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### 21-cm brightness temperature monopole from CAMB

Posted: October 22 2020
Greetings!

I was wondering if it is possible to obtain the monopole of the brightness temperature (as a function of redshift) from CAMB. I am using the Python wrapper for CAMB.

My own attempt:

I have instructed CAMB to compute 21-cm relevant observables with:

pars.Do21cm = True
pars.transfer_21cm_cl = True

Switching these on returns different transfer functions when I then
run get_matter_transfer_data() and get transfer functions out, so it is doing something.

I have found that the 4th transfer function that the command returns
is the "21 cm monopole source". It is indexed by redshift and
wavenumber. However, I have doubts that this is the right place to
be looking as I would not expect a monopole signal to need
information about the primordial power spectrum. I suppose this
transfer function is supposed to be multiplied by the power spectrum and then
integrated/summed.

### Re: 21-cm brightness temperature monopole from CAMB

Posted: October 23 2020
Looks right to me.

### Re: 21-cm brightness temperature monopole from CAMB

Posted: October 23 2020
Thank you, Antony!

To be sure:
- The documentation suggests that the transfer function $\Delta(k,z)$ comes out already divided by $k^2$.
- After multiplying by $k^2$ (in order to get the proper transfer function $\Delta(k,z)$) I then integrate the product of this transfer function (not its square) and the dimensionless primordial power spectrum $\mathcal P(k)$ such that the brightness temperature equals:
$T_b(z) = \int \mathrm{d}\log k \, \Delta(k,z) \mathcal P(k)$,
and it comes out in mK as long as I set pars.use_21cm_mK = True?

Please forgive the nonchalant-reckless handling of the quantities. I am completely new to 21-cm cosmology but more familiar with the CMB part of CAMB and wanted to try to out the 21 cm features of the code.

### Re: 21-cm brightness temperature monopole from CAMB

Posted: October 24 2020
Transfer functions should be squared for the power.