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 1.4 { M _ { \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 0.8 { M _ { \odot } } of the hydrogen envelope remains around the giant star ’ s core .
Our results suggest that the inspiral will continue until another \approx 0.3 { M _ { \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 2.6 { M _ { \odot } } helium-star and a NS with a separation of 3.3-5.7 { R _ { \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 _ { CE } -equivalent efficiency of \approx 5 .