2025MNRAS.536.1736P

The relationship between B-field orientation and density structure in molecular clouds is often assessed using the histogram of relative orientations (HRO). We perform a plane-of-the-sky geometrical analysis of projected B-fields, by interpreting HROs in dense, spheroidal, pre-stellar, and protostellar cores. We use James Clerk Maxwell Telescope POL-2 850 $\mu$m polarization maps and Herschel column density maps to study dense cores in the Ophiuchus molecular cloud complex. We construct two-dimensional core models, assuming Plummer column density profiles and modelling both linear and hourglass B-fields. We find that high-aspect ratio ellipsoidal cores produce strong HRO signals, as measured using the shape parameter $\xi$. Cores with linear fields oriented $<\!\! 45 ^{\circ }$ from their minor axis produce constant HROs with $-1 \lt \xi \lt 0$, indicating that fields are preferentially parallel to column density gradients. Fields parallel to the core minor axis produce the most negative value of $\xi$. For low-aspect ratio cores, $\xi \approx 0$ for linear fields. Hourglass fields produce a minimum in $\xi$ at intermediate densities in all cases, converging to the minor-axis-parallel linear field value at high and low column densities. We create HROs for six dense cores in Ophiuchus. $\rho$ Oph A and IRAS 16293 have high aspect ratios and preferentially negative HROs, consistent with moderately strong field behaviour. $\rho$ Oph C, L1689A, and L1689B have low aspect ratios, and $\xi \approx 0$. $\rho$ Oph B is too complex to be modelled using a simple spheroidal field geometry. We see no signature of hourglass fields, agreeing with previous findings that dense cores generally exhibit linear fields on these size scales.