Source & Spectrum Parameters

Below, we list the parameters that govern the bolometric luminosity of sources as well as their spectral energy distribution. These parameters are relevant to point sources (via the source_* parameters), as well as populations of sources used in global 21-cm signal and/or meta-galactic radiation background calculations (simply replace source_ with pop_).

Source Luminosity

source_type

Options:

  • star: characterized by its temperature, source_temperature, and ionizing photon luminosity, source_qdot

  • bh: characterized by its mass, source_mass etc.

  • toy: completely parameterized

source_temperature

If source_type is star, this is its surface temperature. [Kelvin]

Default: \(10^5 \ \text{K}\)

source_mass

If source_type is bh, this is its mass [\(M_{\odot}\)]

Default: \(10 \ M_{\odot}\)

source_qdot

For toy radiation source, this is the ionizing photon luminosity. [\(\text{s}^{-1}\)]

Default: \(5 \times 10^{48}\ \text{s}^{-1}\)

source_lifetime

Time after which radiation from this source will no longer be considered.

Default: \(10^{10}\) [time_units]

The Source Spectrum

We’ll use \(I_E\) to denote to the SED of sources, which the user supplies via the parameter source_sed or pop_sed. It is proportional to the energy emitted at energy \(E\), NOT the number of photons emitted at energy \(E\), and is normalized (automatically by ARES) such that

\[\int_{\text{source_EminNorm}}^{\text{source_EminNorm}} \text{source_sed} dE = L_{\text{source_EminNorm}-\text{source_EminNorm}}\]

where the luminosity on the right-hand side is that determined by one of the parameters above (e.g., the Eddington luminosity of a source_mass \(M_{\odot}\) BH) or for source populations via the pop_rad_yield parameter. This auto-normalization guarantees the radiative yield of a single source (or source population) at some photon energy is equal to its bolometric luminosity times \(I_E\).

We use square brackets on this page to denote the units of parameters.

source_sed

Options:

  • 'bb': blackbody

  • 'pl': power-law

  • 'mcd'; Multi-color disk (Mitsuda et al. 1984)

  • 'simpl': SIMPL Comptonization model (Steiner et al. 2009)

  • 'qso': Quasar template spectrum (Sazonov et al. 2004)

source_Emin

Minimum photon energy to consider in radiative transfer calculation.

Default: 200 [eV]

source_Emax

Maximum photon energy to consider in radiative transfer calculation.

Default: 3e4 [eV]

source_EminNorm

Minimum photon energy to consider in normalization.

Default: 200 [eV]

source_EmaxNorm

Maximum photon energy to consider in normalization.

Default: 3e4 [eV]

source_alpha

Power-law index of emission. Only used if source_type is pl or simpl. Defined such that \(I_{\nu} \propto \nu^{\alpha}\).

Default: -1.5

Recall that \(I_{\nu}\) is proportional to the energy, not the number of photons, emitted at frequency \(\nu\).

source_logN

Base-10 logarithm of the neutral absorbing column in units of \(\text{cm}^{-2}\).

Default: \(-\infty\)

source_hardening

For non-zero absorbing columns, this parameter determines whether or not the column is applied before or after normalizing the source’s luminosity.

Default: extrinsic

source_Rmax

If source_type is ‘mcd’, this parameter sets the maximum size of the accretion disk being considered.

Default: 1000 [gravitational radii, \(R_g = G M_{\bullet} / c^2\), where \(M_{\bullet}\) is the black hole mass]