GauntFactor#

class fiasco.GauntFactor(hdf5_dbase_root=None, **kwargs)[source]#

Bases: object

Class for calculating the Gaunt factor for various continuum processes.

The Gaunt factor is defined as the ratio of the true cross-section to the semi-classical Kramers cross-section, and thus is essentially a multiplicative correction for quantum mechanical effects. It is a unitless quantity.

Parameters:

  • hdf5_dbase_root (path-like, optional) – Path to built database

  • kwargs – All keyword arguments to fiasco.util.check_database are also supported here

Methods Summary

free_bound(E_scaled, n, l)

The Gaunt factor for free-bound emission as a function of scaled energy.

free_bound_integrated(temperature, ...[, ...])

The wavelength-integrated Gaunt factor for free-bound emission as a function of temperature.

free_free(temperature, wavelength, ...)

The Gaunt factor for free-free emission as a function of temperature and wavelength.

free_free_integrated(temperature, charge_state)

The wavelength-integrated Gaunt factor for free-free emission as a function of temperature.

Methods Documentation

free_bound(E_scaled, n, l)[source]#

The Gaunt factor for free-bound emission as a function of scaled energy.

The empirical fits are taken from Table 1 of Karzas and Latter [KL61]. In CHIANTI, this is used to compute the cross-sections in the free-bound continuum.

Parameters:

  • E_scaled (float) – Rratio of photon energy to the ionization energy.

  • n (int) – The principal quantum number

  • l (int) – The azimuthal quantum number

See also

fiasco.Ion.free_bound

free_bound_integrated(temperature: Unit('K'), atomic_number, charge_state, n_0, ionization_potential: Unit('eV'), ground_state=True)[source]#

The wavelength-integrated Gaunt factor for free-bound emission as a function of temperature.

The wavelength-integrated free-bound Gaunt factor is calculated using the approach of Mewe et al. [MLvandOord86]. The Gaunt factor is not calculated for individual levels, except that the ground state has been specified to be \(g_{fb}(n_{0}) = 0.9\) following Mewe et al. [MLvandOord86]. For more details on this calculation, see The implementation of the total free-bound Gaunt factor in fiasco.

Parameters:

  • temperature (Quantity) – The temperature(s) for which to calculate the Gaunt factor

  • atomic_number (int) – The atomic number of the element

  • charge_state (int) – The charge state of the ion

  • n_0 (int) – The principal quantum number n of the ground state of the recombined ion

  • ionization_potential (Quantity) – The ionization potential of the recombined ion

  • ground_state (bool, optional) – If True (default), calculate the Gaunt factor for recombination onto the ground state \(n = 0\). Otherwise, calculate for recombination onto higher levels with \(n > 1\). See Equation 16 of Mewe et al. [MLvandOord86].

See also

fiasco.Ion.free_bound_radiative_loss

free_free(temperature: Unit('K'), wavelength: Unit('Angstrom'), atomic_number, charge_state)[source]#

The Gaunt factor for free-free emission as a function of temperature and wavelength.

The free-free Gaunt factor is calculated from a lookup table of temperature averaged free-free Gaunt factors from Table 2 of Sutherland [Sut98] as a function of \(\log{\gamma^2},\log{u}\), where \(\gamma^2=Z^2\mathrm{Ry}/k_BT\) and \(u=hc/\lambda k_BT\).

For the regime, \(6<\log_{10}(T)< 8.5\) and \(-4<\log_{10}(u)<1\), the above prescription is replaced with the fitting formula of Itoh et al. [ISK+00] for the relativistic free-free Gaunt factor. This is given by Eq. 4 of Itoh et al. [ISK+00],

\[g_{ff} = \sum_{i,j=0}^{10} a_{ij}t^iU^j,\]

where \(t=(\log{T} - 7.25)/1.25\) and \(U=(\log{u} + 1.5)/2.5\).

Parameters:

  • temperature (Quantity) – The temperature(s) for which to calculate the Gaunt factor

  • wavelength (Quantity) – The wavelength(s) at which to calculate the Gaunt factor

  • atomic_number (int) – The atomic number of the emitting element

  • charge_state (int) – The charge state of the emitting ion

See also

fiasco.Ion.free_free

free_free_integrated(temperature: Unit('K'), charge_state, use_itoh=False)[source]#

The wavelength-integrated Gaunt factor for free-free emission as a function of temperature.

The wavelength-integrated Gaunt factor is primarily used for calculating the total radiative losses from free-free emission. By default, this calculation is done with the form specified in Sutherland [Sut98], which is valid over a wide range of temperatures. The use_itoh option substitutes the form specified by Itoh et al. [ISK+02], which is more accurate but has a more limited range of validity. The difference between the two forms is small, as shown in Young [You19b]. The CHIANTI atomic database only uses the Sutherland [Sut98] form as a result, but includes the data sets for both forms.

Note

The Gaunt factor calculation of Itoh et al. [ISK+02] includes both a relativistic (Eq. 5) and non-relativistic (Eq. 13) form. The relativistic form is valid over the temperature range \(6.0\leq\log_{10}T\leq8.5\) and for charge states \(1\le z\le 28\). The nonrelativistic form is valid over \(-3\leq\log_{10}\gamma^{2}\leq 2\) where \(\gamma^2=z^2\mathrm{Ry}/k_BT\). Outside of these ranges, the form of Sutherland [Sut98] is used.

Parameters:

  • temperature (Quantity) – The temperature(s) for which to calculate the Gaunt factor

  • charge_state (int) – The charge state of the ion

  • use_itoh (bool, optional) – If true, use the Itoh et al. [ISK+02] Gaunt factors over valid ranges. If false (default), use the Sutherland [Sut98] Gaunt factors instead.

See also

fiasco.Ion.free_free_radiative_loss