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Astron. Astrophys. 355, 804-808 (2000)

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3. The origin of the emission polarization in the event of November 2, 1988

High ellipticity of the observed DAM emission forces us to assume both that the emission is generated almost perpendicular to the planetary magnetic field lines in the emission source and the geometrical optics approximation is no longer valid where the polarization of electromagnetic modes is elliptical. Under these conditions, the variation of the polarization along the emission way is described by the following equation (Zheleznyakov, 1995):

[EQUATION]

where [FORMULA] is a function related to the emission polarization ellipticity T by the equation

[EQUATION]

function Q is the ratio of the rate of change of polarization of the electromagnetic modes to the rate of change of the phase difference between the modes,

[EQUATION]

[FORMULA] is the coordinate associated with coordinate z along the ray path by

[EQUATION]

[FORMULA] is the refractive index of extraordinary (x) and ordinary (o) modes, and the parameter q is defined as

[EQUATION]

Gyrofrequency [FORMULA] and the angle between the direction of propagation and the magnetic field lines [FORMULA] in Eq. (5) are functions of space. The parameter q determines the polarization of the electromagnetic modes and the limits of validity of the quasilongitudinal ([FORMULA]) and quasitranverse ([FORMULA]) description of electromagnetic wave propagation within the condition of validity of the geometrical optics approximation.

From Eq. (1) it is easily seen that both the generation condition at the emission point and the variation of function Q along the emission ray determine completely the observed emission polarization. According to the advanced theory of the linear mode coupling (Zheleznyakov 1995), variation of the function Q within the transitional region (TR) exerts appreciable influence on the observed polarization. In the articles of the first group (see Sect. 1) it is assumed that function Q is much greater than unity, [FORMULA], along the part of the emission ray within the Jovian magnetosphere including the source itself and its TR. We are not interested in the part of the emission way within the Io plasma torus and the Earth's ionosphere where the inverse inequality, [FORMULA], is valid. Here, the conditions of the geometrical optics approximation and the quasi-longitudinal propagation are fulfilled, and the variation of the radiation polarization just manifests itself as the rotation of the polarization ellipse without any change in the ellipticity. It is easily seen from Eq. (1) that in the case of [FORMULA] the solution of the transfer equation is independent of the condition along the emission way and is determined by the initial conditions. It means that the observed polarization ellipticity is determined by the angle [FORMULA] between the direction of emission and the magnetic field lines at the generation point. Substituting [FORMULA] into the expression for the degree of circular polarization, which in this case is [FORMULA] (see, for details, Melrose & Dulk 1991), we find that this emission polarization could be observed if the emission generates at angles [FORMULA] relative to the magnetic field lines. However, following Leblanc et al. (1994) it is easily shown that the decametric radiation emitted in the frequency band 27 - 35 MHz at angles [FORMULA] cannot be observed by the ground-based observer. In this case the Earth is out of the emission beam.

Shaposhnikov et al. (1997) assume that inequality [FORMULA] is violated in the decametric emission source and its TR. Within the TR the function Q can reach magnitudes of the order of or less than unity. In this case the observed ellipticity depends on one more parameter: the level of the Jovian magnetospheric plasma density [FORMULA] in TR. Following Shaposhnikov et al. (1997) we calculate the dependence of the degree of circular polarization of the observed emission on the plasma density, [FORMULA], for different values of the angle [FORMULA] and for a fixed emission frequency (Fig. 2).

[FIGURE] Fig. 2. The degree of circular polarization [FORMULA] as a function of plasma density in the transitional region for different values of angle [FORMULA] and for a fixed frequency (f = 30 MHz; [FORMULA] is the value of parameter q at the emission point).

To find the degree of polarization, we use the transfer equation (1) and the simple symmetrical model of the dipole magnetic field. We take into account also the frequency independence of the polarization ellipticity. Specific features of the Jovian magnetic field influence only the position of TR at the magnetosphere and will be taken into further consideration. The degree of the circular polarization is calculated using the following equation (Shaposhnikov et al. 1997)

[EQUATION]

where [FORMULA] is the real part of T. Fig. 2 shows that the observed ellipticity of the emission polarization is mainly determined by the level of plasma density within the TR. Some exceptions occur in the case when TR includes the emission source itself. In this case the influence of the initial condition becomes slightly greater. As it is noted in the previous sections the emission in the great arc has an essentially higher degree of the circular polarization than other parts of the burst, [FORMULA] versus [FORMULA]. This means that the plasma density is about three times greater at the transitional region associated with the source of the great arc than at the transitional regions associated with the sources of the remaining part of the burst.

To understand the reason of the sudden increase of the plasma density within TR we need to trace the variations of TR location in the Jovian magnetosphere during the emission event of Nov.2, 1988. Fig. 3 illustrates schematically the variation of the position of the emission source emitting at fixed frequency f and the associated transitional region at different times, [FORMULA] through [FORMULA]. The variation is due to the motion of the source together with the planet.

[FIGURE] Fig. 3. The tracks (dashed lines) of the source emitting at a fixed frequency and the associated transitional region (schematic view from above the north pole). Asterisks and solid circles show positions of the emission source and of the transitional region, respectively, at different times, [FORMULA] through [FORMULA].

At the emission ray the location of TR is determined from the condition of [FORMULA] (Shaposhnikov et al. 1997). From Eq. (5) it is seen that the value of parameter q depends on angle [FORMULA] between the direction of emission propagation and the local magnetic field lines. This angle, in turn, is determined by angle [FORMULA] between the direction of emission and the magnetic field lines at the emission point. Due both to the planetary rotation and the orbital motion of the Io, angle [FORMULA] changes with time. The variation of [FORMULA] results in a change of both the mutual position of the source and its TR and the location of TR in the magnetosphere. Moreover, there is a situation where TR envelops the emission point (time [FORMULA] in Fig. 3).

The direct way, namely, calculation of parameter q along the emission ray paths, requires the knowledge of the exact source position in the magnetosphere at every moment in time. Up to now the positions of the decametric sources are still not determined exactly. Besides, there is no sufficiently good plasma model for the Jovian low magnetosphere. Therefore, as the first step, we define a magnetosphere region at the way of the emission propagation where plasma density is likely to be enhanced. Then we find positions of the source with the transitional region being located in this magnetosphere region at the time when the highly circularly polarized emission is observed.

It is generally accepted that generation of the decametric emission occurs along the Io flux shells at the active magnetic flux tubes. In general, the active flux tube is not the same as the instantaneous Io flux tube. Note that the concept of the active flux tube is the same as the concept of an active longitude proposed by Dulk et al. (1992). It is also generally accepted that the sources emitting at different frequencies f are situated at heights which correspond to different electron gyrofrequency levels [FORMULA]. The latter implies that the decametric sources are located quite close to the planetary surface, within a few tenths of the Jovian radius. Shaposhnikov et al. (1997) have found that the positions of TR are at distances less than or equal to half of the radius from the source. This estimation was obtained for the simple dipole models of the planetary magnetic field. However, more realistic models of the magnetic field, O4 and O6, considered in place of the simple dipole one, lead to negligible corrections. Near the emission source region, the enhanced density can be reasonably expected only at the Io flux shells themselves. Here the density can be increased due to particle precipitation from the Io plasma torus. Therefore, we conclude that the relevant situation occurs when the transitional region is in the vicinity of the Io flux shells. In other words, we have to find the situation where the condition of [FORMULA] is fulfilled in the vicinity of the source.

Fig. 4a shows the variation of parameter q in the sources plotted as a function of phase ([FORMULA]) of the active flux tube for a fixed CML. The fixed CML corresponds to the moment in time when the emission with a high degree of circular polarization was observed in the event of Nov.2, 1988. For simplicity, we consider the sources which emit at a fixed frequency, e.g. f = 30 MHz. Here and further on we will use the O4 model of the planetary magnetic field. The O6 model as well as a variation of emission frequency from 25 MHz to 35 MHz give negligible differences in the numerical results. From Fig. 4a it can be seen that the required case (coincidence of the position of the emission source and corresponding TR) occurs when the source of the highly circularly polarized emission is situated in the vicinity of the instantaneous Io flux tube. This conclusion is confirmed in Fig. 4b which shows variations of parameter q in the Io flux tube during the event under consideration. Again, we consider the source which emits at 30 MHz. From Fig. 4b it is seen that the positions of TR and of the Io flux tube coincide ([FORMULA]) at the time when the great arc and the highly circularly polarized emission are observed.

[FIGURE] Fig. 4a and b. a Variation of parameter q as a function of the phase of the active flux tube at the moment when CML=248o and [FORMULA]. The asterisk marks the phase of the Io flux tube; b Variation of parameter q and angle [FORMULA] as functions of time at the Io flux tube at the height which corresponds to the 30 MHz gyrofrequency level. The asterisks mark the start and end times of observation of the highly circularly polarized emission at the frequency of 30 MHz.

Thus, we conclude that in the event of Nov. 2, 1988 the highly circularly polarized emission was observed at times when both the emission source and its transitional region were in the Io flux tube. From Fig. 4b, where the variation of the angle between the direction to the remote observer and the magnetic field lines in the source are also shown, it is seen that the angle is about [FORMULA] in the 30 MHz emission source at those times ([FORMULA] for the sources emitting at frequencies 35 MHz [FORMULA] f [FORMULA] 25 MHz). Observations show that a high degree of circular polarization occurs during a very short time interval (about 5 minutes). The short time interval of observation of the circularly polarized emission implies that it is generated in the IFT within a very narrow angle range. For example, at the frequency of [FORMULA] [FORMULA] 30 MHz the diagram beam is about [FORMULA] around the angle [FORMULA]. We can also conclude that the remaining part of the burst is generated in the active tubes which are at a distance from the IFT (see Fig. 4a). We estimate the level of the magnetospheric plasma density which is found as high as [FORMULA] cm-3 in the IFT at the heights corresponding to the 30 MHz gyrofrequency level. This plasma density provides the degree of circular polarization [FORMULA]. Outside of the IFT the plasma density is lower. From [FORMULA] one finds [FORMULA] cm-3.

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© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000
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