# The Complete Evolution of a Neutron-Star Binary through a Common Envelope Phase Using 1D Hydrodynamic Simulations

## TL;DR

This study models the entire common envelope phase of a neutron star and red supergiant using 1D hydrodynamic simulations, revealing how the envelope is ejected and predicting the formation of a close double neutron-star system.

## Contribution

It provides a detailed, self-consistent simulation of the common envelope evolution with a neutron star using MESA, including drag forces and envelope dynamics, which is a novel approach.

## Key findings

- Most of the hydrogen envelope is ejected, forming a large, dusty, optically thick envelope.
- The final binary consists of a 2.6 solar mass helium star and a neutron star with a separation of 3.3-5.7 solar radii.
- The estimated efficiency of envelope ejection is approximately 5, indicating highly efficient common envelope evolution.

## Abstract

Over forty years of research suggests that the common envelope phase, in which an evolved star engulfs its companion upon expansion, is the critical evolutionary stage forming short-period, compact-object binary systems, such as coalescing double compact objects, X-ray binaries, and cataclysmic variables. In this work, we adapt the one-dimensional hydrodynamic stellar evolution code, MESA, to model the inspiral of a 1.4M$_{\odot}$ neutron star (NS) inside the envelope of a 12$M_{\odot}$ red supergiant star. We self-consistently calculate the drag force experienced by the NS as well as the back-reaction onto the expanding envelope as the NS spirals in. Nearly all of the hydrogen envelope escapes, expanding to large radii ($\sim$10$^2$ AU) where it forms an optically thick envelope with temperatures low enough that dust formation occurs. We simulate the NS orbit until only 0.8M$_{\odot}$ of the hydrogen envelope remains around the giant star's core. Our results suggest that the inspiral will continue until another $\approx$0.3M$_{\odot}$ are removed, at which point the remaining envelope will retract. Upon separation, a phase of dynamically stable mass transfer onto the NS accretor is likely to ensue, which may be observable as an ultraluminous X-ray source. The resulting binary, comprised of a detached 2.6M$_{\odot}$ helium-star and a NS with a separation of 3.3-5.7R$_{\odot}$, is expected to evolve into a merging double neutron-star, analogous to those recently detected by LIGO/Virgo. For our chosen combination of binary parameters, our estimated final separation (including the phase of stable mass transfer) suggests a very high $\alpha_{\rm CE}$-equivalent efficiency of $\approx$5.