Where are LIGO's Big Black Holes?

Abstract: In LIGO's O1 and O2 observational runs, the detectors were sensitive to stellar mass binary black hole coalescences with component masses up to $100\,M_\odot$, with binaries with primary masses above $40\,M_\odot$ representing $\gtrsim90\%$ of the total accessible sensitive volume. Nonetheless, of the 5.9 detections (GW150914, LVT151012, GW151226, GW170104, GW170608, GW170814) reported by LIGO-Virgo, the most massive binary detected was GW150914 with a primary component mass of $\sim36\,M_\odot$, far below the detection mass limit. Furthermore, there are theoretical arguments in favor of an upper mass gap, predicting an absence of black holes in the mass range $50\lesssim M\lesssim135\,M_\odot$. We argue that the absence of detected binary systems with component masses heavier than $\sim40\,M_\odot$ may be preliminary evidence for this upper mass gap. By allowing for the presence of a mass gap, we find weaker constraints on the shape of the underlying mass distribution of binary black holes. We fit a power-law distribution with an upper mass cutoff to real and simulated BBH mass measurements, finding that the first 3.9 BBHs favor shallow power law slopes $\alpha \lesssim 3$ and an upper mass cutoff $M_\mathrm{max} \sim 40\,M_\odot$. This inferred distribution is entirely consistent with the two recently reported detections, GW170608 and GW170814. We show that with $\sim10$ additional LIGO-Virgo BBH detections, fitting the BH mass distribution will provide strong evidence for an upper mass gap if one exists.

Summary of "Where are LIGO's big black holes?"

The paper by Fishbach and Holz addresses the apparent absence of detections of binary black holes (BBHs) with component masses heavier than approximately $40 M_\odot$ in the results from LIGO's O1 and O2 observational runs. Despite the detectors' sensitivity to BBHs with masses up to $100 M_\odot$, the most massive detected BBH event (GW150914) had a primary component mass of only $\sim36 M_\odot$, highlighting a discrepancy that warrants investigation.

Fishbach and Holz propose that this lack of heavy BBH detections may be indicative of a theoretical upper mass gap between $50 M_\odot$ and $135 M_\odot$. The existence of such a mass gap aligns with supernova theory, particularly pulsational pair-instability supernovae (PPISN) and pair instability supernovae (PISN) models, which predict substantial mass gaps resulting from stellar core collapses.

The authors enhance the constraints on the BBH mass distribution by adopting a model that incorporates a power-law with an upper mass cutoff. They demonstrate that fitting this model to both actual and simulated BBH detections can confirm the presence of a mass gap, with constraints becoming significantly strong after approximately ten additional LIGO-Virgo BBH detections.

The paper explores the sensitive spacetime volume (VT) concept, elaborating on how LIGO's sensitivity increases with primary component mass $m_1$, and how this impacts the expected frequency of heavy BBH detections under various mass distribution hypotheses. For instance, they find that detection sensitivity scales as $VT \propto m_1^{2.2}$.

Significant numerical results include the Bayes factor calculations, wherein the authors compare model fits with varying upper mass cutoffs. The analysis reveals substantial evidence supporting a cutoff at $M_\mathrm{max} \sim 40 M_\odot$, especially under assumptions that extend LIGO's sensitivity up to total masses of $200 M_\odot$. This finding suggests there is potentially a stellar-formation-driven limit to the masses of BHs in mergers within this range.

Implications of this study extend to refining our understanding of stellar evolution and supernova mechanisms, contributing critical insights into BH formation processes. The anticipation of more BBH detections promises finer granular constraints on both low and high mass gaps. Meanwhile, the existence of BBHs beyond the PPISN or PISN gap remains an open question, demanding further observational data to test the theoretical boundaries of black hole mass and formation models.

Future research may explore additional mass ratio distributions, incorporate redshift evolution considerations more extensively, and investigate the potential existence of subpopulations or primordial BHs beyond the detected mass gaps. This ongoing research will likely shape the theoretical landscape of gravitational-wave astrophysics and inform the strategies for upcoming observational campaigns.