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Re: How can neutron stars form?



My understanding from (a possibly faulty) memory of the formation of
neutron stars is that they form in the centers of type II supernovas
where an iron-rich core of a *high mass* star at the endpoint of it
thermonuclear fusion cycle (which has undergone thermonuclear fusion to
the point where it essentially has the lowest energy, or, equivalently,
the highest nuclear binding energy per nucleon possible, and thus cannot
release any more energy by undergoing further nuclear fusion, and thus
cannot generate the pressure needed to stave off gravitational collapse)
collapses under the gravity (of itself and the inward gravitational
pressure exerted by all the overlying layers of lower nuclear mass
material).

As this iron-rich core is compressed the concentration of the
accompanying (unbound but nearby) electrons increases so much that the
Chandrasekhar (sp?) instability is exceeded where the chemical potential
(or Fermi energy in the low-temp limit approx.) for the electrons
eventually exceeds the mass difference between the rest energy of a
neutron and the sum of the rest energies of a proton + an electron. At
this point it becomes energetically favorable for the highest energy
electrons (those near the Fermi energy) to combine with the available
protons (presumably protons which are not necessarily initially those
tightly bound protons in the iron nuclei, but possibly other extraneous
protons) to form neutrons accompanied by outgoing neutrinos. (Note, my
memory is most hazy here as to just *which* protons initially marry up
with the electrons that are being initially destroyed.)

As this happens the number of electrons decreases and so does the
corresponding electron degeneracy pressure which now has an even harder
time opposing further gravitational collapse. As the collapse proceeds
the inward gravitational forces get ever stronger (i.e., the R in
G*M*M'/R^2 decreases) while the electron degeneracy pressure proceeds to
wimp out due to the destruction of the electrons. This unstably
increases the rate of collapse until the point where the iron nuclei
are close to touching, and at this point *something* (I think a
combination of the gamma rays released in the initial neutronization,
the background thermal photons, the incipient nuclear forces on the
nearby iron nuclei, and the remaining electrons attacking their protons)
cause the nuclei to crumble into separate (but close by) nucleons--the
protons of which immediately undergo further neutronization with the
remaining electrons yielding an immensely concentrated outwardly
expanding shock wave of liberated neutrinos and a core of neutrons.

Since the product of this last neutronization (stimulated inverse Beta
decay) reaction is just a bunch of neutrons that gets compressed to
nuclear densities. Once the neutrons finish getting compressed to this
density *their* degeneracy pressure (neutrons are Fermions too and also
obey the Pauli principle) shoots up *extremely* rapidly making the ball
of neutrons effectively *very* incompressible. This stops the central
collapse in its tracks and its surface provides the hard surface for the
so-called 'bounce' where the rest of the infalling material bounces off
of the neutron core. The bounce from the core, the outgoing neutrinos,
and the gamma rays liberated by in the neutronization stage propel the
rest of the star material outwards as the supernova explosion.

In this explosion various radioactive and high-mass nuclei are formed by
the constituent nuclei colliding together with a high enough relative
kinetic energy that the endothermic fusion reactions which form these
nuclei can proceed as they absorb the needed energy from the explosion's
excessive vigor.

After the explosion has dissipated and cooled (and the short-lived radio
isotopes have mostly decayed away) what remains in the middle is a
neutron star which is the left-over core of neutrons that formed in the
supernova implosion. If this neutron core has an appropriately trapped
magnetic field and if it is spinning with an appropriate alignment
relative to the direction towards Earth then this neutron star might be
observed as a radio pulsar. If the neutron star has a bloated binary
companion (that was not destroyed in the supernova explosion) such that
the neutron star is slowly stealing part of the companion's leaking outer
layer, and this material sprials down onto the neutron star's surface
from an acretion disk, then the neutron star may also be an x-ray source
as well.

Note, if the initial mass of the iron-rich collapsing core in the
beginning of the type II supernova is *too* massive then it is possible
that the central remnant of the supernova is *not* a neutron star but a
black hole. This is because if the ball of neutrons that forms in the
implosion has more than about 3 solar masses, the Oppenheimer-Volkhoff
limit is exceeded. This limit is the largest mass of neutrons that can
support themselves against their own gravity via their degeneracy
pressure and their short distance interparticle repulsion. If this mass
limit is exceeded then the ball of neutrons continues to collapse ever
smaller into a smaller sea of quarks that collapses behind the event
horizon of a black hole. The reason for this is that if the neutron core
is too massive its central compressive gravitational pressure increases
at a faster rate than its opposing degeneracy pressure does upon further
compression. Once the quark soup stage occurs the degeneracy pressure of
the quarks also cannot resist further gravitational compression. If the
neutrons could not resist the gravitational collapse at a larger size
then the quarks can't be expected to do it at a much smaller size when
there is a much stronger gravitational pressure. In the case of the
neutrons the inter-nucleon force is repulsive at short distances that
helps provide rigidity for the neutron ball. But the interaction between
the quarks *weakens* with decreasing distance (this is called asymptotic
freedom) so that at very short distances the quarks act as an ideal gas
of noninteracting (but Pauli-Principle-obeying) particles whose
degeneracy pressure is no match for gravity.

David Bowman
dbowman@georgetowncollege.edu