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 ^ { \prime } -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 .