6.2 Compressive turbulence in the polar wind

Compressive fluctuations in high latitude solar wind have been extensively studied by Bavassano et al. (2004

) looking at the relationship between different parameters of the solar wind and comparing these results with predictions by existing models.

These authors indicated with $N, Pm, Pk,$ and $Pt$ the proton number density $n$ , magnetic pressure, kinetic pressure and total pressure $(Ptot = Pm + Pk)$ , respectively, and computed correlation coefficients $r$ between these parameters. Figure 67 clearly shows that a pronounced positive correlation for $N - Pt$ and a negative pronounced correlation for $Pm - Pk$ is a constant feature of the observed compressive fluctuations. In particular, the correlation for $N - P t$ is especially strong within polar regions at small heliocentric distance. In mid-latitude regions the correlation weakens, while almost disappears at low latitudes. In the case of $Pm - Pk$ , the anticorrelation remains strong throughout the whole latitudinal excursion. For polar wind the anticorrelation appears to be less strong at small distances, just where the $N - Pt$ correlation is highest.

Figure 67:

Histograms of $r(N - Pt)$ and $r(Pm - Pk)$ per solar rotation. The color bar on the left side indicates polar (red), mid-latitude (blue), and low latitude (green) phases. Moreover, universal time UT, heliocentric distance, and heliographic latitude are also indicated on the left side of the plot. Occurrence frequency is indicated by the color bar shown on the right hand side of the Figure (figure adopted from Bavassano et al., 2004

The role played by density and temperature in the anticorrelation between magnetic and thermal pressures is investigated in Figure 68

, where the magnetic field magnitude is directly compared with proton density and temperature. As regards the polar regions, a strong B-T anticorrelation is clearly apparent at all distances (right panel). For B-N an anticorrelation tends to emerge when solar distance increases. This means that the magnetic-thermal pressure anticorrelation is mostly due to an anticorrelation of the magnetic field fluctuations with respect to temperature fluctuations, rather than density (see, e.g., Bavassano et al., 1996a ,b ). Outside polar regions the situation appears in part reversed, with a stronger role for the B-N anticorrelation.

Figure 68:

Solar rotation histograms of $B - N$ and $B - T$ in the same format of Figure 67

(figure adopted from Bavassano et al., 2004

In Figure 69

scatter plots of total pressure vs. density fluctuations are used to test a model by Tu and Marsch (1994

), based on the hypothesis that the compressive fluctuations observed in solar wind are mainly due to a mixture of pressure-balanced structures (PBS) and fast magnetosonic waves (W). Waves can only contribute to total pressure fluctuations while both waves and pressure-balanced structures may contribute to density fluctuations. A tunable parameter in the model is the relative PBS/W contribution to density fluctuations $a$ . Straight lines in Figure 69

indicate the model predictions for different values of $a$ . It is easily seen that for all polar wind samples the great majority of experimental data fall in the $a > 1$ region. Thus, pressure-balanced structures appear to play a major role with respect to magnetosonic waves. This is a feature already observed by Helios in the ecliptic wind (Tu and Marsch, 1994

), although in a less pronounced way. Different panels of Figure 69

refer to different heliocentric distances within the polar wind. Namely, going from P1 to P4 is equivalent to move from $1.4$ to $4 AU$ . A comparison between these panels indicates that the observed distribution tends to shift towards higher values of $a$ (i.e., pressure-balanced structures become increasingly important), which probably is a radial distance effect.

Figure 69:

Scatter plots of the relative amplitudes of total pressure vs. density fluctuations for polar wind samples P1 to P4. Straight lines indicate the Tu and Marsch (1994 ) model predictions for different values of $a$ , the relative PBS/W contribution to density fluctuations (figure adopted from Bavassano et al., 2004

Finally, the relative density fluctuations dependence on the turbulent Mach number M (the ratio between velocity fluctuation amplitude and sound speed) is shown in Figure 70

. The aim is to look for the presence, in the observed fluctuations, of nearly incompressible MHD behaviors. In the framework of the NI theory (Zank and Matthaeus, 1991 , 1993 ) two different scalings for the relative density fluctuations are possible, as $M$ or as $M 2$ , depending on the role that thermal conduction effects may play in the plasma under study (namely a heat-fluctuation-dominated or a heat-fluctuation-modified behavior, respectively). These scalings are shown in Figure 70

as solid (for $M$ ) and dashed (for $2 M$ ) lines.

It is clearly seen that for all the polar wind samples no clear trend emerges in the data. Thus, NI-MHD effects do not seem to play a relevant role in driving the polar wind fluctuations. This confirms previous results in the ecliptic by Helios in the inner heliosphere (Bavassano et al., 1995 ; Bavassano and Bruno, 1995 ) and by Voyagers in the outer heliosphere (Matthaeus et al., 1991 ). It is worthy of note that, apart from the lack of NI trends, the experimental data from Ulysses, Voyagers, and Helios missions in all cases exhibit quite similar distributions. In other words, for different heliospheric regions, solar wind regimes, and solar activity conditions, the behavior of the compressive fluctuations in terms of relative density fluctuations and turbulent Mach numbers seems almost to be an invariant feature.

Figure 70:

Relative amplitude of density fluctuations vs. turbulent Mach number for polar wind. Solid and dashed lines indicate the $M$ and $M 2$ scalings, respectively (figure adopted from Bavassano et al., 2004 ).

The above observations fully support the view that compressive fluctuations in high latitude solar wind are a mixture of MHD modes and pressure balanced structures. It has to be reminded that previous studies (McComas et al., 1995 , 1996 ; Reisenfeld et al., 1999 ) indicated a relevant presence of pressure balanced structures at hourly scales. Moreover, nearly-incompressible (see Section 6.1) effects do not seem to play any relevant role. Thus, polar observations do not show major differences when compared with ecliptic observations in fast wind, the only possible difference being a major role of pressure balanced structures.