Absolute calibration of the polarisation angle for future CMB B-mode experiments from current and future measurements of the Crab nebula

A tremendous international effort is currently dedicated to observing the so-called primordial B modes of the Cosmic Microwave Background (CMB) polarisation. If measured, this faint signal imprinted by the primordial gravitational wave background, would be an evidence of the inflation epoch and quantify its energy scale, providing a rigorous test of fundamental physics far beyond the reach of accelerators. At the unprecedented sensitivity level that the new generation of CMB experiments aims to reach, every uncontrolled instrumental systematic effect will potentially result in an analysis bias that is larger than the much sought-after CMB B-mode signal. The absolute calibration of the polarisation angle is particularly important in this sense, as any associated error will end up in a leakage from the much larger E modes into B modes. The Crab nebula (Tau A), with its bright microwave synchrotron emission, is one of the few objects in the sky that can be used as absolute polarisation calibrators. In this communication, we review the best current constraints on its polarisation angle from 23 to 353 GHz, at typical angular scales for CMB observations, from WMAP, IRAM XPOL, Planck and NIKA data. We will show that these polarisation angle measurements are compatible with a constant angle and we will present a study of the uncertainty on this mean angle, making different considerations on how to combine the individual measurement errors. For each of the cases, the potential impact on the CMB B-mode spectrum will be explored.