Fast radio bursts (FRBs) are bright radio transients with short durations and extremely high brightness temperatures, and their physical origins are still unknown. Recently, a repeating source, FRB 20200120E, was found in a globular cluster in the very nearby M81 galaxy. The associated globular cluster has an age of $sim9.13~{rm Gyr}$, and hosts an old population of stars. In this work, we consider that an FRB source is in a close binary system with a low-mass main sequence star as its companion. Due to the large burst energy of the FRB, when the companion star stops the FRB, its surface would be heated by the radiation-induced shock, and make re-emission. For a binary system with a solar-like companion star and an orbital period of a few days, we find that the re-emission is mainly at optical band, and with delays of a few seconds after the FRB. Its luminosity is several times larger than the solar luminosity, and the duration is about hundreds of seconds. Such a transient might be observable in the future multiwavelength follow-up observation for Galactic FRB sources.
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