Parameterized Models for Sources and Their Spectra

If you want to use ares‘s numerical solvers, but don’t care for the available slew of input options (e.g., spectra, luminosity functions, etc.), you can pass in functions of your own.

There are a few magical override parameters to help you with this:

• pop_spectrum: a Python function of a single variable (photon energy)
• pop_rhoL: a Python function of a single variable (redshift)

You can either supply Python functions for these parameters yourself, or use results from the literature. We’ll demonstrate each approach below.

As always, start with a few imports:

import ares
import numpy as np
import matplotlib.pyplot as pl

User-Defined Models

Create Python functions.

Using Constraints from the Literature

Some SED and luminosity density models will definitely be used over and over again. This motivated the creation of the litdata'' module, which you can use on its own as a convenient way of reading in models from the literature (see :doc:`uth_litdata`) or through more sophisticated calculations, e.g., :doc:`example_crb_uv`. If one of your user-defined models is common in the literature, consider forking *ares* and adding it to the database! See :doc:`uth_litdata` for instructions on how to do that, or simply emulate pre-existing modules in ``$ARES/input/litdata.

For example, to use the template quasar spectrum from Sazonov et al. (2004) and the luminosity density evolution of Ueda et al. (2003), you would modify the parameters from the The Metagalactic UV Background example as follows:

pars = \
{
 'pop_type': 'galaxy',
 'pop_sed': 'sazonov2004',            # NEW
 'pop_rhoL': 'ueda2003',              # NEW
 'pop_kwargs': {'evolution': 'ple'},  # NEW

 'pop_Emin': 1.0,
 'pop_Emax': 5e4,
 'pop_EminNorm': 2e3,
 'pop_EmaxNorm': 1e4,

 # Solution method
 'pop_solve_rte': True,
 'pop_tau_Nz': 100,
 'include_H_Lya': False,

 'sawtooth_nmax': 8,

 'initial_redshift': 6,
 'final_redshift': 3,
}

Notice the aforementioned pop_sed and pop_rhoL parameters, in addition to pop_kwargs, which we have yet to mention. The contents of pop_kwargs will be passed to all functions in associated with the pop_rhoL module, since there are many options to be specified, e.g.:

• Evolution in the luminosity function, in this case, a ‘’pure luminosity evolution’’ ('ple') model. The other options from Ueda et al. (2003) include pure density evolution ('pde') and luminosity-dependent density evolution ('ldde').

Now, initialize a simulation instance and run it in the usual way:

rad = ares.simulations.MetaGalacticBackground(pop_sawtooth=True,
    approx_tau=None, **pars)

# Compute background flux
rad.run()

Instead of extracting fluxes using rad.get_history, as in the The Metagalactic Lyman-Werner Background and The Metagalactic UV Background examples, we’ll use some built-in analysis routines to plot the background intensity at \(z=3\):

anl = ares.analysis.MetaGalacticBackground(rad)
ax = anl.PlotBackground(z=3, color='b')

For a sanity check, let’s use yet another litdata submodule, containing the meta-galactic background as computed in Haardt & Madau (2012) (their ‘’galaxies+quasars’’ model):

hm12 = ares.util.read_lit('haardt2012')
z, E, flux = hm12.MetaGalacticBackground()

# Find element closest to z=3
j = np.argmin(np.abs(z - 3.))

# Plot it on pre-existing axes!
ax.plot(E, flux[j] / 1e-21, color='c')

ax.set_xlim(1, 4e3)
pl.draw()

This is not even close to an apples-to-apples comparison, but let’s worry about that more later.