Healpix question

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Filipe B. Abdalla
Posts: 2
Joined: April 06 2007
Affiliation: UCL

Healpix question

Post by Filipe B. Abdalla » April 06 2007

I am using the c++ version of Healpix and was a bit confused about the definitions of the a_{lm} returned by the function map2alm.

I am using this in the context of galaxy surveys by the way, in this context the a_{lm} are defined by \sum_{gal} Y_{lm}*(\theta,\phi)

when I input a density map in the map2alm function the returned value of the alm is proportional to the sum above with a constant which I cannot work out what it is
and which depends on the number of pixels I use to make the map.

when I input a galaxy overdensity map in the map2alm function I get exactly the sum above divided by the number of galaxies per steradians which is exactly what I would expect.

I was wandering is someone could give me a more precise explanation of what exactly this function is doing and what the definition of the a_{lm} returned is, both in the case I input a density map and an overdensity map, or if they could point me out to where I could find the answer. I couldn't find a precise def on the help page.

Cheers... Fil...

Tommy Anderberg
Posts: 47
Joined: November 24 2005
Affiliation: independent

Re: Healpix question

Post by Tommy Anderberg » April 06 2007

Filipe B. Abdalla wrote:when I input a density map in the map2alm function the returned value of the alm is proportional to the sum above with a constant which I cannot work out what it is
This is probably an immensely stupid question, but since I'm busy procrastinating anyway: have you looked at the source? File alm_map_tools.cc in Healpix_cxx (I'm looking at version 2.01, since that's what I have handy), template<typename T> void map2alm; this line looks interesting:

double normfact = pi/(3*nside*nside);

Ben Gold
Posts: 81
Joined: September 25 2004
Affiliation: University of Minnesota
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Healpix question

Post by Ben Gold » April 06 2007

As previously hinted at, the normalization is [tex]4 \pi / N_{pix}[/tex], where [tex]N_{pix} = 12 N_{side}^2[/tex]. This is documented in the HEALPIX primer:

http://healpix.jpl.nasa.gov/html/intronode6.htm

Filipe B. Abdalla
Posts: 2
Joined: April 06 2007
Affiliation: UCL

Healpix question

Post by Filipe B. Abdalla » April 10 2007

Thanks for the reply, I am still confused as to why I seem to need the normaliastion when I use a density map but I do get the correct answer (compared to a brute force sum over the Y_{lm}) without the normalisation when I use an overdensity map (hope I am not doing something wrong at the moment but it seems to agree with the brute force check...).
Looking at the source I could not work out imediatelly... I am sure I am still missing a detail...

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