fluctuations in the solar wind' A comparison between equatorial and polar observations

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. A6, PAGES 10,659-10,668, JUNE 1, 2001 Radial evolution of outward and inward Alfv6nic fluctuations in the solar wind' A comparison between equatorial and polar observations by Ulysses B. Bavassano Istituto di Fisica dello Spazio Interplanetario, Consiglio Nazionale delle Ricerche, Rome, Italy E. Pie ropaolo Dipartimento di Fisica, Universit dell'aquila, L'Aquila, Italy R. Bruno Istituto di Fisica dello Spazio Interplanetario, Consiglio N azionale delle Ricerche, Rome, Italy Abstract. Ulysses measurements done during the ecliptic phase of the mission are used to investigate the radial evolution of outward and inward Alfv6nic fluctuations at hourly scale in near-equatorial solar wind. This analysis has been stimulated by a recent study on Alfv6nic turbulence in polar wind, showing that at hourly scale different radial regimes develop a,t different distances. In the present analysis a total of 30 time intervals, characterized by highly Alfv6nic fluctuations, are examined, for a total duration of 2558 hours. They are quite uniformly distributed from 1.2 to 5.2 AU along the ecliptic trajectory of Ulysses. The results clearly indicate that in the investigated radial range the energy per unit mass of the dominant outward propagating fluctuations declines, for increasing distance, with approximately the same rate observed for inward fluctuations. In other words, the ratio of inward to outward fluctuation energy roughly remains the same in the examined region. Moreover, the gradient does not vary appreciably with radial distance. These features indicate that between 1 and 5 AU the Alfv6nic fluctuations have a quite different behavior in polar and in near-equatorial solar wind. All this should imply a different role, in the two kinds of wind, of the mechanisms expected to be active in driving the Alfv6nic turbulence evolution at hourly scale. Our results, combined with previous observa,tions by Helios spa, cecraft, also suggesthe likely presence of solar cycle effects. 1. Introduction Alfv nic fluctuations are a relevant feature of the in- terplanetary plasma. They have been the object of extensive studies in the last two decades, with impressive advances both observationally and theoretically. In recent years a new opportunity to investigate Alfvdnic turbulence in the solar wind has been offered by plasma and magnetic field measurements of the Ulysses spacecraft, in the high-latitude fast wind. This is a very regular plasma flow expanding from the large coronal holes that, when the solar activity is not too high, are present in the Sun's polar regions. The polar wind is characterized by an intense flow of Alfv nic fluctuations [e.g., Copyright 2001 by the American Geophysical Union. Paper number 2000JA / 01 / 2000 J A $ ,659 see Goldstein et al., 1995; Horbury et al., 1995; Smith et al., 1995]. As for previous low-latitude observations, a major fraction of these fluctuations is outward propagating, with respect to the Sun, in the solar wind frame. It is well established (see review by Tu and Marsch [1995]) that the outward fluctuations mainly have a solar origin (namely, inside the Alfv n critical point). Conversely, inward propagating fluctuations are obviously generated outside this critical distance. The way the Alfv nic turbulence evolves with radial distance de- pends on the way, if any, fluctuations are locally generated in the interplanetary space. In turn, this depends on solar wind conditions. For instance, velocity gradients are a source for fluctuations; then they can play a role in driving turbulence evolution [e.g., Roberts ½t al., 1991, 1992; Bavassano et al., 1998]. Recently, Bavassano et al. [2000] have investigated the radial evolution of outward and inward Alfv nic

2 10,660 BAVASSANO ET AL.' SOLAR WIND ALFVI NIC FLUCTUATIONS fluctuations in the polar wind between 1 and 5 AU. As well established, polar turbulence is much less evolved than that observed at lower latitudes [Goldstein ½t al., 1995; Hotbury ½t al., 1995; Smith ½t al., 1995], owing to negligible, the parametric instability probably plays a major role in driving Alfv nic turbulence. A detailed discussion about this is beyond the scope of the present study. It will be the object of a forthcoming paper. the lack of strong gradients in velocity. The results of All this has stimulated a reexamination of the radial Bavassano ½t al. [2000] show that hourly-scale Alfvdnic fluctuations in the polar wind exhibit different radial regimes at different distances. Inside 2.5 AU the outevolution of Alfvdnic turbulence in near-equatorial solar wind at. heliocentric distances from 1 to 5 AU, with focus on differences (and similarities) between outward ward fluctuations decrease faster, in terms of energy per and inward fluctuation behaviors. Studies on turbuunit mass, than do the inward ones. This is in agreement with previous low-latitude observations inside 1 AU within the trailing edge of fast streams. As a result of this different gradient, the ratio of inward to outward fluctuation energy rises to near 2.5 AU. Beyond this distance the radial gradient of the inward lence features in this region have been done in the past [e.g., see Bavassano and Smith, 1986; Roberts ½t al., 1987a, 1987b, 1991; Bavassano ½t al., 1998]. However, a separate analysis of outward and inward Atfvdnic fluctuations has never been performed. This is the purpose of the present, paper. fluctuations becomes increasingly steeper, while that of the outward ones does not vary appreciably. A new regime is quickly reached, outside.- 3 AU, where both species decline at almost the same rate. Such behavior 2. Data Analysis Our study is based on plasma and magnetic field data has certainly to be ascribed to the specific mechanism(s) collected by Ulysses during the ecliptic phase of the misactive in the local generation of polar wind turbulence. In this regard, we would like to mention a recent pasion. The plasma data are the fluid velocity vector (averaged over protons and alpha particles), the proton per by Malara ½t al. [2000] on the nonlinear evolution number density, and the alpha particle number density. of the parametric instability for large-amplitude non- The time resolution is either 4 or 8 min, depending on monochromatic Alfvdn waves. Their simulation for the the spacecraft mode of operation. The magnetic data case of a thermal to magnetic pressure ratio equal to 1 closely resembles the polar turbulence behavior observed by Bavassano ½t al. [2000]. Thus it would seem that when the contribution from velocity gradients is are 1-min averages of the magnetic field components and magnitude. Velocity and magnetic field vectors are given in spacecraft-centered solar-heliospheric coordinates v (km/s) ' r (AU) year Figure 1. (top) Daily averages of the solar wind velocity V versus time for the ecliptic phase of the Ulysses mission (from launch, October 1990, to Jupiter flyby, February 1992). (bottom) The investigated intervals in terms of radial distance r versus time.

3 BAVASSANO ET AL.' SOLAR WIND ALFV NIC FLUCTUATIONS 10, V 500 (km/s) 300 N 3 (cm-3) 1 5 (nt) day (1991) Figure 2. Hourly averages of (top to bottom) solar wind velocity V, proton number density N, and magnetic field magnitude B, versus time for a selected period in mid Thick segments on top identify two of the investigated intervals. The computational scheme we use is very simple. For each plasma velocity vector v we compute the corresponding magnetic field vector b by averaging over 4 (or 8) min. After scaling the magnetic field to Alfvdn units, dividing it by (with p the total, protons plus alpha particles, mass density), the Els isser variables are derived. They are defined as z: = v q- b for a background magnetic field with a sunward component along the local spiral direction, or as z: = v = b for the opposite case. With these definitions, z+ always corresponds t.o Alfvdnic fluctuations with an outward direction of propagation (with respect, to the Sun) in the solar wind frame. Conversely, z_ always identifies inward traveling fluctuations. A discussion on the use of Els isser variables in solar wind turbulence studies may be found in the review of Tu and Mar'sch [1995]. Once time series of the Els isser variables are ob- tained, the total variance e+ (e_) of z+ (z_), as given by the sum of the variances along the coordinate axes, is computed for selected averaging times. The values of e+ and e_ give a measure of the energy per unit mass associated with z+ and z_ fluctuations in a given frequency band, determined by the averaging time used to evaluate variances. Several averaging times, from 1 to 48 hours, have been used. Results discussed here refer to hourly variances. This choice vas based on the well-established result [e.g., see Tu and Marsch, 1995] that fluctuations at hourly scale fall in the core of the Alfv nic regime. The ecliptic phase of the Ulysses mission spans from launch (October 1990) to Jupiter flyby (February 1992). Solar wind plasma and magnetic field data have been made available by the principal investigators (D. J. McComas and A. Balogh, respectively) through the World Data Center A for Rockets and Satellites at NASA/Goddard Space Flight Center. The plasma data span from day 322, 1990, to day 33, For magnetic data the available time interval is from 298, 1990, to 33, The top plot of Figure 1 sho vs daily averages of the solar wind velocity magnitude I/for the period of interest. A series of slow and fast streams is observed, as is typical of a near-equatorial vind. However, since solar activity is high during the investigated interval, we are in the presence of a quite irregular pattern. In the bottom plot the investigated intervals are shown as short segments in terms of radial distance r versus time. Thirty intervals have been examined, for a total duration of 2558 hours. They span from 1.2 to 5.2 AU in heliocentric distance and are quite uniformly distributed along the Ulysses trajectory. Their time length depends on the solar wind aor:d turbulence conditions. Most of the selected intervais belong to the trailing edge of streams with relatively high speed, since this is generally the place where the cleanest samples of Alfvdnic turbulence are found. Nevertheless, some of the investigated intervals belong to low-speed regions, as for instance at the beginning of 1991 when the absence of strong velocity gradients allows the persistence

4 10,662 BAVASSANO ET AL.' SOLAR WIND ALFV] NIC FLUCTUATIONS of a highly Alfvdnic character in the observed fluctuations (on this, see Roberts et al. [1987a]). The investigated intervals have been selected by visual inspection of both plots of solar wind data and plots of the Alfvdnic content of hourly-scale fluctuations, as measured by the correlation coefficient between velocity and magnetic field. We have been very careful to not, include t. ransient flows associated with coronal mass ejections and other interplanetary perturbations. An example of the intervals we selected is given in Figure 2, where hourly averages of solar wind velocity, proton density, and magnetic field intensity are given for a period slightly longer than one solar rotation. A stream pattern with welldeveloped corotating interaction regions is clearly apparent. Thick segments on top of Figure 2 indicate two of the analyzed intervals. They belong to the trailing edge of fast flows, where density and magnetic intensity fluctuations are at a relatively low level. It must be underlined that the use of Elshsser's vari- ables may be misleading when compressiv effects are important. In this regard, we show in Figure 3 hourly standard deviations, relative to mean values, of the magnetic field magnitude (S 3, top) and the proton number density (SN, bottom) for the selected intervals. It is seen that. as already known, compressiveffects become relatively more important for increasing distance. Moreover, beyond 2 AU the density variations become more important than the magnetic ones. To reduce the influence of these effects on our analysis, in the following we will apply an upper threshold T 3N to the normal- ized variances S 3 and S v of magnetic field magnitude and proton density. In other words, only hourly intervals with both S 3 and S v below a given value of T 3N will be included in our computations. To evaluate how our results are affected by this selection procedure, three different values (1.0, 0.5, and 0.3) for the threshold T 3N will be used. Incidentally, as a term of comparison, average values of S 3 and SN in the polar solar wind are around 0.09 and 0.07, respectively. 3. Outward and Inward Alfv nic Fluctuations Hourly variances e+ (e_) of z+ (z_) fluctuations for the selected intervals are displayed in Figure 4 (top and bottom, respectively) as a function of time. All data from the examined intervals are reported in Figure 4, without any selection in terms of S and S v. A decreasing trend for increasing time is clearly seen in the data. This is simply understood as an effect of the increasing radial distance (see bottom plot in Figure 1). However, for observations covering more than I year in conditions of high solar activity, we have also to expect strong variations due to temporal changes. This may explain the presence in Figure 4 of departures from a monotonic trend. It is noteworthy that even inside each 1.5 SB SN Figure 3. (top) Hourly standard deviations, relative to mean values, of the magnetic field magnitude versus radial distance for all the analyzed intervals. (bottom) The same for the proton number density.

5 BAVASSANO ET AL.' SOLAR WIND ALFV]5 NIC FLUCTUATIONS 10, e_l - lo 2 (km /s ) ø I,, I i, I f I, I 10 3 e_ lo 2 (kltl2/s2) 01 1 ; :. ' : :' i.? '. ' :::,., 10 ø I ] [ I i ] I i I I, I I I year Figure 4. (top) Time variation of outward fluctuation hourly variances (e+) for the analyzed intervals. (bottom) The same for inward fluctuation hourly variances (e_). 0.8 s<0.s, s<0.s 0.6 e e r (AU) Figure 5. Radial variation of the e_/e+ ratio (Els isser ratio). The plotted data are obtained by averaging, for each of the 30 analyzed periods, e_/e+ values from hourly intervals with both S and S v below 0.5.

6 10,664 BAVASSANO ET AL.' SOLAR WIND ALFVI NIC FLUCTUATIONS of the selected intervals (hence, practically at the same deviation of 0.1). Results do not change significantly if distance and time), the e+ and e_ excursions generally different thresholds (0.3 and 1.0) are used for S and are above one decade. s}. To look for differences, or similarities, in the radial evolution of e+ and e_, we plot in Figure $ the ratio 4. Radial e_/e+ (Els/isseratio) versus the heliocent. ric distance Gradients r. The displayed data have been obtained by averaging, over each of the selected time periods, hourly values of the Elsiisser ratio and using only hourly intervals It has been shown above that e+ and e_ exhibit a similar radial behavior. However, we have still to determine if their gradient, varies with distance. To this with both S and S v below 0.$. No clearadial trend purpose we separately show in Figures 6 and 7 the racomes out in Figure $. Thus the radial decline of e+ and e_ with increasing distance does not appear to lead to any appreciable change in the relative inward t.o outward fluctuation energy. This is a completely different result with respect, to that, obtained by Bavassano et al. dial variation of e+ and e_ on a log-log scale. As for Figure 5, the plotted data are average values, for each of the selected periods, of the hourly variances of z+ and z_, having included only hourly intervals with both S and S v below 0.5. Figures 6 and 7 do not give any [2000] in the polar wind for the same range of heliocen- evidence of a variation of the radial gradient with r. tric distance and at the same scale. Straight lines indicate best fit power la vs over all the The fact that, an almost constant Elsiisser ratio is reached by the near-equatorial turbulence already near 1 AU, namely, well before that for polar turbulence, may be not, surprising. In fact, it. is well established that for a given distance from the Sun the Alfvdnic turbulence in polar regions is less evolved than that near the equator (for instance, see Goldstein ½t al. [1995], Horbury ctal. [1995], and Smith et al. [1995]). However, while in polar wind the Elsiisser ratio becomes as high as 0.5 [Bavassano et al., 2000], the average value of the data shown in Figure 5 is 0.3 (with a standard investigated range of distances. They practically have the same slope, for e+ and for e_. The best fit, slopes change with TBN as listed in Table 1. It, is seen that, (1) the slopes decrease (in absolute value) with increasing TBN and (2) the difference between the e+ and e_ slopes for a given T N value is well below the errors; namely, e+ and e_ have essentially the same slope. It should be noted that the slope variations with T N mainly come from the fact that changes in the threshold value mostly affect data beyond,-03 AU (see Figure 3), rather than all the sample si<0.s, SN<0.S looo e (krn2/s 2) 2OO _ - _r_.53 *. ø 501 i I i i J i I i i I i i i i I i ill IIIIIJlllllllllJlllllllll r (AU) Figure 6. Radial variation of e+ on a log-log scale. The data are obtained by averaging, for each of the 30 analyzed periods, e+ values from hourly intervals with both $' and S v below 0.$. The straight line indicates the best, fit. radial power law.

7 BAVASSANO ET AL.' SOLAR WIND ALFVI NIC FLUCTUATIONS 10, ' s;<0.s, s<0.s 2OO 100 e 1 (kli12/s2) i i i i i i i i i I i i i i i i i i i I i i i i i i i ii IIllllllltllllllllll r (AU) Figure 7. The same as that in Figure 6 but for e_ In Figure 8 we summarize the present results for the ecliptic phase of Ulysses mission, and we conapare them to those of Bavassano et al. [2000] for Ulysses observations in the polar wind and to those obtained by Helios on the ecliptic plane inside 1 AU. The lines drawn in Figure 8 are best fit, lines referring to the different, Ulysses data samples. Solid lines show present results for e+ (thick lines labeled [e+]eq) and e_ (thin lines labelled [e_]eq) for three values (0.3, 0.5, and 1.0) of TBN, with increasing slope for decreasing TB v. The dashed line (labeled[e+]po )indicates the result obtained by Bavassano et al. [2000] for outward fluctuations in the polar wind from 1.4 to 4.3 AU. In that paper the e+ gradient was determined separately for the region inside and outside 2.6 AU. Since the difference between the gradients in the two regions is well below their errors, we used here one fit only for all the radial interval. The same does not hold for inward fluctuations. Their best fit lines inside and outside 2.6 AU are plotted in Figure 8 as dotted lines (with label [e_]pol). From all these Ulysses observations it is clearly apparent. that in addition to the above discussed features for the radial slope, the fluctuation energy levels near the equator are appre- Table 1. Radial Slopes of e+ and e_ (S}, S v) < 0.3 (S}, S v)< 0.5 (S}, S v) < 1.0 e e_ ciably below those typically observed in polar regions. As regards the comparison with Helios 1 and 2 results, we recall that, they refer to power spectra obtained within the trailing edge of fast, streams on the ecliptic plane between 0.3 and 1 AU. The two big squares (diamonds) are average values of energy per unit mass for outward (inward) fluctuations near 0.4 and 0.8 AU [Tit and Marsch, 1990] in a frequency band that corresponds to the 1-hour averaging time used here. With in mind the caveat. that the extrapolation of Ulysses results well inside 1 AU could be invalid, it, is easily seen that as already shown by Bavassano et al. [2000], a good agreement exists between Helios observations and those by Ulysses in the polar wind. In turn, the Ulysses ecliptic results appear different from those of Helios. An overall view of the radial slopes observed by Ulysses for Alfv nic fluctuations in different solar wind regions is given in Figure 9. Squares and diamonds refer to e+ and e_, respectively. Different, columns are for different, regions and situations. The first three columns summarize present findings for different, values of TBN (0.3, 0.5, and 1.0 from left, to right). The last two columns refer to the results of Bavassano et al. [2000] for polar wind turbulence outside and inside 2.6 AU, respectively. In spite of the dependence on TBN, a general agreement exists between slopes in near-equatorial wind and in polar wind outside 2.6 AU (and for e+ also belo v that distance). In other words, the only relevant difference is found for z_ fluctuations in polar wind inside 2.6 AU.

8 10,666 BAVASSANO ET AL.' SOLAR WIND ALFV NIC FLUCTUATIONS 10 4 [e-]pol [e+]pol e +' 10 3 e 1 (km2/s 2) r (AU) Figure 8. A comparison between best fit, lines obtained the present, analysis for near-equatorial wind (thick and thin solid lines labeled [e+]eq and [e_]eq, respectively) and those observed by Bavassano et al. [2000] in polar wind (dashed and dotted lines labeled [e+]pol and [e_]pol, respectively). Thick and thin solid lines are for three different values (0.3, 0.15, and 1.0) of TBN, with slope increasing for decreasing TBN. The two big squares (diamonds) are average values of e+ (e_) as observed by Helios 1 and 2 on the ecliptic plane around 0.4 and 0.8 AU EQ EQ EQ TBN=0.3 TBN=0.5 TBN=1.0 POL r>2.6 POL r< Figure 9. A visual summary of e+ (squares) md e_ (diamonds) radial slopes as observed by Ulysses in different solar wind regions. The tirsthree columns (labeled "EQ") refer to the present near-equatorial wind analysis, for three different choices of TBN. The lastwo columns (labeled "POL") show the results of Bavassano et al. [2000] in the polar solar vind outside and inside 2.6 AU.

9 5. Summary and Conclusion BAVASSANO ET AL.' SOLAR WIND ALFVt NIC FLUCTUATIONS 10,667 Plasma and magnetic field measurements by Ulysses during the ecliptic phase of the mission (from launch, October 1990, to Jupiter flyby, February 1992) have been used to investigate the radial evolution of outward and inward Alfvdnic fluctuations at, hourly scale in nearequatorial solar wind. This analysis has been stimulated by recent findings by Bavassano el, al. [2000] in the polar wind, showing the presence of different radial regimes for the Alfvdnic turbulence at, different dis- tances. In the present study a total of 30 periods have been examined, for a total duration of 2558 hours. The investigated periods span from 1.2 to 5.2 AU in heliocentric distance. They are uniformly distributed along the Ulysses trajectory and have a variable duration, depending on solar wind and turbulence conditions. Hourly variances of the Elsiisser variables z+ and z_ and their average values over each of the analyzed periods are at, the base of our investigation. Since the use of the Elsiisser variables may be misleading if compressive effects are important, all hourly intervals with large variations in plasma density and/or magnetic field magnitude have t,o be rejected. In practice, this selection has been done by requesting that, both S' and 'g v(the normalized hourly variances of magnetic field magnitude and proton density, respectively) are below a given threshold T lv. Three different, values (0.3, 0.5, and 1.0) of T lv have been used to evaluate how the selection procedure affects our findings. The main results of our analysis are that (1) out- ward and inward fluctuations decrease, for increasing distance, with approximately the same gradient,, and (2) this gradient, does not, change appreciably with distance. Its value changes vith that of TBN, becoming steeper vhen TBN decreases. For TBN in the range the gradient is close to that found by Bavassano ½! al. [2000] in far polar vind(i.e., approximately between 2.5 and 5 AU), although the fluctuation energy levels are completely different (much higher in polar vind). As mentioned in section 1, the analysis of Bavassano e! al. [2000] has shown that in the polar vind different regimes of turbulence evolution develop at, different distances. Present, results in near-equatorial wind depict, a completely different situation, with a radial gradient, that is the same for outward and inward fluctuations and has no variations versus distance. The e_/e+ ratio is around 0.3, smaller than that (0.5)in far (2.5-5 AU) polar wind. All this would imply a different role, in the two kinds of vind, of the mechanisms driving the turbulence evolution at hourly scale. However, the interpretation of our results is not, so straightforward. A major point to be considered is the comparison of the Ulysses results to those by Helios 1 and 2 inside 1 AU. Helios observation shown in Figure 8 as squares (for e+) and diamonds (for e_) are representative of turbulence conditions in the trailing edge of near-equatorial fast streams during a period of lo v solar activity. As indicated by Bavassano el, al. [2000], they appear to be in agreement with the radial regime observed by Ulysses in near polar wind (i.e., approximately between 1 and 2.5 AU), characterized by a slower decay of e_ in comparison with that of e+. All this has been interpreted to be indicative of the fact that the Alfv,nic turbulence evolution for low-latitude fast streams under stable interplanetary conditions, as is typical of periods of low solar activity, is not appreciably different from that for the polar solar wind. When the extrapolation inside 1 AU is done for present nearequatorial results, ve find, in comparison with Helios observations, a lower than expected e+ level and a not matching gradient for e_. In Figure 8, Helios results are given in terms of t vo points only. Ho vever, the entire set of Helios observations clearly indicates [see Tit and Marsch, 1995] that the radial decrease of e_ in the region inside i AU is noticeably slower than that for Ulysses ecliptic observations bet veen 1 and 5 AU. Thus, with the caveat that the extrapolation of Ulysses results well inside 1 AU could be invalid, the problem we are left vith is that of the disagreement between near-equatorial observations of Ulysses and of Helios. Since the Ulysses results are for a period of high solar activity, vhile those of Helios have been obtained close to a minimum in the solar cycle, we vould be led to infer that a possible cause might be the different phase in the cycle. Ho vever, this would contradict the fact that Tu and Marsch [1990] found no appreciable difference bet veen z_ spectra obtained during (near solar minimum)and 1980 (near solar maximum). At this point ve could argue that turbulence conditions during periods of not quiet Sun may be different in different solar cycles. Obviously, further evidence on this is needed. It has to be mentioned that the evolution of Alfv,nic fluctuations in near-equatorial solar wind outside 1 AU has been investigated in the past by Roberts et al. [1987a, 1987b] using Voyager 1 and 2 data. A cornparison with their results is made difficult by the different scales examined. While we are looking at fluctuations vith timescales roughly between a few minutes and 1 hour, their analysis is mainly based on hourly averages. When higher-resolution data are used, they study the turbulence evolution in terms of integrated quantities that include timescales as long as 16 hours. This is very probably the reason of the increase, with increasing distance, that they observe for the e_/e+ ratio, reaching values around 0.6 near 5 AU. Our analysis definitely gives smaller values for that ratio. In fact, with the exception of one case, we anvays find values below 0.5, vith most of them in the range from 0.2 to 0.4. Moreover, in our data there is no evidence of an increasing trend vith distance. In conclusion, from the analyzed Ulysses data we have the clear indication that in near-equatorial solar wind the hourly-scale Alfv,nic

10 10,668 BAVASSANO ET AL- SOLAR WIND ALFV NIC FLUCTUATIONS turbulence is vell away from a z+-z_ equipartition also at distances as large as 5 AU [see also Bavassano et al., 1998]. Finally, it should be underlined that the radial gradient ( ) obtained by Bavassano and Smith [1986] for magnetic energy density in the same range of distances with Pioneer 10 and 11 data is in a very good agreement with the values we find vhen TB_N--0.5 is assumed (once the plasma density scaling is taken into account). It is vort. hwhile to recall that this gradient is close to that predicted by Hollweg [1975](in the small-wavelength WKB limit) for the case of rarefaction regions, a flow condition observed for most of the time intervals considered here. Acknowledgments. The use of data of the solar wind plasma analyzer (principal investigator D. J. McComas, Los Alamos National Laboratory, Los Alamos, New Mexico, USA) and of the magnetometers (principal investigator A. Balogh, The Blackett Laboratory, Imperial College, London, UK) aboard the Ulysses spacecraft is gratefully acknowledged. The data have been made available by the World Data Center A for Rockets and Satellites (NASA/GSFC, Greenbelt, Maryland, USA). The present work has been supported by the Italian Space Agency (ASI). Janet G. Luhmann thanks Tim S. Hotbury and another referee for their assistance in evaluating this paper. References Bavassano, B., and E. J. Smith, Radial variation of interplanetary Alfvdnic fluctuations: Pioneer 10 and 11 observations between 1 and 5 AU, J. Geophys. Res., 91, 1706, Bavassano, B., E. Pietropaolo, and R. Bruno, Cross-helicity and residual energy in solar wind turbulence: Radial evolution and latitudinal dependence in the region from 1 to 5 AU, J. Geophys. lies., los, 6521, Bavassano, B., E. Pietropaolo, and R. Bruno, On the evolution of outward and inward Alfvdnic fluctuations in the polar vind, J. Geophys. Res., 105, 15,959, Goldstein, B. E., E. J. Smith, A. Balogh, T. S. Hotbury, M. L. Goldstein, and D. A. Roberts, Properties of magnetohydrodynamic turbulence in the solar wind as observed by Ulysses at high heliographic latitudes, Geophys. Res. Lett., 22, aa9a, Hollweg, J. V., Alfv n wave refraction in high-speed solar wind streams, J. Geophys. Res., 80, 908, Hotbury, T. S., A. Balogh, R. J. Forsyth, and E. J. Smith, Observations of evolving turbulence in the polar solar wind, Geophys. Res. Lett., 22, 3401, Malara, F., L. Primavera, and P. Veltri, Nonlinear evolution of parametric instability of a large-amplitude nonmonochromatic Alfvdn vave, Phys. Plasmas, 7, 2866, Roberts, D. A., M. L. Goldstein, L. W. Klein, and W. H. Matthaeus, Origin and evolution of fluctuations in the solar wind: Helios observations and Helios-Voyager comparisons, J. Geophys. Res., 92, 12,023, 1987a. Roberts, D. A., L. W. Klein, M. L. Goldstein, and W. H. Matthaeus, The nature and evolution of magnetohydrodynamic fluctuations in the solar vind: Voyager observations, J. Geophys. Res., 92, 11,02], 1987b. Roberts, D. A., S. Ghosh, M. L. Goldstein, and W. H. Matthaeus, Magnetohydrodynamic simulation of the radial evolution and stream structure of solar wind turbulence, Phys. Rev. Lett., 67, 3741, Roberts, D. A., M. L. Goldstein, W. H. Matthaeus, and S. Ghosh, Velocity shear generation of solar vind turbulence, J. Geophys. Res., 97, 17,115, Smith, E. J., A. Balogh, M. Neugebauer, and D. McComas, Ulysses observations of Alfvdn vaves in the southern and northern solar hemispheres, Geophys. Res. Lett., 22, 3381, Tu, C.-Y., and E. Marsch, Evidence for a "background" spectrum of solar vind turbulence in the inner heliosphere, J. Geophys. Res., 95, 4337, Tu, C.-Y., and E. Marsch, MHD structures, vaves and turbulence in the solar wind: Observations and theories, Space Sci. Rev., 73, 1, B. Bavassano and R. Bruno, Istituto di Fisica dello Spazio Interplanetario, CNR, Via del Fosso del Cavaliere 100,001aa Roma, Italy. (bavassano@ifsi.rm.cnr.it) E. Pietropaolo, Dipartimento di Fisica, Universitk dell'aquila, via Vetoio, L'Aquila, Italy. (Received December 7, 2000; revised January 26, 2001; accepted February 23, 2001.)