Relationship between nside and CAMB lmax

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
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Evan B
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Joined: February 27 2015
Affiliation: student

Relationship between nside and CAMB lmax

Post by Evan B » December 12 2015

For full-sky map WMAP/Planck products, 'nside' is set to nside=1024 or nside=2048. I have no problem running CAMB outputs up to lmax=2400 or so.

However, I am confused what this means when we degrade the resolution of these maps.

Let's say I degrade a map of nside=2048 (which is a map of around 50e6 pixels) to nside=16 (which is a map of 3072 total pixels). What is the maximum `lmax` at which CAMB outputs remain relevant?

Is there a rule of thumb, or a mathematical correlation here?

Antony Lewis
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Re: Relationship between nside and CAMB lmax

Post by Antony Lewis » December 12 2015

The Healpix rule of thumb (default) is lmax = 3*nside-1.

Evan B
Posts: 13
Joined: February 27 2015
Affiliation: student

Relationship between nside and CAMB lmax

Post by Evan B » December 13 2015

Thanks.

So, when I degrade the map's resolution, there must be significant cosmological information which is lost.

My concrete example in mind is for cosmological parameters. If I am using a sky map nside=16, and lmax=47, can I say anything about cosmological parameters?

Take WMAP, three-year results for polarization. In Appendix D, the full sky maps at set to nside=16, nside=8 to determine \tau. So they used CAMB outputs up to lmax=47, lmax=23? That's very little information.

Can one use the same method to determine cosmological parameters like \Omega_matter? Wouldn't you need CAMB scalar TT C_ell outputs up to lmax=1500 or so?

Another concrete example I run into:
What if I am working with a heavily masked sky map, and I only access 1/4 of the sky map.

How can I think about lmax in this situation? The pixels are at a fairly high-resolution (say, nside=512, total pixels around 3e6). However, I'm only accessing less than 1e6 pixels.

There's some relationship

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