4. The origin of the radio variability
In a previous paper we have shown that the observed flat radio spectra of a sample of Algol-type binary systems cannot be reproduced by a homogeneous source model. We thus proposed a two component model (core-halo) to exemplify the complex morphology of the radio source (Umana et al., 1993). The closed magnetic structures of the lower corona would produce a radio source component, the core , characterized by high values of the magnetic field strength and size comparable to, or less then, the active stellar component.
Eventually, energetic particles in the core diffuse into higher coronal open field structures and produce a more extended tenuous radio source, the halo , characterized by weaker magnetic field and a lower density of energetic electrons. For their physical characteristics, the core emits mostly at higher frequencies, while the halo contributes mainly at low frequencies. The observed radio spectrum is therefore the result of these two different contributions and its shape will vary when the physical conditions of one or both components change as a consequence of, for example, flaring activity.
In our model, the core is assumed to be a compact homogeneous source with constant magnetic field (B ) and number density (), while the halo is assumed to be an extended corona with constant magnetic field and a radial dependence of the electron number density, , being the number density at the coronal base (at ) and r the distance from the center of the K secondary. For both core and halo the emission and absorption coefficients have been computed assuming a power law energy distribution of the relativistic electrons, between KeV and MeV, with (Umana et al. 1993).
A more rigorous model of the radio source should include a radial dependence of the magnetic field of the halo, which, for computational convenience, has instead been assumed to be constant. The core-halo morphology, where the source is sampled in two representative layers of different physical conditions, is to be assumed as a simplification of a probably very complex topology of the coronal magnetic field into two magnetic structures: small, compact loops and larger loops that have dimensions similar to the size of the entire binary system.
By applying the two component model to the RZ Cas data it is possible to determine the combination of physical parameters that best fit the observed spectra (Fig. 3).
In our previous paper (Umana et al., 1993, Fig. 3) we showed that, for a homogeneous gyrosynchrotron radio source of radius R and fixed electronic exponent distribution , the shape of the radio spectrum is maintained, while the frequency at which the spectrum peaks and the flux density of the peak shift toward higher values when B , and R increase. A functional form of these dependences can be expressed by:
with all the exponents and . Slightly different exponents can be found for a variable density distribution, as in the halo model, where the radius R is substituted by the thickness of the layer H. Indeed the same core or halo contributions can be reproduced by different combinations of the radius, magnetic field and energetic particle density of the emitting region.
Although is not possible to derive unique solutions, we have constrained the source parameters in small value intervals proceeding as follows. From the best fit of the observed spectra with a core and halo combination, we found the and for each component. Applying these values in Eqs. 1 and 2, a functional dependence of B and on R can be obtained. Thus, if we give some physical constraint on one parameter, we can derive corresponding ranges of the other ones. Among all the possible solutions we can choose a class that satisfies constraints provided by observational evidences.
Photospheric magnetic fields have recently been derived for active components of RS CVns, from the width of magnetically sensitive lines (Gondoin et al., 1985) and by means of the Zeeman-Doppler imaging technique (Donati et al. 1990; 1992). They obtained photospheric magnetic field values in the range of . Since the radio emission from Algols is very similar to that of RS CVns, and, in both cases, it is related to the magnetic activity of such systems (Umana et al., 1998), we can reasonably use similar magnetic field values for the RZ Cas models.
If we assume that the magnetosphere is mainly dipolar, we can restrict the possible range of B values to be those for which .
The results of the fit of various spectra are summarized in Table 3 and shown in Fig. 4 where the derived values of the magnetic field, size and energetic particles density are plotted for the halo (empty symbols) and the core (filled symbols), as a function of time. When two different spectra were obtained in the same day, a single set of physical parameters was determined, because the differences in flux densities were so small that the solution did not require any significant variation in the choice of , B and of the source dimension.The error bar, associated with each physical parameter determination, represents the range of possible solutions that fit the spectra. In the upper part of the plots, the trend of flux density at the 8.4 GHz (X-band) is also shown. The estimated physical parameters agree very well with those derived from radio spectra of other Algol-type binaries (Umana et al., 1993).
To better appreciate how each component contributes to the observed spectra, we plot in Fig. 5 the ratio of energy emitted by the halo and the core, together with the total luminosity of RZ Cas, as inferred integrating the core-halo spectra from 0 to 40 GHz.
From Fig. 4 and Fig. 5 it appears that the physical characteristics of the two components remain almost constant during the low flux density regime. During those periods, source extension, B and do not show significant variations, and we can assume these values as the stationary properties of the coronal emitting regions.
During the active period (data between dashed vertical lines in Fig. 4) the physical parameters of both the halo and core show significant changes. The magnetic field of the halo is found to considerably increase (about a factor of 6) while the effective size is apparently decreased. The contribution to the total flux becomes greater due to the combination of the increase of the magnetic field and the number density. Thus the halo seems to be characterized by more compact coronal structures, which contribute an almost equal amount as the core to the observed spectrum of the active source (Fig. 5).
The magnetic field and size of the core do not show significant changes with respect to the quiescent period, however the electron density number is increased up to a factor of ten, with large fluctuations. This is not surprising, because the core is probably the site where energetic emitting particles are produced and thus where radio flares originate. Moreover, due to its compact dimension, the core may evolve in a time scale much shorter than the more extended halo.
Probably a flare-like event occured on 13 Feb. The higher values of B and we derived for the core seem to indicate that an energy release was first localized in a very compact region. At this point, i.e. on February 15, it propagated towards external coronal layers, the halo contribution became more important, the radio flux increased at all the observation frequencies but at 22 GHz, which would be the first frequency to suffer the effects of the fading core.
© European Southern Observatory (ESO) 1999
Online publication: February 23, 1999