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We present the 850 $\mu$m polarization observations toward the IC5146filamentary cloud taken using the Submillimetre Common-User Bolometer Array 2(SCUBA-2) and its associated polarimeter (POL-2), mounted on the James ClerkMaxwell Telescope (JCMT), as part of the B-fields In STar forming RegionsObservations (BISTRO). This work is aimed at revealing the magnetic fieldmorphology within a core-scale ($\lesssim 1.0$ pc) hub-filament structure (HFS)located at the end of a parsec-scale filament. To investigate whether or notthe observed polarization traces the magnetic field in the HFS, we analyze thedependence between the observed polarization fraction and total intensity usinga Bayesian approach with the polarization fraction described by the Ricelikelihood function, which can correctly describe the probability densityfunction (PDF) of the observed polarization fraction for low signal-to-noiseratio (SNR) data. We find a power-law dependence between the polarizationfraction and total intensity with an index of 0.56 in $A_V\sim$ 20--300 magregions, suggesting that the dust grains in these dense regions can still bealigned with magnetic fields in the IC5146 regions. Our polarization mapsreveal a curved magnetic field, possibly dragged by the contraction along theparsec-scale filament. We further obtain a magnetic field strength of0.5$\pm$0.2 mG toward the central hub using the Davis-Chandrasekhar-Fermimethod, corresponding to a mass-to-flux criticality of $\sim$ $1.3\pm0.4$ andan Alfv\'{e}nic Mach number of $<$0.6. These results suggest that gravity andmagnetic field is currently of comparable importance in the HFS, and turbulenceis less important.

JCMT BISTRO survey: Magnetic Fields within the Hub-Filament Structure in IC 5146