Stars as Laboratories for Fundamental Physics - MPP Theory Group

The Energy-Loss Argument 21
scalars of
κ x = 2(2π)9/2 αα x
45
Y e T 5/2 e m x/T
m 1/2
x m 4 e
= 4.4×10 −3 cm 2 g −1 × α x Y e m −0.5
keV T 2.5
keV e m x/T , (1.22)
where m keV = m x /keV and T keV = T/keV.
The observed properties of the Sun then allow one to exclude a large
range of parameters in the m x -α x -plane. The energy-loss rate integrated
over the entire Sun must not exceed L ⊙ . Moreover, κ −1
x must not exceed
the standard photon contribution κ −1
γ ≈ 1 g/cm 2 , apart from perhaps
a factor of order unity. Taking a typical solar interior temperature
of 1 keV, these requirements exclude the shaded region in Fig. 1.1.
The dashed line marks the parameters where the mfp is of order the
solar radius.
1.4 General Lesson
What have we learned Weakly interacting particles, if they are not
trapped in stars, carry away energy. For a degenerate object this energy
loss leads to additional cooling, for a burning star it leads to an
accelerated consumption of nuclear fuel. New particles would cause significant
effects only if they could compete with neutrinos which already
carry away energy directly from the interior.
If new particles are trapped because of a short mfp, they contribute
to the energy transfer. They dominate unless their mfp is shorter than
that of photons. Such particles probably do not exist or else they
would have been found in laboratory experiments. This justifies the
usual focus on the energy-loss argument or “free streaming” limit.
Still, the impact of new low-mass particles is maximized for an mfp
of order the stellar radius, a fact which is often not appreciated in the
literature.
If the particles were so heavy that they could not be produced by
thermal processes in a stellar plasma they would be allowed for any coupling
strength. How heavy is heavy The average energy of blackbody
photons is about 3T . Therefore, if m < x ∼ 3T the particle production
will not be significantly suppressed. However, the solar example of
Fig. 1.1 illustrates that for a sufficiently large coupling strength even
a particle with a mass of 30 T could have a significant impact. While
it can be produced only by plasma constituents high up in the tails
of the thermal distributions, the Boltzmann suppression factor e −mx/T