Stars as Laboratories for Fundamental Physics - MPP Theory Group

Two-Photon Coupling of Low-Mass Bosons 189
one finds g aγ B T ω < ∼ 10 −19 eV 2 . For the allowed range of axion masses
this mixing angle is too small to yield a significant conversion effect.
Therefore, this entire line of argument is only relevant for massless
(or at least very low-mass) pseudoscalars which again shall be referred
to as “arions.” Carlson (1995) considered the star α-Ori (Betelgeuse),
a red supergiant about 100 pc away from us. He estimated its arion
luminosity from the Primakoff process, and compared the expected
x-ray flux with data from the HEAO-1 satellite. As a result, a new
limit of g < aγ ∼ 2.5×10 −11 GeV −1 emerged which is more restrictive than
the above bound from globular-cluster stars.
Carlson’s argument yields an even more restrictive limit if applied
to SN 1987A. One may estimate the arion luminosity of the SN core on
the basis of the Primakoff process. If arions couple to quarks or electrons,
the luminosity can only be higher because existing axion limits
already indicate that arions cannot be trapped by these couplings. In
order to evaluate Eq. (5.9) an average temperature of 30 MeV and an
average density of 3×10 14 g cm −3 with a proton fraction of 0.3 is used
(Sect. 13.4.2). The Debye screening scale by the protons is then found
to be 36 MeV so that κ 2 = 1.41 in Eq. (5.10) leading to F = 0.72.
Therefore, the average energy loss rate is about g10 2 1.4×10 16 erg g −1 s −1 .
Taking a core mass of 1M ⊙ = 2×10 33 g and a duration of 3 s one expects
about g10 2 10 50 erg to be emitted in arions which is about 10 −3 g10
2
of the energy emitted in each neutrino flavor.
Typical arion energies are 3T ≈ 100 MeV so that Eq. (5.37) together
with ω P ≈ 10 −11 eV in the interstellar medium reveals that mixing is
nearly maximal for the relevant circumstances. Therefore, the oscillation
length is given by l osc = 4π/g aγ B T which is about 40 kpc for
B T = 1 µG and g aγ = 10 −10 GeV −1 . Therefore, l osc far exceeds the
relevant magnetic field region which is of order 1 kpc as discussed in
Sect. 13.3.3b. The conversion rate is then
prob(a → γ) = ( 1 2 g aγB T l) 2
= 2.3×10 −2 g 2 10 (B T l/µG kpc) 2 , (5.38)
where l is the effective conversion region (distance to source or distance
within magnetic field region), and g 10 ≡ g aγ /10 −10 GeV −1 .
With Eq. (5.38) and an effective magnetic conversion region of l =
1 kpc the expected energy showing up as γ-rays at Earth corresponds
to about 10 −5 g 4 10 relative to the energy in one neutrino species. In
Sect. 12.4.3 the radiative decays of low-mass neutrinos from SN 1987A
was discussed. On the basis of the SMM data it was found that less