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

2. Analysis of the flaring events

2.1. The EXOSAT flare

EXOSAT observed Algol on 18 and 19 August 1983, for a total of  hr. During the observation with the Medium Energy (ME) detector a significant flare was detected, which has been analyzed in detail by van den Oord & Mewe (1989). The ME detector had a bandpass of to  keV and an energy resolution of at 6.7 keV. The spectral fitting to the ME spectra gives a flare peak temperature  MK and a peak emission measure  cm^-3. The main result of the van den Oord & Mewe (1989) analysis is that the flare is found to satisfy the condition for quasi-static decay, with no evidence for prolonged heating (i.e. it is seen as an "impulsive" event), with a resulting loop length  cm, or .

We have analyzed the same flare with the Reale et al. (1997) approach, using the temporal evolution of the temperature and emission measure as determined by van den Oord & Mewe (1989). The results are shown in Fig. 1: the effective decay time of the X-ray count rate ¹ is  ks ², while . Application of Eq. (A.4) yields , showing that the thermodynamic decay time of the loop is significantly shorter than the observed decay time , and therefore that sustained heating is present during the decay phase. The lack of sustained heating was, in van den Oord & Mewe (1989), a result obtained by fitting the data, i.e. was not assumed; thus, the assumptions of the quasi-static heating method may not be appropriate for real stellar flares, and its diagnostic power for the presence of decay-phase heating is likely to be limited. The thermodynamic decay time of the flaring loop is only  ks, while the maximum temperature (from Eq. (A.5)) is  MK and the resulting length of the flaring region is  cm, or .

Fig. 1. The evolution of the EXOSAT Algol flare. The top panel shows the evolution of the emission measure during the flare, together with the best-fit exponential decay, while the bottom panel shows the evolution of the flare's decay in the vs. plane. The dotted line connects the points in their temporal order, while the solid line is the best fit to the decay.

2.2. The GINGA flare

Algol was observed by GINGA with the LAC (Large Area Counter) instrument in January 1989, covering approx. 22 hr elapsed time. The LAC has a passband of 1.2-37 keV, with an energy resolution of 18% FWHM at 5.9 keV. The observation (analyzed by Stern et al. 1992) contains two flares, the largest of which (starting at about Jan. 14 02:00 UT) features a factor of increase in count rate in the LAC.

Stern et al. (1992) have studied the large flare in detail, deriving the temporal evolution of the spectral parameters and analyzing the decay phase to obtain the physical parameters of the flaring regions using the quasi-static approach previously used on the EXOSAT Algol flare by van den Oord & Mewe (1989). The peak temperature of the event is  MK, the peak emission measure  cm^-3, and the e-folding time of the X-ray luminosity 20.0 ks. The EXOSAT analysis has been scaled by Stern et al. (1992) to derive (under the same assumptions) a loop length of  cm () and a density  cm^-3. Later, Stern (1996) plotted the evolution of the same event in the vs. , without however drawing any specific conclusions from it.

Our analysis of the GINGA event within the sustained heating framework uses the temperature, count rate and emission measure values published by Stern et al. (1992). The evolution of the GINGA flare is shown in Fig. 2, where both the light-curve and the vs. diagrams are shown, together with the best fits to the decay phase. The quiescent emission count rate (18 cts s^-1) determined during the same observation has been subtracted from the plotted light-curve. The light-curve e-folding time is  ks, while the slope of the decay in the vs. diagram is , with (derived through Eq. (A.6)). Such large value of implies very strong sustained heating, so that the light-curve is in this case dominated by the temporal evolution of the plasma heating rather than by the natural decay of the flaring loop. The peak temperature of the flaring loop is (from the observed peak temperature  MK and Eq. (A.7))  MK. The resulting loop length is (Eq. (A.1))  cm (); the significant difference with the result of Stern et al. (1992) is due to the dominating influence of sustained heating.

Fig. 2. The evolution of the GINGA Algol flare. The top panel shows the (background-subtracted) flare's light curve, together with the best-fit exponential decay, while the bottom panel shows the evolution of the flare's decay in the vs. plane. The dotted line connects the points in their temporal order, while the solid line is the best fit to the decay.

2.3. The ROSAT PSPC flare

A long observation of Algol was performed with the ROSAT PSPC detector in August 1992, spanning 2.4 orbits of the system ( ks elapsed time), although with an irregular sampling. During the observation a large flare (with a increase in count rate) was observed. The event has been analyzed in detail by Ottmann & Schmitt (1996), using the quasi-static framework. The decay time scale reported by Ottmann & Schmitt (1996) is  ks, and the peak temperature determined through the PSPC is  MK. The quasi-static fit performed by Ottmann & Schmitt (1996) includes (as for the EXOSAT event) allowance for the presence of heating during the decay phase; however the best-fit value of the heating function is zero, so that no sustained heating is evident from the quasi-static analysis. The derived loop lenght is  cm, or . The derived density is  cm^-3.

We have analyzed the Algol PSPC flare, as shown in Fig. 3, adopting the spectral parameters of Ottmann & Schmitt (1996). The top panel of Fig. 3 shows the light curve (together with the best-fit exponential decay, which has  ks), while the bottom panel shows the flare decay in the vs. plane. The decay's slope () implies (through Eq. (A.8)) a ratio , thus showing that significant sustained heating is present, again though the quasi-static analysis (even in its full blown formalism, as used by Ottmann & Schmitt 1996) explicit derives its absence (a situation similar to the one of the EXOSAT flare, Sect. 2.1). The flare's peak temperature (scaled from the maximum measured temperature of 44 MK through Eq. (A.9)) is  MK. Through Eq. (A.1) the derived loop length is  cm, or .

Fig. 3. The evolution of the PSPC Algol flare. The top panel shows the (background-subtracted) flare's light curve, together with the best-fit exponential decay, while the bottom panel shows the evolution of the flare's decay in the vs. plane. The dotted line connects the points in their temporal order, while the solid line is the best fit to the decay.

The temporal coverage of the PSPC flare is rather sparse, in particular the first phase of the decay (immediately following the three points at cts s^-1 in Fig. 3) has not been observed. This introduces a large potential systematic error in the determination of the flare's physical parameters. In particular the decay time of the light curve could be over-estimated: if the flare would have been "hovering" near the peak, during the observing gap, the actual decay would be faster than observed, and thus the flaring loop smaller than derived here. Thus, in this case the derived length should be considered as an upper limit to the actual size of the loop.

2.4. The BeppoSAX flare

The large flare observed by BeppoSAX on Algol in Aug. 1997 was already analyzed in detail, using the Reale et al. (1997) approach, by Favata & Schmitt (1999). Due to the complex evolution of the event (with the temperature rising again midway through the decay) the hydrodynamic modeling yields a wide range of possible values for the loop's length, comprised between 47 and  cm (1.8 and 4.8 ), while the observed eclipse puts an upper limit of  cm (0.9 ) on the loop size (on the assumption of a simple loop geometry, as the actual eclipse constraint is on the maximum height of the flaring region above the stellar surface, which is  cm, or ). Thus, the loop is smaller than the stellar size, and even the hydrodynamic simulation modeling is, if anything, likely to somewhat overestimate the loop's size. Additionally, the eclipse timing (Schmitt & Favata 1999) shows that the event is located above the southern polar cap of the K-type secondary.

2.5. Plasma density and scale height

No direct estimate of the plasma density is produced by the approach used here to analyze the flares. However, a simple estimate can be obtained by dividing the emission measure by the loop volume, i.e.

where is the loop's aspect ratio. In the solar case typically , and this value has often been used (assumed) also for stellar flares. However, recent analyses (Favata et al. 2000a; Maggio et al. 2000) of stellar flares with the same approach used here point to a larger value for stellar flaring loops, with giving a better agreement between the pressure so derived and the pressure obtained by applying the scaling laws of Rosner et al. (1978) to the observed loop sizes and temperatures. We have therefore used both and in computing an estimate for the loop's density, as reported in Table 1. For all flares analyzed here, the plasma densities are typically  cm^-3.

Also, all derived loop sizes are small in comparison with the pressure scale height ³ in the corona of the active star in Algol, which is greater than  cm for all the events discussed here, thus justifying the initial assumption done in the modeling that the flaring loops are isobaric.

© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000
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