No peaks without valleys: The stable mass transfer channel for gravitational-wave sources in light of the neutron star-black hole mass gap

Gravitational-wave (GW) detections are starting to reveal features in the mass distribution of double compact objects. The lower end of the black hole (BH) mass distribution is especially interesting as few formation channels contribute here and because it is more robust against variations in the cosmic star formation than the high mass end. In this work we explore the stable mass transfer channel for the formation of GW sources with a focus on the low-mass end of the mass distribution. We conduct an extensive exploration of the uncertain physical processes that impact this channel. We note that, for fiducial assumptions, this channel reproduces the peak at $\sim9 \mathrm{M_{\odot}}$ in the GW-observed binary BH mass distribution remarkably well, and predicts a cutoff mass that coincides with the upper edge of the purported neutron star BH mass gap. The peak and cutoff mass are a consequence of unique properties of this channel, namely (1) the requirement of stability during the mass transfer phases, and (2) the complex way in which the final compact object masses scale with the initial mass. We provide an analytical expression for the cutoff in the primary component mass and show that this adequately matches our numerical results. Our results imply that selection effects resulting from the formation channel alone can provide an explanation for the purported neutron star--BH mass gap in GW detections. This provides an alternative to the commonly adopted view that the gap emerges during BH formation.