2. Let's estimate the minimum mass of a star. Brown dwarfs are supported by degeneracy pressure before hydrogen fusion starts, preventing them from ever reaching the main sequence. a) (10 points) Derive an expression for the temperature where the electron degeneracy and gas pressures are equal in terms of the mass M and radius R, again assuming constant density. Here the relevant composition is of purely ionized hydrogen. b) (10 points) Hydrogen fusion begins at a temperature T 107 K. Using your result in problem la for the white dwarf radius, calculate the maximum mass where degeneracy pressure supports the star before nuclear fusion begins. 2. Let's estimate the minimum mass of a star. Brown dwarfs are supported by degeneracy pressure before hydrogen fusion starts, preventing them from ever reaching the main sequence. a) (10 points) Derive an expression for the temperature where the electron degeneracy and gas pressures are equal in terms of the mass M and radius R, again assuming constant density. Here the relevant composition is of purely ionized hydrogen. b) (10 points) Hydrogen fusion begins at a temperature T 107 K. Using your result in problem la for the white dwarf radius, calculate the maximum mass where degeneracy pressure supports the star before nuclear fusion begins