Orbital Contraction of Post-Common-Envelope Binaries with a Circumbinary Disk

Abstract

Tight and compact binary systems, such as double neutron star binaries, are believed to undergo a common envelope evolution phase, resulting in strongly bound orbits. During this phase, the outer layers of the primary star are expelled, resulting in orbital shrinkage. However, a part of the expelled material may remain as a circumbinary disk, which can further influence subsequent orbital evolution. In this study, we investigated orbital evolution in the presence of a circumbinary disk within a simplified framework by assuming that orbital contraction and disk dissipation occur over the viscous timescale. The results showed that the orbit of the binary system after the common envelope evolution phase was further contracted by up to $\sim 17 \%$ due to the presence of the circumbinary disk, irrespective of the disk's mass and structure. This additional orbital contraction following the common envelope evolution phase may have significant implications for the formation rate of double neutron star binaries that merge within a cosmic timescale.

Figures (2)

• Figure 1: The relationship between the binary orbital radii and the disk boundary radii. For orbital periods of 1, 5, and 20 h, the sequence of points represents the orbital separation as a function of the total binary mass. Meanwhile, the boundary between the middle and outer regions of the standard disk is shown as a curve for the corresponding binary masses. The lower curve corresponds to a mass transfer rate within the disk of $\dot{m} = 0.1 \dot{m}_{\rm{Edd}}$. Meanwhile, the upper curve corresponds to $\dot{m} = \dot{m}_{\rm{Edd}}$. The figure shows that the binary orbit mostly lies in the outer region. However, the binary orbit may enter the middle region only when the orbital period is significantly short, the disk mass transfer rate is large, and the binary mass is high.
• Figure 2: $\gamma$ as a function of $\alpha_{\rm{CE}}$ computed using Eq. (\ref{['eq:gammanew']}). Results for three mass values ($10 - 20 \rm{M}_{\odot}$) are shown. When $\alpha_{\rm{CE}}$ is small, that is, when the orbit has become sufficiently small through CE evolution, the approximation in Eq. (\ref{['eq:approxalpha']}) holds well. In other words, over a reasonably wide range of parameters, it is reasonable to multiply the value of $\alpha_{\rm{CE}}$ by 0.17 to account for the effect of the CBD.