Astron. Astrophys. 325, 745-754 (1997)

5. Results of the theoretical approach

For the purpose of a comparison with earlier spectral calculations of this type (e.g. Lallement et al. 1993, Clarke et al. 1995) and for the sake of identifying clearly the deviations from our present improved and more sophisticated calculations, we show theoretical results for two different cases:

1. the radiation transport model was used a. adopting a flat solar profile (Fig. 4) b. not taking into account the optical depth (optically thin approximation) c. using an "interface"-free density model that results from the model by Osterbart & Fahr (1992) if the LISM-plasma density vanishes, nearly identical with the density model by Wu & Judge (1979) for an effective solar gravity of (see Sect. 1).

Fig. 4. Different solar Ly emission profiles alternatively used in the radiation transport model by Scherer & Fahr (1996) and also used here.

2. the radiation transport model (Scherer & Fahr 1996) was used a. adopting a realistic solar profile (Fig. 4), resulting by a fit to OSO 8 satellite data Bonnet et al. (1978) b. taking into account the optical depth c. using a density model taking into account the interface effect, assuming a shock position at 80 AU solar distance and an effective solar gravity of (see Sect. 1).

The solar profiles used in the above cases are scaled such that in both cases the area under the curves is equal to unity (see Fig. 4).

In addition in Fig. 5 a Voigt-profile with an assumed temperature of 30000 K is shown as it was used by Clarke et al. (1995) or Lallement et al. (1993). This Voigt-profile is the result of a best fit procedure to the HST data. The maximum of the Voigt-profile is rescaled and shifted, so that its maximum is identical with that of the spectrum calculated with the radiation transport model (case 2).

Fig. 5. Calculated spectra for alternative assumptions: - - - Voigt-profile with 30000 K; case 1: - - radiation transport model by Scherer & Fahr using a flat solar profile and an optically thin approximation (details see text). case 2: - radiation transport model by Scherer & Fahr using a realistic solar profile, angle-dependent redistribution and selfabsorption. The different cases are calculated for the four positions and view directions of the HST (see Table 1).

Between the spectra of case 1 and case 2 there are some remarkable differences evident. The upwind spectra of case 2 are shifted a little bit towards the blue spectral wings. This is caused mainly by the different effective solar gravity used in the different density models. For an attracting gravitational potential operates in the vicinity of the sun which speeds up the neutral hydrogen, and its resonant glow is shifted by the Doppler effect to shorter wavelengths when looking upwind. The opposite relation exists in the downwind direction. Due to the differential depletion of the hydrogen velocity distribution function, the downwind hydrogen glow spectra are shifted by the Doppler effect to longer wavelengths when an attracting solar gravitational potential exists. The different intensities of case 1 and case 2 are caused by the different hydrogen distributions of the density models and the different solar profiles. The influence of the different solar profiles is more clearly seen in calculations of complete sky surveys (see Scherer & Fahr 1995 , 1997).

Re-scaling the spectra of case 1 and case 2 to the same maximum shows that the spectra of case 2 are relatively broader than the spectra of case 1. In case 2, caused by the effective solar gravity, the neutral hydrogen distribution for off axis hydrogen atoms has velocity components perpendicular to the inflow direction. This perpendicular velocity components broaden the hydrogen distribution function in velocity-space and, caused by the Doppler effect, the theoretical backscattering glow spectra also are broadened. The maximum of the case 2 spectrum is lower due to the different solar profiles used by the calculation of case 1 and case 2 (Fig. 4). In a comparison of the theoretical results with the HST data only the widths and spectral location of the maximum of the spectra are important, because the absolute, time-variable solar intensity (solar cycle, etc.) influencing the absolute glow intensities at the event of observation is unknown. In case it would be known for the moment of observation also the absolute value of the HST spectral intensities could be used for H-density determinations. This is why the theoretical results have to be rescaled for comparison with the HST data (see Sect. 6).

The Voigt-profile with 30000 K, resulting by a best fit to the HST data (Clarke et al. 1995) is broader than calculations for the case 2 of the radiation transport model by Scherer & Fahr (Fig. 5). As an explanation we may offer the following reason: the radiation transport model assumes a sharp line of sight in the numerical procedure whereas in reality HST GHRS instrument has a cone with finite opening angle. Therefore, by not taking into account the actual aperture of the HST instrument the line width, calculated with the radiation transport model, underestimates the line width by a small amount.

© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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