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Astron. Astrophys. 329, 792-798 (1998)

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3. Density effects

The aim of this section is to examine the density dependence of the lineshape. According to equation (4), this dependence is contained in the maximum angular momentum [FORMULA], since [FORMULA], with [FORMULA] Debye distance. Let us decompose the profile [FORMULA] of equation (4) into two terms denoted [FORMULA] and [FORMULA] so that:

[EQUATION]

[EQUATION]

and let us put

[EQUATION]

where [FORMULA] is the asymptotic Holtsmark profile, i.e:

[EQUATION]

[FORMULA] which is the object of the next paragraph, is independent of the density. Hence, the density dependence comes from [FORMULA] via the limit [FORMULA]. We have calculated the latter contribution at various densities and temperatures.The results are reported in the Tables 1 to 3. It comes out from these tables that the influence of the density increases with the temperature, and that the density effect is meaningful only in the linecore and the near linewings ([FORMULA] Å). For [FORMULA] greater than 8Å, the profile is linear in density, within an error less than [FORMULA], at densities below [FORMULA] cm-3. This result is accounted for by the convergence of sum (6) at a value of [FORMULA] lower than [FORMULA].


[TABLE]

Table 1. Values of [FORMULA] [FORMULA] at [FORMULA] K and various densities [FORMULA] (in cm-3). Each dash is to be read as the closest number on the right hand side of the same line. [FORMULA] stands for [FORMULA].



[TABLE]

Table 2. Same as table 1 with [FORMULA] K



[TABLE]

Table 3. Same as Table 1 with [FORMULA] K


At higher densities, gets smaller and the region of non-linearity enlarges. However, not too far in the line wings (detunings [FORMULA] Å), [FORMULA] is a good cut-off.

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© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997
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