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Astron. Astrophys. 355, 769-780 (2000)

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7. Cooling of the PFL system

It is generally believed that the post-flare loop plasma cools mainly due to thermal conduction and radiation. To get a simple estimate of the time scale which a hot PFL with temperature of the order [FORMULA] K needs to reach temperature of the order [FORMULA] K, we used a simple formula of vestka (1987) and we applied a correction to the temperature gradient introduced by Varady & Heinzel (1997). The formula was derived from the energy equation under the assumption of static ([FORMULA]), fully ionized plasma. The first and the second term on the right hand side of the equation are approximations of conductive and radiative losses:

[EQUATION]

In this equation [FORMULA] is the correction applied to the temperature gradient, [FORMULA] is the Boltzmann constant, L is the semi-length of the loop, [FORMULA] (in CGS units) is the thermal conductivity coefficient and [FORMULA] and [FORMULA] fit the radiative losses. The latter were taken from Cargill (1994) and are based on the model of Cook et al. (1989):

[EQUATION]

Using the formula above and quantities obtained in previous sections we calculated the theoretical time dependence of plasma temperature in the PFL. The model was calculated for the initial temperature 2.8 MK, which was obtained from the SXT temperature analysis and a constant electron density [FORMULA] cm-3, which corresponds to the value obtained at the top of the loop system using the density sensitive line pair of Fe XIV. The theoretical time dependence of temperature in the loop is shown in Fig. 9. It follows from this model that the total cooling time required to achieve the temperature of the order [FORMULA] K is approximately 750 s. In fact the cooling time will probably be longer, because from the SXT emission measure analysis we have an evidence of a rapid decrease of emission measure in the loop system which reduces the radiative losses.

[FIGURE] Fig. 9. Theoretical time dependence of the temperature of hot PFL, cooled conductively and radiatively from an initial temperature 2.8 MK. The electron density [FORMULA] cm-3 in the loop is assumed to be constant with time.

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© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000
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