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Astron. Astrophys. 333, 970-976 (1998)

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2. Observed spectra during the rising phase

In spite of the difficulties outlined in the introduction, we can extract from the data some interesting examples of flaring activity. Among the available spectra of flares, we have selected those showing an increase in the measured flux density in a time interval of less than a few hours, which can be attributed to the rising phase. The data are plotted in Fig. 1, where different symbols refer to different orbital phases.

[FIGURE] Fig. 1. Observed flux density versus frequency at different times for four flares during the rising phase. a Flare 1: [FORMULA] corresponds to Julian Date 2448965.170; b Flare 2: [FORMULA] corresponds to J.D. 2449462.930; c Flare 3: [FORMULA] corresponds to J.D. 2449467.790; d Flare 4: [FORMULA] corresponds to J.D. 2449478.160

The following considerations are suggested by these figures. First of all, since the emission can increase only if an energy supply (in form of accelerated particles) is present, the time scale of the rise in the flux density gives an idea of the duration of the acceleration mechanism. From our observations we can infer that the particle acceleration can last, in some cases, for as long as two days (a phase difference of 0.01 corresponds to 1.54 hours); however, our data are sampled at long time intervals, and we cannot exclude that particles are accelerated in a succession of short time scale pulses, thus producing a series of bursts of shorter duration. Since we do not have the possibility to know the real substructure of the observed bursts, we will consider them as single flares. An example of "long-lasting energy injection" is shown in Fig. 1c (flare 3) where, at [FORMULA] GHz, the emission increases for as long as 23 hours.

The second important point is that, during active phases, the radiation received from UX Arietis has a positive spectral index ([FORMULA] with [FORMULA]) for 1.4 GHz [FORMULA] 10 GHz, except for flare 4 where [FORMULA] only for 1.4 GHz [FORMULA] 5 GHz. The measured values of [FORMULA] are different from flare to flare and vary with time during the same flare, ranging from 0.31 to 0.73 between 2.7 and 5 GHz, and from 0.13 to 0.38 between 5 and 10.5 GHz, with the exception of flare 4, for which the latter is -0.11. These values agree with the spectral indexes measured in other RS CVn spectra, that, between 1.4 and 5 GHz, are in the range [FORMULA] (Mutel et al. 1987), with higher values corresponding to higher luminosity periods. However, the spectra presented here show only positive spectral indexes in this frequency range, implying that this is a peculiarity of the flare rising phases. In fact, the peak present in the spectra at higher frequencies shifts in time towards lower frequencies and the spectral slope changes sign only when the emission is decreasing.

The common interpretation for positive spectral indexes at radio wavelengths is that of self-absorbed (gyro)synchrotron radiation. Dulk (1985) has derived approximate expressions for gyrosynchrotron emission from an homogeneous source in the case of an isotropic power-law electron energy distribution:

[EQUATION]

in this case the radiation spectrum at radio wavelengths has a positive self-absorbed spectral index

[EQUATION]

peaks at [FORMULA] and decreases for [FORMULA]. However, the values of [FORMULA] measured for UX Arietis strongly deviate from the canonical slope (Eq. (2)). On the other hand, the observed spectrum cannot be interpreted as a consequence of the evolution of the distribution due to energy losses (collisional, radiative or other), since this kind of mechanism only affects the optically thin part of the spectrum (Chiuderi Drago & Franciosini 1993; Franciosini & Chiuderi Drago 1995). In addition, the data show that [FORMULA] deviates from the value 2.5 even when the flux density is increasing; indeed, during the rising phase the features of the spectrum cannot be ascribed to energy loss mechanisms only.

If we assume that gyrosynchrotron emission is the real emission mechanism, as widely accepted, the only possibility to explain the observed spectra is that geometrical effects influence the emitted radiation through the spatial distribution of the magnetic field. In fact, we can imagine the emission from a non-homogeneous source as the superposition of the contribution from many different homogeneous sources. Since the emission from each homogeneous part peaks at [FORMULA], whose value depends mainly on the magnetic field strenght ([FORMULA], see Dulk 1985), the greater is the contribution from regions of high intensity field, the higher is the frequency at which the global spectrum peaks. In other words, the high frequency part of the spectrum comes from regions of strong magnetic field while the low frequency part is mainly due to the emission from regions of weak magnetic field. This implies that the diffuse and compact source components contribute to the emission at low and high frequencies, respectively. The superposition of different spectra can also explain why the optically thick ([FORMULA]) part of the observed spectrum has a slope different from [FORMULA].

The above qualitative interpretation of the observed spectra suggests that a model intended to reproduce their evolution must include at least two features: a non-uniform source, which is necessary both for its influence on the spectral slope and for the observational evidence of a periodic shadowing of the emission (as outlined in the introduction); and a long lasting energy supply, needed to reproduce the increasing radio flux.

The time evolution of the electron population in a non-homogeneous magnetic field, when accelerated electrons are continuously injected in the source, is described in the following section.

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© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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