Black hole mass function from gravitational wave measurements

Abstract

We examine how future gravitational-wave measurements from merging black holes (BHs) can be used to infer the shape of the black-hole mass function, with important implications for the study of star formation and evolution and the properties of binary BHs. We model the mass function as a power law, inherited from the stellar initial mass function, and introduce lower and upper mass cutoff parameterizations in order to probe the minimum and maximum BH masses allowed by stellar evolution, respectively. We initially focus on the heavier BH in each binary, to minimize model dependence. Taking into account the experimental noise, the mass measurement errors and the uncertainty in the redshift-dependence of the merger rate, we show that the mass function parameters, as well as the total rate of merger events, can be measured to < 10% accuracy within a few years of advanced LIGO observations at its design sensitivity. This can be used to address important open questions such as the upper limit on the stellar mass which allows for BH formation and to confirm or refute the currently observed mass gap between neutron stars and BHs. In order to glean information on the progenitors of the merging BH binaries, we then advocate the study of the two-dimensional mass distribution to constrain parameters that describe the two-body system, such as the mass ratio between the two BHs, in addition to the merger rate and mass function parameters. We argue that several years of data collection can efficiently probe models of binary formation, and show, as an example, that the hypothesis that some gravitational-wave events may involve primordial black holes can be tested. Finally, we point out that in order to maximize the constraining power of the data, it may be worthwhile to lower the signal-to-noise threshold imposed on each candidate event and amass a larger statistical ensemble of BH mergers.

Cosmic microwave background limits on accreting primordial black holes

“…In the mean time, there are a number of other interesting astrophysical probes in that mass range. These include future measurements of the stochastic gravitational-wave background [56][57][58][59][60] and of the mass spectrum [61], redshift distribution [62], and orbital eccentricies [63] for future binary-black-hole mergers; lensing of fast radio bursts by PBHs [64]; pulsar timing [65,66]; radio/x-ray sources [67] or the cosmic infrared background [68]; the dynamics of compact stellar systems [54]; strong-lensing systems [69]; and perhaps clustering of GW events [70][71][72][73]. The conclusions of our work suggest that it will be important to pursue vigorously these alternative avenues.…”

Maximum Redshift of Gravitational Wave Merger Events

“…A range of black hole masses is most likely present. The effects of such an assumption have been studied in the context of explaining the current rate of observed black hole merger events with LIGO [48][49][50][51][52][53][54][55]. In our case, such a black hole mass function will alter the shape of N (z), but the effect on z max is negligible since the factors that give rise to the cutoff remain as discussed earlier (namely the shape of the halo mass function and the decline in gas infall at high redshifts).…”

Black Hole Mass Function of Coalescing Neutron Star Black Hole Binary Systems: The Prospect of Reconstruction with the Gravitational Wave Observations

“…where we set the fiducial values to α = 2.35, M gap = 5 M (3 M ; i.e., without the low mass gap), and M cut = 60 M following Abbott et al (2016b) and Kovetz et al (2017). These parameters Λ = {α, M gap , M cut } are called hyperparameters that we try to reconstruct in Sec.2.3.…”

“…We set a typical condition that the S/N of a single interferometer satisfying S/N > 8.0, as the definition of a GW event being "detected." This approximately translates into a network S/N > 12, which is conventionally used as the threshold for a network GW detector to identify the GW signals (Abadie et al 2010;Kovetz et al 2017;).…”

“…Population synthesis expects a high mass cutoff on the power-law mass distribution of black holes (Dominik et al 2015), because massive stars will lose their masses by stellar wind. Thanks to a high merger rate, such characteristics are expected to be identified in merging BBH systems via gravitational wave detection, as demonstrated in Kovetz et al (2017). For merging NSBH binary systems, the BHMF may be more challenging because of the expected smaller number of events.…”