Looking for the parents of LIGO's black holes

Understand

Solutions to the two-body problem in general relativity allow us to predict the mass, spin and recoil velocity of a black-hole merger remnant given the masses and spins of its binary progenitors.

• In this paper we address the inverse problem: given a binary black-hole merger, can we use the parameters measured by gravitational-wave interferometers to tell if the binary components are of hierarchical origin, i.e.
• if they are themselves remnants of previous mergers? If so, can we determine at least some of the properties of their parents? This inverse problem is in general overdetermined.
• We show that hierarchical mergers occupy a characteristic region in the plane composed of the effective spin parameters $\chi_{\rm eff}$ and $\chi_{\rm p}$, and therefore a measurement of these parameters can add weight to the hierarchical-merger interpretation of some gravitational-wave events, including GW190521.