I have a routine that does this for the Tucci et al 2010 C2EX model, which is the model used by the ACT team for this purpose. I am happy to write it into the fgspectra library. It would be helpful for someone who is already working with this package to write a function prototype (i.e. just the definition line for the routine) so that it meshes with the rest of the software in the package,

Great, thanks. We are finalizing the API in these days. Once we are done, I'll prepare a prototype for you.
In the meanwhile people should feel free to provide further inputs.

Sounds great! Like I said in an earlier email, what I have boils down to maybe three or four lines of code, so the work will really be in just setting up the structure to put it into the right place.

Hi both, sorry for being late in responding. People are requesting the ability of predicting radio power given a specific flux cut. Alex you have code for it and in terms of interface with fgspectra this should simply predict the amplitude of the radio sources which would enter as one of the parameters of the full foreground model.

Hi, we have converged on the API (and also the internal structure). We can now prepare a template for this component. In order to do that, we need to know something about the model. In particular, it is important to understand if you can factorize the multipole dependence and the frequency dependence.
@ajvanengelen or someone else, can you give us some information in this respect?

Yes, these sources are just shot noise, so a flat Cl (ell(ell+1)/2piCl in Dl) and scale in frequency with a beta=-0.5 .

So the only variable is the Cl value as a function of the flux cut?

The variable is the amplitude of Cl at ell=3000 (which can be predicted for a given flux cut) but varies as free amplitude for the CMB likelihood. The frequency index can be fixed for now.

I don't know yet. We could think of implementing some automatic calculation going via flux cut but for now I'd keep it simple and give people the option of doing predictions but also varying an amplitude.

In this case we don't need any special tool. We just have to combine a power-law SED with a white cl. We only need the latter, I can take care of it.

Exactly, and that can then be used for dusty sources and radio sources separately.

Ok, so I think we should implement two separate models. One that takes the amplitude of the white spectrum as a free parameter and the another that takes the flux cut as free parameter. Right?
I can easily take care of the former and prepare the skeleton of the latter

Just to check, this should be a power-law in flux units, right? (c.f. Sec. 2.5, Eq. 13 of Dunkley et al 2013) It seems like the power-law implementation in fgspectra currently assumes a power-law in RJ temperature units.

Right, thanks for pointing this out. In this case it is just a redefinition of beta, but we should double check the units for components we recently added

Also ,
I have available radio sources number counts from 2 to 150 GHz , I've used them for Polarbear . can share with you guys if needed.

@giuspugl do you maybe have code for the power spectra that you could contribute here?

Isn't it what I have already implemented in #34 ?

Ah missed it, great!

Thank you Peppe. We should then proceed and merge PR #34
I had a look at your code, I think that before merging

• we should refactor a bit the code to make it coherent with the rest of the FGSpectra APIs -- I can assist you with that.
• Most important, we should double check that the code does what we need.
  • only radio point sources are considered (in particular, no dusty star forming galaxies)
  • the user should provide the flux cut for each of the frequencies to be evaluated
  • regardless of the flux cuts, the sources at different frequencies are assumed 100% correlated

Please @msyriac, and anybody else, confirm that this is OK (and @giuspugl confirm that I'm understanding your code correctly) -- a thumb up is enough. Thanks!

Yes the function estimate_autospectra does exactly that .

Not sure what you mean here by the sources at different frequencies are assumed 100% correlated.

I couldn't find an example or test in #34 to see how the API is meant to be used ; could you add one for the auto and cross?

@msyriac , as I mentioned before, the api should probably change, for coherence with the rest of the library.

@giuspugl , the power in a cross spectrum is the product of the sqrt of the power in the two autos. This is correct if the sources at the two frequencies are exactly the same and have all the same scaling with frequency

@dpole For time being the cross spectra implemented are related to the flux cuts and the observed SED of radio sources. In
https://github.com/giuspugl/fgspectra/blob/edc014a42047b02327a7ceaaf61cea8fbdad7c5c/fgspectra/frequency.py#L167, you can see the current implementation which essentially doesn't rely on the assumption of having the sources 100% correlated, i.e. cross spectrum != product of the sqrt of the power in the two autos. Of course we can discuss if this is a feature we want to include..