B-fields In STar-forming Region Observations (BISTRO): Dual-Wavelength Constraints on Size-Dependent Grain Alignment in Star-Forming Regions
We compared 450 and 850 $μ$m POL-2 observations from the James Clerk Maxwell Telescope at $12.6''$ resolution. The median absolute difference in polarization angle between bands is $6.7^\circ$ across 21 regions. For total intensity $I\proptoν^α$ and polarized intensity $PI\proptoν^γ$, 24-27 of 35 regions have $γ<α$, allowing for $3σ$ limits on weak polarized intensities. The median $γ-α$ is $-0.51$, ranging from $-0.57$ to $-0.45$ under these limits. The ratio of polarization fractions is $P_{450}/P_{850}=0.69\pm0.02_{\rm sys}\pm0.03_{\rm stat}$, with no detected dependence on the angle difference. We suggest that the dependence of alignment on grain size offers the simplest explanation of these findings. For optically thin components sharing a polarization angle and opacity law, temperature mixing reproduces the median $-0.51$ only if the warm dust is polarized less efficiently than the cold dust. If the cold dust is at 10 K or warmer and the warm dust at 40 K or cooler, the median requires a ratio of warm to cold effective polarization efficiencies $r\lesssim0.18$. We tested mixtures with opacity index $β=2$ in four fields against Herschel dust temperatures and Green Bank Ammonia Survey kinetic temperatures. We assumed equal gas and dust temperatures, ammonia tracing cold gas, and model ranges of 3-20 K for cold dust and 25-40 K for warm dust carrying at most half the mass. Mixtures matching both temperatures cannot reproduce $γ-α$ within $1σ$ in three fields, including OMC 2 tentatively, even for $r=0$. Allowing warm dust at 10-100 K and up to 95% of the mass permits solutions only for $r\leq0.041$. To explain these three fields by temperature mixing, we need wider model ranges and a very strong contrast in polarization efficiency. The origin of this contrast remains undetermined.