On the common envelope efficiency

摘要: In this work, we try to use the apparent luminosity versus displacement (i.e., $L_{\rm X}$ vs. $R$) correlation of high mass X-ray binaries (HMXBs) constrain common envelope (CE) efficiency $\alpha_{\rm CE}$, which is a key parameter affecting evolution binary orbit during CE phase. The major updates that crucial for include variable $\lambda$ and new criterion Hertzsprung gap donor stars, both are recently developed. We find that, within framework standard energy formula core definition at $X=10$\%, value i.e., around 0.8-1.0, more preferable, while CE}< \sim 0.4$ likely can not reconstruct observed $R$ distribution. However due an ambiguous boundary in literature, used here still carries almost two order magnitude uncertainty, may translate directly expected CE}$. present detailed components current HMXBs their spatial offsets from star clusters, be further testified by future observations HMXB populations nearby star-forming galaxies.