Reassessing the Spin of Second-born Black Holes in Coalescing Binary Black Holes and Its Connection to the chi_eff-q Correlation

Abstract

The mass ratio q and effective inspiral spin chi_eff of binary black hole (BBH) mergers in GWTC-4.0 show a weaker anti-correlation than in GWTC-3.0, motivating investigation of its physical origin. Within the isolated binary evolution framework, we adopt a recently proposed He-star wind prescription to study the spin of the second-born BH and its impact on the q-chi_eff relation. Using \texttt{MESA}, including the updated He-star wind, internal differential rotation, and tidal interactions, we examine how initial conditions and key processes determine the BH spin. We also perform rapid population synthesis with \texttt{COMPAS} to predict the population-level q-chi_eff correlation. The updated wind prescription is significantly weaker than the standard Dutch scheme, particularly at subsolar metallicity. Detailed binary models of He stars with BH companions show that the resulting BH spin is largely insensitive to the He star's evolutionary stage at the onset of tidal interaction and to the companion mass. Instead, wind mass loss dominates: more massive He-star progenitors produce lower-spinning BHs. Initial stellar rotation has only a minor effect, especially under strong tidal coupling. We provide a fitting formula for the spin of the second-born BH. Combining this formula with rapid population synthesis under default assumptions, we find that 85.8% of BBHs formed via stable mass transfer undergo mass-ratio reversal, compared to only 2.8% in the common-envelope channel. Notably, no correlation between q and chi_eff is found in either channel. Future work will explore alternative physical prescriptions and compare our predictions with BBH mergers reported by the LIGO-Virgo-KAGRA Collaboration.

Figures (13)

• Figure 1: Final masses of He stars as a function of their initial masses with different wind prescriptions (left panel: 1.0 $Z_{\odot}$; middle panel: 0.1 $Z_{\odot}$; right panel: 0.01 $Z_{\odot}$). Circle: SV2023+, square: NL2000. The dashed line indicates where the final mass is equal to the initial mass.
• Figure 2: The color represents the maximum initial orbital period of the BBHs at birth, above which the systems would not merge within a Hubble time. Histograms of the primary component masses (upper panel) and the secondary component masses (right panel).
• Figure 3: The spin magnitude $\chi_2$ of the BH formed via direct core collapse of the He star (left panel) and the corresponding total angular momentum of the progenitor star (right panel) as a function of the central helium abundance. The binary system consists of a He star with an initial mass of 20 $M_{\odot}$ in a 1.0-day orbit, and a BH of varying mass (gray solid line: 3 $M_{\odot}$; cyan solid line: 25 $M_{\odot}$; black dashed line: 40 $M_{\odot}$). The results at 0.01 $Z_{\rm \odot}$ are nearly identical to those at 0.1 $Z_{\rm \odot}$, and are therefore not shown in the paper.
• Figure 4: The synchronization timescale ($T_{\rm sync}$; top panel), the ratio of the He-star spin period to the orbital period ($P_1/P_{\rm orb}$; middle panel), and the BH spin magnitude ($\chi_2$; bottom panel) are shown as functions of the central helium abundance. We consider three He-star models: He ZAMS (solid line), a He star with 10% central helium depleted (dashed line), and a He star with 30% central helium depleted (dash-dotted line). All models assume an initial orbital period of 1.0 day. The first column shows the results at $1.0\,Z_{\odot}$, while the second column shows those at $0.1\,Z_{\odot}$. The results at $0.01\,Z_{\odot}$ are nearly identical to the $0.1\,Z_{\odot}$ case and are therefore not shown in the paper.
• Figure 5: The spin magnitude $\chi_2$ of the BH formed through the direct core collapse of the He star (left panel) and the corresponding total angular momentum of the progenitor star (right panel) as a function of the central helium abundance. The binary system consists of a 20 $M_{\odot}$ BH and a 20 $M_{\odot}$ He star with different initial rotation rates (blue: $\omega_{\rm i} = 0$; orange: initially synchronized with the orbit; green: $\omega_{\rm i} = 0.3\,\omega_{\rm crit}$; red: $\omega_{\rm i} = 0.6\,\omega_{\rm crit}$; purple: $\omega_{\rm i} = 0.9\,\omega_{\rm crit}$). All models assume an initial orbital period of 1.0 d, with the 0.5 d case provided for comparison in Figure \ref{['appendixA_2']}. Results for He stars at 0.01 $Z_{\rm \odot}$ are nearly identical to those at 0.1 $Z_{\rm \odot}$ and are therefore not shown in the paper.