We present our survey for optically faint variable objects using multi-epoch ( 8 - 10 epochs over 2 - 4 years ) i ^ { \prime } -band imaging data obtained with Subaru Suprime-Cam over 0.918 deg ^ { 2 } in the Subaru/XMM-Newton Deep Field ( SXDF ) .
We found 1040 optically variable objects by image subtraction for all the combinations of images at different epochs .
This is the first statistical sample of variable objects at depths achieved with 8-10m class telescopes or HST .
The detection limit for variable components is i ^ { \prime } _ { vari } \sim 25.5 mag .
These variable objects were classified into variable stars , supernovae ( SNe ) , and active galactic nuclei ( AGN ) , based on the optical morphologies , magnitudes , colors , and optical-mid-infrared colors of the host objects , spatial offsets of variable components from the host objects , and light curves .
Detection completeness was examined by simulating light curves for periodic and irregular variability .
We detected optical variability for 36 \pm 2 \% ( 51 \pm 3 \% for a bright sample with i ^ { \prime } < 24.4 mag ) of X-ray sources in the field .
Number densities of variable obejcts as functions of time intervals \Delta { t } and variable component magnitudes i ^ { \prime } _ { vari } are obtained .
Number densities of variable stars , SNe , and AGN are 120 , 489 , and 579 objects deg ^ { -2 } , respectively .
Bimodal distributions of variable stars in the color-magnitude diagrams indicate that the variable star sample consists of bright ( V \sim 22 mag ) blue variable stars of the halo population and faint ( V \sim 23.5 mag ) red variable stars of the disk population .
There are a few candidates of RR Lyrae providing a possible number density of \sim 10 ^ { -2 } kpc ^ { -3 } at a distance of > 150 kpc from the Galactic center .