Gravitational Waves from Coalescing Black Hole MACHO Binaries

TL;DR

This paper investigates whether solar-mass black hole MACHOs (BHMACHOs) formed in the early universe could constitute a significant dark-matter component and serve as detectable gravitational-wave sources. It develops an early-universe binary formation framework, derives the joint distribution of orbital elements f(a,e) and the coalescence-time distribution f_t(t), and uses gravitational-wave emission to predict event rates and detector reach for LIGO/VIRGO/TAMA/GEO. Key findings include a per-galaxy coalescence rate of about 5×10^-2 yr^-1 (potentially up to 3×10^-1 yr^-1 if binaries extend farther) and detectability out to ~15 Mpc with first-generation detectors, with upgrades reaching ~150 Mpc and still yielding a few events per year; a chirp mass of around 0.435 M_sun for equal-mass binaries would help distinguish these events from neutron-star binaries. The work also discusses cosmological implications, noting that forming BHMACHOs requires a blue primordial spectrum with n ≳ 1.6 and specific density perturbation amplitudes, thereby linking dark matter phenomenology with early-universe physics and gravitational-wave astronomy.

Abstract

If MACHOs are black holes of mass about 0.5 solar mass, they must have been formed in the early universe when the temperature was about 1 GeV. We estimate that in this case in our galaxy's halo out to about 50kpc there exist about half billion black hole binaries whose coalescence times are comparable to the age of the universe, so that the coalescence rate will be about five hundredth events/year/galaxy. This suggests that we can expect a few events/year within 15Mpc. The gravitational waves from such coalescing black hole MACHOs can be detected by the first generation of interferometers in the LIGO/VIRGO/TAMA/GEO network. Therefore, the existence of black hole MACHOs can be tested within the next five years by gravitational waves.