A layer inside a low-mass white dwarf has mass density and electron mean molecular…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Quantum statistical mechanics and quantum gases · Quantum statistical mechanics and quantum gases

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

Problem

A layer inside a low-mass white dwarf has mass density

\rho = 1.6\times10^{7}\,\mathrm{kg\,m^{-3}}

and electron mean molecular weight

\mu_e = 2

(fully ionised carbon-oxygen matter, one electron per two nucleons). ((a)) Compute the electron number density

n_e

and the Fermi momentum

p_F

. ((b)) Compute

x = p_F/m_ec

and state whether the non-relativistic limit is justified here. ((c)) Compute the electrons' Fermi kinetic energy

E_F

in keV, using the non-relativistic expression.

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