A carbon-oxygen white dwarf of mass and radius is driven to explosive thermonuclear…

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Stellar death and compact objects · Stellar death and compact objects

Stars from the Inside, Ch Stellar explosions: core collapse, the neutrino-driven shock, radioactive light and remnants

Problem

A carbon-oxygen white dwarf of mass

1.35\,M_\odot

and radius

1800\,\mathrm{km}

is driven to explosive thermonuclear burning, releasing

7.0\times10^{13}\,\mathrm{J\,kg^{-1}}

as its carbon and oxygen fuse to iron-group nuclei. Its net binding energy, the gravitational energy less the electrons' kinetic energy, is about

5\times10^{43}\,\mathrm{J}

. ((a)) Compute the total burning energy released. ((b)) Estimate the gravitational energy from the uniform-sphere value

\dfrac{3}{5}\dfrac{GM^2}{R}

. ((c)) State, with a reason, whether the white dwarf is completely disrupted, and explain why the burning energy does not have to exceed the gravitational energy of part (b).

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