HAWC+/SOFIA Polarimetry in L1688: Relative Orientation of Magnetic Field and Elongated Cloud Structure

We present a study of the relative orientation between magnetic field and elongated cloud structures for $\rho$ Oph A E regions in L1688 Ophiuchus molecular cloud. Combining inferred from HAWC+ 154 $\mu$m observations polarized thermal emission with column density maps created using Herschel submillimeter observations, we find consistent perpendicular alignment at scales $0.02$ pc ($33.6"$ $d \approx 137$ pc) histogram orientations (HRO) technique. This supports conclusions previous work Planck polarimetry extends results to higher densities. this HRO analysis new L1688, transition parallel is observed occur hydrogen approximately $10^{21.7}$ cm$^{-2}$. value agrees well values found nearby clouds via studies only observations. Using existing turbulent, magnetohydrodynamic simulations formed by colliding flows as model conclude that volume associated $\sim10^{4}$ cm$^{-3}$. discuss limitations our analysis, including incomplete sampling dense HAWC+.