The Metagalactic UV Background

In the previous examples, we saw examples of how to initialize stellar and BH populations, e.g., a stellar population:

import ares

pop = ares.populations.StellarPopulation(Tmin=1e4, fstar=0.1)

Such populations will give rise to global radiation backgrounds. In this example, we’ll focus on the UV background that arises from a stellar population.

The “sawtooth” UV Background

The background spectrum between the Lyman-\(\alpha\) line and the Lyman-limit exhibits a series of absorption features due to Lyman series absorption, first illustrated by Haiman et al. (1997).

# Initialize a radiation background
rad = ares.solvers.UniformBackground(pop=pop)

Note that we need not initialize a StellarPopulation object first – we can instead pass keyword arguments directly to the StellarPopulation class, e.g.:

params = \
{
 "source_type": 'star',
 "source_temperature": 3e4,
 "spectrum_type": 'bb',
 "spectrum_Emin": 1.,
 "spectrum_Emax": 13.6,
 "approx_lwb": False,        # this tells ares we'll need to solve the RTE
 "discrete_lwb": False,
 "norm_by": 'lw',
 "Nlw": 1e4,
}

rad = ares.solvers.UniformBackground(**params)

Then, to calculate the background flux:

import numpy as np

# Setup function to compute background intensity at redshift 30
flux = lambda EE: rad.AngleAveragedFlux(z=30, E=EE, energy_units=True)

# Focus on Lyman-Werner-ish band
E = np.linspace(8., 13.6, 500)  # energies in eV

# Compute background and plot it
pl.semilogy(E, map(flux, E))

# Make some nice axes labels
pl.xlabel(ares.util.labels['E'])
pl.ylabel(ares.util.labels['flux_E'])

The Lyman-Werner (and below) background at \(z=30\) that arises from a population of O stars. The dashed line shows the solution obtained if Lyman series absorption is neglected. See ares/tests/solvers/test_lwrb_generator.py for a more complete example.

The keyword argument energy_units converts the fluxes to units of \(\text{erg} \ \text{s}^{-1} \ \text{cm}^{-2} \ \text{Hz}^{-1} \ \text{sr}^{-1}\). By default, fluxes are returned in units of \(\text{s}^{-1} \ \text{cm}^{-2} \ \text{Hz}^{-1}\ \text{sr}^{-1}\).

The dashed line in the above figure shows the solution obtained neglecting Lyman series absorption. It can be obtained by enforcing an optically thin medium with the optional keyword argument tau:

flux = lambda EE: rad.AngleAveragedFlux(z=30, E=EE, energy_units=True, tau=0.0)

pl.semilogy(E, map(flux, E), ls='--')