Stars as Laboratories for Fundamental Physics - MPP Theory Group

504 Chapter 13
While it is clear that a large range of g a values can be excluded,
the quantity ∆t 90% is a relatively crude measure of the length of the
cooling phase. In principle, one should perform a maximum likelihood
analysis for a given range of particle properties. Moreover, one would
need to consider a variety of models for the protoneutron star where the
equation of state (EOS), mass, accretion rate, neutrino opacities, and
perhaps other parameters should be varied to optimize the agreement
with the observed signal when a novel cooling mechanism operates.
Another caveat applies to the “trapping regime” of the new particles.
One may expect that they play a significant role during the
infall phase and shock formation of a SN collapse, an issue that was
addressed only by a small number of authors in the context of majoron
bounds (Fuller, Mayle, and Wilson 1988) and bounds on neutrino dipole
moments (Nötzold 1988). Hence, in general it is not obvious that parameters
allowed by the cooling argument on the trapping side would
remain allowed if one took account of these effects. Moreover, on the
trapping side the novel particles interact about as strongly as neutrinos
and so they could also cause a signal in the detectors. For axions, this
argument rules out the values of g a given in Eq. (13.2).
13.4.2 Analytic Criterion in the Free-Streaming Limit
In order to estimate the impact of a novel cooling channel on the neutrino
signal it is obviously useful to evolve a protoneutron star numerically
with the new physics included, and to calculate the expected
neutrino signal for a varying strength of the new effect. Considering
the many uncertainties involved in this procedure one may well ask if
it is not just as reliable to perform a simple analytic estimate.
At about 1 s after core bounce the neutrino luminosity in all six
(anti)neutrino degrees of freedom together is about 3×10 52 erg s −1 . The
mass of the object is around 1.5 M ⊙ = 3×10 33 g so that its average
energy-loss rate is L ν /M ≈ 1×10 19 erg g −1 s −1 . A novel cooling agent
would have to compete with this energy-loss rate in order to affect the
total cooling time scale significantly. Therefore, the observed signal
duration indicates that a novel energy-loss rate is bounded by
ϵ x ∼ < 10 19 erg g −1 s −1 . (13.8)
It is to be evaluated at typical core conditions, i.e. at a temperature
of around 30 MeV and a density of around 3×10 14 g cm −3 . The nuclear
medium is then at the borderline between degeneracy and nondegeneracy
while the electrons are highly degenerate.