A neutron star is the lingering leftovers of a massive star that has ended its nuclear-fusing “life” in the brilliant and fatal fireworks of a supernova explosion. These extremely dense city-sized objects are actually the collapsed cores of dead stars which, before their violent “deaths”, weighed-in at between 10 to 29 times the mass of our Sun. These bizarre, lingering relics of heavy stars are so extremely dense that a teaspoon full of neutron star material can weigh as much as a herd of elephants. In March 2020, an international research team of astronomers announced that they have obtained new measurements of how big these oddball stars are. They also found that neutron stars unlucky enough to merge with voracious black holes are likely to be swallowed whole–unless the black hole is both small and/or rapidly spinning.

The international research team, led by members of the Max Planck Institute for Gravitational Physics (Einstein Institute: AEI) in Germany, obtained their new measurements by combining a general first principles description of the mysterious behavior of neutron star material with multi-messenger observations of the binary merger of a duo of neutron stars dubbed GW170817. Their findings, published in the March 10, 2020 issue of the journal Nature Astronomy, are more stringent by a factor of two than earlier limits and demonstrate that a typical neutron star has a radius close to 11 kilometers. In addition, they found that because such unlucky stars are swallowed whole during a catastrophic merger with a black hole, these mergers might not be observable as gravitational wave sources, and would also be invisible in the electromagnetic spectrum. Theoretical work in physics and other sciences is said to be from first principles (ab initio) if it originates directly at the level of established science and does not make assumptions such as empirical model and parameter fitting.

Gravitational waves are ripples in the fabric of Spacetime. Imagine the ripples that propagate on the surface of a pond after a pebble is thrown into the water. Gravitational waves are disturbances in the curvature of Spacetime. They are generated by accelerated masses, that propagate as waves outward from their source at the speed of light. Gravitational waves provide a new and important tool for astronomers to use because they reveal phenomena that observations using the electromagnetic spectrum cannot. However, in the case of neutron star/black hole mergers, neither gravitational wave observations nor observations using the electromagnetic spectrum can be used. This is why such mergers may not be observable.

“Binary neutron star mergers are a gold mine of information. Neutron stars contain the densest matter in the observable Universe. In fact, they are so dense and compact, that you can think of the entire star as a single atomic nucleus, scaled up to the size of a city. By measuring these objects’ properties, we learn about the fundamental physics that governs matter at the sub-atomic level,” explained Dr. Collin Capano in a March 10, 2020 Max Planck Institute Press Release. Dr. Capano is a researcher at the AEI in Hannover.

“We find that the typical neutron star, which is about 1.4 times as heavy as our Sun has a radius of about 11 kilometers. Our results limit the radius to likely be somewhere between 10.4 and 11.9 kilometers. This is a factor of two more stringent than previous results,” noted Dr. Badri Krishnan in the same Max Planck Institute Press Release. Dr. Krishnan leads the research team at the AEI.

Strange Beasts In The Stellar Zoo

Neutron stars are born as the result of the fatal supernova explosion of a massive star, combined with gravitational collapse, that compresses the core to the density of an atomic nucleus. How the neutron-rich, extremely dense matter behaves is a scientific mystery. This is because it is impossible to create the necessary conditions in any lab on Earth. Although physicists have proposed various models (equations of state), it remains unknown which (if any) of these models actually describes neutron star matter.

Once the neutron star is born from the wreckage of its progenitor star, that has gone supernova, it can no longer actively churn out heat. As a result, these stellar oddballs cool as time goes by. However, they still have the potential to evolve further by way of collision or accretion. Most of the basic models suggest that neutron stars are made up almost entirely of neutrons. Neutrons, along with protons, compose the nuclei of atoms. Neutrons have no net electrical charge, and have a slightly larger mass than protons. The electrons and protons in normal atomic matter combine to create neutrons at the conditions of a neutron star.

The neutron stars that can be observed are searing-hot and typically have a surface temperature of 600,000 K. They are so extremely dense that a matchbox containing its material would weigh-in at about 2 billion tons. The magnetic fields of these dead stars are about 100 million to 1 quadrillion times more powerful than Earth’s magnetic field. The gravitational field at the bizarre surface of a neutron star is approximately 200 billion times that of our own planet’s gravitational field.

As the core of the doomed massive star collapses, its rotation rate increases. This is a result of the conservation of angular momentum, and for this reason the newborn neutron star–called a pulsar–can rotate up to as much as several hundred times per second. Some pulsars emit regular beams of electromagnetic radiation, as they rapidly rotate, and this is what makes them detectable. The beams of electromagnetic radiation emitted by the pulsar are so regular that they are frequently likened to lighthouse beacons on Earth.

The discovery of pulsars by Dr. Jocelyn Bell Burnell and Dr. Antony Hewish in 1967 was the first observational indication that neutron stars exist. The radiation from pulsars is believed to be primarily emitted from areas near their magnetic poles. If the magnetic poles do not coincide with the rotational axis of the neutron star, the emission beam will sweep the sky. When observed from a distance, if the observer is situated somewhere in the path of the beam, it will appear as regular pulses of radiation emitted from a fixed point in space–hence the “lighthouse effect.” PSR J1748–2446ad is currently the most rapidly spinning pulsar known, and it rotates at the breathtaking rate of 716 times every second, or 43,000 revolutions per minute, giving a linear speed at the surface of almost a quarter of the speed of light.

There are thought to be approximately 100 million neutron stars in our Milky Way. This number was derived by scientists estimating the number of stars that have gone supernova in our Galaxy. The problem is that most neutron stars are not young, wildly spinning pulsars, and neutron stars can only be easily spotted under certain conditions–for example, if they are members of a binary system or if they are youthful pulsars. However, most of the neutron stars dwelling in our Milky Way are elderly–and cold. Non-accreting and slowly-rotating neutron stars are almost undetectable. However, ever since the Hubble Space Telescope discovered RX J185635-3754, a small number of nearby neutron stars that apparently emit only thermal radiation have been spotted. It has been proposed that soft gamma repeaters are a type of neutron star possessing especially powerful magnetic fields, termed magnetars. However, some astronomers think that soft gamma repeaters are really neutron stars with ancient, fossil disks encircling them.

Any main-sequence (hydrogen burning) star, on the Hertzsprung-Russell Diagram of Stellar Evolution, that sports an initial mass exceeding 8 times that of our Sun, has the potential to become the stellar progenitor of a neutron star. As the aging star evolves away from the main-sequence, additional nuclear burning results in an iron-rich core. When all nuclear fuel in the core has been used up, the core must be supported by degeneracy pressure alone. Stars on the hydrogen-burning main-sequence keep themselves bouncy because they experience a very delicate balance between the squeeze of their own gravity and push of radiation pressure. When radiation pressure can no longer be produced by nuclear fuel burning, gravity crushes the dying star.

Additional deposits from shell fuel burning cause the core of the doomed star to exceed what is termed the Chandrasekhar limit. As a result, temperatures of the dying, doomed massive star soar to more than 5X10 to the ninth power K. At these extremely hot temperatures, photodisintegration (the breaking up of iron nuclei into alpha particles by high-energy gamma rays) occurs. As the temperature soars ever higher and higher, electrons and protons merge to create neutrons by way of electron capture. These liberate a flood of neutrinos. When densities reach nuclear density of 4 X 10 to the seventeenth power kg/m cubed, a combination of strong nuclear force repulsion and neutron degeneracy pressure stops further contraction. The infalling outer envelope of the doomed old star is halted and hurled outward by a flux of neutrinos manufactured in the creation of the neutrons. The elderly star has come to the end of that long stellar road, and it goes supernova. If the stellar ghost sports a mass that exceeds about 3 solar masses, it collapses further and becomes a black hole.

As the core of a massive star is squeezed during a Type II (core-collapse) supernova (or a Type Ib or Type Ic supernova), it collapses into a neutron star. The stellar relic retains most of its angular momentum–but because it only possesses a small percentage of its progenitor star’s radius, a neutron star is born with a very high rotation speed. This stellar oddball slows down over a very long span of time.

Sizing Up A Dense Stellar Oddball

Mergers of a duo of binary neutron stars, such as GW 170817, provide a treasure trove of information about how matter behaves under such extreme conditions, as well as the underlying nuclear physics behind it. GW 170817 was first observed in gravitational waves and the entire electromagnetic spectrum in August 2017. From this type of important astrophysical event, scientists can go on to determine the physical properties of these oddball stars, including their radius and mass.

The research team at AEI used a model based on a first-principles description of how subatomic particles dance together at the extremely high densities found inside neutron stars. Remarkably, as the team of scientists discovered, theoretical calculations at length scales less than a trillionth of a millimeter can be compared with observations of an astrophysical object more than a hundred million light-years from Earth.

“It’s a bit mind boggling. GW 170817 was caused by the collision of two city-sized objects 120 million years ago, when dinosaurs were walking around here on Earth. This happened in a galaxy a billion trillion kilometers away. From that, we have gained insight into subatomic physics,” Dr. Capano commented in the March 10, 2020 Max Planck Institute Press Release.

The first-principles descriptions used by the scientists predicts numerous potential equations of state for neutron stars, which are directly derived from nuclear physics. From these possible equations of state, the researchers chose only those that are most likely to explain different astrophysical observations, which agree with gravitational-wave observations of GW 170817. The team used observations derived from public LIGO and Virgo data, which produce a brief hyper-massive neutron star as the result of the merger, and which agree with known constraints on the maximum neutron star mass from electromagnetic counterpart observations of GW 170817. This approach not only enabled the scientists to derive new information on dense-matter physics, but also to obtain the most stringent limits on the size of neutron stars to date.

“These results are exciting, not just because we have been able to vastly improve neutron star radii measurements, but because it gives us a window into the ultimate fate of neutron stars in merging binaries,” noted Stephanie Brown in the March 10, 2020 Max Planck Institute Press Release. Ms. Brown is co-author of the publication and a doctoral student at the AEI Hannover.

The new results suggest that, with an event like GW 170817, the LIGO and Virgo detectors at design sensitivity will be able to distinguish, from gravitational waves alone, whether the duo of neutron stars or duo of black holes have merged. For GW 170817, observations in the electromagnetic spectrum were central in making that important distinction.

The Laser Interferometer for Gravitational Wave Observatory (LIGO) is a large scale physics experiment and observatory to detect cosmic gravitational waves and to develop gravitational wave observatories on an astronomical level. The Virgo interferometer is a large interferometer designed to detect gravitational waves.

The team of scientists also found that for mixed binaries (a neutron star merging with a black hole), gravitational wave merger observations alone will have a difficult time distinguishing these events from binary black holes. Observations in the electromagnetic spectrum or gravitational waves from after the merger will be crucial to distinguish between the two.

However, it turns out that the new results also suggest that multi-messenger observations of mixed binary mergers are unlikely to occur. “We have shown that in almost all cases the neutron star will not be torn apart by the black hole and rather swallowed whole. Only when the black hole is very small or rapidly spinning, can it disrupt the neutron star before swallowing it; and only then can we expecxt to see anything besides gravitational waves,” commented Dr. Capano in the March 10, 2020 Max Planck Institute Press Release.

In the next decade, the existing gravitational wave detectors will become even more sensitive, and additional detectors will begin observing. The research team expects more gravitational wave detections and possible multi-messenger observations from merging binary neutron stars. Each of these mergers would provide wonderful opportunities to learn more about neutron stars and nuclear physics.