Stars as Laboratories for Fundamental Physics - MPP Theory Group

What Have We Learned from SN 1987A 509
recent numerical study by Keil (1994) who used the same axion emission
rates as Burrows, Turner, and Brinkmann (1988) confirmed their
results.
Here, I present the numerical studies of Burrows and his collaborators
where axions were assumed to couple with equal strength to protons
and neutrons. The axial-vector coupling to nucleons is written in
the form (C/2f a ) ψγ µ γ 5 ψ ∂ µ a with a model-dependent numerical factor
C, the Peccei-Quinn energy scale f a , the nucleon Dirac field ψ, and the
axion field a. Under certain assumptions detailed in Sect. 14.2.3 it can
be written in the pseudoscalar form −i g a ψγ 5 ψ where g a = Cm N /f a
is a dimensionless Yukawa coupling (nucleon mass m N ); Burrows et al.
used C = 1. All results will be discussed in terms of g 2 a and as such they
apply to any pseudoscalar particle which couples to nucleons accordingly.
In Sect. 14.4 the available constraints on axions will be expressed
in terms of the axion mass m a .
In the free-streaming limit the energy loss by axions was implemented
according to the numerical rates of Brinkmann and Turner
(1988); limiting cases of these rates were discussed in Sect. 4.2. In the
trapping regime, the transfer of energy by axions as well as axion cooling
from an “axion sphere” was implemented by means of an effective
radiative opacity as discussed in Sect. 4.4. The protoneutron star models
are those of Burrows and Lattimer (1986) and of Burrows (1988b).
In the latter study, cooling sequences were presented for different equations
of state (EOS), and different assumptions concerning the mass
and early accretion rate of the stars. A fiducial case in these studies is
model 55 with a “stiff EOS,” an initial baryon mass of 1.3 M ⊙ , and an
initial accretion of 0.2 M ⊙ .
The compatibility of a given model with the SN 1987A observations
should be tested by a maximum-likelihood analysis of the time and
energy distributions of the events in both the IMB and Kamiokande II
detectors. In practice, it is easier to consider a few simple observables.
Burrows and his collaborators chose the total number of events N KII
and N IMB in the two detectors as well as the signal duration defined by
the expected times t KII and t IMB it takes to accrue 90% of the expected
total number of events. As both detectors measured approximately
10 events each, the time of the last event probably is a reasonable
estimate of t KII and t IMB . Finally, Burrows et al. calculated the total
energy carried away by neutrinos and axions.
The run of these quantities with g a is shown in Fig. 13.4. Recall
from Sect. 11.3.2 that the observed SN 1987A numbers of events
are N IMB = 8 and N KII = 10−12, depending on whether event No. 6