The Subaru/XMM-Newton Deep Survey (SXDS) - V. Optically Faint Variable Object Survey

We present our survey for optically faint variable objects using multi-epoch (8-10 epochs over 2-4 years) $i$-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 $i_{rm{vari}}sim25.5$ 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 $36pm2%$ ($51pm3%$ for a bright sample with $i<24.4$ mag) of X-ray sources in the field. Number densities of variable obejcts as functions of time intervals $Delta{t}$ and variable component magnitudes $i_{rm{vari}}$ 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 ($Vsim22$ mag) blue variable stars of the halo population and faint ($Vsim23.5$ mag) red variable stars of the disk population. There are a few candidates of RR Lyrae providing a possible number density of $sim10^{-2}$ kpc$^{-3}$ at a distance of $>150$ kpc from the Galactic center.