Stars as Laboratories for Fundamental Physics - MPP Theory Group

Particles Interacting with Electrons and Baryons 107
to O(1 MeV), suppressing electron scattering and bremsstrahlung processes
for temperatures below this scale (T < ∼ 5×10 9 K). Bremsstrahlung
of νν pairs from the crust was thought to dominate neutron-star
cooling for some conditions while Pethick and Thorsson (1994) now
find that it may never be important. These findings also diminish
Iwamoto’s (1984) axion bound based on the bremsstrahlung emission
from neutron-star crusts.
3.5.5 Applying the Energy-Loss Argument
One may now easily derive astrophysical limits on the Yukawa couplings
of scalars and pseudoscalars, in full analogy to Sect. 3.2.6 where the
Compton emission rates were used. I begin with the same case that was
considered there, namely the restriction ϵ < ∼ 10 erg g −1 s −1 in the cores
of horizontal-branch stars. For nondegenerate conditions the emission
rates are Eq. (3.30) and Eq. (3.31), respectively. They are proportional
to ρ T 0.5 (pseudoscalar) and ρ T 2.5 (scalar). With ⟨ρ 4 ⟩ = 0.64, ⟨T8 0.5 ⟩ =
0.82, ⟨T8 2.5 ⟩ = 0.48, and a chemical composition of pure helium one finds
α ′ < { 1.4×10 −29 scalar,
∼
1.6×10 −25 pseudoscalar.
(3.43)
Comparing these limits with those from the Compton process Eq. (3.25)
reveals that for scalars the present bremsstrahlung limit is more restrictive,
for pseudoscalars the Compton one.
Because bremsstrahlung is not suppressed in a degenerate plasma,
one can also apply the helium-ignition argument of Sect. 2.5.2 which
again requires ϵ < ∼ 10 erg g −1 s −1 at the same T ≈ 10 8 K, however at a
density of around 10 6 g cm −3 . For these conditions the plasma is degenerate
but weakly coupled (Appendix D) so that Debye screening should
be an appropriate procedure. Therefore, for the emission of pseudoscalars
the emission rate Eq. (3.35) with F from Eq. (3.36) should
be a reasonable approximation. The screening scale is dominated by
the ions, k S = k i = 222 keV, the Fermi momentum is p F = 409 keV so
that κ 2 = 0.15 while β F = 0.77, yielding F ≈ 1.8.
In Fig. 3.6 the energy-loss rate of a helium plasma at T = 10 8 K
is plotted as a function of density, including the Compton process,
and the degenerate (D) and nondegenerate (ND) bremsstrahlung rates.
This figure clarifies that bremsstrahlung, of course, is suppressed by
degeneracy effects relative to the ND rates, but it is not a significantly
decreasing function of density. In this figure a simple interpolation
(solid line) between the regimes of high and low degeneracy is shown