= Linear-density stellar model
{title2=$\rho(r)=\rho_c(1-r/R)$}
An imposed spherical profile $\rho=\rho_c(1-r/R)$ gives $M=\pi\rho_cR^3/3$ in <hydrostatic equilibrium>. For an <ideal gas> with zero surface pressure, $P=P_c(1-x)^2(1+2x-9x^2/5)$ and $T=T_c(1-x)(1+2x-9x^2/5)$, where $x=r/R$, $P_c=5GM^2/(4\pi R^4)$ and $T_c=5GM/(12\mathcal RR)$. The density has a central cusp and temperature initially rises outward, so positive outward <radiative diffusion> with regular positive nuclear heating cannot satisfy this imposed profile near the centre.
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