The theory of the formation and evolution of stars as we understand today cannot form black holes of masses larger than about 50 time Sun’s mass (or solar mass). Indeed, before LIGO and Virgo began discovering black holes, astrophysicists thought that black holes that form when massive stars die in an explosion will likely have masses between 5 and 20 solar masses, but no more than 50. But LIGO and Virgo have not found any hard cutoff on the masses of hundreds of black holes in merging binaries they have discovered so far. So how did they form?

Some researchers have proposed that black holes can grow by repeated mergers, technically called hierarchical growth as illustrated in the adjacent diagram (taken from Mahapatra+). For this to work two things must happen: (1) availability of environments replete with black holes (often called clusters) so that black hole unions can repeat and (2) after a union, black holes must remain in the same environment.

Unfortunately, both of these assumptions have caveats. First, models that posit formation of merging binaries in black hole-rich environments also predict that binaries will be kicked out of the cluster before they merge. Second, in the process of merger the remnant black hole receives a kick that could unbind it from the cluster even if the progenitor binary remained in the cluster. So does hierarchical growth really work and can it explain the observed distribution of masses?

Now in a new study led by graduate student Parthapratim Mahapatra, we looked at the second of these problems and investigated how likely it is for black holes to be retained in clusters so that they can pair up with other black holes and grow hierarchically.

The adjacent diagram shows the distribution of black holes formed by mergers of different generation of black holes assuming some of the black holes can be held by the cluster in spite of the kicks they receive. The encouraging news is that this hierarchical growth might actually explain the distribution of masses in the 3rd gravitational-wave transient catalog (GWTC-3) of LIGO. But the jury is still out if this is the answer to all the questions raised. In fact, I don’t believe we are any where near but this is the first step in formulating models that help us understand how heavier black holes form, how abundant they are and where to find them.