Blog #21: WS7.1, #4

4. Calculate the total energy output, in ergs, of the explosion, assuming that the white dwarf's mass is converted to output energy via fusion of carbon into nickel. Note that the process of carbon fusion is not entirely efficient, and only about 0.1% of this mass will be radiated away as electromagnetic radiation (light). 

Since we're converting mass to energy, we can use \(E=mc^2\), but we have to multiply by 0.001 since it's only 0.1% efficient.
\(E=(1.4*2*10^{30}kg)(3.0*10^8m/s)^2*0.001=2.52*10^{44}J\rightarrow 2.52*10^{51}ergs\)

How does this compare to the total binding energy, in ergs, of the original white dwarf? Does the white dwarf completely explode, or is some mass left over in the form of a highly concentrated remnant? 

To calculate the binding energy of the star, we can use the potential energy as given by the Virial Theorem: \(E_{bind}=U=\frac{-GM^2}{R}\). Since \(M=2M_\odot\) and \(R=12*10^6\), we can simply plug those values in.
\(E_{bind}=U=\frac{-(6.674*10^{-11}m^2kg^{-1}s^{-2})(1.4*2*10^{30}kg)^2}{12*10^6m}=4.36*10^{43}J\rightarrow 4.36*10^{50}ergs\)
Since the energy released is greater than the binding energy, the bonds holding the star's atoms together are broken. These atoms will be blown away, and there won't be anything left over.