Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 85
understood from the relatively steep density dependence of the plasma
neutrino emission rate which is most efficient at the center.
In order to prevent the core mass from exceeding its standard value
by more than 5% (δM c < 0.025 M ⊙ ) one must require F ν ∼ < 3 or
⟨ϵ x ⟩ ∼ < 2⟨ϵ ν ⟩. According to the Sweigart and Gross (1978) red-giant sequences
the neutrino luminosity of the core at helium ignition is approximately
1 L ⊙ so that ⟨ϵ ν ⟩ ≈ 4 erg g −1 s −1 . Therefore, an approximate
analytic criterion to constrain a nonstandard energy loss is
ϵ x ∼ < 10 erg g −1 s −1 , (2.43)
where ϵ x is to be evaluated in a helium plasma at the average density of
the core of about 2×10 5 g cm −3 (the central density is about 10 6 g cm −3 )
and at the almost constant temperature of T = 10 8 K. The standard
neutrino plasma emission rate evaluated at 2×10 5 g cm −3 and 10 8 K
is 3 erg g −1 s −1 , in good agreement with the above average neutrino
luminosity of the Sweigart and Gross models.
Table 2.6. Increase of the core mass at helium ignition because of the emission
of pseudoscalars (Raffelt and Weiss 1995).
α ′ [10 −26 ] δM c [M ⊙ ]
0.0 0.000
0.5 0.022
1.0 0.036
2.0 0.056
A simple application of Eq. (2.43) is the case of bremsstrahlung
emission of pseudoscalars e + 4 He → 4 He + e + a. For a degenerate
medium the emission rate is given in Eq. (3.33); for T = 10 8 K it
is approximately α ′ 2×10 27 erg g −1 s −1 with the “axion fine-structure
constant” α ′ . Then, Eq. (2.43) yields
α ′ ∼ < 0.5×10 −26 . (2.44)
The same case was treated numerically by Raffelt and Weiss (1995)
who implemented the energy-loss rate Eq. (3.33) with varying values
of α ′ in several red-giant evolutionary sequences. 13 They found the
13 In a previous numerical treatment by Dearborn, Schramm, and Steigman (1986)
the correct emission rate had not yet been available and so they overestimated the
energy-loss rate by as much as a factor of 10 at the center of a red-giant core.