1 Introduction

21cmFAST is used to produce different ionization histories. CLASS is then used to produce their temperature and polarization angular power spectra and compare the results. The correctness of the result is however uncertain due to 21cmFAST being undocumented and strange behavior encountered from it, together with the fact that the glue to CLASS is less than perfect.

The code used in this report, including the generation and hosting of this document, is available on GitHub here. The data generated in this study is available on GitHub Releases here.

The canonical viewing format of this document is in HTML because of the use of interactive plots. PDF version is also provided, albeit the plot won’t work there. Links to HTML version of Jupyter notebooks used in the study are included in this report for further reference.

1.1 Understanding CLASS

To ensure CLASS is setup correctly, COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt available from Planck Legacy Archive (Collaboration et al. 2018) is compared. In order to reproduce this result, these files available from CLASS on GitHub (Blas et al. 2011) are used:

• base_2018_plikHM_TTTEEE_lowl_lowE_lensing.ini
• cl_ref.pre

together with setting format = camb.

The Python interface classy is also used to compare class results. Without the format = camb option, they provides identical results. However, with format = camb, classy’s output is not changed, which may be due to a bug in the classy module when parsing the setting. Matching results from with and without format = camb setting, by manually rescaling \(C_l\) to \(D_l\) is not successful due to unknown reason.

Therefore, in this study class is used directly with parameters modified from base_2018_plikHM_TTTEEE_lowl_lowE_lensing.ini with format = camb. cl_ref.pre is not used to sacrifice precision for manageable compute time.

See more from these notebooks:

• class_check.ipynb: used to understand CLASS and reproduce COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt

• class_vs_classy.ipynb: comparing class and classy to make sure they provides identical results.

1.2 Understanding 21cmFAST

21cmFAST is hard to understand, due to the lack of documentations but comments lying within the code base. After running programs listed under Programs/PROGRAM_LIST from 21cmFAST on GitHub (Park et al. 2018), where one program described there is not even available, drive_logZscroll_Ts should be the one to use. For our purpose, since we are interested in the ionization histories, \(x_e\) should be extracted from a file named similar to Output_files/Ts_outs/global_evolution_Nsteps40_zprimestepfactor1.020_L_X3.2e+40_alphaX1.0_f_star100.0500_alpha_star0.5000_f_esc100.0100_alpha_esc-0.5000_Mturn5.0e+08_t_star0.5000_Pop2_200_300Mpc.

The default \(z\) range in the code is from \(6\)–\(30\). drive_logZscroll_Ts.c could be modified to change this, but when the \(z\)-range is changed to \(1\)–\(30\) instead, the output does not make sense. For example, \(x_e\) would continue to rise as \(z\) is decreasing below \(6\), but then drops again. Also, a bunch of other parameters eventually becomes nan as \(z\) gets lower than \(6\). For these reasons the \(z\) range is kept at there default \(6\)–\(30\).

Lastly, to match the cosmological parameters between those used in 21cmFAST and CLASS, 21cmFAST’s header files is modified in a fork of 21cmFAST in this commit to match those defined in base_2018_plikHM_TTTEEE_lowl_lowE_lensing.ini.

See more from these notebooks:

• 21cmfast_understand_output.ipynb: used to understand the output from 21cmFAST

1.3 21cmFAST to CLASS

In CLASS, explanatory.ini and doc/manual/CLASS_MANUAL.pdf documents everything. To inject \(x_e\) from that obtained in 21cmFAST, reio_parametrization should be set to either reio_bins_tanh or reio_inter. reio_bins_tanh is to interpolate using \(\tanh\), while reio_inter linearly.

reio_bins_tanh should in principle be better, however with 76 \(x_e\) values from 21cmFAST’s output, it needs too much memory than available, and after binning to only a few bins, the interpolated \(x_e\) in CLASS is too step-wise to reproduce the input \(x_e\).

reio_inter is not without its problem. From explanatory.ini, a few \(z, x_e\) values are needed to be specified at the boundary of this region. At the left boundary, e.g. if one set \(z = 6\) to \(x_e = -1\), it would interpolate \(x_e\) to 1 linearly between \(z\) steps.

It seems a better approach would be to interpolate linearly within \(z = 6\)–\(30\), and interpolate with \(\tanh\) on the left boundary. But the code provide no such option. In the end, reio_inter is used to interpolate linearly, and setting \(x_e = -2, -1, 0\) at \(z = 0, 6, 30\) according to the documentation, where the \(z = 6\) location is chosen somewhat arbitrarily to coincide with the left boundary of the input such that it would be equivalent to ionized almost instantaneously at \(z = 6\).

Although the resulting spectra from this input does not agree with COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt mentioned in Understanding CLASS, the hope is that the differences between \(x_e\) from \(z = 6\)–\(30\) can be represented in the differences in the final spectra output from CLASS, although we have no ways to verify that in this report.

See more from these notebooks:

• class_custom_x_e.ipynb: preliminary check on the CLASS \(x_e\) using output from 21cmFAST

• classy_trials.ipynb: check \(x_e\) from classy

2 Parameters

Parameters from 21cmFAST is left as default except for those cosmological parameters update mentioned above. CLASS’ parameters from base_2018_plikHM_TTTEEE_lowl_lowE_lensing.ini is used, with the injection of \(x_e\) from 21cmFAST output. In addition, the first 7 parameters¹ from Table 1 (Park et al. 2018, p. 5) are varied, defined as these constants in ANAL_PARAMS.H and HEAT_PARAMS.H:

• STELLAR_BARYON_FRAC
• STELLAR_BARYON_PL
• ESC_FRAC
• ESC_PL
• M_TURNOVER
• t_STAR
• L_X

All these parameters are varied once at each boundary of “Allowed range” defined in Table 1 (Park et al. 2018, p. 5) to get a sense of the possible differences in these ranges. Hence there’s 15 combinations—1 for default; 2 each per parameters, 1 for each boundary of the allowed range.

3 Logistics

In order to reproduce the result of this code, these repositories at respective tag/commit should be used:

• 21cmFAST at commit e81caff (Park et al. 2018)
• CLASS at v2.7.2 (Blas et al. 2011)

3.1 Workflow

Note that the parameters in 21cmFAST are compile time constants, therefore a script to generate header files is used and a recursive makefile is used to compile all the programs first. In addition, modified NUMCORES and RAM in INIT_PARAMS.H to match that of the machine used.

1. within the 21cmFAST directory, created a sub-directory Parameter_spaces, within which

   • notebook/21cmfast_param_gen.ipynb: generates 21cmFAST parameters by writing header files per parameter set,

   • bin/symlink.sh: symlink the rest of code needed to be compiled,

   • bin/makefile: make compile -j to compile drive_logZscroll_Ts per parameter set.

2. bin/makefile: make 21cmfast to run all programs².

3. 21cmfast_get_many_params.ipynb: parses 21cmFAST data and write .ini files for class

4. bin/makefile: make class to generate final spectra³.

5. class_collect_param.ipynb: collect spectra from CLASS

4 results

Note that in 2 set of parameters, 1 of them got non-sensical result from 21cmFAST, and another one request north of 192 GiB memory in class. Therefore the results below contains only 13 sets of parameters.

\(x_e\) as the parameters varies:

Below are the plots per spectrum, with slider across all parameters above. Except for the one labeled, the other parameters are left at the defaults.

From the plots, these spectra, except perhaps dT, are not sensitive to these changes.

It is inconclusive however if the spectra actually is not sensitive to the changes of the parameters, or if the included \(z\)-range of \(6\)–\(30\) is not enough to capture the differences, due to the technical problems encountered mentioned above in 21cmFAST to CLASS.

References