How do you weigh a star? If two stars orbit each other, then we can determine their masses by their orbits. Since each star pulls gravitationally on the other, the size of their orbits and the speed at which they orbit each other allows us to calculate their masses using Kepler’s laws. But if a star is by itself, we have to use indirect methods such as its brightness and temperature to estimate their mass. While this can work reasonably well for main sequence stars like our Sun, it doesn’t work well for neutron stars due their small size and extreme density. But new work in Science Advances has found an interesting way to determine the mass of a type of neutron star known as a pulsar.
Neutron stars have a mass greater than our Sun, but are only about 20 kilometers (12 miles) wide. They are so dense that their magnetic fields are incredibly strong. So strong that they channel lots of radio energy away from their magnetic poles. As a neutron star rotates, these beams of radio energy sweep around like a lighthouse. If the beam is oriented toward Earth, then we observe these beams as short pulses of radio energy. Each pulse marks a single rotation of the star (known as its rotational period). We can measure the timing of these pulses very precisely, and one thing we notice is that period of a pulsar gradually lengthens as its rotation slows over time.
But every now and then the rotational period of pulsar will jump a bit, indicating that its rotation has increased. These jumps are known as glitches, and they are due to interactions between the core of the neutron star and its outer crust. As a neutron star loses energy, it is the crust that slows down over time. The interior of the star is a superfluid, and so continues to rotate at a steady rate. Over time the difference in rotation becomes severe enough that the interior transfers some of its rotational speed to the crust, slowing down the core and speeding up the crust so that the two are more in sync.
Just how much rotation is transferred, and how often such a glitch occurs, depends upon the exact nature of a neutron star’s interior. That’s where this new work comes in. The team took glitch data from the Vela pulsar spanning 45 years, and compared it to several models of neutron star interiors. They found that only one model matched the observed glitches. When they compared this model to another pulsar (PSR J0537−6910) spanning about 14 years, it also agreed with the same model. From the glitch data the team was able to pin down the interior structure of these neutron stars.
What’s interesting about this result is that the superfluid model that fits the glitch data can be used to determine the mass of a pulsar. Since the interior of a neutron star must be below a critical temperature to be superfluid, the glitch data tells us about the internal temperature of the star. Since neutron stars don’t produce heat through fusion like main sequence stars, they gradually cool over time. Larger (more massive) neutron stars cool more slowly than smaller ones. If we know how old the neutron star is (and thus how long it has been cooling) then we can use its age and the critical temperature to determine the mass of the neutron star. Often we can determine the age of a neutron star by studying the remnant of the supernova that formed it, or by using x-ray observations to study its surface temperature.
Since the ages of the Vela pulsar and PSR J0537−6910 are known, the team calculated their masses. They found the Vela pulsar has a mass of 1.5 Suns, and PSR J0537−6910 has a mass of 1.8 Suns. More pulsars will need to be studied to see if their glitch patterns follow the same model, but if the method holds up we’ll be able to determine the mass of a pulsar even when it’s all alone.
This article originally appeared on Forbes.