Stars as Laboratories for Fundamental Physics - MPP Theory Group

506 Chapter 13
The profile of various parameters as a function of the mass coordinate
is shown in Fig. 13.2 for model S2BH 0 of the cooling calculations
of Keil, Janka, and Raffelt (1995); it illustrates typical physical
conditions encountered in the core of a protoneutron star during the
Kelvin-Helmholtz phase. For this model, the average value of (ρ/ρ 0 ) n
with the nuclear density ρ 0 = 3×10 14 g cm −3 and of (T/30 MeV) n is
shown in Fig. 13.3 as a function of n.
Fig. 13.3. Average values for (ρ/ρ 0 ) n with the nuclear density ρ 0 =
3×10 14 g cm −3 and of (T/30 MeV) n for the protoneutron star model of
Fig. 13.2.
As an example one may apply this criterion to the bremsstrahlung
energy-loss rate NN → NNa for the emission of some pseudoscalar
boson a (axion) with a Yukawa coupling g a . The nondegenerate energyloss
rate Eq. (4.8) is ϵ a = ga 2 2×10 39 erg g −1 s −1 ρ 15 T30 3.5 where T 30 =
T/30 MeV and ρ 15 = ρ/10 15 g cm −3 . From Fig. 13.3 one finds that
⟨ρ 15 ⟩ ≈ 0.4 and ⟨T30 3.5 ⟩ ≈ 1.4. The criterion Eq. (13.8) then yields
g < a ∼ 10 −10 , similar to what one would conclude from Fig. 13.1. Using
the degenerate emission rate Eq. (4.10) yields an almost identical result.
Therefore, a simple criterion like Eq. (13.1) is not a bad first estimate
for the import of a novel energy-loss rate.
13.4.3 Trapping Limit
When the new particles (for example, axions) interact strongly enough,
they will be emitted from a spherical shell where their optical depth is
about unity rather than by volume emission. Again, one is concerned