Stars as Laboratories for Fundamental Physics - MPP Theory Group

Processes in a Nuclear Medium 123
Fig. 4.2. Normalized axion spectrum x s(x)e −x /s 1 from nucleon-nucleon
bremsstrahlung emission. The nondegenerate and degenerate functions s(x)
are given in Eqs. (4.7) and (4.9), respectively, while s 1 (ND) and s 1 (D) are
found in Tab. 4.1.
explicitly
Q ND
a
= 128 α aα 2 π
35 √ π
n 2 B T 7/2
,
m 9/2
N
ϵ ND
a = α a 1.69×10 35 erg g −1 s −1 ρ 15 T 3.5
MeV, (4.8)
where ρ 15 = ρ/10 15 g cm −3 , T MeV = T/MeV, and ϵ ND
a
energy-loss rate per unit mass.
= Q ND
a /ρ is the
4.2.4 Degenerate Limit
Details of the nucleon phase space in the degenerate limit can be found
in Friman and Maxwell’s (1979) calculation of νν emission. The axion
energy-loss rate is expressed as in Eq. (4.6). One finds
Γ σ = 4α2 π
3π
p F T 3
n B
and s(x) = (x2 + 4π 2 ) |x|
4π 2 (1 − e −|x| ) , (4.9)
where p F is the nucleon Fermi momentum. As in the nondegenerate case
s(0) = 1 while s(|x|≫1) = |x| 3 /4π 2 . Values for s n = ∫ ∞
0 x n s(x) e −x dx
are given in Tab. 4.1. The normalized axion spectrum is shown in
Fig. 4.2 (dotted line), the average energy is ⟨ω a ⟩/T = s 2 /s 1 ≈ 3.16.