Stars as Laboratories for Fundamental Physics - MPP Theory Group

What Have We Learned from SN 1987A 501
with K = 0 representing the Lorentzian, K = 1 the Galilean law of
adding velocities. For photons, the most stringent laboratory bound is
K < γ ∼ 10 −4 derived from the time of flight of decay photons π ◦ → 2γ
from a pulsed π ◦ source (Alväger et al. 1964). A much more stringent
constraint (K < γ ∼ 2×10 −9 ) obtains from an analysis of the photon signal
from a pulsed x-ray source (Brecher 1977).
The absence of dispersion of the ν e pulse can be used to derive constraints
on K ν (Atzmon and Nussinov 1994). The observed SN 1987A
neutrinos were produced by microscopic processes involving nearly relativistic
nucleons, and subsequently scattered several times on such
nucleons before leaving the star. If the last nucleon on which they
scatter is considered the source with v S ≈ 0.2 c their laboratory speed
c ′ ν will be represented by a distribution of approximate width 0.2 K ν
around c because of the random orientation and distribution in magnitude
of v S . Thus one derives a bound K < ν ∼ 10 −11 from the absence of
a spread in arrival times exceeding about 10 s.
Atzmon and Nussinov (1994) warn, however, that this simple argument
may be too naive as the motion through the progenitor’s envelope
may cause the particles of the envelope to be the true source of
the “neutrino waves” as there is a substantial amount of refraction between
the neutrino sphere and the stellar surface. If one follows Atzmon
and Nussinov’s reasoning, there remains only a much weaker bound of
K < ν ∼ 10 −5 from the absence of an anomalous time delay between the
neutrino signal and the optical sighting of the SN.
13.4 Duration of Neutrino Emission
13.4.1 General Argument
The most intricate way to use SN 1987A as a laboratory arises from the
observed duration of neutrino cooling. While the neutrino luminosity
during the first few 100 ms until the shock has been revived is largely
powered by accretion and by the contraction and settling of the bloated
outer core, the long tail is associated with cooling, i.e. emission from
the neutrino sphere which is powered by energy originally stored deep
in the inner core. If a direct cooling channel existed for that region,
such as the emission of r.h. neutrinos or axions, the late cooling phase
would be deprived of energy. Put another way, a novel cooling channel
from the inner core would leave the schematic neutrino light curves
of Fig. 11.3 more or less unchanged before about 1 s while the long
Kelvin-Helmholtz cooling phase would be curtailed.