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cl2map synthesizes CMB temperature maps from spherical harmonic coefficients $a_{{\ell}m}$.

\Delta T(\theta, \phi) = \sum_{{\ell}=2}^{\max}\sum^{{\ell}}_{m=-{\ell}} a_{{\ell}m}Y_{{\ell}m}(\theta,\phi)
\end{displaymath} (3)

Inversely, cl2map can decompose an input CMB temperature map into its spherical harmonic coefficients $a_{{\ell}m}$ and/or power spectrum:
C_{{\ell}}=\frac{1}{2{\ell}+1}\sum_{m=-{\ell}}^{{\ell}} \vert a_{{\ell}m}\vert^2.
\end{displaymath} (4)

D_{{\ell}}=\frac{ {\ell}({\ell}+1)C_{{\ell}}}{2 \pi T_0^2}.
\end{displaymath} (5)

where $T_0 = 2.726$ K. If necessary, dipole can be calculated and included.

To synthesize a map, cl2map can process an $a_{{\ell}m}$ file either in FITS Binary Extension-like or in ASCII format, or can process ASCII $a_{{\ell}m}$ strings.

If the input is a power spectrum $C_{{\ell}}$ or $D_{{\ell}}$, cl2map generates a Gaussian map of CMB anisotropies by assigning the $a_{{\ell}m}$ = COMPLEX($\Re$, $\Im$) mutually independent Gaussian-distributed real ($\Re$) and imaginary part ($\Im$), both with a standard deviation $\sqrt{C_{{\ell}}/2}$ at each ${\ell}$ harmonic.

To decompose an input map for its $a_{{\ell}m}$ coefficients, cl2map processes the FITS Binary map with position and temperature $T(\theta, \phi)$ with 3 sections:

  1. $x =\cos(\theta)$, the center-position of the rings as a function of the polar angle (nx positions),

  2. nx numbers with the number of pixels, nphi, in the corresponding ring,

  3. $T(\theta, \phi)$organized in one row using Point 1 as the major index and Point 2 as the minor index.


  1. Synthesizing a map from given spherical harmonic coefficients:

  2. Gaussian random map simulation from a given angular power spectrum:

  3. Map decomposition for its angular power spectrum and/or spherical harmonic coefficients:

next up previous
Next: cmap Up: GLESP Description and Examples Previous: alm2dl
Gauss Legendre Sky Pixelization