Aseyhe t1_j2kty6j wrote on January 2, 2023 at 1:53 AM

Reply to comment by amaurea in Is any "movement" visible in the fluctuations of the CMB over time, or does it appear static? by JarasM

I just lazily took pi/l for l=2500, the largest l that Planck papers plot. Indeed, the ground-based telescopes push to somewhat higher l.

Hmm, around 1 degree (where the fluctuation power peaks), the time scale for the CMB to change would be of order a billion years, or one part in ~10^(9) per year. I wonder how far off that kind of sensitivity is.

amaurea t1_j2kuo6l wrote on January 2, 2023 at 1:59 AM

Yes, they typically plot out to l=10000, but all the power out there comes from point sources (if one doesn't clean those away). I used 360°/l, but if I use 180°/l the ACT foreground cleaned spectrum becomes too faint to be detectable at 2.9 arcmin.

amaurea t1_j2m8d9y wrote on January 2, 2023 at 10:33 AM

(Actually, come to think of it, shouldn't the formula be sqrt(4pi)/(lmax+1)? Alms from 0 to lmax have (lmax+1)² degrees of freedom (sum_0^lmax (2l+1)). This is enough information to split the full sky into (lmax+1)² pixels, which would then have a side length of sqrt(4pi)/(lmax+1). This works out to 1.13*pi/l, so very close to your formula and far from the 2pi/l I had been using.)