A layer in a carbon white dwarf has density and temperature

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 layer in a carbon white dwarf has density

\rho = 1.0\times10^{10}\,\mathrm{kg\,m^{-3}}

and temperature

T = 1.0\times10^{7}\,\mathrm{K}

. The carbon ions have charge

Z=6

and mass number

A=12

. ((a)) Find the ion spacing

a = (3/4\pi n_i)^{1/3}

, where

n_i

is the number density of ions. ((b)) Find the Coulomb coupling parameter

\Gamma = \dfrac{Z^2e^2}{4\pi\epsilon_0 a k_B T}

and state whether this layer has crystallised, given that carbon crystallises near

\Gamma \approx 175

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