Astron. Astrophys. 342, 709-716 (1999)

5. Physical properties of the radio corona

RZ Cas was first detected in the soft X-ray range by Mc Cluskey & Kondo (1984). Recently its coronal X-ray emission has been the object of an extensive study by Singh et al. (1995), based on both ASCA and ROSAT observations. In particular they observed RZ Cas in the energy band between 0.1 and 4 KeV with the PSPC on board the ROSAT satellite, in two different epochs, on 1991 September (two scans) and on 1992 February (two scans).

These observations demonstrated that the source is highly variable in the X-ray domain, showing three different regimes of X-ray emission, that the authors define as low, mid and high state. The counts/s measured during the high state were almost a factor of six higher than those of low emission levels.

From spectral analysis of their data Singh et al. (1995) derived that the X-ray emission is consistent with the contribution of two different isothermal components, characterized by different volume emission measures (EM ). The possibility to better fit the observed X-ray spectra with two isothermal components instead of using a continuous power-low distribution of EM has been pointed out in several X-ray observations of active binaries (Schmitt et al., 1990; White et al., 1994). This seems to indicate the presence of a highly structured, perhaps bimodal, corona.

The X-ray observations, performed on 1992 February 5, are almost simultaneous to our microwave spectrum, obtained just 2 hr before the first X-ray acquisition. During these observations the X-ray source was at the mid state. Since in the two X-ray scans, obtained more than 10 hrs apart, the same fluxes were observed, we may assume that the source was constant over hours and that the X-ray emission was due to optically thin gas, in near equilibrium between radiation and heating. In the following, we will therefore utilize the physical parameters, determined by Singh et al. (1995), to further constrain the structure of the radio emitting corona.

From spectral analysis of the February 5 observations Singh et al. (1995) derived for the first component and ] and for the second component and ]. There is still a very active debate as to whether in active binaries the bulk of high-temperature X-ray emission comes from high density, very compact loops (Schrijver et al., 1995) or is associated to large, low density coronal structures (Siarkowski et al., 1996) and there is observational evidence that supports both possibilities.

In the following, we will assume that the dimensions of the higher temperature component are bigger than those of the lower temperature component. If the X-ray and the radio sources are co-spatial, the coronal emission regions can be separated into two separate kinds of magnetic structures: low temperature, smaller loops, which are associated with the core, and higher temperatures, larger loops, associated with the halo.

There are two principal requirements that a co-spatial model of the source must satisfy: first, the magnetic field should be able to contain the source, i.e., the density of magnetic energy should be greater than the kinetic energy of the local thermal plasma; second, the local plasma must have such a density that should not affect the radio emission by absorption.

In this scenario we can therefore derive the thermal plasma density from the X-ray data and check if the magnetic field, as determined from the radio data, can contain the X-ray source. If the plasma density is uniform in a volume V, we can write . Thus, assuming that the X-ray emission arises from a spherically symmetric source of radius equal to the radio source we can estimate the thermal plasma density in the core and in halo, which result to be and respectively. The range of values corresponds to the possible solutions for the radius of the source (see Sect. 4).

Because the plasma must be confined by the magnetic field, the plasma , defined as the ratio between the density of kinetic energy to the density of magnetic energy, must be less than unity. We can write as:

where P represents the pressure of the thermal plasma. By replacing for P , and using the values of magnetic field, as derived from radio observations, we will obtain for the core and for the halo, i. e., the magnetic pressure exceeds the gas pressure, and thus the magnetic field is strong enough that the core and halo components can be stable structures.

We consider now the possible effects that the ambient thermal plasma might have on the propagation of the radio emission. Gyrosynchrotron emission will be suppressed whenever the refractive index is significantly smaller than unity (Razin effect), i.e. at frequencies below the critical value given by:

When the proper values for the core and the halo are substituted in Eq. 4, the result is that in both cases the observation frequencies are well above the critical frequency .

In conclusion, the structures assumed for the radio source are stable, i.e. using parameters consistent with the almost simultaneous X-ray observations, they can be contained by the magnetic field. Moreover, the local plasma densities, as derived from X-ray observations, assuming the source dimensions determined from our core-halo radio model, allow the propagation of the radio waves in the corona.

We reobserved the system on February 6, just 7 hours after the last X-ray observations. We found a slight difference in the high frequency part of the radio spectra, obtained in the two consecutive days, consistent with a higher contribution of the core to the resultant radio flux density. This conclusion is supported by the fact that the physical characteristic of the halo did not change between the two radio observations (see Fig. 4).

The high frequency part of the radio spectrum is strictly related to the energy content of the emitting population. Thus, a variation of the slope in this range of frequency will reflect how the energy of the relativistic electrons varies as a consequence of the energy loss mechanism operating in the radio emitting region. The different contribution of the core on February 6 can be therefore ascribed to a higher efficiency of the loss mechanism in more compact magnetic structures. However the overall observed flux density remained at a comparable level to Feb 5. If we assume as the quiescent or basal flux density of RZ Cas the level measured on 1991 Oct 5 or 1992 Apr. 25 ( [mJy]), we may conclude that, as in the X-ray regime, in the period between Feb 5 and 6, the radio emis sion of RZ Cas showed a kind of "middle state" of energy level.

Gyrosynchrotron emitting electrons, injected in loops filled by thermal plasma of density , will thermalize in a time scale given by (Benz & Gold, 1971):

where E represents the electron energy expressed in MeV. This time, for electron energies in the range between , will be minutes for the halo and minutes for the core. This means that to maintain the observed mid state level for up to two days a continuous ejection of relativistic electrons in the coronal regions is necessary.

© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999
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