Next: polalm
Up: GLESP Description and Examples
Previous: ntot
Description
polmap synthesizes CMB temperature and polarization
maps from
spherical harmonic coefficients
and polarization mode coefficients
and
.
 |
(6) |
To synthesize a map,
polmap
can process an
file either in FITS Binary Extension-like or
in ASCII format, or can read
an ASCII string of
.
If the input is a power spectrum
or
(where the
ASCII
data have
to be in units of
, and
unitless),
polmap generates
a Gaussian map of CMB anisotropies by assigning
the
= COMPLEX(
,
) mutually independent Gaussian-distributed
real (
) and imaginary part (
), both with a standard
deviation
at each
harmonic.
To synthesize polarization maps of Stokes-parameters Q and U,
polmap
can process 3-alm file containing
,
and
data, separate
and
files and file either
in FITS Binary Extension-like or
in ASCII format, or can read
an ASCII strings of
and
.
Maps of the Stokes parameters
and
are calculated with the potentials
and
as follows:
 |
(7) |
and operators
and
are:
 |
(8) |
where
.
![\begin{displaymath}
S={1\over\sqrt{2\pi}}\sum_{l=2}^{l_{max}}\left(s_{l0}
f^0_l(...
...(x)[s_{lm}^c\cos(m\varphi)-
s_{lm}^s\sin(m\varphi)]\right) ,
\end{displaymath}](img56.png) |
(9) |
![\begin{displaymath}
P={1\over\sqrt{2\pi}}\sum_{l=2}^{l_{max}}\left(
f^0_l(x)+2\s...
...(x)[p_{lm}^c\cos(m\varphi)-
p_{lm}^s\sin(m\varphi)]\right) ,
\end{displaymath}](img57.png) |
(10) |
 |
(11) |
Here
and
are the associated Legendre
functions (ordinary and normalized) and
and
(of B and E-modes) are the coefficients of decomposition
characterizing properties of polarization.
See other details in the correpsnoding paper of GLESP 2.0.
Examples
- Synthesizing an anisotropy map from given spherical harmonic
coefficients (-a, -as)
-
polmap -a alm.fits -t map.fits -nx 250 -np 500 -lmax 100
synthesizes the map from input FITS file 'alm.fits' and writes to the
file '
map.fits' with resolution (250,500). The maximum multipole
number
is 100.
-
polmap -as "2,1,1,0" -t map.y21.fits -nx 100 -np 200 -lmax 4
synthesizes a map from the
string '"2,1,1,0"' (
)
and writes to the
file '
map.y21.fits'.
The resolution of the map is (100,200).
The maximum multipole number
is 4.
-
polmap -a alm.txt -L 1 -t map.dipole.fits -nx 50 -np 100
synthesizes the dipole map from the input ASCII file '
alm.txt' and
writes to the file '
map.dipole.fits'.
The resolution of this dipole
map is (50, 100).
- Gaussian random map simulation from a given angular
power spectrum (-Dl, -Cl):
- Synthesizing maps of Q and U Stokes parameters
unisg given scalar and pseudosacalar harmonic
coefficients (E and B-modes)
Next: polalm
Up: GLESP Description and Examples
Previous: ntot
Verkhodanov Oleg
2009-04-01