|
In 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.
Figure 5:
Coordinate conventions for HEALPix (lhs panels) and IAU (rhs panels). The
upper panels illustrate how the spherical coordinates are measured, and the
lower panel how the Q and U Stokes parameters are identified in the
tangential plan.
|
|
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
right-handed 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 right-handed
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 FITS keyword POLCCONV has been introduced in HEALPix 2.0 to describe the
polarisation coordinate convention applied to the data contained in the file. Its value is either COSMO for files following the Healpix/CMB/Planck convention (default
for sky map synthetized with Healpix routine synfast) or IAU for those
following the IAU convention, as defined above. Absence of this keyword is
interpreted as meaning COSMO.
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
2010-06-18
|
|
