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4. Results

The differences between static models and those with velocities are mainly in the emergent intensities. Including the velocities in the NLTE model calculations affects also the level populations as the velocity appears in radiative rates evaluation (Eqs. (7 (click here)), (8 (click here)), (9 (click here))).

Figures 2 (click here), 3 (click here), 4 (click here) and 5 (click here) show the tex2html_wrap_inline1398 line profiles and departures of the level populations from the static case tex2html_wrap_inline1726. The lefthand columns contain the profiles for each model together with the static and therefore symmetric profiles. The right-hand columns plot the population departures of the first three levels and protons only for the model with the highest velocity (i.e. for the velocity parameter tex2html_wrap_inline1656), because the population departures for models with lower velocity have the same structure and only their amplitudes are lower. This indicates that a velocity increase amplifies the population departures from static case without changing their height structure. For models with velocities tex2html_wrap_inline1730, which is approximately the velocity of thermal motions, the differences rarely exceed 5%, maximum 10%. To reproduce an observed asymmetry for velocities that are close to the thermal velocity, one can use the static model and perform the formal solution of radiative transfer equation with line absorption shifts caused by the macroscopic velocity. Figure 6 (click here) shows the tex2html_wrap_inline1398 line for F1 gradient models m10 and m50. While for the model m10 the emergent tex2html_wrap_inline1398 line intensities computed using static population and using the right ones are identical, those for model m50 are different.

For almost all computed models the level populations depart from the static case in two regions. Only the models with non-zero velocities in lower heights have these two regions identical. The first region corresponds to the height of the moving material and therefore depends on the model, while the second one is model-independent and lies in the heights with tex2html_wrap_inline1736. The common feature of all models is an overpopulation of the first level and under-population of the second and third level in the moving material.

The collisional rates are the same for the static model as well as for models with velocities as their temperature structure is identical. Thus all differences are due to changes in the radiative rates caused by the shift of the absorption coefficient in the moving material. To find out the changes in the radiation field we selected the layer model in the upper part of the chromosphere with velocity parameter tex2html_wrap_inline1656 and F1 temperature structure, where these two regions are clearly seen. For this model we computed the specific intensity in the tex2html_wrap_inline1740, tex2html_wrap_inline1742 and tex2html_wrap_inline1398 lines for all depths and for upward and downward directions (i.e. for tex2html_wrap_inline1746 and -1) and divided it by the corresponding intensity from the static model. Obtained intensity departures (Fig. 7 (click here)) show that incoming radiation (tex2html_wrap_inline1750) plays a crucial role in the atmosphere. In the moving layer (tex2html_wrap_inline1752, the tex2html_wrap_inline1398 wing-line intensity increases by a factor of 104, while in the wing of the Lyman lines it is 103 times. This depopulates the second level (with respect to the static case) and, via tex2html_wrap_inline1742, overpopulates first level. The incoming line intensities look different in the middle region. The wing-intensity of the tex2html_wrap_inline1742 line exhibits the largest increase, 200 times, in the tex2html_wrap_inline1398 line, 100 times, while the intensity in tex2html_wrap_inline1740 increases only 10 times. This force electrons leave the first level and overpopulate the third level. To summarize, the changes of the populations are connected with the increase of the lines intensities. The amount of these changes depends on the ratio of the intensity increases in different lines. If the increase dominates for the resonance lines, the ground level becomes underpopulated and the upper levels overpopulated. If the intensity increase of subordinate lines is stronger, under-population appears in the upper levels while the ground level is now overpopulated.

Figure 6: tex2html_wrap_inline1398 line computed using static (dotted line) and dynamic (solid line) populations for F1 gradient m10 (upper) and m50 (lower) models

Line asymmetries arise as a result of changes in the optical depth scale for different line frequencies due to shift of the line absorption coefficient. The emergent intensity is approximately equal to the source function at optical depth tex2html_wrap_inline1770. From the computations we performed it follows that the shift of the line absorption coefficient in the moving material causes a substantial increase of the opacity in the line wing. Height corresponding to tex2html_wrap_inline1772 moves up to heights with a different source function. The value of the source function determines whether the emergent intensity will be higher or lower than for the static case.

It should be noted that the line intensity in the blue wing does not differ from the static case because the optical depth scale for the blue wing frequencies remains unaffected. This leads us to the conclusion that if the velocities in the flare atmosphere have downward direction, the moving material influences only the red wing of the lines. The same statement holds for upward velocities and the blue wing. Whether the line asymmetry will be blue or red depends on the run of the source function in the atmosphere.

Figure 8 (click here) shows the run of the outgoing line intensity with height for some models. The asymmetry of the outgoing line intensity always arises at heights where the velocities become significant, i.e. comparable to the thermal velocity. For layer models it is in the moving layer where the line asymmetry increases and reaches its maximum at the top of the layer. The line asymmetry for the gradient models increases with height as the velocity increases and reaches its maximum at the top of the atmosphere.

4.1. F1 models

The source function of tex2html_wrap_inline1398 for static F1 model decreases with height. The asymmetric tex2html_wrap_inline1398 line profiles of F1 models with velocities show the blue asymmetry because the red-wing intensity is lowered. In F1 layer models, the moving region appears in the tex2html_wrap_inline1398 profile as a self-absorption dip with central wavelength corresponding to the velocity in the layer. For F1 gradient models tex2html_wrap_inline1398 red wing exhibits an intensity decrease that extends from the line center up to the wavelength corresponding to the maximum velocity of the material on top of the atmosphere.

4.2. F2 models

The source function of tex2html_wrap_inline1398 line for static F2 models increases with depth and falls down at the top of the atmosphere. tex2html_wrap_inline1398 blue asymmetry for F2 upper and middle layer models is caused by the shift of the optical depth tex2html_wrap_inline1770 towards the heights where the source function drops. The same mechanism holds for tex2html_wrap_inline1398 line F2 gradient models with velocity parameter V0 10 and tex2html_wrap_inline1794. tex2html_wrap_inline1398 for F2 gradient models with velocity parameter tex2html_wrap_inline1798 exhibits a red asymmetry because the optical depth tex2html_wrap_inline1770 for wavelengths tex2html_wrap_inline1802 moves up where the source function is larger than in the static case.

  Figure 7: tex2html_wrap_inline1740, tex2html_wrap_inline1742 and tex2html_wrap_inline1398 line intensity departures for incoming radiation for F1 layer u50 model

  Figure 8: The tex2html_wrap_inline1398 line intensity with outward direction (tex2html_wrap_inline1746) as a function of the optical depth for F1 layer m50 (upper left), F1 gradient m50 (upper right), F2 layer m50 (lower left) and F2 gradient m50 (lower right) models

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