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Massive star-forming galaxies in the high-redshift universe host largereservoirs of cold gas in their circumgalactic medium (CGM). Traditionally,these reservoirs have been linked to diffuse H I Lyman-$\alpha$ (Ly$\alpha)$emission extending beyond $\approx 10$ kpc scales. In recent years,millimeter/submillimeter observations are starting to identify even colder gasin the CGM through molecular and/or atomic tracers such as the [C II]$158\,\mu$m transition. In this context, we study the well-known J1000+0234system at $z=4.54$ that hosts a massive dusty star-forming galaxy (DSFG), aUV-bright companion, and a Ly$\alpha$ blob. We combine new ALMA [C II] lineobservations taken by the CRISTAL survey with data from previous programstargeting the J1000+0234 system, and achieve a deep view into a DSFG and itsrich environment at a 0.2" resolution. We identify an elongated [C II]-emittingstructure with a projected size of 15 kpc stemming from the bright DSFG at thecenter of the field, with no clear counterpart at any other wavelength. Theplume is oriented $\approx 40^{\circ}$ away from the minor axis of the DSFG,and shows significant spatial variation of its spectral parameters. Inparticular, the [C II] emission shifts from 180 km/s to 400 km/s between thebottom and top of the plume, relative to the DSFG's systemic velocity. At thesame time, the line width starts at 400-600 km/s but narrows down to 190 km/sat top end of the plume. We discuss four possible scenarios to interpret the [CII] plume: a conical outflow, a cold accretion stream, ram pressure stripping,and gravitational interactions. While we cannot strongly rule out any of thesewith the available data, we disfavor the ram pressure stripping scenario due tothe requirement of special hydrodynamic conditions.

The ALMA-CRISTAL survey. Discovery of a 15 kpc-long gas plume in a $z=4.54$ Lyman-$\alpha$ blob