Are neutron stars truly squishy? Perhaps not

By Cameron Scott

Imagine compressing some hydrogen gas. The volume occupied by the gaseous vapour shrinks and the interactions between the constituent hydrogen molecules strengthens. At a certain pressure, the hydrogen molecules coalesce and transition into liquid hydrogen. Compress it further and the liquid solidifies. What would happen if we continued applying greater pressure?

With further compression, the atoms making up the hydrogen solid would approach so close that they combine, producing helium and releasing energy. Nuclear fusion has occurred. This is exactly the process by which stars operate. The universal attraction of gravity gathers, compresses, and fuses hydrogen, releasing energy that we receive in the form of visible light and other forms of electromagnetic radiation. The energy from fusion also acts as a kind of pressure pushing against the compressive grip of gravity. For small enough stars like our own, the outward pressure of fusion can counter the compression completely and the star remains steadily fusing hydrogen for many billions of years.

But what about larger stars? In this case, the energy from fusion is not sufficient to halt gravitational compression and the star continues to feel the squeeze. Helium is then fused together to form heavier elements, and these go on to form progressively heavier elements with each step in the fusion ladder producing diminishing energy and struggling to stave off gravity.

Two vastly different masses of star have the same size. What does this mean?

Eventually, the pressures become so great that the individual protons and electrons constituting these elements are combined into neutrons in a last-ditch effort to prevent gravitational collapse. The resulting objects has a mass approximately equal to that of our Sun but is now compressed into something around the size of the island of Manhattan. This miraculous density is one of the defining characteristics of the neutron star.

Naturally, the questioning could continue. What if the energy released during the formation of the neutron star is still insufficient to prevent further compression? Are the neutrons somehow combined into some unimaginably dense material or does the story end in neutrons? The former case is intriguing. It implies that as the neutrons are forced together, their components– quarks and gluons – would form a sea of much greater density than the neutron star. This phase of matter would presumably be the most compact thing possible. The latter option implies that instead of undergoing this phase transition, a neutron star too dense to remain stable would continue collapsing into a black hole.

In order to determine which of the two outcomes are the correct, two pieces of information must be very carefully measured. The mass of the neutron star is the first of these and can be ascertained by observing the motions of light that passes nearby. The more massive the star, the greater the deflection of light. Detection of the deflection determines the mass.

The second piece of crucial information is the diameter of the star. Obtaining this value is much more subtle and is predicated on the fact that a large star is rotating at a constant rate. Upon collapsing into a neutron star, this rotation must continue (the principle of conservation of angular momentum) but as the neutron star is now considerably smaller than the original, the rate of rotation must be much higher. In fact, the rotation of the neutron star becomes so fast that charged particles near the surface are accelerated to huge speeds. This leads to another key piece of physics – accelerating charged particles emit huge amounts of electromagnetic radiation. The observational puzzle is completed when you realise that this radiation must, like light, be bent by the strong gravitation field of the star. The gravitational field of the neutron star is so strong that radiation originally emitted in a direction away from Earth will be bent round and sent towards Earth. The delay in radiation signals from the Earth-facing side against the other side provides some measure of the size of the neutron star.

Exactly these kinds of measurements have been performed using NASA’s Neutron star Interior Composition Explorer (NICER) X-ray Telescope mounted to the International Space Station. Data recorded from J0740, a neutron star three thousand light-years away from the Earth, was analysed by two independent teams. J0740 has a mass of 2.1 solar masses (the largest neutron star currently known) and was calculated to have a diameter of around 26km. Compare this with results from J0030, a neutron star of about 1.4 times the mass of the Sun and a diameter also about 26km across. Two vastly different masses of star have the same size. What does this mean?

If the hypothesised quark sea were to form in the larger star, you would expect the heavier star to have a smaller size – the quark sea makes the star squishier. This has not been observed. Clearly a neutron star of 2.1 times the mass of the Sun is not heavy enough to create this novel phase or if it does form, it can only possibly form in the very centre of the core with a negligible effect on the star’s overall size. Unfortunately, the experimental results indicate that this fascinating form of super dense material remains tantalisingly out of reach even in this most extreme of locales.

Image: Generated by OpenAI’s Dall-E 2

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