We present an optical polarimetry study of the nearby star-forming region Lambda-Orionis to map the plane-of-the-sky magnetic field geometry to understand the magnetized evolution of the HII region and the associated small molecular clouds. We made multiwavelength polarization observations of 34 bright stars distributed across the region. We also present the R-band polarization measurements that focused on the small molecular clouds, bright-rimmed clouds (BRC), BRC 17, and BRC 18, which are located at the periphery of the HII region. The magnetic field lines exhibit a large-scale ordered orientation consistent with the Planck submillimeter polarization measurements. The magnetic field lines in the two BRCs are found to be roughly in north-south directions. However, a larger dispersion is noted in the orientation for BRC 17 compared to BRC 18. Using a structure-function analysis, we estimate the strength of the plane-of-the-sky component of the magnetic field as ∼28 μG for BRC 17 and ∼40 μG for BRC 18. The average dust grain size and the mean value of the total-to-selective extinction ratio (RV) in the HII region are found to be ∼0.51 ± 0.05 μm and ∼2.9 ± 0.3, respectively. The distance of the whole HII region is estimated as ∼392 ± 8 pc by combining astrometry information from Global Astrometric Interferometer for Astrophysics (Gaia) early data release 3 (EDR3) for young stellar objects associated with BRCs and confirmed members of the central cluster Collinder 69.
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