Context: WISE J085510.83-071442.5 (W0855) is a unique object: with Teff ca. 250 K, it is the coldest known brown dwarf (BD), located at only ca.2.2 pc form the Sun. It is extremely faint, which makes any astronomical observations difficult. However, at least one remotely similar ultra-low-mass object, the M9 dwarf TVLM 513-46546, has been shown to be a steady radio emitter at frequencies up to 95 GHz with superimposed active states where strong, pulsed emission is observed. Aims: Our goal is to determine the millimeter radio properties of W0855 with deep observations around 93 GHz (3.2 mm) in order to investigate whether radio astrometry of this object is feasible and to measure or set an upper limit on its magnetic field. Methods: We observed W0855 for 94 min at 85.1-100.9 GHz on 24 December 2019 using 44 of the Atacama Large millimeter Array (ALMA) 12 m antennas. We used the standard ALMA calibration procedure and created the final image for our analysis by accommodating the Quasar 3C 209, the brightest nearby object by far. Furthermore, we created a light curve with a 30 s time resolution to search for pulsed emission. Results: Our observations achieve a noise RMS of 7.3 {mu}Jy/beam for steady emission and of 88 {mu}Jy for 30 s pulses in the aggregated bandwidth (Stokes I). There is no evidence for steady or pulsed emission from the object at the time of the observation. We derive 3 {sigma} upper limits of 21.9 {mu}Jy on the steady emission and of 264 {mu}Jy on the pulsed emission of W0855 between 85 GHz and 101 GHz. Conclusions: Together with the recent non-detection of W0855 at 4-8 GHz, our constraints on the steady and pulsed emission from W0855 confirm that the object is neither radio-loud nor magnetospherically particularly active.
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