The Common Envelope Evolution Outcome -- A Case Study on Hot Subdwarf B Stars

Abstract

Common envelope evolution (CEE) physics plays a fundamental role in the formation of binary systems, such as mergering stellar gravitational wave sources, pulsar binaries and type Ia supernovae. A precisely constrained CEE has become more important in the age of large surveys and gravitational wave detectors. We use an adiabatic mass loss model to explore how the total energy of the donor changes as a function of the remnant mass. This provides a more self-consistent way to calculate the binding energy of the donor. For comparison, we also calculate the binding energy through integrating the total energy from the core to the surface. The outcome of CEE is constrained by total energy conservation at the point at which both component's radii shrink back within their Roche lobes. We apply our results to 142 hot subdwarf binaries. For shorter orbital period sdBs, the binding energy is highly consistent. For longer orbital period sdBs in our samples, the binding energy can differ by up to a factor of 2. The CE efficiency parameter $β_\mathrm{CE}$ becomes smaller than $α_\mathrm{CE}$ for the final orbital period $\log_{10} P_{\mathrm{orb}}/\mathrm{d} > -0.5$. We also find the mass ratios $\log_{10} q$ and CE efficiency parameters $\log_{10} α_{\mathrm{CE}}$ and $\log_{10} β_{\mathrm{CE}}$ linearly correlate in sdBs, similarly to De Marco et al. (2010) for post-AGB binaries.