A team of astrophysicists from Italy and the United Kingdom has calculated that in the observable Universe, a sphere of diameter around 90 billion light-years, there are at least 40*1018 stellar-mass black holes.
An artist’s impression of a group of stellar-mass black holes. Image credit: NASA / ESA / Hubble / N. Bartmann.
The formation and evolution of black holes in the Universe is one of the major issues to be addressed by the modern research in astrophysics and cosmology.
In the mass range between 5 and 150 solar masses, black holes are originated from the final, often dramatic stages in the evolution of massive stars.
At the other end, in the range between 106 and 1010 solar masses, supermassive black holes grow mainly by gaseous accretion that energizes the spectacular broadband emission of active galactic nuclei. Such an activity can have a profound impact on galaxy evolution.
The intermediate-mass range between 103 and 106 solar masses is the most uncertain. So far, only tentative evidence of these systems has been identified. However, the chase is open in view of their astrophysical relevance.
“One of the most fundamental quantities for demographic studies of the black hole population is constituted by the relic mass function, namely the number density of black holes per comoving volume and unit black hole mass, as a function of redshift,” said Dr. Alex Sicilia of the Scuola Internazionale Superiore di Studi Avanzati and colleagues.
“We provide an ab initio computation of the stellar black hole relic mass function across cosmic times, by coupling the state-of-the-art stellar and binary evolutionary code SEVN to redshift-dependent galaxy statistics and empirical scaling relations involving metallicity, star formation rate and stellar mass.”
The researchers estimate a relic mass density of stellar-mass black holes in the local Universe of 5*107 solar masses per cubic megaparsec, which exceeds by more than two orders of magnitude that in supermassive black holes.
“The innovative character of this work is in the coupling of a detailed model of stellar and binary evolution with advanced recipes for star formation and metal enrichment in individual galaxies,” Dr. Sicilia said.
“This is one of the first, and one of the most robust, ab initio computation of the stellar black hole mass function across cosmic history.”
The scientists also explored the various formation channels for black holes of different masses, such as isolated stars, binary systems and stellar clusters.
“The most massive stellar black holes originate mainly from dynamical events in stellar clusters,” they said.
“Such events are required to explain the mass function of coalescing black holes as estimated from gravitational wave observations by the LIGO/Virgo Collaboration.”
“Our work provides a robust theory for the generation of light seeds for (super)massive black holes at high redshift, and can constitute a starting point to investigate the origin of heavy seeds,” said Dr. Lumen Boco, a researcher with the Scuola Internazionale Superiore di Studi Avanzati and the IFPU – Institute for fundamental physics of the Universe.
The study was published in the Astrophysical Journal.
Alex Sicilia et al. 2022. The Black Hole Mass Function Across Cosmic Times. I. Stellar Black Holes and Light Seed Distribution. ApJ 924, 56; doi: 10.3847/1538-4357/ac34fb