Rethinking Thorne-\.Zytkow Object Formation: The Fate of X-ray Binary LMC X-4 and Implications for Ultra-long Gamma-ray Bursts

We present a start-to-end simulation aimed at studying the long-term fate of high-mass X-ray binaries and whether a Thorne-\.Zytkow object (T\.ZO) might ultimately be assembled. We analyze results from a 3D hydrodynamical simulation that models the eventual fate of LMC X-4, a compact high-mass X-ray binary system, after the primary fills its Roche lobe and engulfs the neutron star companion. We discuss the outcome of this engulfment within the standard paradigm of T\.ZO formation. The post-merger angular momentum content of the stellar core is a key ingredient, as even a small amount of rotation can break spherical symmetry and produce a centrifugally supported accretion disk. Our findings suggest the inspiraling neutron star, upon merging with the core, can accrete efficiently via a disk at high rates ($\approx 10^{-2}M_\odot/{\rm s}$), subsequently collapsing into a black hole and triggering a bright transient with a luminosity and duration typical of an ultra-long gamma-ray burst. We propose that the canonical framework for T\.ZO formation via common envelope needs to be revised, as the significant post-merger accretion feedback will unavoidably unbind the vast majority of the surrounding envelope.