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Astron. Astrophys. 321, 549-556 (1997)

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3. Discussion

Modern computational techniques allow us to investigate with confidence the response of the atmosphere to the impulsive heating. Now we have the numerical method, that takes into account all the main physical processes such as thermal conduction, radiative cooling, stellar gravity, etc, and which gives an adequate description of the flare process for a given mechanism of heating and a chosen initial model of the stellar atmosphere. This paper presents one typical variant of the computation for a flare on AD Leo where conditions are favourable for the appearance of flare optical radiation.

Two features of this gas-dynamic modelling should be pointed out.

First, these results remain valid when impulsive heating is located in layers which include the upper chromosphere (under the transition region). This is significant if the flaring process is considered in a real outer atmosphere of a late-type star containing a chromosphere and a corona. It is fulfilled in our numerical modelling because we consider an outer atmosphere with a transition region at [FORMULA] (the column mass [FORMULA]), and a maximum of the energy release of accelerated electrons with [FORMULA], below or near the transition region.

In fact, the initial atmospheric model adopted here relates to a quiescent red dwarf (dM) star (without emission in its optical spectra) as seen in a set of chromospheric models by Houdebine et al. 1995. Thus, flare optical continuum is generated effectively when accelerated electrons with [FORMULA] impact on the chromosphere with a moderate activity level ([FORMULA], see Houdebine et al. 1995) or electron beams of higher energies impact onto the active dense chromosphere ([FORMULA]). In the case when heating doesn't expand the upper chromopshere, we obtain the solution that is close to one given by Cheng & Pallavicini (1991). Then, when heating occurs in coronal layers, the [FORMULA] ratio should exceed the value corresponding to our solution, given in Fig. 3.

Second, we consider here a level of heating by accelerated electrons, for which thermal fluxes during the developing gas-dynamic process don't exceed the corresponding saturated heat flux. This condition limits the energy flux of these particles to [FORMULA] for the hard spectrum we have chosen ([FORMULA]). In addition, we suggest that the energy of the flux of accelerated particles isn't limited by the return currents that can arise when intensive electron beams are injected into the chromosphere. These circumstances allow us to apply the results of these numerical simulations to the interpretation of simultaneous multi-wavelength observations of stellar flares of any power other than the most powerful ones (with [FORMULA]).

The gas-dynamic model presented here allows us to interpret observations of flares on red dwarf stars. One of the most important points is the evidence for the thermal origin of flare optical continuum radiation. The calculations show that the source of the optical continuum is formed within several tenths of a second after the flare onset. If the heating is turning-off when the optical radiation appears, this source continues to exist until the shock wave dissipates due to the propagation through a medium with increasing density. The time for the dissipation is about of 0.5 s. Therefore, the duration of the fastest bursts of optical continuum should be less than 0.5 s.

On the other hand, really large impulsive flares can be presented as a series of elementary bursts. An injection of accelerated electrons into the chromosphere can occur as a sequence of fast pulses, partly overlapping in time. The gas-dynamic response then takes place at the footpoints of various low-lying loops. In principle, this numerical modelling gives the possibility to predict the behaviour of light curves in different spectral ranges.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998