The existence of neutron stars was predicted in December 1933 by Walter Baade and Franz Zwicky, shortly after the discovery of the neutron by James Chadwick less than two years prior . However, it was not until 1967 that Jocelyn Bell Burnell observed regular weak pulses from a radio source, each lasting 0.3 seconds with a constant period of 1.337 seconds. Initially labelled as LGM-1 (Little Green Men) with the belief that the observation could be a possible sign of extra-terrestrial life, other examples were shortly discovered of this “pulsating radio star”, dubbed a pulsar . This was confirmation of the existence of neutron stars.
Neutron stars are typically formed in the final stage of stellar evolution of stars with initial mass of 8 to 20-30 times the mass of the Sun (solar mass M☉ being defined as 2×1030 kg). Initial masses of significantly less than 8 M☉ will form a white dwarf, while those significantly greater than 20-30 M☉ will become a black hole. In an eligible massive star, hydrogen fusion followed by other fusion reactions involving heavier elements yields an iron core. The fusion releases energy, providing the electron degeneracy pressure necessary to counter gravity and keep the star from collapsing. When the iron core is formed, no more fusion can occur as at low pressures Iron-56 has the highest of any binding energy per nucleon – therefore fusion or fission would require an energy input .
The core accumulates until it reaches the maximum mass which can be supported against gravity by electron degeneracy pressure: the Chandrasekhar mass, MCh ≈ 1.4 M☉(2s.f) . After this point the core collapses under the pull of gravity, producing pressures high enough for protons and electrons to form neutrons and a flood of neutrinos. The collapse is stopped when the nuclear density of 4×1017 km/m3 is reached – exceeding that of an atomic nucleus – allowing mutual electromagnetic repulsion and neutron degeneracy pressure to combat gravity . Neutron degeneracy creates a pressure as no two neutrons can occupy the exact same state. The falling outer layers of the star are flung outward due to a rapid release of gravitational energy carried mostly by neutrinos, causing an explosion transferring energy outwards with a shock wave, in a Type II supernova explosion (a stellar explosion produced at the endpoint of the evolution of stars whose mass exceeds roughly 10 times that of the Sun) . What remains after only seconds is a neutron star.
Neutron stars are not large in size, with diameters falling within the range of 15-30 kilometres . On average, they have a mass of 1.4 M☉. Masses are at least 1.1 M☉, and while the upper limit of mass for a neutron star – the Tolman-Oppenheimer-Volkoff limit – is around 2.1 M☉, a more recently updated estimate puts this limit at 2.16 M☉ . Density is given by:
Such great mass accompanied by small volume results in density within an order of magnitude of that of an atomic nucleus. If a radius of 15km and mass of 1.4 are used, an estimate for density is returned as 2.0×1026km/km3, in comparison to the Earth’s meagre density of 5.0×1022 kg/km3. A 6ml imperial teaspoon of neutron star material would have a mass of around 900 billion kg . However, this assertion is conflicted with sources claiming other volumes such as that of a sugar cube, thimble or tablespoon would equal 900 billion kg. Regardless of this detail, the fact that neutron stars are the densest observed object in the universe safely conveys the great magnitude of the density.
The density of a neutron star gives it an incredibly high surface gravity of up to 7×1012 m/s2, with the typical value of any neutron star being of order 1012m/s2. Calculated using Newton’s law of universal gravitation this is given by:
where G is the universal gravitational constant, M is the mass of the star and r is its radius . This is approximately 1011 times what we experience on Earth. Due to this, neutron stars have an escape velocity of around 1×105km/s, which is about a third of the speed of light (c = 3×105km/s (1s.f)). This escape velocity is given by:
where G is the universal gravitational constant, M is the mass of the body being escaped from, and r the radius. Hypothetically, an object released from rest 1m above the surface of a neutron star with a radius of 12km would hit the surface at 1400 km/s . However, in reality, the tidal force – the gravitational effect stretching a body of mass towards the centre of mass of another object due to a difference in strength in gravitational field – would cause a process called spaghettification to compress this object into long thin shapes before it could reach the surface.
Gravity is strong enough to bend radiation emitted from the star in a process called gravitational lensing, allowing observers to see some of the back side of the star .
Neutron stars inherit the magnetic field of their progenitor star, which, conserved in an object so small, means they possess very strong magnetic fields of over 1012 gauss in contrast to the Earth’s 1 gauss . Variations in magnetism allow different types of neutron stars to be distinguished, and magnetism aids the explanation of the periodic pulses by which neutron stars were first discovered.
Magnetars are highly magnetised neutron stars, with their magnetic fields falling between 1014 and 1015 gauss. This gives them the strongest magnetism yet recorded in the universe. Scientists have only discovered about 30 magnetars so far . The magnetic field is strong enough to interfere with sub-atomic particles: “X-ray photons readily split in two or merge. The vacuum itself is polarized, becoming strongly birefringent, like a calcite crystal. Atoms are deformed into long cylinders thinner than the quantum-relativistic de Broglie wavelength of an electron” . Some magnetars are known as ‘soft gamma repeaters’, or SGRs, due to their sporadic releases of large bursts of low energy gamma rays and X-rays, typically during time periods of the order of 1×10-1 seconds . Magnetars also differ from other neutron stars in that their period of rotation lasts longer at 2-10 seconds, whereas a typical neutron star would rotate once in less than a few seconds. This is due to the resulting drag from the strength of the magnetic field. In addition, their active lives are short – the strong magnetic field will decay after about 10,000 years.
Magnetism is partly responsible for the observed “pulses” from pulsars, another type of neutron star. The neutron star is formed with a very high rotation speed. The combination of this with the strong magnetic field produces electric fields with electric potential of over 1 trillion V. 1m3 of the magnetic field of one example – the Crab pulsar – contains more energy than human life has generated to date . These fields accelerate electrons to high velocities, which produce high-energy radiation emissions called magnetospheric radiation in reference to the magnetosphere around the pulsar. This radiation is thought to be produced somewhere above the magnetic poles – the two regions, north and south, at which the field is most intense. “Pulsing” bursts are observed when this area above the magnetic pole is visible. The pulses come at the same rate as the rotation of the neutron star and so appear periodic, similar to a lighthouse.
(Fig.1: The magnetic field, represented by the red belts emanating from its surface, and electrical fields accelerate electrons to nearly the speed of light, causing them to emit beams of radio waves and other forms of radiation. As the pulsar rotates, these beams sweep across space. If the beams intersect the Earth, the pulsar can be seen switching ‘on’ and ‘off,’ like a lighthouse. Source: https://www.nrao.edu/pr/2002/3c58/pulsars/ .)
Neutron stars rotate rapidly once formed due to the conservation of angular momentum:
where L is the angular momentum, m is mass, v is velocity and r the radius. As the radius shrinks with the compression of the star, velocity of rotation increases. This same conservation is seen in spinning ice-skaters pulling their arms in to increase speed of turn.
(Fig.3 The conservation of angular momentum demonstrated by the model of a spinning ice-skater. Source: https://socratic.org/questions/when-a-spinning-star-shrinks-in-radius-it-speeds-up-why-does-this-happen .)
Over time, the rotational velocity of a neutron star slows at a very small constant rate. The spin-down rate (P-dot) is the derivative of P – the periodic time for one rotation – with respect to time :
P-dot = dP/dt > 0
The unit for P-dot, the periodic increase per unit time, is s•s-1. Eventually, the neutron star will rotate too slowly for the emission of magnetospheric radiation to occur and so becomes undetectable.
Due to the strong magnetic and gravitational fields of neutron stars, occasionally matter orbiting nearby stars can be absorbed. This adds to the mass of the star, therefore increasing the velocity of rotation in accordance with the conservation of angular momentum.
The fastest rotating neutron star discovered to date is named PSR J1748-2446ad, with a frequency of 716 revolutions per second .
Density increases with depth into a neutron star. The outer atmosphere is thought to consist of a thin layer – mere micrometres in thickness – of mostly light nuclei of elements such as hydrogen and helium, as heavier elements sink beneath the surface.
Current consensus is that there is an outer crust (although there is much conflict between sources of its thickness), consisting of a lattice of atomic nuclei and a sea of free-roaming electrons. It is believed that further down, an inner crust contains a lattice of even closer-packed ionised elements. The crust is extremely strong and hard due to the tight compression and pressure. Additionally, it is very smooth, due to the extreme gravitational field preventing any surface irregularities over roughly 5mm .
Deeper in, it is thought that most protons merge with electrons to form neutrons as increased density squeezes nuclei closer together. It is postulated that a type of degenerate matter referred to as nuclear pasta exists between the crust and core of a neutron star. Competing nuclear attraction between protons and neutrons, electric repulsion of the protons, and the pressure at this depth in the star is thought to trigger the formation of a variety of structures made up of neutrons and protons. The name “nuclear pasta” refers to the geometry of these theoretical structures, resembling types of pasta. The density of this material means it would be the strongest material in the universe. “To shatter a plate of nuclear pasta, it could take about 10 billion times the force needed to shatter steel.” .
The main area of interest regarding the structure of a neutron star is the contents of its core. Numerous suggestions including strange matter of strange, up and down quarks, Bose-Einstein condensate and hyperon particles have been made. However, given the limited space to discuss each possibility, this essay will focus on the potential existence of a quark-gluon plasma.
Quarks are what protons and neutrons are made of, held together tightly by gluons which carry the strong nuclear force binding most ordinary matter together. Experiments in CERN’s Large Hadron Collider in Switzerland have found, by colliding heavy ions at high energy, that at high pressures and temperatures quarks can be freed from the gluons. The result is a free-flowing quark-gluon plasma. The fleeting example of this achieved in 2012 by CERN set the record for the highest temperature material made in a laboratory – exceeding 5 trillion degrees Celsius. It is possible that the pressure due to density in the core of a neutron star would have a similar impact in overcoming the strong force of the gluons, forming this quark-gluon plasma or “goo” .
(Fig.2: A cross-sectional illustration of the various layers of a neutron star: the thin outer atmosphere, outer and inner crust including nuclear pasta, and the unknown inner core. The short 10km radius is also illustrated, alongside relative approximated thicknesses of each layer. Source: https://physicsforme.com/2018/05/08/a-short-walk-through-the-physics-of-neutron-stars/ .)
Neutron stars hold great significance in the extremity of their properties and conditions. They offer intriguing test cases that have the capability to help physicists understand the possibilities of what can exist in this universe.
There is much that is left to be explained and discovered regarding neutron stars. In many cases, breakthroughs and technological advancements by projects such as NICER and LIGO, while providing explanations to some phaenomena, bring about a whole new set of unanswered questions. The composition of the inner core, feasibility of nuclear pasta and the cause of the RRAT (rotating radio transients) phenomenon are among several such matters. NICER aims to look at X-rays coming from rotating neutron stars to try to more accurately predict measurements of their mass and radii. LIGO hopes to detect gravitational waves produces by the merger of two neutron stars, gaining insight into the properties of the dense matter. Further advancement in understanding in the coming years is eagerly anticipated.
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