= Central stellar temperature bound from the virial theorem
{title2=$T_c\ge\langle T\rangle_M>\mu m_pGM/(6k_BR)$}
For spherical <hydrostatic equilibrium> with negligible surface <pressure>, <ideal gas> support and constant <mean molecular weight> $\mu$, the <stellar virial theorem> gives $3k_B\int T\,dm/(\mu m_p)=\int Gm\,dm/r$. Since $r<R$ throughout the interior, the right side exceeds $GM^2/(2R)$. Division by $M$ gives the stated mass-weighted <temperature> bound. The central bound additionally assumes that the central <temperature> is maximal. A central <pressure> lower bound alone is insufficient without controlling central <mass density>.
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