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Astron. Astrophys. 334, 1136-1144 (1998)

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4. Astrophysical consequences

To date, several diagnostic methods for low energy proton beams have been considered:

  • The first one, valid for low energy protons, is based on proton-hydrogen charge exchange. Excitation by a charge exchange process could give rise to very fast hydrogen atoms that produce Doppler shifted emission and consequently enhancements of the line wings of chromospheric lines (Fang et al. 1995).
  • The H [FORMULA] emission enhancement in the line centre and the line central reversal disappearance have been interpreted as due to energy deposition by proton beams in the highest chromosphere layers (Henoux et al. 1993). But the very large broadening of the lines implies macroscopic velocities whose origin is not clearly explained.
  • The third one is based on the proton beams property to keep their anisotropic angular distribution velocity when bombarding the solar chromosphere. The resulting anisotropic collisional atoms excitation generates the emission of a polarized line. Such polarization has been observed during solar flares (Henoux et al. 1990).

From our results, we can deduce accurate information on these different diagnostic methods which are discussed hereafter.

4.1. Line profiles and Doppler effect

According to the cross sections values, the charge exchange process is important when low energy protons ([FORMULA] keV) are present at the chromospheric level. The subsequent Doppler shifted emission has been calculated by Fang et al. (1995) who deduce that, due to the continuum background which is larger by several orders of magnitude, the nonthermal H [FORMULA] emission would not be detectable. But the nonthermal emission in the red Ly [FORMULA] and Ly [FORMULA] wings is significantly high and can be used as a diagnostic. The presently calculated cross sections for excitation with charge exchange into the [FORMULA] and [FORMULA] levels agree with the values used by Fang et al. (1995) and we confirm their conclusions. Due to the very fast spontaneous emission process and the low particles density in the chromosphere, charge exchange of the excited atoms with the ambient protons is negligible and consequently no population transfer between fast atoms (excited by charge exchange) and slow atoms (excited directly by the beam) significantly contributes to the statistical populations equilibrium.

Considering the differential excitation cross sections (without capture), we have shown that the protons deflection angle [FORMULA] can be of the order of a few degrees for the lowest considered energies. Consequently the excited atoms recoil velocity [FORMULA], given by [FORMULA] for incident protons with velocity [FORMULA], is important compared to the thermal velocities: for a 1 keV proton beam and a 1 degree deflection angle, [FORMULA] is between 7 and 40 [FORMULA]. This recoil velocity is approximatively perpendicular to the incident protons direction, and according to the line of sight, may produce an important macroscopic broadening of the emitted line.

Of course, for a quantitative interpretation of the observed profilesone would need to account of the angle [FORMULA] between the line of sight and the direction of the magnetic field and of the beam pitch angle of the oblique incident proton beam, both for the wings (Zhao et al. 1997) and for the line centre.

4.2. Polarization

Linear H [FORMULA] line polarization has been observed in solar flares (Henoux et al. 1990). The observed polarization degree can be as high as [FORMULA] for a flare located near the limb, it can be explained as [FORMULA] level anisotropic collisional excitation by vertical proton beams. The observed polarization parallel to the incident proton beam, corresponds to a positive sign of our calculated polarization fraction. For a quantitative comparison between the calculated and the observed polarization, one needs to consider all the processes that contribute to the population equilibrium of the atomic Zeeman sublevels. Apart from the nonthermal excitation by the beam, radiative excitation as well as population collisional transfer by the ambient particles must be taken into account. These two last processes effectively depolarize the line so that excitation by the beam is the only polarizing mechanism. Considering the polarization degree energy variation (see Fig. 11c and Werner & Schartner 1996), we can deduce that, at the chromosphere level, the protons energy is certainely lower than 200 keV and probably less than 50 keV to produce highly polarized lines as were observed. At the same energies, the sign of the polarization fraction for the Lyman [FORMULA] line is negative, and thus simultaneous observation of the H [FORMULA] and Lyman [FORMULA] polarization would offer a decisive test of the interpretation of such polarization as due to collisional excitation by a proton beam.

It is important to remark that excitation by a neutral beam of electrons and protons with the same velocity (a 50 keV proton has the same velocity as a 30 eV electron) leads to the same conclusion since the polarization fraction of due to electron impact excitation is positive at low energies and becomes negative at 80 eV (Aboudarham et al. 1992) which corresponds to 150 keV protons.

Our calculations show no significant polarization fraction variation as a function of the deflection angle. Consequently no frequency dependence of the polarization is expected in the line centre. In the far wings, formed by nonthermal emission, the emission at a given position [FORMULA] is directly related to the particle energy in the incident beam (Zhao et al. 1997), thus the polarization fraction frequency dependence should only reflect the beam energy distribution (see Figs. 11 a,b,c). H [FORMULA] spectropolarimetric observations were performed by Firstova et al. 1996 but the accuracy of these measurements is not sufficient to conclude quantitatively on the proton beam distribution energy. More observations are needed and will be available in the near future with THEMIS.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998