Thermal Evolution of the Central Star in Pa 30

Abstract

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 $ΔM\approx0.02-0.04\,M_\odot$. 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.

Figures (11)

• Figure 1: Diagram of a quadrant of the central star in Pa 30. The blue region represents the hot envelope with mass $\Delta M$ and the orange/red region represents the cooler core with mass $M_c$. As we derive in Section \ref{['sec:hot envelope']}, for a constant luminosity $L$ though the envelope and energy carried by radiative diffusion, this layer has a $T\propto r^{-1}$ and $\rho\propto r^{-3}$ profile. As $L$ goes down with time, the surface radius $R_s$ contracts as the layer heats.
• Figure 2: Profiles of $T$, $\rho$ and the carbon-carbon burning rate $\epsilon_{\rm CC}$ for a cooling envelope model with $M_c=1.25\,M_\odot$, $\Delta M=0.03\,M_\odot$, and $R_c=7\times10^8\,{\rm cm}$. Each color line represents a different $\chi$ (see text for the specific values), which in turn corresponds to a different time during the cooling as shown in the bottom panel. The vertical black dashed line represents the surface of the core.
• Figure 3: Time evolution of the luminosity $L$ and the envelope radius $R_s$, each keeping $M_c=1.25\,M_\odot$ and $\Delta M=0.03\,M_\odot$ fixed, while varying $R_c$ with values indicated by the different colored lines. This demonstrates that, over the timescales of interest, $L$ varies only slightly, with a larger $L$ for smaller $R_c$. The radius $R_s$ depends very sensitively to $R_c$, with an inverse relationship between the two (although at sufficiently late times these lines cross and a smaller $R_c$ will asymptote to a smaller $R_s$).
• Figure 4: Similar to Figure \ref{['fig:rcore']}, but this time fixing $\Delta M=0.03\,M_\odot$ and $R_c=7\times10^8\,{\rm cm}$, while varying $M_c$. Here, the main change is in the luminosity, with larger $M_c$ corresponding to a larger $L$. Since the dynamic range of possible $M_c$ values is relatively small, the impact on the $R_s$ evolution is not very strong.
• Figure 5: Similar to Figure \ref{['fig:rcore']}, but this time fixing $M_c=1.25\,M_\odot$ and $R_c=7\times10^8\,{\rm cm}$, while varying $\Delta M$. Here we see that the observed radius can vary dramatically with envelope mass, and at sufficiently large $\Delta M$ it does not change appreciably over the observational time period.