Stars as Laboratories for Fundamental Physics - MPP Theory Group

502 Chapter 13
Of course, this reasoning is identical with the energy-loss argument
previously studied for normal stars in Chapters 1 and 2. The main
difference is that neutrinos are trapped so that particles which interact
more weakly can dominate the thermal evolution by volume emission.
In normal stars, photons are trapped and neutrinos can dominate the
energy loss by volume emission as, for example, in the early cooling of
a white dwarf.
This general argument is best illustrated with axion emission. These
particles are pseudoscalars which for the purpose of this argument are
taken to interact with neutrons and protons with a common Yukawa
coupling strength g a which is the only free parameter in the problem.
For very small values of g a axions will play no role, but with an increasing
coupling strength their emission from the inner core by bremsstrahlung
processes, NN → NNa, will begin to compete with neutrino cooling.
Of course, if g a exceeds some critical value axions will be trapped
and emitted from an “axion sphere” at about unit optical depth. Beyond
some large coupling they will be trapped so effectively that their
contribution to the cooling of the SN core is, again, negligible and the
neutrino signal assumes its standard duration. This general behavior is
shown in Fig. 13.1 on the basis of the numerical cooling calculations 85
of Burrows, Turner, and Brinkmann (1989) and Burrows, Ressell, and
Turner (1990). These authors used the quantity ∆t 90% as a measure of
the cooling time; it represents the time at which 90% of the expected
number of events have arrived at a detector. ∆t 90% was calculated separately
for Kamiokande II and IMB; in Fig. 13.1 an average relative
signal duration is shown, normalized to the value when axions are not
important. It is apparent that a large range of g a values can be excluded
on the basis of the observed duration of the neutrino signal.
One is here considering the time scale of neutrino emission at the
source while the detectors register a pulse which conceivably could have
been lengthened by dispersion effects. However, in view of the recent
laboratory limits of m < νe ∼ 5 eV this is not a serious concern.
If one contemplates nonstandard neutrinos, a relatively short emission
time scale at the source is compatible with the observations if ν µ ’s
85 In the free-streaming regime these calculations were based on axion emission
rates which do not take the high-density multiple-scattering effects into account
that were discussed in Sect. 4.6.7. Therefore, the free-streaming part of Fig. 13.1
probably overestimates the import of axion emission. For the present purpose of
discussing the general aspects of a novel cooling channel, however, this problem is
of no concern. The axion case is the only one where numerical cooling calculations
are available for both the volume-emission (free-streaming) and the trapping limit.