Stars as Laboratories for Fundamental Physics - MPP Theory Group

86 Chapter 2
Fig. 2.27. Increase of the core mass of a red giant at helium ignition due
to the emission of pseudoscalars according to Tab. 2.6 (Raffelt and Weiss
1995).
core-mass increases given in Tab. 2.6 and shown in Fig. 2.27. The requirement
that the core not exceed its standard value by more than 5%
reproduces the analytic bound. This example nicely corroborates the
surprising precision of the simple criterion Eq. (2.43).
Another important case where a detailed numerical study is available
is the emission of neutrinos by the plasma process γ → νν when
they have nonstandard magnetic dipole moments µ ν . The emission
rates are derived in Sect. 6.5.5 and the simple criterion Eq. (2.43) is
applied in Sect. 6.5.6. It yields a limit µ < 12 ∼ 2 where µ 12 = µ ν /10 −12 µ B
with the Bohr magneton µ B = e/2m e . The numerical variation of the
core mass with µ ν is shown in Fig. 2.28 according to Raffelt and Weiss
(1992). An analytic approximation is
[
δM c = 0.025 M ⊙ (µ
2
12 + 1) 1/2 − 1 − 0.17 µ 3/2 ]
12 . (2.45)
The requirement δM c ∼ < 0.025 M ⊙ then translates into
µ ν ∼ < 3×10 −12 µ B , (2.46)
a result which, again, is almost identical with the analytic treatment,
supporting the power of the simple criterion stated in Eq. (2.43).