Widening of Binaries via Non-conservative Mass Transfer as a Formation Channel for Gaia Black Hole System

TL;DR

The paper tackles the puzzle of Gaia BH1 and Gaia BH2, whose wide, eccentric orbits are hard to reconcile with standard isolated binary evolution. It tests a formation channel based on fully non-conservative mass transfer, where all transferred mass exits the system carrying the donor's center-of-mass angular momentum, avoiding excessive angular-momentum loss and enabling orbital widening. Using the MESAP code with a Jeans-mode mass-loss prescription, the authors show that this mechanism can reproduce the observed orbital periods for Gaia BH1 and BH2 across a broad range of initial conditions with little fine-tuning. If borne out, this scenario offers a plausible formation pathway for these systems and potentially broad applicability to other post-mass-transfer binaries, with significant implications for binary evolution theory and gravitational-wave progenitors.

Abstract

The detected Gaia systems hosting compact objects challenge standard models of binary star evolution. In particular, if the observed black hole (BH) systems evolved in isolation, it is expected that they underwent a mass transfer phase. Given their highly unequal mass ratios, such mass transfer is dynamically unstable within standard models, leading to either a stellar merger or a final binary with a very short orbital period. In contrast, the observed systems have much wider orbits than predicted, making their formation within conventional evolutionary frameworks difficult to reconcile. With the aid of detailed binary evolution calculations, we test whether fully non-conservative mass transfer, where mass is lost from the system carrying the specific angular momentum of the donor's center of mass, can explain the properties of two of the Gaia BH systems. This mass-loss geometry differs from the standard isotropic re-emission model, which assumes mass loss from the accretor's vicinity. We find that our mass-loss model, without the need for fine-tuning, reproduces the observed orbital periods of the two Gaia BH systems remarkably well across a wide range of initial conditions. This scenario, therefore, offers a plausible formation pathway for these systems. We speculate that orbital widening during mass loss could result from the unequal Roche-lobe sizes of the components and eruptive mass loss driven by the donor's high-opacity subsurface layers. Similar mass loss may also be relevant for all other classes of post-mass-transfer binaries that face analogous evolutionary challenges, including Gaia neutron star and white dwarf systems, binaries hosting stripped-envelope Wolf-Rayet stars, and low-mass X-ray binaries.

Figures (4)

• Figure 1: Evolution of the Gaia BH1 progenitor system. The top panel shows the evolution of the donor’s mass, with the red, yellow, and blue curves representing the hydrogen-rich envelope, helium core, and carbon--oxygen core, respectively. The middle panel presents the evolution of the donor’s radius, along with the Roche lobe radius $R_{\rm L}$ and the sizes corresponding to the inner Lagrange point L1 $\approx a \,(1 - (M_{\rm acc} / (3 M_{\rm don}))^{1/3})$ and outer Lagrange point L3 $\approx a (1 + 5/12 \, (M_{\rm acc} / M_{\rm don}))$ located behind the donor (see Fig. \ref{['Fig: cartoon']}). The bottom panel shows the evolution of the orbital period. The green line corresponds to the model assuming mass loss carrying the specific angular momentum of the donor’s center of mass (orbital widening), while the orange dashed line represents the standard assumption of isotropic re-emission from the accretor (rapid orbital shrinkage). The black dashed line marks the observed properties of the Gaia BH1 system. The timescale is expressed as the logarithm of the remaining time until the end of evolution, defined as the point of central helium depletion.
• Figure 2: Illustration of the geometry of systems at the onset of RLOF for three different mass ratios, all with the same orbital separation and total components mass. The left panel shows a system with a donor-to-accretor mass ratio $M_{\rm don}/M_{\rm ac}=20$, as in case of Gaia BH1 and BH2 progenitors. For comparison, cases with equal-mass components ($M_{\rm don}/M_{\rm ac}=1$) and with the opposite extreme mass ratio ($M_{\rm don}/M_{\rm ac} =$0.05) are also presented.
• Figure 3: Opacity profiles of the donor stars at the early stages of RLOF from MESA simulations, shown as a function of mass above a given layer (left panels) and radius normalized by the stellar Roche-lobe radius (right panels). Results are shown for the Gaia BH1 progenitor system -- upper panels, black line and the Gaia BH2 progenitor system -- lower panels, grey line. For comparison, the Eddington opacity for the presented stars would be $\sim 1.66 \, \rm{cm}^2 \rm{g}^{-1}$ and $\sim 1.53 \, \rm{cm}^2 \rm{g}^{-1}$ for Gaia BH1 and BH2 respectively. Those opacity limits would be lower for a rotating star, as the additional centrifugal force reduces the effective gravity.
• Figure 4: Evolution of the progenitor system of Gaia BH2. The physical assumption and figure description are the same as for Figure \ref{['Fig: Mass_evolution_1']}.