  We obtained linear polarization photometry ($J$-band) and low-resolution
spectroscopy ($ZJ$-bands) of Trappist-1, which is a planetary system formed by
an M8-type low-mass star and seven temperate, Earth-sized planets. The
photopolarimetric monitoring campaign covered 6.5 h of continuous observations
including one full transit of planet Trappist-1d and partial transits of
Trappist-1b and e. The spectrophotometric data and the photometric light curve
obtained over epochs with no planetary transits indicate that the low-mass star
has very low level of linear polarization compatible with a null value.
However, the "in transit" observations reveal an enhanced linear polarization
signal with peak values of $p^* = 0.1\,\%$ with a confidence level of 3
$\sigma$, particularly for the full transit of Trappist-1d, thus confirming
that the atmosphere of the M8-type star is very likely dusty. Additional
observations probing different atmospheric states of Trappist-1 are needed to
confirm our findings, as the polarimetric signals involved are low. If
confirmed, polarization observations of transiting planetary systems with
central ultra-cool dwarfs can become a powerful tool for the characterization
of the atmospheres of the host dwarfs and the validation of transiting planet
candidates that cannot be corroborated by any other method.
