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 three structural properties - core mass M-core, envelope mass M-env, and core composition. This approach allows us to connect these properties of stellar interiors to the luminosity and effective temperature T-eff in a more systematic way than with stellar evolution models. We compute core-H burning models with total masses of M-total = 8-60 M-circle dot and central H mass fractions from 0.70 to 0.05. Using these, we derive an analytical relationship between M-core, M-total, and central H abundance that can be readily used in rapid stellar evolution algorithms. In contrast, core-He burning stars can have a wide range of combinations of M-core, M-env, and core compositions. We compute core-He burning models with M-core = 2-9 M-circle dot, M-env = 0-50 M-circle dot, and central He mass fractions of 0.50 and 0.01. Models with M-core/M-total from 0.2 to 0.8 have convective envelopes, low T-eff and will appear as red supergiants (RSGs). For a given M-core, they exhibit a small variation in luminosity (0.02 dex) and T-eff (similar to 400 K) over a wide range of M-env (similar to 2-20 M-circle dot). This means that it is not possible to derive RSG masses from luminosities and T-eff alone. We derive the following relationship between M-core and the total luminosity of an RSG during core He burning: log M-core similar or equal to 0.44log L/L-circle dot - 1.38. At M-core/M-total approximate to 0.2, our models exhibit a bistability and jump from an RSG to a BSG structure. Our models with M-core/M-total > 0.8, which correspond to stripped stars produced by mass-loss or binary interaction, show that T-eff has a strong dependence on M-env, M-core, and the core composition. We constrain the mass of one of these stripped stars in a binary system, HD 45166, and find it to be less than its estimated dynamical mass. When a large observational sample of stripped stars becomes available, our results can be used to constrain their M-core, M-env, mass-loss rates, and the physics of binary interaction.