## Presentation

## Hydrogen Stark broadening calculation for astrophysical applications

The Stark line profiles are calculated using the Model Microfield Method of Brissaud and Frisch (J. Quant. Spectrosc. Rad. Transfer 11, 1767 (1971) )
which includes the effects of the motions of the plasmas ions. Such effects are important in the line centers.

The online calculation is performed for a plasma composed of electrons and protons.

The details of the model and the numerical methods are given in [2,3]:

In this preliminary online version, the tabulations are given in alfa units (Angstroms/ues) , which are defined by Delta_alfa = Delta_lambda (Angstroms) / F0 ,
where F0 is the the normal Holtsmark field F0 defined by F0 = e/R0^2 = 1.25 10-9 Ne^(2/3) ( ues, cm-3) ( see ref 2) .

The area normalized profile includes the contributions of electrons and protons. The line shape recovers in the far line wings the well known static limit in
I(Delta_alfa) = Kalpha/| Delta_alfa |^2.5 . The calculation gives the pure Stark broadened profile and also the convolution with the Doppler profile.
Only the half profile (positive values of Delta_alfa) is given.

This online calculation can be used alternatively to the existing tabulations at CDS
(http://cdsweb.u-strasbg.fr/cgi-bin/qcat?VI/98) with appropriate interpolation in the tables.

We encourage the users to cite references 2 and 3 for publication purposes.

**Two calculations will be proposed (beta test) :**

- a detailed (more precise) calculation which takes into account the tensorial form of the electron contribution to the line shape. It is proposed for Lyman (1 – n’, with n’ =2,3,4,5,6) and Balmer lines ( 2=n’, with n’=3,4,5)
- a simplified calculation (soon available), for the other Balmer and Paschen lines. It supposes that the electron contribution has a scalar form and allows a faster computation. The accuracy is discussed in [2,3].

Note that the Debye approximation is supposed to be valid. This means that the input temperature T(K) and electron density Ne (cm-3) should satisfy the relation 0.9 Ne^0.1666/T^0.5 < 1

**References :**

- [1] Theory of Stark broadening , Exact line profile with model microfield., Brissaud and Frisch , J. Quant. Spectrosc. Rad. Transfer 11, 1767 (1971)
- [2] Extensive MMM tabulations of Hydrogen Lyman and Balmer lines, Stehle C., Hutcheon R., Astron, Astrophys. Suppl. 140, 93 (1999)
- [3] Paschen Lines of Hydrogen and He+ ion, Stehle C., Physica Scripta, T65, 183-187, (1996).

Contacts :

Chantal Stehle , Sylvain Fouquet

## Tables of Stark broadened hydrogen lines

Access## Exact hydrogenic oscillator strengths and einstein coefficients computation

Contacts :

Dy HOANG BINH