  As the first and till date the only one multiple planet hosting dwarf star
that is sufficiently cool to form condensate cloud in it atmosphere, Trappist-1
provides unique opportunity to test the efficiency of image polarimetry as a
tool to detect and characterize exoplanets around L- and late M-dwarfs and
Exomoons around directly imaged self-luminous giant exoplanets. Although
scattering of light by atmospheric dust particles should produce significant
amount of linear polarization in the far optical and near infra-red, the
disk-averaged net detectable polarization of the star must be zero owing to
spherical symmetry. However, the transit of its planets would give rise to
significant asymmetry and produce phase-dependent polarization with the peak
polarization occurring at the inner contact points of planetary transit ingress
and egress epoch. Adopting the known stellar and planetary physical parameters
and employing a self-consistent cloudy atmosphere model of M8 dwarf star, the
transit polarization profiles and the expected amount of polarization of
Trappist-1 during the transit phase of each individual planets as well as that
during simultaneous transit of two planets are presented in this paper. It is
emphasized that the amount of polarization expected is within the detection
limit of a few existing facilities. If polarization is detected confirming the
prediction, time resolved image polarimetry will emerge out as a potential tool
to detect and characterize small planets around cloudy ultra-cool dwarfs.
