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tokens: Heyer et al. 2008 ; Chapman et al. 2011 ). Using the Chandrasekhar-Fermi method, Chapman et al. (2011) estimated a magnetic field strength of about 25 G in the cloud surrounding the B211 filament, concluding that the former is magnetically supported. Fig. 4 Same as Fig. 1 for part of the Taurus molecular cloud around the B211 (north-west) and the L1506 (south-east) filaments. The numbers and white lines on the total intensity map correspond to the positions of the different cuts used to derive the radial profiles shown in Figs. 5 and 6 . Fig. 5 Same as Fig. 2 for the Taurus B211 filament. Here corresponds to the southern side of the filament crest. The filament is clearly seen in and is located in the area of a steep variation of the emission. The dispersion of the emission is small along the length of the filament. Fig. 6 Same as Fig. 2 for L1506. Here corresponds to the south-eastern side of the filament crest. Figure 4 shows the Planck 353 GHz Stokes parameter maps of the TMC around the B211 and L1506 filaments. The B211 filament is well detected in the and maps, as a structure distinct from its surrounding. On the map, on the other hand, the filament is not seen as an elongated structure, but it is perpendicular to a large gradient that separates two regions of almost uniform . The emission is negative on the northern side of the filament while it is positive on the southern side. This indicates that the -field orientation varies in the cloud surrounding the B211 filament. This variation can be seen very clearly in the radial profiles perpendicular to the filament crest, shown in Fig. 5 . These profiles are derived as explained in the previous section (for the Musca filament). The four and profiles (shown in the middle and right-hand panels of Fig. 5 ) are derived by averaging the cuts within a distance along the filament crest of 3 times the Planck beam (3 4.8). The cloud intensity () increases from the southern to the northern side of the filament, while the emission is similar on both sides of the filament crest. The (negative) emission of B211 is very clearly seen in the radial profiles. The different profiles show the approximate invariance of the emission along the filament crest. The total and polarized emission components are remarkably constant along the length of B211. 3.3. The Taurus L1506 filament The L1506 filament is located on the south-east side of B211 (see Fig. 4 ). Stellar polarization data are presented by Goodman et al. (1990) . The density structure and the dust emission properties have been studied by Stepnik et al. (2003) , and more recently by Ysard et al. (2013) using Herschel data. This filament has mean column densities comparable to those of the Musca filament. Star formation at both ends of L1506 has been observed with the detection of a few candidate prestellar cores ( Stepnik et al. 2003 ; Pagani et al. 2010 ). Figure 6 shows the radial profiles perpendicular to its crest. The colour profiles numbered from