Polarization fraction of Planck Galactic cold clumps and forecasts for the Simons Observatory

We measure the mean-squared polarization fraction of a sample of 6282 Galactic cold clumps at 353 GHz, consisting of Planck Galactic cold clump (PGCC) catalogue category 1 objects [flux densities measured with signal-to-noise ratio (S/N) > 4]. At 353 GHz, we find the mean-squared polarization fraction, which we define as the mean-squared polarization divided by the mean-squared intensity, to be (4.79 ± 0.44) × 10^-4 equation to an $11\, \sigma$ detection of polarization. We test if the polarization fraction depends on the clumps' physical properties, including flux density, luminosity, Galactic latitude, and physical distance. We see a trend towards increasing polarization fraction with increasing Galactic latitude, but find no evidence that polarization depends on the other tested properties. The Simons Observatory, with angular resolution of order 1 arcmin and noise levels between 22 and $54\, \mu$K-arcmin at high frequencies, will substantially enhance our ability to determine the magnetic field structure in Galactic cold clumps. At $\ge 5\, \sigma$ significance, we predict the Simons Observatory will detect at least ~12 000 cold clumps in intensity and ~430 cold clumps in polarization. This number of polarization detections would represent a two orders of magnitude increase over the current Planck results. We also release software that can be used to mask these Galactic cold clumps in other analyses.