The unprecedented sensitivity provided by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) could shed light on studies of the magnetic field and plasma properties of brown dwarfs by catching polarized radio flares. With the FAST L-band 19-beam receiver, we observe a nearby dwarf stellar system 2MASSW J0746425 + 200032 which has been reported to show 4.86 GHz and 8.46 GHz radio flare emission. The L-band radio signals from the target are searched in both total intensity and circular polarization during the entire 147 min tracking observation. No radio flare down to a sensitivity of ∼13 mJy and ∼2 mJy (5σ) in Stokes I and V can be identified. The non-detection may lie in the intrinsic physical condition of the stellar system, e.g., the magnetic field strength and the electron density distribution and/or the sampling rate, which should be higher to reveal the sub-second structures but are smeared out with a lower rate in our observations.
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