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Thorne–Żytkow objects (TŻOs), originally proposed by Thorne and Żytkow, may form as a result of unstable mass transfer in a massive X-ray binary after a neutron star (NS) is engulfed in the envelope of its companion star. Using a rapid binary evolution program and the Monte Carlo method, we simulated the formation of TŻOs in close binary stars. The Galactic birth rate of TŻOs is about $$1.5\times...