30 has been identified as the nebular remnant of the historical SN 1181. It is host to a hot ($\approx200,000\,{\rm K}$) central star (WD J005311) with a fast wind ($\approx16,000\,{\rm km\,s^{-1}}$) radiating at roughly the Eddington luminosity for a solar mass ($\approx1.5\times10^{38}\,{\rm erg\,s^{-1}}$). We explore the thermal evolution of this star to understand how it progressed toward the state it is observed as today as well as to constrain its underlying physical properties. We develop a semi-analytic two-component model, which approximates the central star as a hot radiating envelope contracting and cooling above a relatively cool core. Comparing this model with the observed luminosity and radius requires a core mass $M_c\approx1.15-1.4\,M_\odot$ with a core radius $R_c\approx(6-8)\times10^8\,M_\odot$, and a hot envelope mass $\Delta M\approx0.02-0.04\,M_\odot$. The small envelope mass is the best constrained of these parameters due to the need to reach the observed radius of $\approx0.15\,R_\odot$ in a timescale of $\approx845\,{\rm yrs}$. These results favor a picture where SN 1181 involved the merger of O/Ne and C/O white dwarfs, and where the majority of the latter was ejected in the explosion. We also explore which models ignite carbon burning at the base of the hot envelope, demonstrating that this is possible but not necessarily required to explain the current thermal state of the central star.