A case for Case A: detailed look at binary black hole formation through stable mass transfer

TL;DR

The paper investigates the formation of binary black hole mergers through stable mass transfer (SMT) using the POSYDON framework, spanning eight metallicities and focusing on Case A mass transfer during both STAR+STAR and STAR+BH phases. It demonstrates that SMT predominantly produces BBHs via Case A interactions, with a strong metallicity dependence arising from wind-driven orbital widening that suppresses mergers above $Z\approx 0.2Z_\odot$ unless natal kicks are present. The work reveals characteristic population features, including mass-ratio reversal leading to near-unity mass ratios, dual peaks in $\chi_{\mathrm{eff}}$, and long delay times that increase with metallicity; natal kicks introduce a low-mass, unequal-mass subpopulation that can merge at higher metallicities. These findings contrast with outcomes from rapid population synthesis codes and underscore the necessity of detailed binary modeling to accurately predict SMT BBH populations and their observational signatures. The results have implications for interpreting LVK BBH data and pave the way for integrating cosmic star formation history and remnant prescriptions in future work.

Abstract

In isolated binary evolution, binary black hole (BBH) mergers are generally formed through stable mass transfer (SMT) or common envelope evolution. In recent years, the SMT channel has received significant attention due to detailed binary models showing increased mass transfer stability compared to previous studies. In this work, we perform a full zero-age-main-sequence to compact object merger analysis using detailed binary models at eight metallicities between $10^{-4}Z_\odot$ and $2Z_\odot$ to self-consistently model the population properties of BBH mergers in the SMT channel, determined their progenitor initial conditional, and investigate the binary physics governing their formation and metallicity dependence. We use the population synthesis code POSYDON to determine the population of BBH mergers from SMT. Using its extended grids of MESA binary models, we determine the essential physics in the formation of BBH mergers. SMT produces BBH mergers predominantly from systems with $P_{ZAMS}\leq10$ days. In these systems, both the initial mass transfer between two stars and the subsequent interaction between the remaining star and the first-born BH take place while the respective donor star is on the main-sequence (Case A). We find a limited contribution from wider Case B/C systems. Without a natal kick, the SMT channel does not produce BBH mergers above $Z>0.2Z_\odot$ due to orbital widening from stellar wind mass loss. The primary BH mass distribution shows a strong dependence on metallicity, while the mass ratio prefers unity independent of metallicity due to mass ratio reversal. Additionally, the $χ_{eff}$ distributions contain peaks at $χ_{eff}=0$ and ~0.15 of which the former disappears at high metallicities. A mass-scaled natal kick leave this sub-population unchanged but introduce a low-mass, unequal mass ratio sub-population that merges due to their high eccentricity.

Figures (13)

• Figure 1: Representative binary from the SMT channel leading to a BBH merger at $10^{-4}Z_\odot\xspace$ with $M_1=32M_\odot\xspace$, $M_2=27M_\odot\xspace$, and $P=1.9$ days at ZAMS. The time series is divided into different scales to show details in the evolution on shorter timescales. The top row shows the mass evolution of the primary (blue) and secondary (red), while the bottom row shows their stellar radius evolution. The shaded regions are when RLO occurs, colored according to the donor star. The black solid line tracks the orbital separation, and the vertical dashed lines mark the times of core collapse for each component. Between 5.58 Myr and 5.59 Myr, the first mass transfer phase starts. After a fast thermal timescale interaction, the mass ratio flips, and the mass transfer continues on a nuclear timescale. At ${\sim}7.68$ Myr, the detached binary with an eccentricity of 0.001 is circularized and matched to the nearest CO-HMS_RLO grid model, causing the slight increase in mass, period, and radius. The steep drop afterwards is caused by thermal timescale mass transfer. The small changes in radii at $6.2$ Myr and $8.05$ Myr are from readjustment after core hydrogen depletion in the primary and secondary, respectively. In the top row, the He-core ($M_\mathrm{He}$) and CO-core ($M_\mathrm{CO}$) masses are shown with dashed and dotted lines, respectively. This system is evolved with the same simulation setup as the population models, but the nearest-neighbor method (matching to the closest down-sampled precomputed track) is used instead of initial–final interpolation to show the evolution over time Fragos+23. The orange bars indicate the POSYDON step or grid that is used for the evolution of the binary.
• Figure 2: Example grid slices at $10^{-4}Z_\odot\xspace$ for fixed $M_\mathrm{donor}\xspace = 19.3M_\odot\xspace$ (left), $33.9M_\odot\xspace$ (middle), and $59.4M_\odot\xspace$ (right) for the CO-HMS_RLO grid, where the models start at RLO. The diamonds indicate unstable mass transfer with $L_2$ overflow (orange) and $\dot{M}_\mathrm{max}$ (red) separated. Stable mass transfer is indicated with squares with mergers (light blue) and non-mergers (dark blue) within the Hubble time based on the same remnant mass calculation as our default population. The STAR+BH systems evolved in a POSYDON population with $\Delta M \pm 2$ around $M_\mathrm{donor}$ going into this grid slice are shown as a 2D histogram behind the grid markers, as well as dots for the exact systems. The darker the shading, the higher the density of systems. The black contour contains 100% of the STAR+BH system that produces BBH mergers, showing the overlap between the evolved population and region that leads to BBH mergers in the CO-HMS_RLO grid. The latter can be slightly off from the exact location of progenitor properties due to underlying histogram binning, but also due to the 4-dimensional nature of the grids. It provides an indicator of the parameter space region of the BBH mergers progenitors.
• Figure 3: Grid slices of the HMS-HMS grid at $q=0.60$, $0.85$, and $0.99$ for $Z=10^{-4}Z_\odot\xspace$. We do not show the grid below $M_1 < 15 M_\odot\xspace$ because such systems do not contribute to the BBH merger rate. The non-converged (or initial RLOF), unstable, and reverse stable mass transfer Briel+25 models are marked with black dots, red diamonds, and pink circles, respectively. Models without mass transfer are marked with gray squares. SMT systems are marked with four different colored squares, where the exact color indicates a contact phase during the MS (gray squares), Case A (light blue), Case B (teal), or Case C mass transfer (dark green) as the first interaction of the binary. We show the ZAMS properties of BBH merger progenitors by encircling all of them with a black contour, based on a smoothed 2D histogram.
• Figure 4: Evolution of $M_1=32M_\odot\xspace$ and $q=0.85$ example binaries with different $P_\mathrm{ZAMS}$, as a function of time till carbon depletion. The top panel shows the mass evolution for the primary and secondary, while the bottom panel shows the period evolution. Similar to the model in Figure \ref{['fig:example_binary']}, the mass transfer starts with a rapid phase, which shrinks the orbit, causing the dips in the period evolutions. However, the mass ratio flips, and the orbit widens again. In general, a tighter initial orbit leads to a shorter period and a more massive companion at carbon depletion, while the helium core mass is independent of $P_\mathrm{ZAMS}$. The STAR+BH conditions of these binaries are marked with a star in Figure \ref{['fig:MBH_grid_slice']}.
• Figure 5: CO-HMS_RLO grid slice for a fixed $M_\mathrm{BH}\xspace\approx15M_\odot\xspace$, which is the remnant mass of the primary in the example models ($M_\mathrm{1,ZAMS}\approx 32M_\odot\xspace$) from Figure \ref{['fig:period_dependence']}. The star markers are the properties of the example models with $q=0.85$ after the first supernova for different initial periods, where the coloring is the same as in Figure \ref{['fig:period_dependence']}. The squares and circles are models with the same $P_\mathrm{ZAMS}$ and $M_\mathrm{1, ZAMS}$ but with $q=0.99$ and $q=0.60$, respectively. The markers and colors of the models from the CO-HMS_RLO grid are the same as in Figure \ref{['fig:example_Mdonor']}, but here $M_\mathrm{BH}$ is fixed instead of $M_\mathrm{donor}$. As $P_\mathrm{ZAMS}$ increases, the STAR+BH binaries move outside the SMT BBH merger regime.