Artist’s impression of a black hole-neutron star merger, by Carl Knox, OzGrav-Swinburne University

In our recently accepted paper, we examined the black hole-neutron star merger called GW200115, second observed by LIGO and Virgo in January 2020. Curiously, GW200115’s black hole could have been spinning rapidly, with its spin misaligned with respect to the orbital motion. This is strange because it implies that the system would have formed in pretty unexpected ways.

So, is there something we’re missing? In our paper we show that the puzzling black hole spin is probably due to something that was *added* to the LIGO-Virgo measurements instead. It has to do with things called ‘priors’ which encode assumptions about the population of black hole-neutron star binaries based on our current knowledge. We argue that a better explanation for the GW200115 merger is that the black hole was not spinning at all, and consequently, we place tighter constraints on the black hole and neutron star masses.

**What is a prior?**

Imagine you want to know the probability of having drawn an Ace from a deck of cards, given that the card is red. You’d need to know the separate probabilities of drawing an Ace and a red card. The probability of drawing an Ace, independent of the data (“the card is red”) is the ‘prior’ probability of drawing an Ace. Astronomy is similar to a game of cards: we can think of observed gravitational-wave signals as having been dealt to us randomly by the Universe from a cosmic deck of cards. The prior should express our current best knowledge of this deck *before we make a measurement,* because it‘s used to calculate the probability of each possible black hole spin. In the LIGO-Virgo analysis of GW200115, it was assumed that all black hole spins are equally likely. This is fine if we have no strong preference for any value, but we do: observation and theory tell us we shouldn’t expect a rapidly spinning black hole to be paired with a neutron star. This information is key to accurately measuring the properties of GW200115.

In our paper, we begin by demonstrating that *if* GW200115 originated from a black hole-neutron star binary with zero spin, the unrealistic LIGO-Virgo prior (which assumes the black hole can equally likely spin with any magnitude and direction) generates preference for a large misaligned black hole spin. We do this by simulating a gravitational-wave signal from a non-spinning binary, placing it into simulated (but realistic) LIGO-Virgo noise, and inferring its properties assuming any spin value is equally likely. Our simulated experiment yields a similar spin measurement to LIGO-Virgo’s and we’re able to explain analytically why signals from black hole-neutron star binaries with zero spin will generically yield such measurements when very broad spin priors are assumed. While this doesn’t prove that GW200115 is non-spinning, it suggests that the puzzling LIGO-Virgo spin measurement is probably due to their unrealistic priors.

Next, we look to astrophysics to figure out a more realistic prior. We use current theoretical modelling to suggest that there’s roughly a 95% probability that black hole-neutron star binaries do not spin at all, and only around 5% do spin. We use this astrophysical prior to update the LIGO-Virgo measurements of GW200115’s spins and masses. When we do this, we find that there is almost zero probability that the black hole had any spin at all. While this might seem circular at first glance—after all, we’re giving zero-spin almost 20 times more weight than non-zero spin—it’s also a reflection of the fact that the data don’t strongly support a rapidly spinning black hole. Additionally, we show that our prior reduces the uncertainty on the black hole and neutron star masses by a factor of 3. Reassuringly, the mass of the neutron star looks significantly more like those found in double neutron star systems in the Milky Way.

Written by Rory Smith and Ilya Mandel, Monash University