

Relation with IAU conventionIn a cartesian referential with axes x and y, the Stokes parameters for linear polarisation are defined such that +Q is aligned with +x, Q with +y and +U with the bisectrix of +x and +y. Although this definition is universally accepted, some confusion may still arise from the relation of this local cartesian system to the global spherical one, as described below [Hamaker & Leahy, 2003], and as illustrated in Fig. 5.
The polarization conventions defined by the International Astronomical Union [IAU, 1974] are summarized in [Hamaker & Bregman, 1996]. They define at each point on the celestial sphere a cartesian referential with the x and y axes pointing respectively toward the North and East, and the z axis along the line of sight pointing toward the observer (ie, inwards) for a righthanded system. On the other hand, following the mathematical and CMB litterature tradition, HEALPix defines a cartesian referential with the x and y axes pointing respectively toward the South and East, and the z axis along the line of sight pointing away from the observer (ie, outwards) for a righthanded system. The Planck CMB mission follows the same convention [Ansari et al, 2003]. The consequence of this definition discrepency is a change of sign of U, which, if not accounted for, jeopardizes the calculation of the Electric and Magnetic CMB polarisation power spectra.
How HEALPix deals with these discrepancies
The change_polcconv IDL facility is provided to add this keyword or change/update its value and swap the sign of the U Stokes parameter, when applicable, in an existing FITS file. The facility anafast will crash if the map to analyze follows the 'IAU' convention, and issue a warning if the convention used can not be determined. Eric Hivon 20100618 



