## 3. Flare modellingBoth models that we will apply to the X-ray light curve of the 1994 flare of HU Virginis were initially developed to describe solar flares. Since they approach the problem from two different sides it is very interesting to see how consistent the results will be. Earlier applications of these models to ROSAT observations of long duration flares were discussed by Schmitt (1994) and Kürster & Schmitt (1996). ## 3.1. Rebinning the light curveSince both flare models just describe the long-term trend in the light curve and cannot account for the fine structure in the onset and at the beginning of the maximum, we rebinned the data into one point per ROSAT-observation "slot" (which typically lasts for 2000 seconds) by taking the mean of all original points weighted with the inverse error. As a conservative approach we adopted the standard deviation of all (original) data points within a slot from the slot mean value as the error of the new points. These rebinned values are shown in Figs. 4 and 5.
## 3.2. Model 1: a quasi-static cooling flareThe quasi-static cooling loop model of van den Oord & Mewe (1989) assumes that a single coronal loop cools via X-ray emission whitout any further heating (conductive cooling is negligible). This model provides information only for the decay phase of the flare light curve and does not consider the flare onset and thus the heating mechanism. A more detailed description of the model can be found in the paper by van den Oord & Mewe (1989). The radiative energy per unit time released during the flare is given by: where is the radiated energy at the peak of
the flare, is the temperature at the peak of the flare,
the particle density and
() the emissivity or radiative cooling function.
From a -fit to the decay phase, using
and as free parameters,
we obtain the best value for the radiative cooling time of
= sec and
= cts sec This best-fit model is plotted along with the observed decay phase
of the flare in Fig. 4. Since we have no spectral information
with the HRI detector we must estimate the peak temperature
and the emission measure
by using values from PSPC observations of similar X-ray flares on
other RS CVn-type stars. We adopt = 5.8
K and = 7.3
cm ## 3.3. Model 2: a two-ribbon flareThe two-ribbon flare model (Kopp & Poletto 1984) describes a
quite different astrophysical scenario. Most importantly, further
heating is implicitely accounted for. The model describes the
two-ribbon type flares observed on the Sun where reconnection of an
open magnetic field structure delivers the energy from which a certain
fraction goes into X-rays. The open field structure was created before
the flare by a disruptive event and the emission occurs in an arcade
of "post-flare loops". Actually, the energy reservoir of the flare is
the difference between the non-potential magnetic field where , and is the
Legendre polynomial of the order where is the time it takes the neutral point
to reach its maximum height
( is the stellar radius). The parameter If one could fit the model to the observational data to distinguish
between different values of
Four values for © European Southern Observatory (ESO) 1997 Online publication: March 26, 1998 |