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An Accurate Determination of the Optical Periodic Modulation in the X-Ray Binary SAX J1808.4-3658

We report on optical imaging of the X-ray binary SAX J1808.4-3658 with the 8-m Gemini South Telescope. The binary, containing an accretion-powered millisecond pulsar, appears to have a large periodic modulation in its quiescent optical emission. In order to clarify the origin of this modulation, we obtained three time-resolved $r'$-band light curves (LCs) of the source in five days. The LCs can be described by a sinusoid, and the long time-span between them allows us to determine optical period P=7251.9 s and phase 0.671 at MJD 54599.0 (TDB; phase 0.0 corresponds to the ascending node of the pulsar orbit), with uncertainties of 2.8 s and 0.008 (90 % confidence), respectively. This periodicity is highly consistent with the X-ray orbital ephemeris. By considering this consistency and the sinusoidal shape of the LCs, we rule out the possibility of the modulation arising from the accretion disk. Our study supports the previous suggestion that the X-ray pulsar becomes rotationally powered in quiescence, with its energy output irradiating the companion star, causing the optical modulation. While it has also been suggested that the accretion disk would be evaporated by the pulsar, we argue that the disk exists and gives rise to the persistent optical emission. The existence of the disk can be verified by long-term, multi-wavelength optical monitoring of the source in quiescence, as an increasing flux and spectral changes from the source would be expected based on the standard disk instability model.