Authors: Cecilia Sgalletta, Michela Mapelli, Lumen Boco, Filippo Santoliquido, M. Celeste Artale, Giuliano Iorio, Andrea Lapi, Mario Spera
First Author’s Institution: SISSA, via Bonomea 365, I–34136 Trieste, Italy
Status: Submitted to A&A [open access]
Lives and deaths of stars
The lives of stars have changed continuously throughout the evolution of the universe. Before stars existed, the Universe was still hot and bubbling with the first atoms of hydrogen, helium, and lithium forming. Then came the era of the first stars, hundreds of times the mass of our Sun, fusing together heavier elements for the first time. Now we live in a time where stars live and die coincidently, and dying stars feed the gas clouds which form new suns in the galaxies around us. Throughout the evolution of the Universe, the number of stars forming, their masses, their elemental compositions and their formation environments have all been changing.
A small subset of these stars – massive stars orbiting other massive stars – will go on to merge as two black holes at the end of their lives, forming an even more massive black hole. We see the ripples that these dead stars send through the Universe as gravitational waves (GWs). The number of binary black hole (BBH) mergers we observe per unit observing time per unit volume of the Universe is called the merger rate density of BBHs. It depends on how the number of stars which have formed has changed through cosmic time, and the fraction of these stars that merge as black holes. We can measure this merger rate density as far out into the Universe as we can detect BBHs with GWs, up to about a redshift of 1.5, about 9.5 billion years back in time.
Balancing the details with the big picture
Comparing the measured merger rate density to models of how we expect the merger rate density to evolve throughout the age of the Universe can tell us about the stars that went on to form the BBHs we detect. Modeling the BBH merger rate density is complicated – we have to take into account the larger scale influences such as the overall star formation rate (SFR) and how this varies from galaxy to galaxy; as well as physics on the scale of individual stellar systems, considering various aspects of binary stellar evolution.
Today’s paper builds a set of detailed model universes taking these various aspects of the merger rate density into account in order to compare to current measurements. In their models, the authors simulate populations of binary stars, varying the initial conditionals for each system. They base these initial conditions on a series of analytic relationships – the initial mass function of stars, and the distributions of their orbital periods and eccentricities.
The authors then populate their simulated universes with a number of galaxies, placing each binary system from their simulated population into different host galaxies. These galaxies also get assigned related properties – total stellar mass, redshift, SFR, and metallicity. As star forming gas gets recycled through more generations of stars, each generation creates more metals when they die. The newer generations are more enriched with a higher metal content, so metallicity depends on stellar mass, SFR and redshift. SFR depends on how many stars have already been made in a galaxy and how much star forming gas is left, so it depends on stellar mass and redshift. The authors investigate a range of different analytic models for the relations of these quantities. They can then calculate the merger rate density from their BBH populations and galaxy relations.
A universe overflowing with black holes
A comparison of the rate of BBH mergers the authors calculate for their assumed galaxy relations to the observed rate from GWs is shown in figure 1. This shows the merger rate density for five different sets of galaxy relations (coloured lines), for different assumptions about binary stellar evolution of their BBH progenitors (panels). Of their detailed models, the B18 model describing the SFR-stellar mass relationship best matches with observations (grey band). But this model disagrees with direct observations we have of the SFR, meaning it effectively extrapolates above a redshift of ~0.9. The merger rate from all of the author’s detailed models is much higher than the observed rate at low redshifts. This is where we have the best measurements from GWs, but it just doesn’t line up with theory. This is a problem not only with the models in today’s paper, it’s consistent with other results which use different assumptions when modelling BBH populations.

So what’s happening?? These models are considering more realistic prescriptions of the merger rate density than ever before, and yet they way overestimate the rate that we detect. Furthermore, the authors assume that the BBHs we detect come only from massive binary stars, but we might see BBHs from other formation pathways in our observations, such as dynamical encounters in stellar clusters. These other environments would just add to the rate that today’s paper models. How do we get rid of some of these black holes from our models?
Turning down the dial on black hole production
The authors have a couple of suggestions that could help reconcile their results.
- When black holes form, they can receive a kick from the supernova explosion that forms them. This could tear them apart from their stellar companion. If BBHs are disrupted by much higher kick velocities when they form, this reduces the rate BBH mergers sufficiently to match with observations, without having to alter any of the other parameters governing the merger rate density evolution, as shown in the left of Figure 2.
- One subset of formation of the BBH population may be over-contributing to the rate density much more than others. The modelled rate of mergers is made up of different formation channels that go through different evolutionary stages to eventually make BBHs. In the right of Figure 2, the purple channel is the one over-contributing to the rate density. Could it be that we don’t model the particular astrophysics involved in this formation channel well enough?

Overall, the tension between modelled BBHs and observations is still going strong, with models flooding the Universe with BBHs that we don’t observe. This paper shows that it probably isn’t the larger scale influences such as the SFR or metallicity evolution that contributes to this tension. Rather, in order to understand the big picture of BBH formation history, we need to better understand the smaller details in the evolution of binary stars. So let’s create just a few more BBH populations and try to pin this down. I think there should be space to put them right over there…
Astrobite edited by Archana Aravindan
Featured image credit: Storm Colloms