SNAPSHOT: Connections between Internal and Surface Properties of Massive Stars

We introduce SNAPSHOT, a technique to systematically compute stellar structure models in hydrostatic and thermal equilibrium based on 3 structural properties - core mass $M_{\rm core}$, envelope mass $M_{\rm env}$ and core composition. This approach allows us to connect these properties of stellar interiors to the luminosity and effective temperature $T_{\rm eff}$ in a more systematic way than with stellar evolution models. For MS models, we derive an analytical relationship between $M_{\rm core}$, $M_{\rm total}$ and central H abundance that can be used in rapid stellar evolution algorithms. Core-He burning models with $M_{\rm core}/M_{\rm total}$ from 0.2 to 0.8 have convective envelopes, low $T_{\rm eff}$ and will appear as red supergiants. For a given $M_{\rm core}$, they exhibit a small variation in luminosity (0.02 dex) and $T_{\rm eff}$ ($\sim 400\,\mathrm{K}$) over a wide range of $M_{\rm env}$ ($\sim 2 - 20\,\mathrm{M}_{\odot}$). This means that it is not possible to derive red supergiant masses from luminosities and $T_{\rm eff}$ alone. We derive the following relationship between $M_{\rm core}$ and the total luminosity of a red supergiant during core He burning: $\log M_{\rm core} \simeq 0.44 \log L/L_{\odot} - 1.38$. At $M_{\rm core}$/$M_{\rm total} \approx 0.2$, our models exhibit a bi-stability and jump from a RSG to a BSG structure. Our models with $M_{\rm core}/M_{\rm total} > 0.8$, which correspond to stripped stars produced by mass loss or binary interaction, show that $T_{\rm eff}$ has a strong dependence on $M_{\rm env}$, $M_{\rm core}$ and the core composition. We find the mass of one of these stripped stars in a binary system, HD 45166, to be less than its dynamical mass. When a large observational sample of stripped stars becomes available, our results can be used to constrain their masses and the physics of binary interaction.