virial_temperature
plain-language theorem explainer
Virial temperature supplies the central stellar temperature scaling as M over R in units where the gravitational and thermal constants are normalized to one. Modelers of main-sequence stars cite this when combining hydrostatic equilibrium with nuclear burning to obtain the mass-luminosity relation. The definition proceeds by direct assignment of the ratio after the prefactor G m_p over k_B is set to unity.
Claim. The virial temperature is defined by $T_c(M,R) := M/R$ in units where $G m_p/k_B=1$, with $M$ the stellar mass and $R$ the radius.
background
The StellarEvolution module builds the Hertzsprung-Russell diagram from Recognition Science by combining the virial theorem for central temperature with the Gamow energy for nuclear rates. virial_temperature implements the proportionality $T_c ∝ G M m_p/(k_B R)$ after rescaling units so that the constant prefactor equals one. Upstream results include the RS-native gravitational constant $G=λ_rec² c³/(π ℏ)$ from the J-cost functional equation.
proof idea
The definition is a direct one-line assignment of the mass-to-radius ratio in the chosen natural units.
why it matters
It feeds the theorem temp_increases_with_mass that proves central temperature rises with mass at fixed radius. The declaration fills the virial-theorem step listed in the module key results for the RS_Stellar_Evolution_HR_Diagram paper. It anchors the temperature input to the luminosity scaling that emerges from nuclear burning equilibrium combined with radiative transport and hydrostatic equilibrium.
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