Astron. Astrophys. 332, 732-738 (1998)

5. Conclusions

In this work we have carried out a full quantum mechanical calculation for the Ly scattering phase and polarization functions. The hyperfine level structure of the hydrogen atom and the populations established by the Ly light are taken into account. The resulting phase functions, and thus measured intensities, differ in the case of a realistic model for the density from the widely used fine structure phase function by 10%. This difference is quite large and should thus be detectable in the data. The Ly mapper SWAN on the SOHO satellite will probably provide data good enough to make a comparisons between the different phase functions possible. However, as many other factors (like multiple scattering and the density distribution used) are also of importance in interpreting the data, this comparison may not be straightforward.

We saw that in order to explicitly evaluate the scattered intensity one needs the frequency profile of the incoming light and the velocity distribution of the atoms. We have throughout been assuming a flat frequency profile, but have not, except in Sect. 3.3., specified the form of the velocity distribution. By measuring the spectrum of the scattered light we can obtain information about the parallel component of the velocity distribution. In the case of a pure Maxwell-Boltzmann distribution this would directly give us the temperature of the scattering gas. For an asymmetric velocity distribution, the spectrum would be smeared out by the LOS integration. In our calculations we have also neglected the effects of multiple scattering. If multiple scattering is of importance our LOS integrals are no longer valid. Keller (1981) have estimated, by using Monte Carlo methods, that the optically thin approximation underestimates the scattered intensity from the nearby interstellar medium by 5 to 35%, depending on the direction of the LOS. Scherer & Fahr (1996) has used a more analytical approach to the multiple scattering problem and taken into account an angle-dependent partial frequency redistribution. As input in their calculations they have used the phase function of Brand and Chamberlain. On the basis of our numerical simulations one would then expect a 10% change in their integrated intensity when using our phase functions. Also the temperature inferred from the line width of the scattered light is effected due to the line broadening caused by the multiple scattering. Quémerais & Bertaux (1993) estimates that temperature is off by about 30 %. Although our LOS integrals are not accurate enough under these circumstances, the phase functions listed in Table 1 will still be useful, as they apply to the scattering from a single atom, and thus can be used as a starting point in the numerical simulations.

© European Southern Observatory (ESO) 1998

Online publication: March 23, 1998
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