Stars as Laboratories for Fundamental Physics - MPP Theory Group

16 Chapter 1
even if the luminosity L x in “exotics” is as large as the photon luminosity
(δ x = 1 ) the overall changes in the stellar structure remain moderate.
The predominant effect is an increased consumption of nuclear
2
fuel at an almost unchanged stellar structure, leading to a decreased
duration of the hydrogen-burning phase of
δτ/τ ≈ −δ x . (1.14)
The standard Sun is halfway through its main-sequence evolution so
that a conservative constraint is δ x < 1.
2
In general, the exotic losses do not have the same temperature and
density dependence as the nuclear burning rate, implying a breakdown
of the homology condition. However, to lowest order these results will
remain valid if one interprets δ x as a suitable average over the entire
star,
δ x = L x /(L x + L γ ), (1.15)
with the photon luminosity L γ and that in exotics L x . To lowest order
L x can be computed from an unperturbed stellar model.
For a convective structure (M < ∼ 0.25 M ⊙ main-sequence stars)
Frieman et al. found by a similar treatment
δR
R =
−2δ x
2ν + 11 ,
δL
L =
−5δ x
2ν + 11 ,
δT
T =
2δ x
2ν + 11 . (1.16)
These stars also contract, and the internal temperature increases, but
the surface luminosity decreases.
1.3.2 Application to the Sun
For the Sun, the radius and luminosity are very well measured and
so one may think that small deviations δR and δL from a standard
model were detectable. This is not so, however, because a solar model
is defined to produce the observed radius and luminosity at an age
of 4.5 Gyr. The unknown presolar helium abundance Y initial is chosen
to reproduce the present-day luminosity, and the one free parameter
of the mixing-length theory relevant for superadiabatic convection is
calibrated by the solar radius.
In a numerical study Raffelt and Dearborn (1987) implemented axion
losses by the Primakoff process in a 1 M ⊙ stellar model, metallicity
Z = 0.02, which was evolved to 4.5 Gyr with different amounts
of initial helium and different axion coupling strengths. Details of the
emission rate as a function of temperature and density are studied in