Simple Physical Models for the Global 21-cm Signal

To begin, first import ares:

import ares

To generate a model of the global 21-cm signal, we need to use the ares.simulations.Global21cm class. With no arguments, default parameter values will be used:

sim = ares.simulations.Global21cm()

See the Parameter Listing page for a listing of parameters that can be passed to ares.simulations.Global21cm as keyword arguments.

Since a lot can happen before we actually start solving for the evolution of IGM properties (e.g., initializing radiation sources, tabulating the collapsed fraction evolution and constructing splines for interpolation, tabulating the optical depth, etc.), initialization and execution of calculations are separate. To run the simulation, we do:

sim.run()

The main results are stored in the attribute sim.history, which is a dictionary containing the evolution of many quantities with time (see Field Listing for more information on what’s available). To look at the results, you can access these quantities directly:

import matplotlib.pyplot as pl

pl.plot(sim.history['z'], sim.history['dTb'])

Or, you can access convenience routines within the analysis class, which is inherited by the ares.simulations.Global21cm class:

sim.GlobalSignature(fig=2)
https://www.dropbox.com/s/gkbc0e15namryh3/ares_gs_default.png?raw=1

One possible realization for the global 21-cm signal. You should get something that looks like this, but may not be exactly the same depending on what version of ARES you’re using.

If you’d like to save the results to disk, do something like:

sim.save('test_21cm', clobber=True)
pl.savefig('ares_gs_default.png')

which saves the contents of sim.history at all time snapshots to the file test_21cm.history.pkl and the parameters used in the model in test_21cm.parameters.pkl.

Note

The default format for output files is pkl, though ASCII (e.g., .txt or .dat), .npz, and .hdf5 are also supported. Use the optional keyword argument suffix.

To read results from disk, you can supply a filename prefix to ares.analysis.Global21cm rather than a ares.simulations.Global21cm instance if you’d like, e.g.,

anl = ares.analysis.Global21cm('test_21cm')

See analysis for more information about readily available analysis routines.

DIY Parameter Study

To do simple parameter study, you could do something like:

ax = None
for i, fX in enumerate([0.1, 1.]):
    for j, fstar in enumerate([0.1, 0.5]):
        sim = ares.simulations.Global21cm(fX=fX, fstar=fstar)
        sim.run()

        # Plot the global signal
        ax, zax = sim.GlobalSignature(ax=ax, fig=3, z_ax=i==j==0,
            label=r'$f_X=%.2g, f_{\ast}=%.2g$' % (fX, fstar))


ax.legend(loc='lower right', fontsize=14)
pl.savefig('ares_gs_diy_param_study.png')
https://www.dropbox.com/s/m0no9b8ynvhc18y/ares_gs_diy_param_study.png?raw=1

Four realizations of the global 21-cm signal, varying the normalization of the \(L_X\)-SFR relation and the star formation efficiency.

These parameters, along with Tmin, Nlw, and Nion round out the simplest parameterization of the signal (that I’m aware of) that’s tied to cosmology/galaxy formation in any way. It’s of course highly simplified, in that it treats galaxies in a very average sense. For more sophisticated models, check out More Realistic Galaxy Populations.

Check out Population Parameters for a listing of the most common parameters that govern the properties of source populations, and Simple Parameter Study: 2-D Model Grid for examples of how to run and analyze large grids of models more easily. The key advantage of using the built-in model grid runner is having ARES automatically store any information from each calculation that you deem desirable, and store it in a format amenable to the built-in analysis routines.

A Note About Backward Compatibility

The models shown in this section are no longer the “best” models in ARES, though they may suffice depending on your interests. As alluded to at the end of the previous section, the chief shortcoming of these models is that their parameters are essentially averages over the entire galaxy population, when in reality galaxy properties are known to vary with mass and many other properties.

This was the motivation behind our paper in 2017, in which we generalized the star formation efficiency to be a function of halo mass and time, and moved to using stellar population synthesis spectra to determine the UV emissivity of galaxies, rather than choosing \(N_{\mathrm{LW}}\), \(N_{\mathrm{ion}}\), etc. by hand (see More Realistic Galaxy Populations). These updates led to a new parameter-naming convention in which all population-specific parameters were given a pop_ prefix. So, in place of Nlw, Nion, fX, now one should set pop_rad_yield in a particular band (set by pop_Emin and pop_Emax). See Population Parameters for more information about that.

Currently, in order to ensure backward compatibility at some level, ARES will automatically recognize the parameters used above and change them to pop_rad_yield etc. following the new convention. This means that there are three different values of pop_rad_yield: one for the soft UV (non-ionizing) photons (related to Nlw), one for the Lyman continuum photons (related to Nion), and one for X-rays (related to fX). This division was put in place because these three wavelength regimes affect the 21-cm background in different ways.

In order to differentiate sources of radiation in different bands, we now must add a population identification number to pop_* parameters. Right now, fX, Nion, Nlw, Tmin, and fstar will automatically be updated in the following way:

  • The value of Nlw is assigned to pop_rad_yield{0}, and pop_Emin{0} and pop_Emax{0} are set to 10.2 and 13.6, respectively.
  • The value of fX is multiplied by cX (generally \(2.6 \times 10^{39} \ \mathrm{erg} \ \mathrm{s}^{-1} \ (M_{\odot} \ \mathrm{yr}^{-1})^{-1})\) and assigned to pop_rad_yield{1}, and pop_Emin{0} and pop_Emax{0} are set to 200 and 30000, respectively.
  • The value of Nion is assigned to pop_rad_yield{2}, and pop_Emin{0} and pop_Emax{0} are set to 13.6 and 24.6, respectively.
  • pop_Tmin{0}, pop_Tmin{1}, and pop_Tmin{2} are all set to the value of Tmin. Likewise for fstar.

Unfortunately not all parameters will be automatically converted in this way. If you get an error message about an “orphan parameter,” this means you have supplied a pop_ parameter without an ID number, and so ARES doesn’t know which population is meant to respond to your change. This is an easy mistake to make, especially when working with parameters like Nlw, Nion etc., because ARES is automatically converting them to pop_* parameters.