The use of a grid of non-LTE models to perform inversions of observed line profiles allows one to circumvent the problem of converging towards the smallest minimum of an appropriate merit function (e.g. ) by use of iterative algorithms. This is especially true when fast inversions are sought, or the need to systematically reduce huge amounts of data arises. Indeed, the problem of the uniqueness of the inverted profile is eliminated altogether in the case of a grid of models, since the grid enables a complete exploration of the space of parameters, therefore discriminating between local and true global minima. Even when the profiles are inverted by e.g. calculating the corresponding response functions numerically (Socas-Navarro et al. 1998), the use of a grid as a first step may save significant computing time.
In the procedure presented in this study, steps have been taken to ensure that further extensions of the grid will be easily carried out in the future. Those include the calculation by the MALI code of the source functions, and not of the profiles themselves. This allows one to vary within certain limits. Another is the choice of an electronic density constant with depth as a free parameter. Hydrogen is the largest contributor of electrons to the prominence plasma, and solving the equilibrium equations for this element will certainly provide us with an excellent approximation to the true . This value, in turn, can be used as input to calculate the non-LTE formation of other spectral lines from chemical elements other than hydrogen, whose contributions to are negligible. Further extensions of the grid to include spectral lines from other elements will in this way be straightforward. Finally, as it has been pointed out in Sect. 2 above, a constant allows us to use CRD for the formation of the Lyman lines, which speeds up the computations.
Implicit through our study is the assumption that the portion of the solar atmosphere underneath the filament is structureless, and can be well approximated by a mean H profile, such as that of David (1961). In general, this will not be the case. Features below the filament with non-zero longitudinal velocities have a varying degree of influence on the observed filament profiles. If the optical thickness of the observed portion of the filament is small, the effect of that velocity can be important, and will modify the line profile in a complicated fashion. Firstly, the light illuminating the cloud from below will be Doppler-shifted with respect to the cloud itself, changing the conditions under which line profiles are formed in its interior. Secondly, the partially-absorbed background profile which will reach the observer will give rise to an asymmetry in the composed observed profile (i.e. background + cloud). Notice also that not only one, but many chromospheric structures with different velocities will contribute to the line profile impinging on the cloud from below, complicating matters further. The analysis above will therefore be greatly aided in the future with the use of more than one spectral line. In the case of H, one could aim at observing simultaneously with H, which forms in similar conditions but is optically thinner. This would in turn help modeling the background illumination more accurately. Calculating H, nonetheless likely requires a more complete hydrogen model atom, such that atomic populations (at least, those which give rise to the two first Balmer lines) are calculated with high precision.
An extension of the grid to account for cooler plasma regions (lower T) is desirable. Very dark, optically thick regions of the filament clearly require T's which are probably as low as 4 500 K, as recommended in the Hvar model (see above). New calculations should also rise V's range up to at least 10 km s-1. We plan to increase the parameters' range in the near future.
© European Southern Observatory (ESO) 1999
Online publication: April 19, 1999