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We present models for the complete life and death of a 60 solar mass starevolving in a close binary system, from the main sequence phase to theformation of a compact remnant and fallback of supernova debris. After corehydrogen exhaustion, the star expands, loses most of its envelope by Roche lobeoverflow, and becomes a Wolf-Rayet star. We study its post-mass transferevolution as a function of the Wolf-Rayet wind mass loss rate (which iscurrently not well constrained and will probably vary with initial metallicityof the star). Varying this mass loss rate by a factor 6 leads to stellar massesat collapse that range from 3.1 to 10.7 solar masses. Although the iron coremasses at collapse are generally larger for stars with larger final masses,they do not depend monotonically on the final stellar mass or even the C/O-coremass. We then compute the evolution of all models through collapse and bounce.The results range from strong supernova explosions for the lower final massesto the direct collapse of the star into a black hole for the largest finalmass. Correspondingly, the final remnant masses, which were computed byfollowing the supernova evolution and fallback of material for a time scale ofabout one year, are between 1.2 and 10 solar masses. We discuss the remaininguncertainties of this result and outline the consequences of our results forthe understanding of the progenitor evolution of X-ray binaries and gamma-rayburst models.Comment: 23 pages total (including 11 figures), submitted to Ap

The Limiting Stellar Initial Mass for Black Hole Formation in Close Binary Systems