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The dependence of polarization fraction $p$ on total intensity $I$ inpolarized submillimeter emission measurements is typically parameterized as$p\propto I^{-\alpha}$ $(\alpha \leq 1)$, and used to infer dust grainalignment efficiency in star-forming regions, with an index $\alpha=1$indicating near-total lack of alignment of grains with the magnetic field. Inthis work we demonstrate that the non-Gaussian noise characteristics ofpolarization fraction may produce apparent measurements of $\alpha \sim 1$ evenin data with significant signal-to-noise in Stokes $Q$, $U$ and $I$ emission,and so with robust measurements of polarization angle. We present a simplemodel demonstrating this behavior, and propose a criterion by whichwell-characterized measurements of polarization fraction may be identified. Wedemonstrate that where our model is applicable, $\alpha$ can be recovered byfitting the $p-I$ relationship with the mean of the Rice distribution, withoutstatistical debiasing of polarization fraction. We apply our model to JCMTBISTRO Survey POL-2 850$\mu$m observations of three clumps in the OphiuchusMolecular Cloud, finding that in the externally-illuminated Oph A region,$\alpha\approx 0.34$, while in the more isolated Oph B and C, despite theirdiffering star formation histories, $\alpha \sim 0.6-0.7$. Our results thussuggest that dust grain alignment in dense gas is more strongly influenced byincident interstellar radiation field than by star formation history. Wefurther find that grains may remain aligned with the magnetic field atsignificantly higher gas densities than has previously been believed, thusallowing investigation of magnetic field properties within star-forming clumpsand cores.

JCMT BISTRO Survey observations of the Ophiuchus Molecular Cloud: Dust grain alignment properties inferred using a Ricean noise model