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Astron. Astrophys. 342, 756-762 (1999)

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3. NLTE calculations

Simultaneous solution of the radiative transfer and statistical equilibrium equations has been realized using MULTI-code (Carlsson, 1986) in the approximation of complete frequency redistribution for all the lines. Taking into account that this code was initially exploited for rather cool stars, it was modified with the aim to apply it for early-type stars' analysis. In particular, we have added the opacity sources from ATLAS9 program (Kurucz, 1992). It enabled us to calculate more precisely a continuum opacity. At the same time, a possibility to take into account an absorption in the great number of spectral lines (especially within the region of the near-UV) allowed to calculate much accurately an intensity distribution in the region 900-1500 Å, that plays a key role in the determination of the radiative rates of [FORMULA] transitions. In addition, we changed a code to have a possibility to calculate the combined profile of the blending lines taking into account the star rotation and instrumental profile.

Atmosphere model was selected from the grid calculated with the help of ALTLAS9 (Kurucz, 1992). From the spectrum of program star we have selected N ii lines that are formed due to transitions between different levels and situated in the different spectral regions (Table 1).

Such a choice gives a guarantee that an accordance between calculated line profiles and observed ones results from the sufficiently complete description of the nitrogen atom model.

3.1. Parameters of the nitrogen atom

We employed the model of nitrogen atom consisting of 109 levels: 3 ground levels of N i, 93 levels of N ii with [FORMULA] and [FORMULA]. A detailed structure of the multiplets was ignored and each LS multiplet was considered as a single term. Next ionization stage includes 12 levels and ground state of N iv. A list of energy levels is given in Table 2. They were selected from compilative catalogue by Hirata & Horaguchi (1995).


[TABLE]

Table 2. Energy levels included in nitrogen atom model


Within the described system of the nitrogen atom levels we considered the radiative transitions between the first 43 levels of N ii, 5 N iii levels and ground level of N iv. Only transitions having [FORMULA] were selected for the analysis. Transitions between the rest levels were not taken into account and they were used only in the equations of particle number conservation. After the numerous test calculations, 92 [FORMULA] transitions were included in the linearization procedure. These transitions quite satisfactory describe a formation of the lines of interest. The other transitions were treated as those having fixed radiative rates.

Photoionization cross-sections were mainly taken from the Opacity Project (Yan et al., 1987) keeping a detailed structure of their frequency dependence, including resonances. For some important [FORMULA] transitions, the cross-section structure is extremely complicated that makes it difficult to describe it using only simple approximation like [FORMULA]. Other photoionization cross-sections were estimated with the help of quantum defect method.

Oscillator strengths were selected from the extensive compilative catalogue by Hirata & Horaguchi (1995), from survey of the lines which are formed as transitions from the ground level by Verner et al., (1994) and from 23 CD-ROM by Kurucz (1994). Some information was obtained through the Opacity Project. As we ignored a multiple structure of all the levels, the oscillator strengths for each averaged transition were calculated as [FORMULA]. Results are gathered in Table 3 and Table 4.


[TABLE]

Table 3. Linearized transitions



[TABLE]

Table 4. Fixed transitions


After the combined solution of radiative transfer and statistical equilibrium equations, the averaged levels have been splitted with respect to multiplet structure, then level populations were redistributed proportionally to the statistical weights of the corresponding sublevels and finally the lines of the interest were studied.

A certain problem is linked with a correct accounting of the line broadening due to a quadratic Stark effect. Some estimates of the broadening constants were taken from Kuruczs CD-ROM 23. For the rest transitions we used a classic expression for radiative broadening constant and Stark broadening constant was adopted to be equal to [FORMULA].

Together with the broadening constants, we have also taken into account the microturbulence parameter. It is important to note that all the broadening mechanisms were included in both the statistical equilibrium and line formation calculations.

Collisional ionization was described using Seaton's formula (Seaton, 1962):

[EQUATION]

were [FORMULA] - threshold value of the cross-section, [FORMULA], [FORMULA] - energy of ionization, [FORMULA] and [FORMULA]-electron concentration and temperature respectively. For Gaunt factor we adopted value of 0.3. For all allowed [FORMULA] transitions we used van Regemorter (1962) formula:

[EQUATION]

where [FORMULA] - hydrogen ionization potential, [FORMULA] - first-order integral exponential function. Collisional rates for the forbidden transitions were calculated with the help of semiempirical formula (Allen, 1973):

[EQUATION]

with collisional force of 1.

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999
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