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alm2dl

Description

alm2dl reads $a_{{\ell}m}$ and calculates $C_{{\ell}}$ and $D_{{\ell}}$ where

\begin{displaymath}
C_{{\ell}}=\frac{1}{2{\ell}+1}\sum_{m=-{\ell}}^{{\ell}} \vert a_{{\ell}m}\vert^2.
\end{displaymath} (1)


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

where $T_0 = 2.726$K, $C_{{\ell}}$ is output in unit of $T^2$ and $D_{{\ell}}$ is unitless. alm2dl can read the input $a_{{\ell}m}$ file either in FITS or in ASCII formats. The FITS binary format should contain 3 fields: index= ${\ell}\times {\ell}+{\ell}+m+1$ (in HEALPix definition), $a_{{\ell}m}$ real part ($\Re$) and imaginary part ($\Im$). The ASCII format should contain 4 entries : L, M, Re, Im, where L is the ${\ell}$-multipole and M is the $m$-multipole. It can also read data from a single 3-$a_{{\ell}m}$ file ($a_{{\ell}m}$, $e_{{\ell}m}$ and $b_{{\ell}m}$) to calculate correlation spectra BB, EE, TE or TB between $a_{{\ell}m}$ and $e,b_{{\ell}m}$-coefficients. If the input file contains only $a_{{\ell}m}$-coefficients, to calculate TE or TB-spectra, a file with $e_{lm}$ or $b_{lm}$-coefficients should be added in the command string.

alm2dl calculates $a_{{\ell}m}$ amplitudes: $\vert a_{{\ell}m}\vert$ and phases defined as $\arctan(\Im/\Re)$ in $[0,2\pi]$.

alm2dl also lists the values of the FITS $a_{{\ell}m}$ coefficients, which can be output either to a file or to the standard output device for display.

Examples

  1. Calculating $C_{{\ell}}$ or $D_{{\ell}}$:

  2. Listing $a_{{\ell}m}$:

  3. Calculating amplitudes:

  4. Calculating phases:

  5. Calculating polarizatiom modes $B_{{\ell}m}$ and $E_{{\ell}m}$ :


next up previous
Next: cl2map Up: GLESP Description and Examples Previous: GLESP Description and Examples
Verkhodanov Oleg 2009-04-01