A carbon-oxygen white dwarf of mass has (fully ionised carbon and oxygen)

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Astrophysics & Cosmology · Stellar death and compact objects

Stars from the Inside, Ch White dwarfs: the relativistic polytrope, the Chandrasekhar mass and a cooling clock

Problem

A carbon-oxygen white dwarf of mass M=0.4 M⊙M = 0.4\,M_\odot has μe=2\mu_e = 2 (fully ionised carbon and oxygen). Using the non-relativistic mass-radius relation R≈1.05×104 km (M/0.6 M⊙)−1/3(μe/2)−5/3R \approx 1.05\times10^{4}\,\mathrm{km}\,(M/0.6\,M_\odot)^{-1/3}(\mu_e/2)^{-5/3}, ((a)) find its radius RR. ((b)) given that the central density scales as ρc∝M/R3\rho_c \propto M/R^3 and that a 0.6 M⊙0.6\,M_\odot star of this composition has ρc≈1.5×109 kg m−3\rho_c \approx 1.5\times10^{9}\,\mathrm{kg\,m^{-3}}, find ρc\rho_c for this 0.4 M⊙0.4\,M_\odot star.

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