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WOCS 4540 is the longest orbital period (P_orb= 3030 days) blue straggler star (BSS)—white dwarf (WD) pair in the old open cluster NGC 188. It also contains one of the most luminous BSS in the cluster. Prior Hubble Space Telescope Cosmic Origins Spectrograph spectroscopy measured a WD mass of 0.53M_⊙, indicative of a carbon–oxygen WD and suggesting previous mass transfer from an asymptotic giant branch (AGB) star. Detailed modeling of the system evolution, including red giant branch phase wind mass transfer, AGB wind Roche-lobe overflow, and regular Roche-lobe overflow, is done with Modules for Experiments in Stellar Astrophysics. The best-fit model produces excellent agreement with a wide array of observational constraints on the BSS, the WD, and the binary system. To produce the observed luminosity and effective temperature of the BSS, all three donor mass-transfer mechanisms contribute similarly to build a 1.5M_⊙BSS. The overall mass-transfer efficiency is 55%. Regular Roche-lobe overflow occurs only during the largest AGB thermal pulse, but yields a very high accretion rate at 75% efficiency and briefly (less than 1 Myr) a very high luminosity boost from the accretor.

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