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

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5. Discussion

To explain the radio continuum and the X-ray emissions from young magnetic B stars and Bp-Ap stars, André et al. (1988) proposed a model where the stellar wind plasma flows out near the magnetic poles along the field lines. Far from the star, such a wind draws the field lines near the equator into current sheets which should be location of particle acceleration. Mildly relativistic electrons return to regions near the star by traveling along the magnetic field lines, emitting gyrosynchrotron radiation. This model has been applied by Linsky et al. (1992) to explain the flat spectra of the MCP stars.

The characteristics of the polarized component of the radio emission at 1.4 GHz from CU Vir, that show high degrees of circular polarization and high directivity, can be explained in terms of coherent emission. The two major mechanisms that have been suggested to explain coherent radio emission are plasma radiation due to Langmuir waves and cyclotron maser. Plasma radiation has been invoked in several cases, such as solar microbursts at 1.4 GHz (e.g. Bastian 1991), solar millisecond spikes (e.g. Wentzel 1993) and radio bursts from the flare star AD Leo (Abada-Simon et al. 1997). The theory of Electron Cyclotron Maser Emission (ECME) (e.g. Wu & Lee 1979or Melrose & Dulk 1982) seems to be the favourable emission mechanism to explain coherent radiation from the magnetosphere of Jupiter, solar spike bursts and flare stars, like M dwarfs and RS CVn binary systems.

5.1. Plasma radiation

Plasma radiation is a two-stage process where longitudinal waves in the plasma (Langmuir waves) are first generated and later their energy is converted into radiation (e.g. Dulk 1985). The frequency of the radiation is the plasma frequency ([FORMULA] Hz, with [FORMULA] the plasma density number in [FORMULA]) or its second harmonic. To be observed at 1.4 GHz, [FORMULA] or [FORMULA] respectively for [FORMULA]. Plasma radiation can occur when the magnetic field is relatively weak ([FORMULA], where [FORMULA], with B in gauss). This gives an upper limit for the magnetic field B in the region where the radiation is generated: [FORMULA] ([FORMULA]) or [FORMULA] gauss ([FORMULA]). Assuming a dipolar topology of the magnetic field, [FORMULA], with [FORMULA] gauss, we get that the region where plasma emission occur must be located at [FORMULA] ([FORMULA]) or [FORMULA] ([FORMULA]).

However, the theory of plasma radiation does not foresee any high directivity. For this reason this mechanism is not suitable to explain our observations.

5.2. Electron cyclotron maser emission

Following the theory of the ECME, electrons reflected by the magnetic mirrors can develop a pitch angle anisotropy (or loss cone anisotropy), becoming candidates for cyclotron maser emission if the local plasma frequency is relatively small ([FORMULA]). The frequency of the maser emission is given by [FORMULA], being s the harmonic number and [FORMULA] the gyrofrequency. The faster growth rate is for the first few harmonic number ([FORMULA]) in the extraordinary mode (x-mode). The radiation generated where the magnetic field intensity is [FORMULA] has a frequency [FORMULA]; when crossing a more external layer with [FORMULA], it can be suppressed by the gyromagnetic absorption of the thermal plasma. Melrose & Dulk (1982) show that the [FORMULA] harmonic is generally suppressed, while the [FORMULA] can escape from layers absorbing at higher harmonic numbers. The ECME is confined in a hollow cone of half-angle [FORMULA] with respect to the line of the magnetic field, with [FORMULA] and v the speed of the emitting electrons. The thickness of the hollow cone is [FORMULA]. If the maser is emitted in a region of constant magnetic field, the relative bandwidth is [FORMULA]. However, if the emission comes from a layer where the magnetic field ranges from [FORMULA] to [FORMULA], then the observed bandwidth will be much larger, ranging the radiation from [FORMULA] to [FORMULA]. In this case, the angle [FORMULA] and the thickness of the hollow cone of radiation [FORMULA] do not change, depending only on [FORMULA].

5.2.1. The main peaks

We observe that the two main peaks a and d are beamed at an angle [FORMULA] with respect to the axis of the dipole, and have a full width half maximum (FWHM) of about [FORMULA] (Fig. 10). This strongly suggests that we are in presence of ECME.

We propose the following scenario: the electrons accelerated in the current sheets out of the Alfvén radius flow toward the photosphere close to the magnetic pole; they are eventually mirrored back by the increasing magnetic field, traveling along field lines almost parallel to the axis of the dipole. After the reflection, they develop a loss cone anisotropy because of the interaction with the thermal plasma, leading to electron cyclotron maser emission. In this hypothesis the angle [FORMULA] is just the angle [FORMULA] of the ECME theory. Since [FORMULA] and [FORMULA], we get [FORMULA].

If the magnetic field of CU Vir is a dipole, we should expect a symmetry in the ECME with the stellar phase. The absence of any beamed emission at [FORMULA] (i.e. at [FORMULA] from the direction of the south pole) suggests an asymmetry of the magnetosphere. The presence of a quadrupole component, that has been observed in other MCP stars like HD 32633 and HD 175362 (Mathys 1991), or of a decentered dipole, as recently proposed for CU Vir (Hatzes 1997), could explain the observed asymmetry of the ECME. In fact, the presence of a quadrupole, as for example shown by Michaud et al. (1981) in their Fig. 1d, can inhibit the wind, and so the radio emission, from the magnetic south pole. The interpretation of an asymmetry in the wind is not new. In fact Brown et al. (1985), from the behavior of the UV lines of the MCP star HD 21699, inferred that the wind flows from "only one of the magnetic poles".

5.2.2. The secondary peaks

The secondary peaks b, c, e and f are, like the main peaks a and d, also circularly polarized. The maximum flux density that they show is about 3 mJy in the Stokes V, as it is possible to see inspecting Fig. 12. Peak b lasts for 2 minutes (half power to half power) and a further rise is possible. It has been detected on June 6 at phase 0.5; at the same phase, on June 11, no flux enhancement has been observed, meaning that probably peak b is a transient phenomenon. Peak c lasts about 3-4 minutes and is followed by the rise of the main peak d. Peak e is very short in duration, about one minute, and peak f is about 4 minutes. While the main peaks a and d are detected in all the three days of observation, we cannot say if b, c, e and f are sporadic impulsive emissions or if they are stable as the main ones. Further observations are needed to clarify this point.

[FIGURE] Fig. 11. Proposed picture for the emission of the main peaks. Accelerated in the current sheets and flowing back to the surface following the magnetic field lines (dashed lines from the pole) electrons are reflected by magnetic mirrors close to the star; they develop a loss cone anisotropy and emit cyclotron maser when going outward; the location of the possible region of the maser emission at 1.4 GHz are the circular rings centered around the axis of the dipole (vertical straight line); each ring is marked with the corresponding harmonic number s. The shaded areas represent the escaping radiation if generated, for example, at harmonic s=2. The angle [FORMULA] is also shown.

[FIGURE] Fig. 12. Secondary peaks. See text for details.

5.2.3. The bandwidth

Our observations have been performed at two bands of 50 MHz separated by 80 MHz. No difference of flux between the two bands has been found. So, the bandwidth of the masing radiation is [FORMULA]. Since in the ECME theory [FORMULA], with [FORMULA] we expect a bandwidth of about 10 MHz. This apparent incongruence can be explained if the region where the maser emission is generated covers a wide range of magnetic field strength. The observed radiation is the envelope of a continuous series of maser spots along the field lines, the higher frequency being emitted in regions closer to the star, according to [FORMULA]. In a dipole [FORMULA]; with [FORMULA] gauss, [FORMULA] GHz. To be observed at 1.4 GHz, the maser spots are located at [FORMULA], with [FORMULA]. On the contrary, we did not observed any coherent emission at 5 GHz, as we will discuss in a following paper. So, no condition for the maser mechanism is expected close to the star. The maser mechanism is efficient at a distance [FORMULA]. Probably the electrons are thermalized close to the star, due to a higher density.

5.2.4. Why only right hand circular polarization?

The Stokes parameter V is always positive, that means the radiation is right hand polarized. The theory of the ECME foresees that the radiation is almost entirely polarized in X-mode, as observed for the auroral kilometric radiation (AKR) and for the Jupiter's decametric emission (DAM) (Wu & Lee 1979, Melrose 1976). In fact, in the x-mode the sense of rotation of the electric vector is the same as the helicity of the emitting particles. Electrons moving in a magnetic field directed toward us are seen to rotate in counter clockwise, as the right hand circular polarization. In a perfectly symmetric configuration, the electrons mirrored outward move in the same direction as the magnetic field lines in the north hemisphere, in opposite direction in the south hemisphere, emitting respectively in right and left hand polarization.

Our data show no LCP enhancement at any rotational phase. This suggests that there is no condition for cyclotron maser emission at 20 cm in the magnetic south hemisphere. Again, this can be imputed to an asymmetry in the magnetosphere of CU Vir.

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Online publication: October 30, 19100