## 5. Energy requirementsOne of the main objectives of this kind of atmospheric modelling is to constrain the amount of chromospheric heating required to sustain the atmosphere of the stars, i.e., to balance the radiative losses due to the different spectral lines and continua. Here we compute the radiative cooling rate (ergs cm-3 s-1), i.e. the net amount of energy radiated at a given depth by the atmosphere, which is given by In this paper we computed the contributions due to , H, He I, Mg I and II, Ca I and II, Fe I, Si I, Na I, Al I and CO. The overall results and the most important individual contributions are presented in Fig. 6. A positive value implies a net loss of energy (cooling), and a negative value represents a net energy absorption (heating).
As can be seen, the cooling rate for both stars is very similar,
well within the error in the calculations due to differences in the
depth grid. The larger temperature of our model for Gl 628 for
In the temperature minimum region, the
cooling rate is negative, driving the total rate to negative values.
In this case there is a missing This results can be compared with the ones shown in Fig. 9 of Paper I, which shows that the dMe star AD Leo has a much larger cooling rate in the high chromosphere, which implies that much more heating is needed to sustain the higher temperature (see Fig. 1). In the mid and high-chromosphere the energy balance is determined by the hydrogen cooling rate and the Mg II rate. In Fig. 7 we show a detail of the cooling rates in the high
chromosphere, that can be compared with Fig. 10 of Paper I. We note
that line cooling is positive for all three stars, and it is the most
important radiative loss for the cooler stars. In the transition
region, for temperatures larger than 15000 K, is
the most important cooling agent, whereas at lower temperatures the
Balmer lines become dominant. In this region, cooling in the
line is three times larger than in
, and ten times larger than for
to H
© European Southern Observatory (ESO) 1997 Online publication: April 20, 1998 |