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Degenerate Objects

Neutrinos from Neutron Stars

The energy locked within a neutron star is radiated away as neutrinos—the fundamental particle that interacts weakly with matter, that is, that interacts with neutrons and protons through the weak force.  Neutrinos are rapidly created throughout a neutron star's core, and, because matter is transparent to them, even at neutron star densities (> 1014 gm cm−3), they easily escape into space.  The power in radiated neutrinos far outstrips the electromagnetic radiation generated by the tiny photosphere for all but the coldest neutron stars.

The processes that generate neutrinos in a neutron star are quite different from the plasma neutrino process that generates neutrinos in a degenerate dwarf.  Neutrinos are created in a neutron star through three principal processes: the direct Urca process, the modified Urca process, and neutrino bremsstrahlung.[1]

The direct Urca process is neutron decay and its inverse within a neutron star.  A free neutron in space is unstable, decaying with a half life of about 10 minutes to a proton, an electron, and an electron neutrino.  This decay is possible because the neutron is more massive than the proton by slightly more than the mass of the electron.

The decay of a neutron can be suppress if there is no low-energy state available for the proton or the electron in the decay.  This suppression is possible because protons and neutrons are Fermions.  Under quantum mechanics, when there are many particles about, the particles can have only very specific values for their energies.  These specific energies are energy states, and they increase by specific increments from a minimum value—the ground state—up to infinity.  Only two Fermions of the same type can occupy any given energy state.  This means that only two protons can occupy any energy state at the same time.  The same is true for neutrons, which have their own set of energy states.  As a consequence, a total of four nucleons—two protons and two neutrons—can occupy the ground states for neutrons and protons.

This environment of quantized energy states exists inside an atomic nucleus.  In nuclei in which there are no unoccupied low-energy states for protons created in the decay of a neutron, the neutrons are stable.  For instance, helium-3 (3He) and helium-4 (4He) nuclei are stable because the proton ground state is filled with two protons.  Because the neutrons in these nuclei are also in the ground state, a neutron could only decay if the first excited proton energy state were above the neutron ground state by less than the energy difference between the rest mass energy of a neutron and the rest mass energies of a proton and an electron.  This is not the case, so the neutrons in the (3He) and (4He) isotopes are stable.  Neutrons in some isotopes, on the other hand, are not stable, and such nuclei change through beta decay into isotopes with the same number of nucleons but with one-more proton than their parent nuclei; the neutron releases an electron and an electron neutrino to become a proton in an available low-energy state.  This type of decays called beta decay.

Within an atom, an inverse to neutron decay can occur if the number of protons greatly exceeds the number of neutrons.  In this case, the proton in its high energy state has more energy than a neutron in the lowest available energy state.  If the proton energy exceeds the neutron energy by the mass of the electron, the proton can decay into a neutron, a positron, which is the antiparticle to the electron, and an electron antineutrino, which is the antiparticle to the electron neutrino.

Within the core of a neutron star, because the energy states of free neutrons and protons are quantized, much as they are inside an atomic nucleus, a similar set of processes occur.  As within an atom, the neutron can decay into a proton, an electron, and an electron neutrino.  The inverse process proceeds when a proton absorbs an electron to become a neutron, with an electron antineutrino emitted in the process.  These reactions are as follows:

n → p + e + ν

p + e → n + ν

where p is the proton, n is the neutron, e is the electron, ν is the neutrino, and ν is the antineutrino.  This is the direct Urca process, and it is effectively beta decay by the neutron star.  The process works as long as the star is not fully degenerate, so that there are a small number of protons and neutrons with energies above the Fermi energy, and there are open energy states below the Fermi energy.

The direct Urca process is called a fast neutrino process.  It is most effective at the very core of the most massive neutron stars (2.5 solar masses), where the density is extremely high, and the density of protons exceeds the density of neutrons by a small amount.  This higher proton density is required by the second reaction, which converts protons into neutrons, to work.

In the outer layers of a neutron star and in the cores of light neutron stars (1.5 solar masses), slow neutrino processes rather than the direct Urca process are cooling the neutron star.  These processes are the modified Urca process and the neutrino bremsstrahlung process.

The modified Urca process is similar to the Urca process in that a neutron becomes a proton and then becomes a neutron again, emitting a neutrino-antineutrino pair.  The difference is that in the modified Urca process another nucleon catalyzes the reaction.

n + N → p + N + e + ν

p + N + e → n + N + ν

In these reaction, N is a nucleon, either a neutron or a proton.  By being a source or sink of kinetic energy and momentum, the catalyst allows the reaction to occur under situations where the direct Urca reaction would be blocked because it violates conservation of energy and momentum.

Neutrino bremsstrahlung is similar to a process called photon bremsstrahlung, in which an electron passing by an atomic nucleus emits light.  In neutron bremsstrahlung, however, a nucleon, either a proton or a neutron, collides with another nucleon to create an electron neutrino-antineutrino pair.

N + N → N + N + ν + ν

The matter inside a neutron star is an excellent conductor—in fact, when the temperature that is about 10% of the Fermi energy, the matter is a superconductor—so the temperature within a neutron star is uniform.  Only in the outer layer, where the material is composed of atomic nuclei rather than degenerate neutrons and protons, does the temperature vary with radius.  This outer layer insulates the neutron star core, so the photospheric temperature is much less than the core temperature.  Typically, the core of a young neutron star is a little less than 1 billion °K, but the photosphere is only several million °K.  In this state, the neutron star loses much more energy by generating neutrinos than by emitting x-rays from its photosphere.  Only when the neutron star is cold does radivative cooling dominate neutrino cooling.

Massive neutron stars lose most of their energy through the direct Urca process working at the very center of the star, although the slow neutrino processes are also at work throughout the star.  The less massive stars lose their energy through the slow neutrino processes.  Regardless of the process, the generation of neutrinos cools the interior of a neutron star on a 100,000 year timescale, which is comparable to the lifetime of a radio pulsar.  The drop in core temperature causes the photospheric temperature to drop below 1 million °K, which makes the neutron star too cool to emit thermal x-rays.  Isolated neutron stars older than about 100,000 years are effectively invisible to us.

[1]Yakovlev, D.G., and Pethick, C.J.  “Neutron Star Cooling.”  Annual Reviews of Astronomy and Astrophysics 42 (2004): 169–210.

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