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

1. Introduction

The study of the decay of large, long-duration stellar flares is one of the key tools for deriving information about the spatial structure of stellar coronae. In the past a variety of techniques has been applied, most of which contain, either explicitly or implicitly, the assumption that the flaring plasma, after an initial more or less impulsive heating event, decays freely by a combination of radiative and conductive cooling. This has often been justified by analogy with impulsive solar events, which are confined to a single loop and which are thought to freely decay after an initial impulsive heating event. These techniques, when applied to intense, long-lasting stellar flares, invariably yield very large flaring loops, with sizes comparable to, or at times much larger than, the star itself. For active binaries these result have prompted the idea of inter-binary loops, with magnetic structures linking the two stars (Uchida & Sakurai 1983). While in the case of the Sun many large flares belong to a different type (the so-called two-ribbon events) in practice the formalism with which they have been described (e.g. Kopp & Poletto 1984) requires many assumptions to be made when applied to spatially unresolved stellar events, so that it has not been possible to use it to obtain well-constrained information about the spatial structuring of stellar coronae.

More recently, a different approach to derive the size of the flaring region from the analysis of the flare decay has been developed by Reale et al. (1997), based on a line of work on the solar corona going back to the classic Rosner et al. (1978), through the studies of e.g. Serio et al. (1991), Sylwester et al. (1993) and Reale et al. (1993). This approach is based on hydrodynamic simulations of decaying loops, and explicitly considers the presence of (decaying) sustained heating also during the decay phase of the flare. Its validity has been shown first on the Sun (Reale et al. 1997), where the availability of Yohkoh images of the flaring events has allowed to compare the decay-derived size with the actual geometrical size, and later on the flare observed on Algol by BeppoSAX (Favata & Schmitt 1999), in which the presence of a total eclipse has allowed to derive the size of the flaring region from geometrical considerations, without any a priori assumption on the characteristics of the flaring region itself. In both cases this approach has proven to have a much better diagnostic power than approaches based on the assumption of free decay. For example, the quasi-static method of van den Oord & Mewe (1989) predicts, for the Algol BeppoSAX flare, much larger loop sizes than actually observed through the flare eclipse.

One of the key results obtained through the application of this approach both on solar and stellar events is the almost ubiquitous presence of sustained heating during the decay of flares. Sylwester et al. (1993) and Reale et al. (1997) have shown that sustained heating is also present in many compact solar flares, so that their classification as "impulsive events" is actually deceptive. The application of the same approach on stellar flares, on a range of different stellar types - i.e. Reale & Micela (1998), Favata et al. (2000b) and Favata et al. (2000a) on flare stars, Favata & Schmitt (1999) on Algol, Maggio et al. (2000) on AB Dor - has shown that sustained heating is invariably present in all the events studied. In many cases (specially for the large flares) the decay is actually dominated by the time-profile of the heating rather than by the behavior of the flaring loop. An immediate consequence of the presence of sustained heating during the decay phase is that the size of the coronal structures in which the flaring plasma is confined is significantly reduced: previous estimates based on the assumption of free flare decay normally resulted in loops as large or larger than the star itself. Once the presence of sustained heating is accounted for the loops invariably become smaller, with typical sizes . The smaller inferred loop sizes implies that for very active stars the filling factor of stellar coronae needs not be very high to explain the observed coronal luminosity: in the case of the flare star AD Leo (Favata et al. 2000a) even rather small filling factors (a few percent) can explain the observed coronal luminosity.

Algol is a binary system with of a B8 V primary and a K2 IV secondary (plus a more distant tertiary component, with a period of  yr and a spectral type A or F). The basic parameters are (Richards 1993) , and  cm, , with orbital inclination  deg. The orbital period is  d. The separation is 14.14 , or times the radius of the K star.

Algol is a key object for the study of stellar activity: late B stars are not expected to have neither the outer convective envelope required to sustain a dynamo and thus a corona nor the strong, shocked stellar wind which is thought to be responsible for the X-ray emission observed in O and early B stars. Indeed late B stars are in general observed to be X-ray dark (Grillo et al. 1992). The X-ray emission seen in a minority of late-B stars is normally explained as coming from an unseen, low-mass nearby companion. Thus, the high level of magnetic activity observed in Algol is expected to be confined to the K-type secondary, in which the deep convection zone coupled with the rapid rotation will sustain a vigorous dynamo. Therefore complex, inter-binary magnetic loops are unlikely to be present, and the corona will likely have the same structure as the one of a single star with comparable levels of activity. The high activity level and proximity to Earth of Algol allow for high spectroscopic observations to be performed. The presence of the X-ray-dark B-type primary which eclipses the active K-type secondary has allowed to obtain, for the first time, a geometrical estimate of the size of a flaring structure on a star other than the Sun (Schmitt & Favata 1999). Its high radio luminosity (Mutel et al. 1998) allows detailed VLBI imaging, making a comparison of the radio and X-ray corona possible. Also, the high frequency of large flares on the active K-type secondary makes it a target of choice: indeed by now a significant database of X-ray observations of Algol exists, and four large flaring events have been observed (by EXOSAT, GINGA, ROSAT and BeppoSAX), so that the frequency of (large) flares can be estimated as approximately one every two orbits, i.e.  d (Ottmann & Schmitt 1994). The orbital period is 2.87 d, and each optical eclipse lasts approximately 10 hr.

In the present paper we aim to characterize the corona of Algol by studying all known large X-ray flares in a homogeneous way, using the approach based on hydrodynamic simulations of the decaying loops of Reale et al. (1997), together with the published studies on the radio corona of Algol and on its quiescent X-ray emission. Through this systematic approach we obtain a consistent picture of Algol's corona, and verify that the conclusions obtained by Schmitt & Favata (1999) and Favata & Schmitt (1999) from the analysis of the BeppoSAX flare have a far more general applicability. The flaring events studied here have been analyzed in the past with a consistent methodology, the so-called quasi-static approach, which van den Oord & Mewe (1989) originally applied to the EXOSAT Algol flare. The GINGA flare was analyzed by Stern et al. (1992), while the ROSAT one was studied by Ottmann & Schmitt (1996), in both cases using the same method as used for the EXOSAT event. In all cases the size of the coronal structure responsible for the flaring event was found to be larger than the stellar radius (see Table 1). Although the van den Oord & Mewe (1989) approach considers the possibility of heating during the decay phase, the fit to the EXOSAT and ROSAT events did not require sustained heating (which, as we show in the following, is actually present). For the GINGA event the lack of sustained heating was actually assumed, rather than derived from the data.

Table 1. A comparison of the physical parameters derived for different flares on Algol from the GINGA, EXOSAT, ROSAT and BeppoSAX flares. : observed maximum temperature during the flare. : observed temperature at the beginning of the flare's decay (i.e. at the peak of the flare's emission measure or count rate). : peak emission measure of the flare. : decay time of the flare's light curve (or emission measure), as determined here. : density of the flaring plasma at the beginning of the decay phase as determined by the quasi-static analyses in the original papers. : ratio between the observed luminosity decay time and thermodynamic free decay time of the loop . : length of the flaring loop determined by the quasi-static analyses of the original papers: : length of the flaring loop determined here. n: density derived through the observed peak emission measure and the loop length ; the first value assumes loops with aspect ratios while the second one assumes . Numerical subscripts indicate the power of 10 by which the relevant quantity has been scaled.

The present paper is so structured: Sect. 2.1, 2.2 and 2.3 contain the analysis of the Algol flares observed by EXOSAT, GINGA and ROSAT, respectively; the essential results from the BeppoSAX flare are recalled in Sect. 2.4; Sect. 3 discusses the available evidence from radio observations, comparing it with the information from X-ray observations, while Sect. 4 presents a consistent scenario for Algol's corona explaining both the X-ray and radio observations. A brief Appendix contains the detailed prescriptions for application of the Reale et al. (1997) method to flaring events observed with the EXOSAT ME and the GINGA LAC instruments, as well as for events observed with the ROSAT PSPC which have sufficient statistics for the flare decay to be resolved into individual spectra.

© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000
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