We present sensitive and high angular resolution ($sim$0.2-0.3$$) (sub)millimeter (230 and 345 GHz) continuum and CO(2$-$1)/CO(3$-$2) line archive observations of the disk star system in UX Tauri carried out with ALMA (The Atacama Large Millimeter/Submillimeter Array). These observations reveal the gas and dusty disk surrounding the young star UX Tauri A with a large signal-to-noise ratio ($>$400 in the continuum and $>$50 in the line), and for the first time is detected the molecular gas emission associated with the disk of UX Tauri C (with a size for the disk of $<$56 au). No (sub)millimeter continuum emission is detected at 5$sigma$-level (0.2 mJy at 0.85 mm) associated with UX Tauri C. For the component UX Tauri C, we estimate a dust disk mass of $leq$ 0.05 M$_oplus$. Additionally, we report a strong tidal disk interaction between both disks UX Tauri A/C, separated 360 au in projected distance. The CO line observations reveal marked spiral arms in the disk of UX Tauri A and an extended redshifted stream of gas associated with the UX Tauri C disk. No spiral arms are observed in the dust continuum emission of UX Tauri A. Assuming a Keplerian rotation we estimate the enclosed masses (disk$+$star) from their radial velocities in 1.4 $pm$ 0.6 M$_odot$ for UX Tauri A, and 70 $pm$ 30 / $sin i$ Jupiter masses for UX Tauri C (the latter coincides with the mass upper limit value for a brown dwarf). The observational evidence presented here lead us to propose that UX Tauri C is having a close approach of a possible wide, evolving and eccentric orbit around the disk of UX Tauri A causing the formation of spiral arms and the stream of molecular gas falling towards UX Tauri C.
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