Core of a neutron star

The extreme conditions inside neutron stars suggest all kinds of unusual matter might make them up. From neutronium, to nuclear pasta, to soups of strange quarks, neutron stars are a rich source of interesting physics. This episode I will take you on a journey through the star’s layers to the heart of the monster: the core of a neutron star. Here, we will witness the tenets of particle physics break down under the immense pressure, as quarks deconfine and decay. We might see droplets of strange matter fly out and infect the universe. Finally, I’ll touch on the search for experimental evidence to determine which type of matter neutron stars are most likely to keep bubbling away in their cores.

https://whatwedontknow.buzzsprout.com/

Hello everyone, welcome to the fourteenth episode of ‘What We Don’t Know’, a podcast that explores the boundaries of human knowledge, investigating the unanswered questions and theories that unravel them at the frontiers of science. During this podcast I hope to get you interested in new areas of science, maths and technology, teaching you about existing concepts and igniting a curiosity for the things we have yet to know.

When a massive star dies, it explodes in a breathtaking supernova, throwing off its outer layers and leaving behind a small, dense core. The mass in this core contracts due to gravity. If the total mass is greater than around 2.2 solar masses - 2.2 times the mass of the sun - then the core will contract into an infinitely small point: a black hole. If not, outward forces will balance the strong inward pull of gravity, and a neutron star will be born.

Neutron stars are one of the most extreme astronomical objects in the universe. They are so dense that a single teaspoon, if you were strong enough to collect it, would weigh 4 billion tons. They can spin as fast as 43,000 times per minute, and their magnetic field - for reference, Earth’s magnetic field is around 1 gauss - reaches a trillion gauss. If a neutron star is lucky enough to have close company, two neutron stars can spiral into each other and collide in a ‘kilonova’, sending gravitational waves rippling across space-time and ejecting some of the stars’ inner material. Many astronomers believe that these collisions are the source of much of the universe’s gold, platinum, and other elements heavier than iron. We like to say that us humans are made of stardust. But it seems that our jewellery is made of neutron stardust.

Picture a neutron star as a small spinning star, with a diameter of about 12.5 miles, surrounded by a very strong magnetic field. Some neutron stars have jets of materials and radiation streaming along this magnetic field, visible as high-powered beams that flash like a lighthouse as the star spins. These are pulsars. Pulsars and regular neutron stars have thin atmospheres mostly consisting of hydrogen and helium, which cover a thin crust, around 1-2cm thick, made of atomic nuclei - bundles of protons and neutrons held together by the strong force - and free-roaming electrons.

Beneath this crust, the inward force of the neutron star compresses the nuclei and electrons into a dense lattice, then compresses the material further until the pressure becomes so great that protons and electrons fuse into neutrons. This kind of substance, made purely of neutrons, gives neutron stars their name, and can only exist under their immense gravity. It is called ‘neutronium’ or ‘element zero’: a hypothetical form of matter with no protons and an atomic number of zero.

Ice, water, and steam are three phases of the same substance. Neutronium also exists in phases. Near the surface, neutronium is homogenous, meaning that it is in the same phase everywhere. Deeper, small spheres form, which look like gnocchi. Deeper still, the gnocchi is compressed into cylindrical rod-like structures that look like spaghetti, then flat sheets, comparable to lasagna, emerge. This fabulous variety of shapes theorised to populate a neutron star’s interior is known as nuclear pasta. Whether it sounds appetising is probably a matter of personal taste.

If we dig even deeper, matter becomes even less normal. But to understand why the next form of matter is weird, first you must know how matter usually behaves in neutrons and other fermions.

Neutrons and protons are made of even smaller particles called quarks. There are six types, also known as ‘flavours’ of quark: up, down, strange, charm, top, and bottom, which differ in mass and charge. The last four are unstable, so the majority of regular matter is made of up and down quarks. Quarks, along with leptons and bosons, make up the Standard Model of particle physics, a highly successful theory classifying all known elementary particles and describing three of the four known fundamental forces. These four forces are electromagnetism, carried by photons, the strong interaction, carried by gluons, the weak interaction, carried by W and Z bosons, and gravity, which is currently unexplained by the Standard Model. Also, every particle has an antiparticle with the same mass and opposite charge.

The strong interaction, also known as the strong nuclear force, holds quarks together in composite particles called hadrons (hence the name Large Hadron Collider at CERN). A neutron is made of two down quarks and one up quark. A proton is made of two up and one down. All three quarks and their interactions via gluon exchange can be described using the field of quantum chromodynamics.

Importantly, quarks really hate to be alone. They tend to come in groups of three (baryons like protons and neutrons) or quark-antiquark pairs (mesons). You will never observe a quark by itself: the harder you try to pull them apart, the more the strong force will stick them together, and if you put in enough energy when pulling, this energy is just used to create new quarks. This phenomenon is known as quark confinement.

In neutronium, quarks are confined inside neutrons as we expect. But remember, neutron stars have immense mass (around 1.4 solar masses) packed inside a tiny volume (around 4300 km3). This results in an astonishingly high density and pressure that increases the deeper we delve into the star. The confining radius of quark interaction determines the size of a neutron. When the matter density reaches the point where the average separation between neutrons is lower than their confining radius, neutrons ‘overlap’ and lose their individuality. The neutrons ‘dissolve’ into a uniform bath of quarks which we call quark matter.

We can actually establish the transition of baryonic matter to quark matter: the neutron to quark first-order phase transition is estimated to start at densities of around 1.4-4 x1015 g/cm3. The density of a neutron star ranges from 8x1013 to 2x1015. Therefore, although quark matter wouldn’t form in the outer layers of a neutron star, it could be hidden away at the ultradense centre.

In fact, neutron stars are not the only place we can find quark matter. Nucleons melt into their components under high pressure, but also under high temperatures: above around 2x1012 Kelvin. In the first 40 microseconds of the universe’s life, conditions would have been hot enough, so quarks and gluons may have been deconfined in a ‘quark-gluon plasma’. This is not purely theoretical. In 2000, researchers at CERN managed to create a state of matter where quarks were deconfined, showing that it is possible. Even so, it is very difficult to replicate the internal conditions of a neutron star in a laboratory on Earth.

Perhaps the core of a neutron star is just quark matter. This is already exciting. But what if the core is even stranger?

The Pauli exclusion principle prevents fermions - matter particles like quarks - from occupying the same energy level and position. When the particle density in a substance is high enough, like it could be at the centre of a neutron star, all energy levels below the available thermal energy are occupied, so to increase the density further, some particles must be raised to higher, yet unoccupied energy levels. Energy is needed to cause more compression. This energy manifests as a pressure called degeneracy pressure. Similarly, electron gas becomes ‘degenerate’, and experiences a much higher pressure than predicted by classical physics, when the mean spacing between electrons approaches the de Broglie wavelength. Closer than the de Broglie wavelength, and the electrons violate the Pauli exclusion principle.

Usually, the degeneracy pressure of down quarks dominates the quark matter, because it formed from neutrons, which contain twice as many down quarks as up quarks. But if the energy level required to relieve the degeneracy pressure is high enough, half of the down quarks will be transmuted, i.e. changed through nuclear processes, into strange quarks. Here, the weak force is responsible. A strange quark has a higher rest mass than a down quark, which represents an energy cost, but the transmutation is ultimately effective because strange quarks open another set of energy levels, allowing the average energy per particle to be lower, and the matter system becomes more stable.

In fact, down quarks could, theoretically, transmute into charm, top, or bottom quarks. However, their much higher rest masses make this energetically unfeasible.

Strange matter isn’t the most inventive name. It refers to any quark matter containing strange quarks. The ‘forbidden soup’ of up, down, and strange quarks, deconfined and in equal parts, potentially brewing in the depths of neutron stars, is called strange matter. A neutron star containing strange matter is called a strange star.

Since the strange quark has a higher mass than up and down quarks, it spontaneously decays into an up quark via the weak interaction. This means that particles containing strange quarks, such as the lambda hyperon which is made of an up, a down, and a strange quark, usually decay into lighter particles without strange quarks. Under normal conditions, a hyperon will decay and lose its strangeness. But under the immense pressure of a neutron star, deconfined strange matter may be the most stable form of matter. The stability occurs because of the Pauli exclusion principle and the lower energy states that strange quarks provide.

Strange matter may even be the true ground state of all matter. This would make it the ideal form: perfectly dense, perfectly stable, and indestructible. So stable that it could exist outside neutron stars. So stable that anything it touched would be converted.

The conversion would be like a deadly infection, or a forest fire ripping through the land. A droplet of strange matter, endearingly termed a strangelet, would ‘burn’ through any matter around it, lowering its energy level, converting it into strange matter, kickstarting a chain reaction that ended with everything dissolving into a strange quark bath. If strange matter fell to Earth, it would disintegrate every proton and neutron in an instant.

Ah, but remember the very, very strong gravitational field of a neutron star? It is second only to a black hole. If strange matter did happen to form inside neutron stars, surely it would be stuck deep within the core, unable to escape and contaminate the ordinary matter of the universe with its enticing stability?

Chances are you are listening to this on a phone, or maybe using a computer. Those electronic devices contain surprising amounts of heavy and precious metals like copper, gold, and palladium. Maybe you’re also wearing a silver necklace. You’re surrounded by the evidence of neutron star collisions: extraordinary astronomical events where two neutron stars in a binary system spiral inwards, collide, and expel their contents in a kilonova. Kilonovae are the source of many of the heavy elements on Earth. They could also fling out strangelets into the vast vacuum of space. These droplets of strange matter would hurtle across the galaxy for millions of years until they, by chance, encountered a planet or star, where they would burn through the material until nothing was left but a dense bath of quarks.

In fact, some physicists argue that strangelets are common, that our distant skies are littered with tiny specks of strange matter. Strangelets may even have formed just after the big bang when everywhere in the universe was very hot and very dense. These ancient remnants of more unforgiving conditions could persist to this day, accumulating around galaxy cores where the mass is concentrated.

There’s no need to worry though. The existence of interstellar strangelets is, for now, speculatory.

First, there are mathematical barriers to understanding quark matter. It is difficult to estimate the critical density for a transition from nuclear to quark matter because calculations involving the strong interaction are complex and unwieldy.

While theoretical physicists work on this, and the other mathematical obstacles in quantum chromodynamics, experimentalists search the heavens for observable signatures of neutron stars. Although we cannot actually peer into a neutron star to measure its core, the different possibilities for the matter there - neutronium, quark matter, strange matter - push against gravity in unique ways, generating different internal pressures, and increasing or decreasing the radius of the star accordingly. By examining the mass to radius ratio of a neutron star, we could determine what type of matter makes it up. Most measurements in the past have not been precise enough to convincingly confirm one theory over another. There have, however, been some exciting recent developments.

In 2019, the Neutron Star Interior Composition Explorer (NICER for short) on the International Space Station made measurements of neutron stars’ radii to within half a kilometre, allowing researchers to narrow down models of the stars’ cores. For example, NICER’s data suggested that J0030+0451, a lone pulsar spinning around 1100 light years away from Earth, has a mass of 1.3-1.4 solar masses and a radius of 13km. The new precision is promising, but unfortunately, the results could support both mundane and exotic predictions about neutron star matter. In the future, some researchers hope that NICER may find two neutron stars with the same mass but different radii, indicating a critical transition point where small changes in conditions cause exotic matter to form.

Secrets about neutron stars may also be revealed when they rotate around each other and collide. Gravitational wave detectors such as the Virgo detector in Italy and the Laser Interferometer Gravitational-Wave Observatory (LIGO) in the US can measure the gravitational waves emitted during binary neutron star rotation, as well as the amount of distortion due to gravity that both stars experience. The type of matter inside each star influences its malleability, which, in turn, influences the star’s shape.

This episode I introduced you to neutron stars: the very small, very dense stars left in the wake of a supernova, whose intense pressure compresses all their matter to neutrons, and whose speed of rotation and strong magnetic fields can produce pulsing beams of radiation that light up space. We dug deep through a pantry of nuclear pasta and arrived at the core of a neutron star. Here, the pressure became so great that the conventions of particle physics started to crumble. I explained the Standard Model’s elementary particles and fundamental forces, emphasising the confinement of quarks into composite particles called hadrons, then I revealed that due to the pressure inside neutron stars, individual neutrons might deconfine into a soup of up and down quarks. As if quark matter wasn’t interesting enough, the core might become even stranger when we consider the Pauli exclusion principle and the resulting degeneracy pressure from high quark densities. To relieve this degeneracy pressure, some down quarks may turn into strange quarks, forming a theoretically ultrastable, ideal form of matter known as strange matter. Neutron star collisions provide an opportunity for strangelets to escape the core. If droplets of strange matter are expelled during kilonovae, they, like strangelets remaining from the early universe, may be flying around space, waiting to contact a planet and convert it into more strange matter. On the other hand, neutron star collisions also provide an opportunity to experimentally understand the material in their cores.

Much of astronomical condensed matter physics is theoretical. Neutron stars are rare, their collisions even rarer, and the mathematics that models their interiors can be difficult to decipher. But physicists are taking steps to discover more about what lies in the core of neutron stars. By understanding how matter behaves in such extreme conditions, we’ll be able to better understand the early universe and the ordinary matter that makes up atoms, us, and the universe we inhabit today.

Thank you for listening.

References:

What We Don't Know

Core of a neutron star

Listen to this podcast on