Magnetic field morphology and physical properties of two small molecular clouds: L1604 and L121

Magnetic fields play an important role in star formation but are often difficult to observationally probe in small star-forming molecular clouds. We study two such clouds, L1604 (towards the Galactic anticentre) and L121 (towards the Galactic centre), using R-band polarimetry to investigate their envelope magnetic field (θ Bᵉⁿᵛ) morphology, physical structure, and internal energetics. We find a key distinction: θ Bᵉⁿᵛ in L1604 is effectively parallel to the Galactic plane, while it is offset by ~ 70^∘ ± 1^∘ in L121. Additionally, θ Bᵉⁿᵛ is misaligned with the core minor axes (derived from sub-millimeter data) by ~ 47^∘ ± 1^∘ for L1604 and ~ 74^∘ ± 1^∘ for L121. However, for L121, a much smaller offset of ~ 17^∘ ± 1^∘ is found when compared with its minor axis obtained from optical data in the literature, suggesting scale-dependent variations in magnetic field geometry. The distances are calculated with using the near-infrared (NIR) photometry technique (which uses Two Micron All Sky Survey and Gaia DR3) are found to be 816± 11\, pc for L1604 and 124± 1\, pc for L121. We use the PNICER technique to create extinction maps and derived physical parameters using Herschel Spectral and Photometric Imaging Receiver (SPIRE) data. The mean column densities are ~ (2.2± 1.1)× 10²¹ cm⁻² for L1604 and ~ (1.3± 0.6)× 10²¹ cm⁻² for L121. The plane-of-sky magnetic field strengths (Bₚₒₛ), estimate using the Davis–Chandrasekhar–Fermi method, are ~ (47± 17)\, μG for L1604 and ~ (72± 23)\, μG for L121. Both clouds exhibit sub-critical mass-to-flux ratios and sub-Alfvénic conditions, indicating magnetic dominance over gravity and turbulence. Our results highlight that envelopes are magnetically supported, while cores may become supercritical, demanding high-resolution data to trace the envelope-to-core magnetic influence.