Neutron stars are some of the most extreme objects in the universe. Formed from the collapsed cores of supergiant stars, these stars are heavier than our Sun, but compressed into a sphere the size of a city. The dense cores of these exotic stars contain matter compressed into unique states that we can’t reproduce or study on Earth. That’s why NASA is on a mission to study neutron stars and the physics that govern the matter inside them.

My colleagues and I helped them. We used radio signals from a rapidly spinning neutron star to measure its mass. This allowed scientists working with NASA data to measure the star’s radius, giving us the most accurate information yet about the strange material inside.

What’s inside a neutron star?

The matter in the core of a neutron star is denser than an atomic nucleus. The densest and most stable form of matter in the universe has been crushed to its limit and is on the verge of collapsing into a black hole. Understanding how matter behaves under these conditions is a critical test of our fundamental theories of physics. NASA’s Neutron Star Internal Composition Exploration (NICER) mission is trying to unravel the mysteries of this extraordinary matter.

More beautiful — The X-ray telescope on the International Space Station. It detects X-rays from hot spots on the surfaces of neutron stars, where temperatures can reach millions of degrees. Scientists are modeling the timing and energy of these X-rays to map the hot spots and determine the mass and size of the neutron stars.

Knowing how the size of neutron stars relates to their mass will reveal the “equation of state” of the matter in their cores. This tells scientists how soft or hard the neutron star is, how “compressible” it is, and therefore what it’s made of.

A more moderate equation of state would assume that the neutrons in the core would dissolve into an exotic soup of smaller particles. A more stringent equation of state would imply neutron dragging, which would lead to larger neutron stars. The equation of state would also determine how and when neutron stars would break apart during a collision.

Solving mystery with neutron star neighbor

One of NICER’s primary targets is a neutron star called PSR J0437-4715, the nearest and brightest millisecond pulsar.

Pulsar It is a neutron star that emits bursts of radio waves, which we observe as a pulse with each rotation of the neutron star. This particular pulsar spins 173 times a second (as fast as a blender). We have been observing it for almost 30 years with CSIRO’s Murriyang radio telescope in Parkes, New South Wales.

Working with NICER data, the team encountered a problem with this pulsar. X-rays from a nearby galaxy made it difficult to accurately model hot spots on the surface of the neutron star. Fortunately, we were able to use radio waves to find an independent measurement of the pulsar’s mass. Without this important information, the team would not have been able to obtain the correct mass.

The weight of a neutron star depends on time

To measure the mass of a neutron star, we rely on an effect called the Shapiro delay, described by Einstein’s theory of general relativity. Massive, dense objects like pulsars (and in this case, their companion star, a white dwarf) warp space and time. The pulsar and its companion orbit each other every 5.74 days. By the time the pulses from the pulsar reach us through the compressed space-time around the white dwarf, they are delayed by microseconds.

Such microsecond delays can be easily measured from pulsars such as Murriyang and PSR J0437-4715. This pulsar and other millisecond pulsars are regularly observed by the Parkes Pulsar Timing Array project, which uses these pulsars to detect gravitational waves.

Because PSR J0437-4715 is relatively close to us, from our perspective its orbit wobbles slightly as the Earth orbits the Sun. This wobble gives us more details about the geometry of the orbit. We use this, along with the Shapiro delay, to find the masses of the white dwarf companion and the pulsar.

Mass and size of PSR J0437-4715

The mass of this pulsar was calculated to be typical for a neutron star, 1.42 times the mass of our Sun. This is important because the size of this pulsar would also be about the size of a typical neutron star. Working with the NICER data, scientists were then able to determine the geometry of the X-ray hotspots and calculate the radius of the neutron star to be 11.4 kilometers. These results provide the most accurate reference point for the equation of state for neutron stars at intermediate densities.

Our new picture already rules out the softest and hardest equations of state for a neutron star. Scientists will continue to figure out what this means for the presence of exotic matter in the inner cores of neutron stars. Theories suggest the problem could involve quarks escaping from their normal homes and into larger particles, or rare particles known as hyperons.

This new data also completes a new model of neutron star interiors based on observations of gravitational waves from colliding neutron stars and the associated explosion called a kilonova. Murriyang has a long history of helping NASA missions and was known to have been used as the primary video receiver for much of the Apollo 11 moonwalk. We have now used this iconic telescope to “weigh in” on the physics of neutron star interiors and expand our fundamental understanding of the universe.