Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 51
F which includes Coulomb screening by ion correlations and electron
relativistic corrections one may easily “integrate” over the entire star.
For an assumed equal mixture of carbon and oxygen one finds for the
luminosity in pseudoscalar “exotica”
L x = α 26 2.0×10 −3 L ⊙ (M/M ⊙ ) ⟨F ⟩ T 4 7 , (2.12)
where α 26 = α ′ /10 −26 and T 7 = T/10 7 K (internal temperature T ).
Further, ⟨F ⟩ ≈ 1.0 within a few 10% (Sect. 3.5.2).
This energy-loss rate varies with internal temperature almost as
the surface photon luminosity of Eq. (2.7). If L x dominates in Mestel’s
cooling law Eq. (2.11) the slope 10 M 35 bol is replaced with the almost
identical value 12 M 35 bol. Thus, for a given WD birthrate the main
impact of pseudoscalars is to reduce the amplitude of the luminosity
function. Conversely, the inferred birthrate is larger by about a factor
1 + L x /L γ ≈ 1 + α 26 . Because the formation rate of planetary nebulae,
the progenitors of WDs, agrees with the standard inferred birthrate to
within a factor of about 2, one finds α < 26 ∼ 1. 9
The observed break of the luminosity function at the faint end
(Fig. 2.10) has been interpreted as the beginning of WD formation.
If boson cooling were dominant the faintest luminosities would have
been reached in a shorter amount of time, reducing the inferred age of
the galactic disk; standard cooling implies t gal = 8−12 Gyr. Even the
solar system is 4.5 Gyr old and so a reduction of t gal by more than a
factor of 2 is ruled out. This implies L x < L γ so that α 26 < 1.0 as
before.
The galactic age constraint appears to be much more reliable than
the one based on the formation rate of planetary nebulae. The former
could be avoided if the observations reported by Liebert, Dahn, and
Monet (1988) were crudely incomplete at the faint end of the luminosity
function, i.e. if many faint WDs had been overlooked so that the
break in the luminosity function of Fig. 2.10 were a major observational
selection effect. Barring this remote possibility the limit on α 26 is conservative.
Even for a much smaller value of α 26 , the inferred value for
t gal is reduced by an approximate factor (1 + α 26 ) −1 which may still be
significant.
Wang (1992) calculated numerical 1 M ⊙ WD sequences with varying
amounts of pseudoscalar cooling while Blinnikov and Dunina-Barkovskaya
(1994) performed a more detailed study for 0.6 M ⊙ WDs.
9 In the original derivation (Raffelt 1986b) ion correlations were ignored, leading
to ⟨F ⟩ ≈ 3 and to the limit α 26 ∼
< 0.3.