The 21cm global signal and 3D power spectrum from the dark ages

 Posts: 5
 Joined: November 01 2017
 Affiliation: Tel Aviv University
The 21cm global signal and 3D power spectrum from the dark ages
We have been using CAMB, and have several questions about getting from it the 21cm global signal and the 21cm power spectrum during the dark ages.
How do we get the 21cm global signal (i.e., mean 21cm brightness temperature) T_b as a function of redshift directly from CAMB? We can get it indirectly by running once with use_21cm_mK = True and once with use_21cm_mK = False, and taking the ratio of the monopole transfer functions in the two cases. Is there a better way?
The 21cm power spectrum: Our aim is to generate the (total) 21cm power spectrum P(k) and its angular decomposition terms P_mu^0, P_mu^2, and P_mu^4 using CAMB. We find the following possibly relevant parameters for 21cm. Please let us know if we missed anything. Other parameters are kept at their default values.
• WantCls – (False)
• Do21cm – (True)
• Evolve_baryon_cs – (boolean) Evolve a separate equation for the baryon sound speed rather than using background approximation
• Evolve_delta_xe – (boolean) Evolve ionization fraction perturbations
• Evolve_delta_Ts – (boolean) Evolve the spin temperature perturbation (for 21cm)
• line_phot_dipole – (boolean) Dipole sources for 21cm
• line_phot_quadrupole – (boolean) Quadrupole sources for 21cm
• line_basic – (boolean) Include main 21cm monopole density/spin temperature sources
• line_distortions – (boolean) Redshift distortions for 21cm
• line_extra – (boolean) Include other sources
We set Evolve_baryon_cs and Evolve_delta_xe to True, but we are not sure about Evolve_delta_Ts. We ran CAMB with Evolve_delta_Ts=False and with Evolve_delta_Ts=True. We found that the monopole transfer functions are the same for both cases. However, we found that the run time for Evolve_delta_Ts=True is 2 orders of magnitude higher than for the Evolve_delta_Ts=False case. Does this make sense?
We have a fundamental question: Does Transfer_monopole for the 21cm monopole transfer function give P_mu0 ~ (Transfer_monopole)^2, i.e., the 21cm power spectrum without the velocity effect? Is there a way to get from CAMB the total 21cm power spectrum including the velocity effect?
We also set line_basic to True, and varied line_phot_dipole, line_phot_quadrupole, line_distortions, and line_extra. But, we found that the monopole transfer function does not depend on these parameters. Are any of them relevant to us, or do they all have an insignificant effect?
Thanks for any help.
How do we get the 21cm global signal (i.e., mean 21cm brightness temperature) T_b as a function of redshift directly from CAMB? We can get it indirectly by running once with use_21cm_mK = True and once with use_21cm_mK = False, and taking the ratio of the monopole transfer functions in the two cases. Is there a better way?
The 21cm power spectrum: Our aim is to generate the (total) 21cm power spectrum P(k) and its angular decomposition terms P_mu^0, P_mu^2, and P_mu^4 using CAMB. We find the following possibly relevant parameters for 21cm. Please let us know if we missed anything. Other parameters are kept at their default values.
• WantCls – (False)
• Do21cm – (True)
• Evolve_baryon_cs – (boolean) Evolve a separate equation for the baryon sound speed rather than using background approximation
• Evolve_delta_xe – (boolean) Evolve ionization fraction perturbations
• Evolve_delta_Ts – (boolean) Evolve the spin temperature perturbation (for 21cm)
• line_phot_dipole – (boolean) Dipole sources for 21cm
• line_phot_quadrupole – (boolean) Quadrupole sources for 21cm
• line_basic – (boolean) Include main 21cm monopole density/spin temperature sources
• line_distortions – (boolean) Redshift distortions for 21cm
• line_extra – (boolean) Include other sources
We set Evolve_baryon_cs and Evolve_delta_xe to True, but we are not sure about Evolve_delta_Ts. We ran CAMB with Evolve_delta_Ts=False and with Evolve_delta_Ts=True. We found that the monopole transfer functions are the same for both cases. However, we found that the run time for Evolve_delta_Ts=True is 2 orders of magnitude higher than for the Evolve_delta_Ts=False case. Does this make sense?
We have a fundamental question: Does Transfer_monopole for the 21cm monopole transfer function give P_mu0 ~ (Transfer_monopole)^2, i.e., the 21cm power spectrum without the velocity effect? Is there a way to get from CAMB the total 21cm power spectrum including the velocity effect?
We also set line_basic to True, and varied line_phot_dipole, line_phot_quadrupole, line_distortions, and line_extra. But, we found that the monopole transfer function does not depend on these parameters. Are any of them relevant to us, or do they all have an insignificant effect?
Thanks for any help.

 Posts: 1943
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: The 21cm global signal and 3D power spectrum from the dark ages
I don't think there is a better way to get Tb, you're welcome to add a PR to add a python wrapper function to get Tspin, Tb etc for the 21cm case, e.g. following the pattern of get_background_time_evolution (GetBackgroundThermalEvolution in fortran), You can see where Tb is calculated from the recombination model outputs in equations.f90 (Tb = (1exp(tau_eps))*a*(TspinTrad)*1000).
When Evolve_delta_Ts is false, Delta T_s is calculated assuming Eq 32 of our paper, assuming equilibrium. If it is true, I think it evolves the full equation (perturbed version of Eq 28). But the approximation is very accurate (better than other approximations, like neglecting the velocitydependence of the spin temperature).
Not sure I understand which velocity effect: line_distortions parameter determines whether RSD are included in the total power.
When Evolve_delta_Ts is false, Delta T_s is calculated assuming Eq 32 of our paper, assuming equilibrium. If it is true, I think it evolves the full equation (perturbed version of Eq 28). But the approximation is very accurate (better than other approximations, like neglecting the velocitydependence of the spin temperature).
Not sure I understand which velocity effect: line_distortions parameter determines whether RSD are included in the total power.

 Posts: 5
 Joined: November 01 2017
 Affiliation: Tel Aviv University
Re: The 21cm global signal and 3D power spectrum from the dark ages
You wrote: "line_distortions parameter determines whether RSD are included in the total power."
How do we get the total 21cm power out of CAMB, and not just the monopole transfer function?
How do we get the total 21cm power out of CAMB, and not just the monopole transfer function?

 Posts: 1943
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: The 21cm global signal and 3D power spectrum from the dark ages
Code: Select all
transfer_21cm_cl=True

 Posts: 5
 Joined: November 01 2017
 Affiliation: Tel Aviv University
Re: The 21cm global signal and 3D power spectrum from the dark ages
Thank you for your response.
We have a (most probably) final question about the normalization of the 21cm monopole power spectrum. For example, we are doing the following at z=40
Is this the right way to get the dimensionless squared fluctuation from the transfer function?
We have a (most probably) final question about the normalization of the 21cm monopole power spectrum. For example, we are doing the following at z=40
Code: Select all
pars.set_matter_power(kmax=20, redshifts=[40.])
results = camb.get_results(pars)
trans = results.get_matter_transfer_data()
k = trans.transfer_data[0,:,0]*results.Params.h
primordial_PK = results.Params.scalar_power(k)
Transfer_monopole=4
mono = trans.transfer_data[Transfer_monopole1,:,0]
Pk21cm = primordial_PK*mono**2.*k**4.