A mystery lurks inside the corpses of dead stars. Neutron stars, formed when certain types of stars die in supernova explosions, are the densest form of matter in the universe; black holes are the only thing denser, but they have so fully escaped the bounds of normal physics that they are not matter anymore. The atoms in neutron stars have been squeezed so tightly by gravity that they have broken down, the protons and electrons inside them smushing together to create neutrons, leaving objects the size of small cities that contain masses larger than the sun. Some 95 percent of the mass of a neutron star is pure neutrons, but physicists wonder what happens at the very center, where the density peaks. Do neutrons break down further into their constituent quarks and gluons? Do some of the quarks transform from their normal “up” and “down” flavors to become weirder and heavier “strange quarks” not found in ordinary matter? Do the particles form an extreme state of matter called a superfluid that sloshes with no viscosity, never slowing down?

Scientists have come a step closer to understanding the inner workings of these bizarre bodies by studying the light and gravitational waves that result when two neutron stars slam into each other and become a black hole. Gravitational waves are folds in spacetime carved out when large masses move around. Scientists only gained the ability to detect gravitational waves in 2015, and have spotted just a handful of events involving neutron stars so far (the others have been collisions of black holes). But studying the properties of these waves—their frequency and how they change over time—can tell scientists a lot about the objects that created them. Physicists seek accurate measurements of neutron stars’ masses and radii, which would help reveal their “equation of state”—the relationship between pressure and density within these stars. Knowing the neutron star equation of state would in turn indicate what kind of matter hides inside them.

In a new study, an international team of researchers combined gravitational wave measurements from two neutron star collisions, as well as the light signals that arrived along with one of them (the other was dark), with estimates of neutron star masses and radii from watching rapidly spinning neutron stars called pulsars. “The big advantage is it’s a very coherent picture,” says study member Tim Dietrich of the University of Potsdam in Germany, who co-authored a paper reporting the results published today in Science. “We combine all the things we know currently, including gravitational waves and electromagnetic waves, information from single neutron stars, and theoretical computations from nuclear physics.” The equation of state they derived predicted that a neutron star containing the mass of 1.4 suns would have a radius of about 11.75 kilometers, plus or minus .81 to .86 km. That’s a bit more than half the length of Manhattan. “The size of the neutron star directly depends on the behavior of matter inside the core, so this gives us a better understanding about the properties of the neutron star material,” Dietrich says.

For instance, if neutrons remain intact in the core of these stars, they would push out against the outer layers, potentially leading to a slightly larger radius. If, on the other hand, the neutrons break down into a soup of quarks, the core would be squishier and the whole star would sink in a bit, resulting in a smaller radius.

The new measurement is in general agreement with earlier studies that have looked at gravitational wave data and other ways to measure neutron star size. “This paper is a nice joint reanalysis of previous studies, and doesn't change the overall impression that has been in place for the last few years, that the radius of a neutron star is about 11 to 13 km,” says Mark Alford, a physicist at Washington University in St. Louis. Anna Watts, an astrophysicist at the University of Amsterdam, says this type of combined analysis “is clearly the way forward,” but that none of the measurements “are yet good enough to really pin down the nature of dense matter.” The field will need to wait for future data to really understand what’s happening inside neutron stars.

“I think it’s a very nice analysis,” says physicist James Lattimer of Stony Brook University, who was not involved in the research. He cautions that in modeling how well different possible equations of state fit the data, the team may have mistakenly eliminated too many equations that produce neutron stars with large radii, however. “I think they’ve underestimated their uncertainty. But in some sense, it’s a matter of opinion and how much faith you place in different statistical methods.”

Besides revealing secrets of neutron stars, the study also produced a measurement of the Hubble constant, which reflects the expansion rate of the universe. To derive the constant, the scientists used the amplitude of the gravitational waves coming from one of the collisions to estimate how far away the crash occurred. They then compared their distance measurement with the known speed of the collision’s host galaxy, which was measured by looking at the galaxy’s redshift—how much its light has slid toward the red end of the spectrum. The Hubble constant they found, 66.2 kilometers per second per megaparsec, is not precise enough to decide between the competing measurements that already exist, but adds another data point to the hotly contested question of how fast the cosmos is growing.

The scientists hope to apply the same type of analysis to future neutron star collisions that appear. “We made this first step and now we’ll push forward,” says team member Sarah Antier of the University of Paris, an astronomer who searches for light signals accompanying gravitational wave events. “My task is to connect different observatories to provide a network to make immediate observations” when gravitational wave detectors find a new signal.

Physicists are biding their time until the next generation of gravitational-wave detectors, such as the Cosmic Explorer in the U.S. and the Einstein Telescope in Europe, come online in the 2030s. These machines should be much more sensitive, allowing them to capture many more signals from more events and offering higher precision data. Future projects such as the Enhanced X-ray Timing and Polarimetry Mission (eXTP) and the Athena X-ray Observatory should also gather more accurate measurements of pulsars.

Scientists have learned so much in the short time since gravitational wave data became available, the future promises to greatly expand our knowledge of extreme matter under intense pressure. “The last four years have been remarkable,” Lattimer says. “It shows the potential that we are going to be getting in the future. We should have many more measurements from gravitational wave events, and as we add each new event the results are going to converge.”