An unevolved star of mass and radius is modelled as an polytrope

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar structure, energy generation and evolution · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Pressure against gravity: the equation of state, polytropes and the Lane-Emden equation

Problem

An unevolved star of mass M=2 M⊙M = 2\,M_\odot and radius R=1.6 R⊙R = 1.6\,R_\odot is modelled as an n=3n=3 polytrope, for which ξ1=6.8968\xi_1 = 6.8968, −ξ12θ1′=2.018-\xi_1^2\theta_1' = 2.018 and ρc/ρˉ=54.18\rho_c/\bar\rho = 54.18. Take μ=0.61\mu = 0.61. ((a)) Compute the central pressure Pc=WnGM2/R4P_c = W_n GM^2/R^4. ((b)) Compute the mean density ρˉ\bar\rho and the central density ρc\rho_c. ((c)) Compute the central temperature TcT_c.

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