A New Way To Weigh A Star
Authors: Nils Andersson, Wynn Ho
Affiliation: Mathematical Sciences and STAG Research Centre, University of Southampton, UK.
You probably have a pretty good idea of your own weight. And if you need an exact answer it is relatively easy to find out. Get the bathroom scales out, step up and read off the result. But have you ever asked yourself what was actually involved in that measurement? Have you considered that what actually happened was that gravity’s pull was countered by the electromagnetic interaction of the atoms that make up the surface of the scale, and what you actually measured was how hard the atoms had to work to push back on your feet? Possibly not, and the chances are that you have never really considered how one would weigh a distant star, either.
As it turns out, this question has a fairly straightforward answer, which also involves gravity, electromagnetism… and a bit of luck. If you want to figure out how heavy a particular star is, and you are lucky enough that this star has a close companion, then all you need to do is track the star’s motion. The orbital motion of a double-star system is dictated by gravity and you can figure out how much the stars weigh using the same arguments that we use to figure out the mass of the moon (going around the Earth) and the Earth (circling the Sun). If you want to be a bit more precise you should use Einstein’s curved spacetime theory for gravity rather than Newton’s inverse square-law, but this may be a luxury in this exercise.
Using this technique, astronomers have weighed many stars with great precision and they have also managed to work out the masses of a number of pulsars . This is particularly exciting as these systems stretch our understanding of several aspects of fundamental physics.
A pulsar is a highly magnetised rotating neutron star formed when a massive star runs out of nuclear fuel. At this point it can no longer hold itself up against gravity and it starts falling in on itself. This leads to a spectacular explosion – a supernova – the remains of which may be either a neutron star or a black hole. Neutron stars are nature’s own counterparts to the Large Hadron Collider . In essence, they provide a link between astronomy and laboratory work in both high-energy and low-temperature physics. By weighing these stars we gain insight into physics under extreme conditions .
Pulsars are named for their rotating beam of electromagnetic radiation, which is observed by telescopes as it sweeps past the Earth, just like the familiar beam of a lighthouse . They are renowned for their incredibly stable rate of rotation , but young pulsars occasionally experience so-called glitches where they are found to speed up for a very brief period of time . The prevailing idea is that these glitches provide evidence of exotic states of matter in the star’s interior . The glitches arise when a rapidly spinning superfluid within the star transfers rotational energy to the star's crust, a solid outer layer like a bowl containing a mysterious soup; the component that is tracked by observations. Imagine the bowl spinning at one speed and the soup spinning faster. Friction between the inside of the bowl and its contents, the soup, can cause the bowl to speed up. Whenever this happens, the more soup there is, the faster the bowl will be made to rotate.
Interestingly, it seems that the superfluid soup provides us with a new way of weighing these stars. This new technique is very different from the usual approach as it is not based on gravity, but nuclear physics, and it can also be used for stars in isolation. The star does not have to have a companion.
In a recent paper in Science Advances , we have developed this exciting new idea, which relies on a detailed understanding of neutron star superfluidity and the dynamics of the quantum vortices - a kind of ultra-slim tornadoes - by means of which these systems mimic large-scale rotation. Our results are promising and have important implications for the generation of revolutionary radio telescopes, like the Square Kilometre Array (SKA ) and the Low Frequency Array (LOFAR ), that are being developed by large international collaborations. The discovery and monitoring of many more pulsars is one of the key scientific goals of these projects. We now have a set of scales that may allow us to figure out how much these stars weigh, as well.
 See, for example, the list maintained at stellarcollapse.org.
 See Large Hadron Collider.
 J.M. Lattimer, M. Prakash, "The Physics of Neutron Stars", Science, 304, 536-542 (2004). Abstract.
 The discovery of pulsars was recognized with the Nobel prize in physics in 1974.
 Gravity tests using the stability of the timing of pulsars was recognized with the Nobel prize in physics in 1993.
 A catalog of glitches is maintained by Jodrell Bank Centre for Astrophysics.
 W.C.G. Ho, C.M. Espinoza, D. Antonopoulou, N. Andersson, "Pinning down the superfluid and measuring masses using pulsar glitches," Science Advances, 1, e1500578 (2015). Full Article.
 See Square Kilometre Array.
 See LOFAR.