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Astron. Astrophys. 357, 767-776 (2000)

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3. Atmosphere models and scattered light

We wish to combine the simple escape probability and absorption factor techniques with atmosphere models to predict both the emergent spectral line fluxes and flux ratios. Spectral emission from quiet sun regions of the upper chromosphere and transition zone is dominated by spicule-like inhomogeneities and so one would expect any successful model to account for these features.

We consider four models: firstly we consider emission following the [FORMULA] function 1 with a transition-zone layer based on constant conductive flux from the corona to the chromosphere. [FORMULA] and [FORMULA] follow the quiet sun atmosphere model of Vernazza et al. (1981). Secondly, following the approach of Kastner & Bhatia (1992), an emission layer of constant (adjustable) thickness and density is envisaged. This model is a simple parametric adjustment which does not attempt to capture anything of the nature of the spicules. It is, nevertheless, useful to consider such a model in order to put the success of any other simple model in context. Thirdly, a layer of density which falls off exponentially with adjustable scale height is envisaged. That is, the density falls off as [FORMULA] for some constants H and B. This is motivated by the findings of Mariska et al. (1978) who considered models where the dominant contribution to the EUV signal was due to transition-zone sheaths around isolated cylindrical H[FORMULA] spicules but showed that `above the emission peak the amount of emitting material in the line of sight for any spectral line must decrease exponentially with height with a scale height that depends on temperature'. Furthermore this is identical, in essence if not approach, to the model of Withbroe & Mariska (1976). Finally we consider a composite of models 1 and 3, i.e. a thin layer plus a layer of exponentially decaying density of adjustable scale height. The relative magnitude of the thin layer to the other is adjusted to optimise the fit to the data but the quality of the fit is insensitive to this parameter.

In summary the models considered are

  1. Thin transition region based on the VAL atmosphere model

  2. Spherical shell of constant density

  3. Layer of density that falls off exponentially with height

  4. Composite of models 1 and 3

3.1. Scattered light

In all four models it was necessary to consider the effects of instrumentally scattered light - light that reflects off the interior of the telescope prior to passing through the entrance slit. The entire disk contributes to the scattered light signal with the contribution from each point being characterised by the instrument point spread function, psf, (Fig. 4) - the relative intensity of a point source as a function of lateral distance from the slit. David et al. (1997) have shown that the pre-launch point spread function is still effective so it was this that was used to complete the calculation. Thus the emitted flux, [FORMULA], from position h is given by

[EQUATION]

where [FORMULA] is the true signal [FORMULA].

[FIGURE] Fig. 4. The SUMER pre-launch point spread function (stars) (Lemaire 1998) - relative intensity of a point source vs lateral distance from source to slit centre. The dotted line is a fit to the measured points used in the analysis described.

In practice we have evaluated this integral along a radius rather than over the whole disk. This introduces an error in that the scattered contribution is underestimated at each point by a maximum factor of [FORMULA] but this error is not sufficient to explain the C III emission beyond [FORMULA] 970 arc sec. The calculation captures well the dependance of the off-limb line ratios on scattered light.

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000
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