A Path to Constraints on Common Envelope Ejection in Massive Binaries: Full Evolutionary Reconstruction of Three Black Hole X-ray Binaries

TL;DR

This study reconstructs the evolution of three black hole X-ray binaries to constrain the common envelope ejection efficiency, revealing that high efficiency parameters are necessary and suggesting the need for additional energy sources or formalism revision.

Contribution

It provides the first systematic constraints on common envelope efficiency parameters for massive binaries using detailed evolutionary reconstructions.

Findings

Minimum CE efficiency parameters are greater than 4.2 to 6.7 depending on energy considerations.

No solutions found with CE efficiency below unity, even with reduced envelope binding energy.

Substantial natal kicks are required for the formation of one of the studied binaries.

Abstract

The massive binary common envelope (CE) phase plays a pivotal role in the formation of close black hole/neutron star (BH/NS) binaries, yet significant uncertainties remain in our understanding of this process. In this study, we aim to constrain the massive binary CE phase by systematically reconstructing three observed BH X-ray binaries (BHXBs): GRO J1655-40, SAX J1819.3-2525, and 4U 1543-47. Through comprehensive binary evolution simulations and parametric supernova (SN) modeling, we establish lower limits for the CE efficiency parameters under different energy considerations within the standard energy formalism. Specifically, we derive minimum values for three cases: $\alpha_{\rm 0.5U}$ and $\alpha_{\rm U}$ representing CE efficiencies with half and all of the internal energy contributing to the envelope ejection, respectively, and $\alpha_{\rm H}$ accounting for the envelope's enthalpy. Our analysis reveals that the self-consistent formation of these three BHXBs requires CE efficiency parameters satisfying: $\alpha_{\rm 0.5U}\gtrsim 6.7$, $\alpha_{\rm U}\gtrsim 4.2$ and $\alpha_{\rm H}\gtrsim 1.7$. Notably, we find no viable solutions with CE efficiency values below unity, even when considering the most extreme scenarios in which the envelope binding energy is significantly reduced through enthalpy inclusion. {Our results strongly imply that either additional energy sources are required, or the formalism itself must be revised.} Furthermore, we quantitatively assess the impact of BH natal kicks on our results. A key finding is that 4U 1543-47's formation requires substantial natal kicks ($\gtrsim 50 \;\rm km/s$), as lower kick velocities are incompatible with isolated binary evolution.