Polarization angle requirements for CMB B-mode experiments : Application to the LiteBIRD satellite

Abstract

A methodology to provide the polarization angle requirements for different\nsets of detectors, at a given frequency of a CMB polarization experiment, is\npresented. The uncertainties in the polarization angle of each detector set are\nrelated to a given bias on the tensor-to-scalar ratio $r$ parameter. The\napproach is grounded in using a linear combination of the detector sets to\nobtain the CMB polarization signal. In addition, assuming that the\nuncertainties on the polarization angle are in the small angle limit (lower\nthan a few degrees), it is possible to derive analytic expressions to establish\nthe requirements. The methodology also accounts for possible correlations among\ndetectors, that may originate from the optics, wafers, etc. The approach is\napplied to the LiteBIRD space mission. We show that, for the most restrictive\ncase (i.e., full correlation of the polarization angle systematics among\ndetector sets), the requirements on the polarization angle uncertainties are of\naround 1 arcmin at the most sensitive frequency bands (i.e., $\\approx 150$ GHz)\nand of few tens of arcmin at the lowest (i.e., $\\approx 40$ GHz) and highest\n(i.e., $\\approx 400$ GHz) observational bands. Conversely, for the least\nrestrictive case (i.e., no correlation of the polarization angle systematics\namong detector sets), the requirements are $\\approx 5$ times less restrictive\nthan for the previous scenario. At the global and the telescope levels,\npolarization angle knowledge of a few arcmins is sufficient for correlated\nglobal systematic errors and can be relaxed by a factor of two for fully\nuncorrelated errors in detector polarization angle. The reported uncertainty\nlevels are needed in order to have the bias on $r$ due to systematics below the\nlimit established by the LiteBIRD collaboration.\n