Are Binary Black Hole Spins and Mass Ratios Correlated?

When researchers scour the detections of merging black holes made by gravitational wave observatories, they use models and statistics to make careful inferences about the population of black holes in our universe. In a recent article, researchers explored whether an emerging trend in gravitational wave data is real or an artifact of previous analysis methods.

A New Window on the Universe

Illustration of the first black hole merger detected by LIGO

Illustration of the first black hole merger detected by LIGO. [Aurore Simmonet (Sonoma State University)]

The detection of gravitational waves from merging black holes in 2015 by the Laser Interferometer Gravitational-Wave Observatory (LIGO) gave scientists a new way to investigate black holes. By analyzing the spacetime ripples from colliding black holes, researchers hope to understand how the black holes formed (through the collapse of massive stars or the successive mergers of existing black holes?) and how they came to exist in binary systems (by first belonging to a stellar binary system or by forming solo and linking up with another black hole later?).

One potential result that has emerged from several analyses of gravitational wave signals is that the effective spins and the ratios of the masses of merging black hole binaries appear to be anticorrelated. But as with all results that are extracted delicately, statistically from complex data sets, it’s important to ask if this is a real feature of the data, with real implications for how black hole binary systems are assembled, or if it’s a result of our models or statistical analyses.

a diagram illustrating positive and negative effective spin

Top: The black hole spins are aligned with the system’s orbital angular momentum (positive effective spin). Bottom: The black hole spins are misaligned with the system’s orbital angular momentum (negative effective spin). [Kerry Hensley]

Statistical Investigation

Christian Adamcewicz (Monash University and OzGrav) and collaborators approached this question by applying a new statistical treatment to detections of black hole mergers. This new treatment features a new model for effective spin and allows for a subpopulation of black hole binaries with zero effective spin, which hasn’t yet been ruled out and might have an impact that hasn’t been accounted for.

The team applied their population model to the third catalog of gravitational wave signals from the LIGO and Virgo detectors and used Bayesian statistical methods to extract the properties of the overarching population of black holes. They found that the previously reported anticorrelation between effective spin and mass ratio is likely real, ruling out the possibility of there being no correlation at 99.7% probability.

More Work, a Paradox, and Astrophysical Possibilities

Adamcewicz and collaborators acknowledge that this work doesn’t provide a final verdict on this question (as they put it, “a modeler’s job is never done”), and that other statistical effects need to be rooted out. One lingering possibility is that this result is due to the amalgamation paradox, which arises when trends present in different factors disappear or flip when the factors are considered together.

If the observed anticorrelation holds up to further statistical scrutiny, a number of astrophysical phenomena could be responsible for this effect. Extensive mass transfer between black hole progenitor stars, stars evolving within a common envelope and accreting matter at a high rate, or even black hole binary systems assembled within the accretion disks of active galactic nuclei should all be investigated with future black hole population models.


“Evidence for a Correlation Between Binary Black Hole Mass Ratio and Black Hole Spins,” Christian Adamcewicz et al 2023 ApJ 958 13. doi:10.3847/1538-4357/acf763