11 Continuum radiation

CHIANTI v. 2.0 allows the calculation of continuum radiation according to the Gronenschild & Mewe (1978) model. Here we provide only the formulas adopted for the calculation, and further details can be found in the quoted paper.

The computation includes free-free, free-bound and two-photon continuum and the results are given in units 10^-20 erg cm³ s^-1 Å^-1.

An IDL routine is supplied together with the database which allows one to calculate the continuum radiation for temperatures between 10⁴ to 10⁸ K and to convolve the result with a selected DEM in order to calculate the continuum radiation synthetic spectrum.

The approximations used in the adopted model are accurate to better than 15%.

It is important to note that the Gronenschild & Mewe (1978) model for continuum emission adopted in the present version of CHIANTI has been successively improved by Mewe & Kaastra (1994). The improvements include:

• Free-free radiation: the approximation to the correction for relativistic effects based on the calculations of Kylafis & Lamb (1982) and the interpolation of the results given by Carson (1988) which replace the older Karzas & Latter (1961) calculations;
• Free-bound radiation: the full energy dependence of the Gaunt factor has been taken into account;
• Two-photon emission: The accuracy of the calculation has been improved to better than $\simeq$ 1%.

These improvements will be included in a future release of the CHIANTI database.

11.1 Free-free radiation

The free-free continuum energy emitted by a plasma of a given chemical composition per unit time, volume and wavelength band in the hydrogenic approximation is given by

$$\begin{eqnarray} {{\rm d}P_{\rm ff}{\left({\lambda,T}\right)}\over{{\rm d}\lambd... ...N{\left({H}\right)}} {z^2}{g_{\rm ff}{\left({z,\lambda,T}\right)}}\end{eqnarray}$$ (1)

$\lambda$ is the radiation wavelength (in Å), $N_{\rm e}$ is the electron density (in cm^-3), $N{\left({Z^{+z}}\right)}\over{N{\left({Z}\right)}}$is the ion Z^+z abundance relative to the total abundance of the element, ${{N{\left({Z}\right)}}\over{N{\left({H}\right)}}}$ is the element Z abundance relative to hydrogen and $C_{\rm ff}=2.051\;10^{-19}$. $g_{\rm ff}{\left({z,\lambda,T}\right)}$ is the temperature-averaged free-free hydrogenic Gaunt factor, evaluated in the same way as Gronenschild & Mewe (1978).

In the present version only H I, He I and He II are included in the computation.

11.2 Free-bound radiation

The free-bound continuum energy emitted by a plasma of given chemical composition per unit time, volume and wavelength band is given by

$$\begin{eqnarray} {{\rm d}P_{\rm fb}{\left({\lambda,T}\right)}\over{{\rm d}\lambd... ...H}\right)}}} {N{\left({H}\right)}}{{\rm e}^{I_{Z,z-1,n}\over{kt}}}\end{eqnarray}$$ (2)

with

$${I_{Z,z-1,n}\over{kt}} \le {{hc}\over{\lambda k T}}$$ (3)

where $I_{Z,z-1,n}=I_H{z^2\over n^2}$ is the ionization energy of the n state of the recombined ions, $\eta_{Z,z,n}$ is the number of position of the $n^{\rm th}$ shell of the recombining ion free to be occupied by the captured electron. The free-bound Gaunt factor $g_{\rm fb}$ is equal to 1 following Karzas & Latter (1961) and taking into account contribution of recombination to excited levels also.

The elements to be included in the computation may be selected via an option on the chemical abundance.

11.3 Two-photon radiation

The two-photon continuum energy emitted by a plasma composed by hydrogen and helium-like ions per unit time, volume and wavelength band is given by

$$\begin{eqnarray} {{\rm d}P_{\rm 2ph}{\left({\lambda,T}\right)}\over{{\rm d}\lamb... ...left({y}\right)}} \quad {\left({\lambda \ge \lambda_{Z,z}}\right)}\end{eqnarray}$$ (4)

where

$$\Phi{\left({y}\right)}=2.623\cdot {\sqrt{\cos{\left[{\pi{\left({y-1/2}\right)}}\right]}}}$$ (5)

and f_Z,z and $\lambda_{Z,z}$ are the absorption oscillator strength and the wavelength of the [1s ]-[2s ] transition, g_Z,z is the averaged Gaunt factor and $y = {\lambda_{Z,z} \over \lambda}$.

I_Z,z,n and $\eta{\left({Z,z,n}\right)}$ for the free-bound continuum and f_Z,z , $\lambda_{Z,z}$ and g_Z,z for the two-photon continuum are supplied in a proper file. Reduction of the two-photon continuum emission by depopulation of the [2s ] level via collisional de-excitation is taken into account. For this purpose the electron density selection is allowed.