Astron. Astrophys. 362, 628-634 (2000)

Appendix A: calibration of the flare analysis method

The flare analysis method of Reale et al. (1997) needs to be separately calibrated for each detector, due the different spectral bandpass and resolution. In the present Appendix we present the calibration for the EXOSAT ME and for the GINGA LAC detectors, as well as for the ROSAT PSPC when flares can be broken into temporal segments with sufficient statistics as to be individually fit (an alternate approach optimized for low-statistics PSPC flares is discussed by Reale & Micela 1998). The details of the method used here are discussed in Reale et al. (1997).

For each individual detector, the ratio between the observed decay time of the light curve and the "natural" thermodynamic cooling time of the loop without additional heating (Serio et al. 1991) needs to be calibrated as a function of the slope of the flare decay in the vs. plane. This allows to derive from the observed quantities and and thus to derive the loop length from the relationship

where and is the actual peak temperature of the plasma in the flaring loop, which in turn needs to be calibrated as a function of the maximum temperature determined through spectral fitting of the observed flare spectrum . For each instrument thus the two functions that need to be determined are

and

with T in K as in all the following equations.

In general, implies that sustained heating is present during the decay of the flare, and thus that the assumption of free decay of the flare will lead to overestimate the size of the flaring region, by a factor roughly comparable to itself. In practice this means a shallow decay in the vs. plane, i.e. the temperature of the flaring plasma decays more slowly than its emission measure. When , the size of the flaring region estimated assuming free decay will be very similar to the size estimated with the present approach.

Using temperatures and emission measures determined by spectral fitting to EXOSAT ME data the function is

where the range of validity for the relationship is also given. The peak temperature is given by

For the GINGA LAC detector the corresponding relationships are

with , , . The actual peak temperature of the plasma in the flaring loop is related to the observed peak temperature of the flare through

Finally, if ROSAT PSPC-derived temperatures and emission measures are used,

while

© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000
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