Neutron Star
NeutronStar
Neutron stars are the core remnants of moderately massive stars that have undergone violent stellar death via
tremendous
supernova explosions after leaving the Main Sequence. The cores of such large stars are too
massive to exist as white dwarfs. If the remnant has more mass than the critical 1.44 times the Sun's mass
(called
Chandrasekhar limit) than it can not exist as a white dwarf but collapses further to a smaller and even
denser neutron
star.  A teaspoonful of neutron star matter may weigh as much as 10 billion tonnes!
There's really nothing even to compare it to try and visualize it. The core collapses to such immense densities
because the gravitational field is so enormously strong that normal matter is crushed and destroyed and even
extremely dense white dwarf matter is crushed and destroyed. Very massive stars leave heavier remnants that
can not even exist as neutron stars, but collapse into mysterious entities known as black holes. During its Main
Sequence
lifetime the pressure of the radiation emitted by nuclear reactions stops the core from collapsing, but
when the star runs out of fuel, the core collapses until it reaches a state of matter that can resist further
collapse.

In the case of a neutron star, this matter is very strange and not entirely understood, but appears to be mostly
composed of neutrons.
Atoms are composed of a nucleus of one or more protons and neutrons and one or
more
electrons in shells around the nucleus. Free neutrons, when removed from the nucleus, are very unstable
and decay into electrons, protons and anti-electron neutrinos:
In some radioactive nuclei, there are too many neutrons which makes the nucleus unstable. In this case,
neutrons inside the nucleus may also decay into a proton, electron and anti-electron neutrino in a process
called
beta-decay, which releases the highly energetic electron from the nucleus as ionising radiation. The
number of free neutrons halves every ten minutes as the neutrons decay. (This is the principle of the neutron
bomb - irradiate an area with energetic neutrons, killing all the inhabitants, and within a day it is safe to move in
and occupy the area). However, in a neutron star the immense pressure forces this equation to the left, as
electrons (e) and protons (p) are squeezed into neutrons (n), so that neutrons become stable and a neutron
star is made up mostly of neutrons (there are about 200 neutrons for every electron). This material can be
conveniently called
neutronium.

How does a neutron star get turned from ordinary matter into neutronium?

The neutron star is enormously compressed by its immense gravitational field, and is only about 10 to 20
kilometres in diameter (about the size of a city) but is still very hot and luminous. To see what is happening we
shall examine the best physical model we have of its structure. Its atmosphere is only about one metre thick and
beneath this is a solid crust which is one to two kilometres thick and composed of atomic nuclei and electrons,
and so is relatively normal matter which is nevertheless extremely dense and heavy and very hot. The surface
gravity is about 2 hundred billion to 3 thousand billion times that on the surface of the Earth. Thus, an average
man standing on the surface of a neutron star would weigh as much as 200 billion tonnes or more! Clearly, his
body would be squashed to nothing!

The interior, beneath the crust, is thought to be liquid and is composed of neutron rich nuclei as the increasing
pressure starts to convert electrons and protons into neutrons. As we move deeper into the neutron star the
pressure rises considerably. The enormous pressure starts to pull neutrons from the neutron rich atomic nuclei
(a process called
neutron drip) so we have a liquid of nuclei, neutrons and electrons which is very hot and
dense. Deeper in, the nuclei completely dissolve into a sea of neutrons, with some electrons and protons (there
are about 200 neutrons to each proton, so the bulk of the neutron star is essentially a superhot and
super-dense neutron fluid. Superhot by our standards that is, but compared to the high density the neutrons
are expected to behave as if they are cold, and so may resemble a solid in many respects. It is possible that the
neutrons form degenerate matter, which is a special state of matter not normally encountered, but comprises
particles that are squeezed into their least energetic states. Only the fact that two neutrons cannot have the
exact same set of quantum numbers (they belong to a type of particle called fermions) prevents them from
merging together, in fact this purely quantum mechanical phenomenon maybe all that stops the neutron star
from collapsing further - in other words the neutrons don't want to be any closer together and so they exert a
pressure which holds the star up against gravity which is trying to pull it in.

In the neutron star core the pressures far exceed the maximum pressures that can be produced in a laboratory,
so we have to speculate. The core might consist of neutrons, or the neutrons may  collapse into particles called
pions, muons and hyperons (and possibly kaons). Hyperons contain strange quarks (normal protons and
neutrons contain quarks but no strange quarks) and are referred to as a type of
strange matter. At even
greater pressures this strange matter may collapse into a quark liquid.

The neutrons inside a neutron star are expected to be
ultrarelativistic, which means that they are moving
close to the speed of light! (Light moves at about 2.998 hundred million metres per second in a vacuum!). The
liquid is also predicted to be a
superfluid. Superfluids are very strange things, they move without friction and
can flow uphill and also behave as if they are a single particle (if you lift a portion out in a ladle, then it will flow
up over the sides of the ladle to join up with the rest, as if it likes to be a single entity!).

There is speculation that especially heavy neutron stars may contain predominantly strange matter (a so-called
strange star) and neutron stars more than 2 to 3 times the Sun's mass (the Tolman-Oppenheimer-Volkoff
limit
) may be composed almost entirely of free quarks, a so-called quark star.

When a neutron star is formed in a massive supernova explosion, the neutron star is typically slung across
space at immense speeds and often rotates at tremendous rates. A rotating neutron star is a
pulsar and is
considered in more detail in the pulsar section.

Degenerate Matter

Neutron stars are, like white dwarfs, degenerate stars. Degenerate means that a number of particles have the
same energy value. In particular, degenerate matter consists of particles called
fermions, such as electron,
protons and neutrons. Fermions generally have spin 1/2. Spin refers to the rotational angular momentum of a
particle, in classical terms this is due to a particle rotating on its axis, in quantum mechanics (QM) this is not the
case, though it is helpful to think of it as rotation or spin. Angular momentum, like other properties of confined
quantum systems, is quantised, meaning that only a few very discrete values are possible, as in, for example,
the energy levels of an atom (see atomic spectra). In a spin 1/2 particle, the angular momentum due to rotation
can take one of only two possible values: +1/2 or -1/2 (which you can imagine to be like spinning clockwise and
spinning counterclockwise) also referred to as spin-up and spin-down. According to the Pauli Exclusion
Principle, fermions cannot coexist in the same region of space with the same values of their quantum numbers
(the values of their quantised energy and momenta), such as energy or spin. This can also be viewed in terms
of Heisenberg's Uncertainty Principle, in which both the spatial position and momentum of a particle cannot be
simultaneously known to an arbitrary degree of accuracy. Particles are systems of quantum-mechanical waves
and they don't like to be made to sit still with perfectly defined exact values of momentum. The more you
attempt to confine the momentum of a particle to a certain specific value, the more uncertain its spatial position
becomes, and likewise the more you confine its spatial position, the more its momentum becomes uncertain.

In neutron stars, the neutrons are highly compressed by an immense gravitational field, such that they almost
exclusively occupy the lowest available energy levels or ground states. In normal matter, thermal energy excites
particles to lie above their ground states (they move about with thermal kinetic energy) and gaps are left in the
then many available energy levels as particles move up-and-down between the many available states. In
degenerate matter, thermal energy can barely excite the particles at all and they sit neatly huddled together as
tightly as possible. This restricts their energy and momenta, such that many particles occupy each available
energy and momentum level. For this reason, degenerate matter is called cold matter, though it is still very hot
as it stores immense potential heat energy. However, confining their momentum in this way, causes the spatial
positions of each particle to become more uncertain, and being fermions no two neighbouring particles in the
same energy level can occupy the same region of space, therefore, QM prevents the particles being pressed
any more closely together. The particles resist compression by applying pressure. In normal matter, pressure,
say in a gas, is caused by the thermal motion of the particles jostling them about so that they collide with the
walls of their container and impart energy and momentum to the walls - this is thermal pressure. In degenerate
matter, the pressure is purely quantum-mechanical and is called the
Fermi pressure. Matter in this state is
extremely dense!

In white dwarfs, the Fermi pressure is provided by degenerate electrons, whilst in neutron stars it is provided by
degenerate neutrons
.

Degenerate matter can consist of non-relativistic, relativistic or ultrarelativistic particles. Non-relativistic particles
are like those encountered in ordinary matter - they move at speeds well below the speed of light. Relativistic
particles have enough energy to move at speeds a substantial fraction of the speed of light, and ultrarelativistic
(or extreme relativistic) particles have enough energy to move at speeds very close to the speed of light. The
degenerate neutrons in a neutron star are
ultrarelativistic. This affects the approximate equations that are
used to determine the energy per particle and the Fermi pressure. The matter in any star can be modeled by a
state equation (
equation of state) which describes the relationship between the various properties of the
system like pressure, volume, temperature, mass, energy and chemical composition. (Specifically a state
variable, like temperature, is one that depends only on the current state of the system and not on its history).
Finding a reliable state equation that accurately describes neutron stars is an ongoing area of research.

In a vacuum, the least energetic and most stable atomic nucleus is iron-56 (iron atoms with 26 protons and 30
neutrons, or a total of 56 nucleons in their nucleus). This is the stable end-result of normal nuclear fusion
reactions in the cores of massive giant stars. The immense density inside a neutron star, however, shifts the
point of stability to more neutron-rich nuclei and as density increases, the process of
neutronisation occurs,
in which neutrons add on to the atomic nuclei as they form by reverse beta-decay. The presence of electrons,
tightly squeezed into a small volume too, helps reverse the beta-decay by blocking the normal forward process
of beta-decay by preventing the emission of electrons (there are very few spare energy levels for extra
electrons to move into, so extra electrons tend not to be produced). Neutronisation occurs (at zero degrees K)
at a density between about 2E+07 (20 million) g/cubic cm to 4E+11 (400 billion) g/cubic cm. (Recall that the
normal density of water is 1 g/cubic cm). This is expected to result in the formation of large clusters of nucleons
(neutrons and protons) embedded in a neutron fluid.

As density increases still further, deeper inside the neutron star, the energy of a neutron inside a nucleon
cluster exceeds that of a neutron in the surrounding fluid, resulting in a phase change resulting in the formation
of nucleon clusters embedded in a noninteracting neutron fluid (the neutrons in the fluid do not interact with the
clusters but prefer to stay outside). As density approaches that of an atomic nucleus, the clusters grow and
overlap, resulting in another phase change, which results in a
fluid of neutrons, protons and electrons, but
mostly neutrons (the number of protons roughly equals the number of electrons which roughly equals one tenth
the number of neutrons, so 80% of the fermions are neutrons). The presence of the electrons stabilises the
neutrons, by inhibiting beta-decay.

When the density reaches about half that of nuclear matter, the average kinetic energy of an electron exceeds
the rest-mass energy of muon (mu leptons) and many electrons transform into muons:
Electron = muon + electron neutrino + anti-muon neutrino
Neutron + electron = sigma-minus + electron neutrino
At twice the density of nuclear matter, electron-capture occurs - neutrons capture electrons to form hyperons
(particles composed of three quarks (baryons), like neutrons and protons, but with a strange quark
incorporated) such as the negatively-charged sigma particle (dds, made of two down and one strange quark)
and the neutral lambda particle (uds, one up, one down and one strange quark), the neutral sigma particle
(also uds) and also negatively charged delta particles (ddd). Hyperon formation:
Thus, the core of a neutron star is expected to consist of neutrons (n), protons (p), hyperons, an electron
fluid and a muon fluid. Furthermore, under these pressures, neutrons and protons can pair together, forming
nn and pp pairs. About 10% of the nucleons are predicted to do this. The
pp pairs are positively charged
and
superconducting, even at these immense temperatures. A superconductor is a material that conducts
electricity with essentially zero resistivity. Some metals become superconducting at atmospheric pressure
when cooled to very low temperatures and this superconductivity is due to the formation of electron pairs, ee,
called Cooper pairs that can move freely within the metal without being scattered from the ion lattice. (The
electrons have like electric charges and so will normally repel one-another, but they form very loosely bound
pairs in these conditions by exchanging a phonon, a quasiparticle (pseudoparticle) which is a quantum of
vibrational energy). In neutron stars, the pp pairs similarly superconduct. The
nn pairs are superfluid,
meaning that they can flow around inside the neutron star in very strange ways, without friction, behaving like
a single particle in many ways. These superfluid neutrons are
excellent thermal conductors, distributing
heat around the neutron star. This, coupled with the neutron degeneracy, makes the interior of a neutron
star approximately
isothermal, that is at the same temperature. The temperature drops in the region of the
neutron star crust. Neutron stars slowly cool by losing thermal radiation into space.
neutron star composition
Above: a model of a neutron star, showing the composition of matter and the variation in density with
fraction of the radius and mass. The crust is a solid, permeated by a fluid of ultrarelativistic particles, whilst
the core is fluid and composed mostly of electrons, nucleons (neutrons, n, and protons, p) and more
massive baryons and hyperons. The inner core might contain superfluid neutron and superconducting
proton fluids, and may be solid in less massive neutron stars. In the most massive neutron stars, the inner
core may comprise a fluid of quarks, as the nucleons and other baryons begin to break-down, with their
constituent quarks separating, at least partially. The latter hypothetical stars are also called
strange stars
or
quark stars. According to the theory of colour confinement (a theory not proven but for which no
violations have been observed) the quarks that make-up the nucleons and other hadrons (a hadron is a
particle composed of quarks and/or anti-quarks) can not exist in isolation since they possess a
colour
charge
. Colour charge is like electric charge, except that whereas electric charge is associated with the
electromagnetic force, colour charge is associated with the much shorter range
strong force which holds
hadrons together. Whereas there are two types of electric charge, designated plus (+) and minus (-), there
are three colour charges, designated red (r), green (g) and blue (b). Colour charge has nothing to do with
visual colour, but since there are three strong force charges and three primary colours, 'colour charge' is a
suitable term. Colour confinement states that the overall colour charge must be neutral or colourless. In the
case of a nucleon, which contains three quarks, one quark must be red, one green and one blue, since
mixing red, green and blue light gives white light - hence the analogy to colour is useful here. However,
under immense pressures, the nucleons (or their wavefunctions) overlap and they emerge into a continuous
system in which the quarks can move around as if free in a gas. The strong force, which acts between the
colour charges of quarks, is conveyed by particles called gluons, which quarks constantly exchange, and so
the resultant state of nuclear matter is called a
quark-gluon plasma. This kind of matter could exist in the
inner core of heavy neutron or quark stars.

Atmosphere

Above the surface of the crust is an atmosphere of plasma, which becomes less dense further from the
surface, falling from the density of the crust to the density of interstellar matter. With the immense
gravitational field of the neutron star, however, the atmosphere is very compressed and only a metre or two
in height!

Magnetosphere

Outside the crust is a region dominated by the neutron star's gravitational field, called the magnetosphere,
which extends to several times the star's radius into space. Neutron stars typically have very strong
magnetic fields, with B > 10^9 gauss (G) (10^5 tesla, T) and with typical values in
pulsars of 10^9 T (10^13
G)! [1 T = 10^ G = 10 000 G]. B is the magnetic flux density and is a measure of the intensity of the field
(though is not strictly the same thing as magnetic field 'intensity' or 'strength'). In comparison the Earth's
magnetic field is 0.3 G to 0.6 G and very strong superconducting magnets are around 13.5 T and pulsed
magnets at 72 T. Some neutron stars have unusually strong magnetic fields at ~10^11 T (10^15 G) and are
then called
magnetars. Pulsars are stars that emit periodic pulses of radio energy at a frequency of around
once per second or higher. Pulsars (or at least most of them) are thought to be rapidly rotating neutron
stars with strong magnetic fields.

The magnetic field of neutron stars is so immense that it can pull electrons and protons out from the crust,
except near to the poles, these charged particles follow the magnetic field lines back down to the star's
surface, these field lines forming a toroidal belt around the star's equator. At the poles, charged particles
would have to move faster than light to make it back down and so instead the field lines detach and the
particles stream away, electrons closest to the pole, emitted in cones, surrounded by protons slightly further
from the pole, at least according to one model anyway. As the charged particles spiral around these
magnetic field lines at near-light speeds, they emit radio frequency radiation, so-called
synchrotron emission.

Furthermore, the magnetic field is so intense that the
electron orbitals in the atoms of the crust are
distorted, being narrower in the direction Normal (perpendicular) to the magnetic field lines as they emerge
from the crust, such that rather than being spherical, the atoms should be prolate spheroids (like rugby balls
standing upright):
One consequence of this arrangement is that the electrons are closer to the nucleus and so are more tightly
bound and it takes considerable energy to ionise the atoms and remove the electrons (for a magnetic field
of B = 10^12 G, it requires a temperature of about 10^9 K to ionise the atoms). The atoms are also tightly
packed, resulting in a tight crystal lattice that is very strong. The crust also has anisotropic (different in
different directions) electrically conductivity - conducting well in one direction, whilst acting as a good
insulator in another direction.

Pulsars - rapidly rotating, strongly magnetic neutron stars.