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Astron. Astrophys. 362, 281-288 (2000)

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4. The 1.4 GHz emission

The observed 1.4 GHz emission is shown in Fig. 2 as a function of the phase during the three days of observation separately. In Fig. 3 a summary of the behavior of other three frequencies as a function of the phase for the whole observing run is reported. The smooth variations of the radio flux and of the circular polarization at the higher frequencies will be discussed elsewhere, together with a numerical model for the continuum radio emission from MCP stars.

[FIGURE] Fig. 2. Flux density (Stokes I) at 1.4 GHz as a function of rotational phase, computed with the Pyper et al. (1998) ephemeris, in the three days of observation.

[FIGURE] Fig. 3. Radio emission at 15, 8.4 and 5 GHz during the three days of observation as a function of the rotational phase. No strong enhancement of the emission has been observed at any of those frequencies, rather a modulation is evident. Moderate circular polarization (Stokes V) has been detected at 8.4 and 5 GHz, with a percentage not greater than 10%, in the range of phases 0-0.3 and 0.8-1, slowing variating with the phases.

4.1. Correlation with the magnetic field

Since Leone & Umana (1993) reported a correlation between radio emission and effective magnetic field in HD 37017 and HD 37479, we look first at a similar correlation for our data. Fig. 4, upper panel, shows the 1.4 GHz emission as a function of the rotational phase. This emission is characterized by two or three components: a basal flux of [FORMULA] mJy and very large increments of the flux around phases 0.35-0.45 and 0.75-0.85, where it goes up to 15 mJy, and secondary peaks of up to 7 mJy, further discussion of which is deferred to Sect. 5.2.2. Only in two moments, at phase 0.85 and 0.97, the intensity drops below 1 mJy. Phasing the magnetic data from Borra & Landstreet (1980) and Pyper et al. (1998) (Fig. 4, lower panel), we found that those peaks of the radio emission coincide approximately with the the null magnetic field, i.e. when the axis of the dipole is almost perpendicular to the line of sight. The peak visible at phase 0.35-0.45 is defined by the observations on June 2 (maximum) and 6 (rising phase), and the 0.75-0.85 one on June 2 (rising phase) and 11 (maximum) (see also Fig. 2). According to the accuracy of the period given by Pyper et al. (1998), our data are phased with respect to the magnetic data better than [FORMULA].

[FIGURE] Fig. 4. Upper panel: 1.4 GHz emission from CU Vir; Lower panel: Longitudinal magnetic field measurements from Borra & Landstreet (1980) and from Pyper et al. (1998) (open and filled circles respectively) as a function of the rotational phase. 1.4 GHz radiation maxima correspond approximately with the null magnetic field.

It is worthy to note that the flux density of the peaks is about five times larger than those previously reported in the literature at this frequency for MCP stars. Previous observations of CU Vir reported by Leone et al. (1996) show that the 1.4 GHz flux is 2.6 mJy, in agreement with the "out of peaks" emission here reported.

The high flux increment, that occurs at the particular orientation of the magnetosphere, indicates an emission mechanism that is not explainable with the emission models up to now proposed. In the following, we will analyze further characteristics of this emission.

4.2. Polarization

A further exceptional aspect of the 1.4 GHz is its high degree of circular polarization. Fig. 5, where the Stokes V parameter (V = 1/2(RCP-LCP)) is plotted versus the rotational phase, shows that the increment of the flux occurs only in the right-hand circular polarization. Six peaks, denoted with the letters from a to f  in Fig. 5, are visible, the largest and broad emission being detected in peaks a and d , that occur in coincidence with the null magnetic field. Outside the peaks, the Stokes parameter V is statistically null. The percentage of polarization [FORMULA] goes up to 80% during the main peaks a and d . If we subtract the continuum radio emission, that contributes for about 3 mJy, we get [FORMULA]%.

[FIGURE] Fig. 5. Stokes parameter V versus rotational phase in the 3 days of observation. No polarization is seen outside the peaks denoted with the letters from a to f. The higher fluxes (a and d ) are visible when the magnetic axis is perpendicular to the line of sight.

In order to verify if the behavior of the right-hand circular polarization was not due to an instrumental problem, we looked for other sources in the field of our star to be monitored for the polarization at the same times of our observations. Leone et al. (1996) found in the 6 cm VLA frames centered at the CU Vir position a radio source with coordinates: [FORMULA] and [FORMULA], that they used to check possible instrumental effects. This field source is visible also in the 1.4 GHz map showed in Fig. 6 and has a flux density (Stokes I) of about 3 mJy, comparable with CU Vir outside the peaks. By comparing the polarizations (Stokes V) of the field source and of CU Vir, we can rule out any instrumental effects (Fig. 7).

[FIGURE] Fig. 6. The 1.4 GHz radio map of CU Vir showing the field source used to check possible instrumental effects.

[FIGURE] Fig. 7. Stokes V for the field radio source as function of the corresponding rotational phase of CU Vir. The Stokes I is 3 mJy. The absence of variability in the polarization confirms that no instrumental problem occurred during the observations.

4.3. Directivity of the radio emission

Since the polarized peaks have been observed in the three different days of observation, we can conclude that this radiation is stable at least in a period of weeks. The observed variations can be due to the different inclination that the oblique dipole forms with the line of sight as the star rotates. In a particular geometric configuration, highly beamed radiation is emitted toward the Earth, producing the observed peaks. As already pointed out, the main peaks of the right-hand circular polarization corresponds almost to the zero of the average magnetic field over the surface of the star. This means that the maxima of this emission occur when the magnetic axis is almost perpendicular to the line of sight.

Borra & Landstreet (1980) found that the magnetic curve is delayed with respect to the light curve. Assuming that the two main peaks occur in two symmetric orientations of the magnetosphere, we can compute this shift with good accuracy: from our data, peaks a and d show their maxima at phases [FORMULA] and [FORMULA] respectively, and therefore


Once the geometry of the magnetosphere of the star has been defined by the values of the inclination i and the obliquity [FORMULA] (see Table 1), we can find the angle [FORMULA] that the line of sight forms with respect to the axis of the dipole, defined by:


The error of [FORMULA] estimated from this relation and from the uncertainty in the angles i and [FORMULA] is about [FORMULA] when [FORMULA] and [FORMULA] when [FORMULA] and [FORMULA]. Fig. 8 shows the change of the orientation of the star, and so of the angle [FORMULA], with the rotation.

[FIGURE] Fig. 8. Changes of the geometry of CU Vir as a function of the rotational phase. The point V at the center of the star is the intersection of the stellar surface with the line of view; the point R close to the top is the rotational pole; the points denoted with N and S represent the North and South magnetic poles; the arc V-N subtends the angle [FORMULA]. [FORMULA] and [FORMULA] are indicated in each panel. The main peaks are visible when the star is oriented as in the two framed panels at [FORMULA] (peak a) and at [FORMULA] (peak d).

Fig. 9 shows the behavior of the polarized component of the emission as a function of the angle [FORMULA] in a polar view. The main peaks are emitted at an angle of about [FORMULA] with respect to the axis of the dipole (indicated as the arrow B), and have a high degree of directivity, with an half power beam width of about [FORMULA]. For the less intense peaks [FORMULA] and f, the beams have a narrower width of about [FORMULA]. Fig. 10 shows the details of the main peaks as a function of the angle [FORMULA]. It is important to note that the magnetic longitude of the line of sight during the two main peaks are different, since in these configurations the star shows opposite hemispheres (see Fig. 8). This means that the observed phenomenon is not related to an active longitude, depending only on [FORMULA]. It seems to be similar to the pulses observed in pulsars, the magnetic fields of which are, like MCP stars, typically characterized by oblique dipole geometries.

[FIGURE] Fig. 9. Polar representation of the emission, showing the very high directivity of the coherent components. The arrow B represents the axis of the dipole; the emission is plotted as a function of the angle [FORMULA] formed by the line of sight and the axis B.

[FIGURE] Fig. 10. The main peaks a and d as a function of the angle [FORMULA].

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100