Stars as Laboratories for Fundamental Physics - MPP Theory Group

602 Appendix D
D.2.4
Hot Nuclear Matter
In a supernova core right after collapse the temperature is so high (several
tens of MeV) that the nucleons are nearly nondegenerate. Moreover,
the neutrinos are trapped so that locally a fixed value for Y L
determined by initial conditions is assumed. Most of the lepton number
will reside in electrons, causing the proton concentration Y p to be
approximately equal to Y L . A more accurate determination requires a
numerical solution of Eqs. (D.18) and (D.19).
In Figs. D.7 (a)−(c) the results of such an exercise are presented
for Y L = 0.3, which is a typical value for the material in a SN core just
after collapse. The proton concentration Y p , the difference between the
neutron and proton chemical potentials, and the degeneracy parameters
for neutrons and protons are shown. In each case, a solid line refers
to the assumption of an effective nucleon mass as in Fig. 4.10 while
a dotted line refers to the vacuum mass. As expected, the reduced
effective mass increases somewhat the medium’s degeneracy.
Because µ n − µ p = µ e − µ νe , the contours of Fig. D.7 (b) also give
the difference between the surfaces of the electron and neutrino Fermi
seas. Note that the leptons are much more degenerate than the nucleons
because they are essentially massless. This remark does not apply to the
upper-left corner of the plots where actually an excess of antineutrinos
is enforced—there are more protons than leptons (Y p > Y L )!
Fig. D.7. (a) Contours for Y p in hot neutron-star matter with Y L = 0.3.
Solid lines for the effective nucleon mass as in Fig. D.7, dotted lines for the
vacuum mass.