Stars as Laboratories for Fundamental Physics - MPP Theory Group

508 Chapter 13
region where their energy flux is set. Put another way, for fermions the
concept of blackbody emission from a neutrino sphere is not adequate,
making it impossible to apply the Stefan-Boltzmann in a simplistic way.
The transport of r.h. neutrinos in the trapping limit is an equally complicated
problem as that of l.h. ones! Therefore, a proper treatment of
the trapping limit is generally a tricky subject; axions are the only case
where it has been studied in some detail.
Occasionally one may wish to construct a particle-physics model
that avoids the SN limit. It would be incorrect to believe that this
is achieved when the interaction strength has been tuned such that
the mean free path is of order the neutron star radius. On the contrary,
when this condition obtains the impact on the cooling rate is
maximized. This is analogous to the impact of novel particles on the
structure and evolution of the Sun as depicted in Fig. 1.2; the cooling
rate is maximized when the mfp corresponds to a typical geometric dimension
of the object. In the trapping regime a new particle is harmless
only if it interacts about as strongly as the particles which provide the
standard mode of energy transfer.
13.5 Axions
13.5.1 Numerical Studies
The most-studied application of the SN cooling-time argument is that
of invisible axions as these particles are well motivated (Chapter 14).
Moreover, they have attracted much interest because they are one of
the few particle-physics motivated candidates for the cosmic dark matter.
Early analytic studies in the free-streaming limit are Ellis and Olive
(1987), Raffelt and Seckel (1988), and Turner (1988) who also discussed
the trapping regime; his line of reasoning was presented in Sect. 13.4.3
above. Numerical studies in the free-streaming limit were performed
by Mayle et al. (1988, 1989) and by Burrows, Turner, and Brinkmann
(1989) while the trapping regime was numerically studied by Burrows,
Ressell, and Turner (1990). The numerical studies by different workers
in the free-streaming limit used different assumptions concerning
the axion couplings, emission rates, and other aspects. In my previous
review (Raffelt 1990d) I have attempted to reduce the results of
these works to a common and consistent set of assumptions; apart from
relatively minor differences which could be blamed on different input
physics (e.g. softer equation of state and thus higher temperatures in
the Mayle et al. papers) the results seemed reasonably consistent. A