Stars as Laboratories for Fundamental Physics - MPP Theory Group

Anomalous Stellar Energy Losses Bounded by Observations 39
that even neutrinos are trapped. Therefore, energy and lepton number
are lost approximately on a neutrino diffusion time scale of several
seconds. The neutrinos from stellar collapse were observed for the first
and only time when the star Sanduleak −69 202 in the Large Magellanic
Cloud (a small satellite galaxy of the Milky Way) collapsed. The
subsequent explosion was the legendary SN 1987A.
After the exhaustion of hydrogen, massive stars move almost horizontally
across the Hertzsprung-Russell diagram until they reach their
Hayashi line, i.e. until they have become red supergiants. However, subsequently
they can loop horizontally back into the blue; the progenitor
of SN 1987A was such a blue supergiant.
The SN rate in a spiral galaxy like our own is thought to be about
one in a few decades, pessimistically one in a century. Because many
of the ones occurring far away in our galaxy will be obscured by the
dust and gas in the disk, one has to be extremely lucky to witness
such an event in one’s lifetime. The visible galactic SNe previous to
1987A were Tycho’s and Kepler’s in close succession about 400 years
ago. Both of them may have been of type I—no pulsar has been found
in their remnants. 7 Of course, in the future it may become possible to
detect optically invisible galactic SNe by means of neutrino detectors
like the ones which registered the neutrinos from SN 1987A.
2.1.9 Variable Stars
Stars are held in equilibrium by the pull of gravity which is opposed
by the pressure of the stellar matter; its inertia allows the system to
oscillate around this equilibrium position. If the adiabatic relationship
between pressure and density variations is written in the form δP/P =
γ δρ/ρ, the fundamental oscillation period P of a self-gravitating homogeneous
sphere (density ρ) is found to be 8 P −1 = [(γ − 4)G 3 Nρ/π] 1/2 .
This yields the period-mean density relationship P (ρ) 1/2 ≈ const.
which is often written in the form P (ρ/ρ ⊙ ) 1/2 = Q with the average
solar density ρ ⊙ = 1.41 g cm −3 and the pulsation “constant” Q. It is
in the range 0.5−3 h, depending on the adiabiatic coefficient γ and the
7 Observationally, type I and II SNe are distinguished by the absence of hydrogen
spectral lines in the former which is explained by their progenitor being an accreting
white dwarf which explodes after carbon ignition. Therefore, it is difficult to
establish the type of a historical SN unless a pulsar is detected as in the Crab.
8 For γ < 4/3 the star is dynamically unstable. We have already encountered
this magic number for the relationship between pressure and density of a degenerate
relativistic electron gas where it led to Chandrasekhar’s limiting white-dwarf mass.