B-fields In STar-forming Region Observations (BISTRO): Technical Foundations for Quantitative 450/850 $\mu$m JCMT SCUBA-2/POL-2 Polarimetry

Abstract

We present five technical validations of SCUBA-2/POL-2 polarimetry on the James Clerk Maxwell Telescope at 450 and 850 $\mu$m, using 174 archival fields in 69 molecular cloud regions and subsets appropriate to each test. Extended-source calibration avoids a deterministic shift of $\Delta \beta =-1.05$ in the dust emissivity index $\beta$ that would result from calibrating extended emission using peak brightness. We modeled Stokes $I$ noise with additive and signal-dependent components. The measured median ratio of surface-brightness noise at 450/850 $\mu$m is 25. Independent tests of Stokes $Q,U$ noise support approximately equal additive variances and weak error correlations, providing a basis for propagating polarization uncertainties. Corrections determined for individual fields reduce additive zero-level offsets of order $1$ mJy arcsec${}^{-2}$ in the 450 $\mu$m Stokes $Q$ and $U$ intensities. The three-step regression leaves a median combined residual amplitude of $0.07$ mJy arcsec${}^{-2}$. Independent comparisons with SOFIA/HAWC+ at 154 and 214 $\mu$m support the correction in strongly affected fields. We matched the 450 $\mu$m maps to the modeled 850 $\mu$m beam and the common $12.6^{\prime \prime }$-$300^{\prime \prime }$ range of angular scales. We compared three reductions of the same 450 $\mu$m observations across 30 sources. Taking the median angular residual relative to the final product for each source, we find that beam matching reduces the median over sources from $6.3^{\circ }$ to $4.7^{\circ }$. After matching, 29 of the 30 sources have median residuals below $10^{\circ }$. We also quantified how residual $Q/U$ offsets propagate in ratios of polarization fractions, differences in spectral indices, and polarization angles. These validations provide procedures and quantitative references for interpreting POL-2 measurements and combining them with polarimetry at other wavelengths.

arXiv comment75 pages, 33 figures, 10 tables. Submitted to PASJ. Paper T of a series of three (Papers T, S1, and S2); Paper S1 is posted at the same time, and Paper S2 will be posted in November 2026. The submitted versions of all three papers are available at https://github.com/450um1G/PASJ2026