CosmoCoffee

I'm making simulated maps of the CMB with SZ effect.
I want to add Gaussian noise and convolve the image with a Gaussian
instrument beam.

The standard lore is that the effect of noise and beam
is to add a noise term with a simple power spectrum depending
on noise amplitude and beam FWHM.

Is this also true in the case with SZ contamination in the map?
In other words, will the noise covariance of my simulated maps,
after adding CMB and noise in each pixel then beam smearing,
be the same as the usual noise covariance?

Also, should I add noise to the pixels then beam smear, or the other way
round (or does it not matter)?

Maybe somebody who's done this before can let me know the secret.
Cheers.

Well, I think that the right procedure is: simulate prefect CMB, add SZ clusters, smear with beam (i.e. in simplest case just mulitplity by the smearging function in the alm space) and then finally add noise according to the noise mask (or constant for simplicity). I think the noise is independent from pixel to pixel, even if the map is oversampled (in which case, signal is highly correlated for two adjacent pixels). Would be interested to hear from people, who disagree.

Jamie Portsmouth wrote:Also, should I add noise to the pixels then beam smear, or the other way
round (or does it not matter)?

As Anze said, you have to first smear, then add noise. The noise is instrument specific, and not connected to the sky at all:

data = convolution(beam, sky) + noise

or, as you usually will see it, in a matrix form:

d = A * s + n

where A is the beam, s is the sky and n is noise.

I agree, I wd add noise after smearing (noise is at detector level, not sky).