A ONE-SIDED ASPECT OF ALFVENIC FLUCTUATIONS IN THE SOLAR WIND

Ever since pioneering studies by Coleman (1968) and Belcher & Davis (1971) it has been known that the solar wind is both turbulent and filled with Alfvénic-type fluctuations. Belcher and Davis noted that the fluctuations propagate predominantly away from the Sun along the magnetic field, B, in the solar wind rest frame, suggesting that they are largely the evolved remnants of Alfvénic fluctuations that originate inside the point where the solar wind flow becomes super-Alfvénic. Most subsequent observational studies of these fluctuations have employed statistical methods (for example, correlation analysis, power spectra analysis, structure functions, cross helicity, etc.) to discern and understand the nature of the fluctuations and their evolution with distance from the Sun (see, for example, reviews by Marsch 1991; Goldstein et al. 1995; and Tu & Marsch 1995). These studies commonly employ quantities such as variances and the Elsasser variables (Elsasser 1950), and typically assume that the fluctuations in B and velocity, V, are about suitably obtained average values of those quantities. Such studies have confirmed the general outward (from the Sun) sense of propagation of the fluctuations in the solar wind rest frame, but have also revealed that the fluctuations become less Alfvénic with increasing heliocentric distance with the apparent development of mixed and partially sunward-directed Alfvénic components (e.g., Roberts et al. 1987). Various authors (e.g., Roberts et al. 1987; Marsch 1991) have warned that the apparent sunward-directed component arising from various statistical analyses might not correspond to actual discrete sunward-propagating Alfvénic fluctuations, but might result instead from something else such as a combination of outward-propagating Alfvénic fluctuations and convective structures (e.g., Tu & Marsch 1993). Nevertheless, some recent studies (e.g., Scudder et al. 2008, 2009) assume that the solar wind near 1 AU is filled with discrete sunward-propagating rotational discontinuities (RDs).

We have recently been engaged in studies (e.g., Gosling et al. 2005, 2006, 2007; Gosling 2007) of coupled solar wind V and B fluctuations in an attempt to identify signatures of magnetic reconnection in the solar wind in the form of Petschek-like exhausts (Petschek 1964), i.e., roughly Alfvénic plasma jets propagating away from reconnection sites and bounded by pairs of back-to-back RDs. In order to identify that characteristic signature of reconnection, we have made detailed component-by-component examinations of combined V and B fluctuations in the solar wind obtained by a variety of spacecraft covering many years of observations at different heliocentric distances and latitudes. This examination has revealed a common one-sided nature to variations in the r or t (heliocentric r, t, n coordinates) components of V and B in these fluctuations that, although having an obvious interpretation, has not previously been considered in any detail to the best of our knowledge. Our study has also revealed that in the absence of magnetic connection to reverse shocks, including Earth's bow shock, or magnetic reconnection there are few, if any, discrete RDs propagating sunward along B in the solar wind rest frame at 1 AU. Here, we briefly document and discuss these important aspects of Alfvénic fluctuations in the solar wind using 64 s data from the SWEPAM (McComas et al. 1998) and MAG (Smith et al. 1998) experiments on Advanced Composition Explorer (ACE), which is in orbit about the L1 point ∼0.01 AU upstream from the Earth.

Figure 1 shows solar wind plasma and magnetic field data from ACE obtained during a time when the spacecraft was embedded within the core of a high-speed stream from a coronal hole. Throughout this interval the solar wind electron strahl (not shown), which carries the electron heat flux away from the Sun, was centered at a pitch angle of 0°, consistent with the predominant positive B_r values observed. Fluctuations in all components of V and B were strongly anticorrelated throughout the interval, indicating that the fluctuations were all Alfvénic and propagating antisunward along B in the solar wind rest frame since changes in V and B are anticorrelated (correlated) for Alfvénic fluctuations propagating parallel (antiparallel) to B. Proton density and |B| were relatively constant, with small changes in these quantities being generally uncorrelated with one another.

The fluctuations in V_r evident in Figure 1 appear as one-sided pulses, rather than wavelike structures, and were of variable duration; notably, all produced relatively short-lived increases in V_r above a slowly varying base value that ranged between ∼650 and ∼670 km s⁻¹. Exceptions occurred when a brief fluctuation occurred during a fluctuation of longer duration such as in the intervals from ∼ 0515 to ∼0645 UT, from ∼1330 to 1410 UT, and from ∼1510 to 1600 UT, in which case V_r typically rose from and/or returned to the level associated with the broader fluctuation. Similarly, the associated fluctuations in B_r were all one-sided toward less positive values relative to a slowly varying base value ranging between ∼ +5 and ∼ +6 nT. Since the average and median |B| during this interval were 6.27 and 6.32 nT, respectively, the base B_r was the dominant r, t, n component of B during this interval. The spiral field angle associated with a base B_r of 5.5 nT and the average |B| of 6.27 nT is 29°, close to but somewhat more radial than the 1 AU Parker spiral angle of 33° associated with a solar wind speed of 660 km s⁻¹. Isolated RDs were not present in the data since all increases (decreases) in V_r (B_r) had associated decreases (increases).

Zoom In Zoom Out Reset image size

Figure 2 demonstrates the high degree of correlation between changes in V and B (in Alfvén speed units) on a 64 s point-by-point basis for the first 3 hr of the interval shown in Figure 1 and is representative of the data for the entire 12 hr. Observed changes in the velocity components were comparable to, but slightly less than, that predicted for pure Alfvénic fluctuations as has been found in numerous previous studies (e.g., Marsch 1991). We also note that both the predicted and the observed changes in V_r were generally smaller than the predicted and observed changes in the other two components.

The above noted one-sided and positive nature of V_r fluctuations above a base value is characteristic of Alfvénic fluctuations observed in the high-speed wind from coronal holes when B_r is the dominant r, t, n component of the background B, which is usually the case at 1 AU, independent of the sign of B_r and even when the base value of V_r is itself temporally variable. Similarly, at such times the associated fluctuations in B_r are all one-sided relative to reasonably well-defined base levels with the B_r fluctuations being toward less positive (less negative) values when the base B_r is positive (negative). However, one-sided fluctuations in the solar wind are not limited to the r components of V and B; they can also be observed in the t components when B_t is the dominant component of the background field. Figure 3 shows ACE data for another 12 hr interval when the spacecraft was again embedded within a high-speed stream from a coronal hole. Throughout this interval the electron strahl (not shown) was centered at a pitch angle of 0°, consistent with the predominant negative B_t values observed during this interval. Fluctuations in all components of V and B were strongly anticorrelated throughout, indicating that they were all Alfvénic and propagating antisunward along B in the solar wind rest frame. Proton density and |B| were relatively steady throughout with changes in these quantities being generally uncorrelated with one another. Point-by-point comparisons of observed and predicted changes in solar wind V (not shown) for this 12 hr interval reveal the same level of agreement as demonstrated in Figure 2 for the 2003 May 12 interval with the predicted changes in the V components again typically being somewhat greater than the observed changes and both the predicted and observed changes in V_t generally being less than observed changes in the other two components.

Zoom In Zoom Out Reset image size

Virtually all of the fluctuations in the Figure 3 interval produced relatively short-lived decreases in V_t relative to a slowly varying base value of ∼+20 km s⁻¹. Similarly, the associated fluctuations in B_t were all one-sided toward more positive values relative to a slowly varying base ranging between ∼−5 and ∼−4 nT. Since the average and median values of |B| were 5.16 and 5.20 nT, respectively, the base B_t was the dominant component of B during this interval. The spiral field angle associated with a base B_t of −4.5 nT and the average |B| is 61°, considerably greater than the Parker spiral angle of 30° expected for a 750 km s⁻¹ wind. In general, we find that when B_t is the dominant component of the background B and regardless of the sign of the base B_t, fluctuations in both B_t and V_t tend to be one-sided with the fluctuations in V_t always being toward less negative values, consistent with Alfvénic fluctuations propagating outward from the Sun along B.

Zoom In Zoom Out Reset image size

Figure 4 shows data for a 16 hr interval when fewer large-amplitude Alfvénic fluctuations were observed than in the previous examples shown. The base V_r level was not as well determined as in Figure 1, particularly in the interval from ∼2300 UT on January 23 to ∼0700 UT on January 24 when proton density and magnetic field strength were strongly anticorrelated. Nevertheless, a base B_r level of ∼−4 nT was evident in the magnetic field data for much of this interval and the electron strahl (not shown) was centered at pitch angle 180°, as expected. For the most part, fluctuations in V and B were correlated in the 16 hr interval, with excursions in V_r being above the base value and excursions in B_r being to less negative values, in contrast to Figure 1 example. An exception to this occurred from ∼0600 UT to ∼0700 UT on January 24 when a broad B_r fluctuation had no associated V_r fluctuation, and more notably in the interval from ∼0800 UT to ∼0935 UT, highlighted by the red horizontal bar in the top panel of the figure, when changes in V and B were anticorrelated rather than correlated, and the changes in V_r were decreases below the local base value of ∼560 km s⁻¹. These anticorrelated V, B pulses, although not entirely Alfvénic (note, for example, the associated dips in field strength and increases in proton density associated with the two largest fluctuations in this interval), were thus clearly propagating sunward in the solar wind rest frame and must have been generated upstream of the spacecraft and then been blown back over the spacecraft by the super-Alfvénic solar wind flow. We are reasonably confident that these anticorrelated, sunward-propagating pulses were produced by backstreaming ions from Earth's bow shock since energetic bow shock ions (bottom panel of Figure 4) and suprathermal electrons from the bow shock were observed throughout much of the 0800–0935 UT interval as well as in the preceding hours.

Using ACE 64 s data we have shown that Alfvénic fluctuations in the solar wind propagating out from the Sun along B typically produce one-sided fluctuations in the r or t components of V and B relative to more slowly varying base values when B_r or B_t, respectively, is the dominant background field component. The associated pulses in V_r (V_t) are always positive (negative) independent of the sign of the base value of B_r(B_t). We have also observed this effect in solar wind data sets obtained at different heliocentric distances (e.g., Helios, Ulysses) and at higher latitudes (Ulysses). The one-sided nature of V_r and B_r fluctuations is particularly prominent in the Helios data near 0.3 AU where the background B tends to be more nearly radial than at 1 AU and the one-sided nature of V_t and B_t fluctuations is particularly prominent in the Ulysses data obtained well beyond 1 AU at relatively low heliographic latitudes where the background B tends to be more transverse to the radial direction than at 1 AU.

These effects can be explained as a natural consequence of the transverse nature of outward-propagating Alfvénic fluctuations in which |B| is ∼ constant (see, for example, the stochastic model of Alfvénic fluctuations in the solar wind proposed by Barnes (1981) in which the tip of the field vector varies randomly over a hemisphere of constant radius). If one considers the simple case of an underlying radial magnetic field directed outward from (inward toward) the Sun, fluctuations in either or both of the transverse field components necessarily means that B_r must become less positive (less negative) so as to keep |B| ∼ constant. In either case, the fluctuations also must include increases in V_r relative to an underlying base value since changes in V and B are anticorrelated (correlated) for Alfvénic fluctuations propagating parallel (antiparallel) to B. One can show that in this case the magnitude of the changes in V_r and B_r should be less than the magnitude of the changes in the total transverse component for field fluctuations that are less than 90° from the underlying field direction. The relevant variations in V_r and B_r are thus relative to base values rather than average values as is assumed in most statistical analyses of Alfvénic fluctuations in the solar wind. For example, the variances in V_r and B_r will not be normally distributed about the average values for an underlying radial B and the direction of minimum variance for field rotations less than 90° from the underlying B should coincide precisely with the direction of the underlying radial magnetic field.

A similar situation prevails for the t components of V and B if the underlying field direction is transverse to the radial direction in the solar equatorial plane. For more general orientations of B the situation is more complicated and the effect is more difficult to observe using data in r, t, n coordinates since even when B lies in the equatorial plane the r and t components are usually mixtures of parallel and transverse components of B. The one-sided nature of the fluctuations in the field component that defines the underlying background field direction only becomes obvious in r, t, n coordinates when either the r or the t component of B is the dominant component as in the examples shown in this paper. In the high-speed wind at 1 AU, the Parker spiral B usually has a dominant r component, which is why the one-sided nature of V_r fluctuations is so common at and inside 1 AU throughout much of the high-speed wind from coronal holes.

Sunward-propagating (in the solar wind rest frame) Alfvénic fluctuations and/or RDs produce the opposite sense of correlation between changes in V and B compared to antisunward-propagating disturbances. In addition, when B_r is the dominant component of the background B they should produce decreases in V_r below the nominal base level, as in the Figure 4 example. A limited search for both these types of signatures in the ACE data indicates that discrete sunward-propagating fluctuations are relatively rare in the pristine solar wind at 1 AU. Thus far we have identified sunward-propagating Alfvénic fluctuations in the ACE data only (1) in events such as that in Figure 4, which are associated with backstreaming ions from Earth's bow shock and which produce pulselike rather than single-step decreases in speed, (2) immediately up and down stream from reverse shocks associated with corotating interaction regions or disturbances driven by interplanetary coronal mass ejections where the fluctuations are usually wavelike, and (3) in events identified as reconnection exhausts, in which case the sunward-propagating RDs are always paired with RDs propagating in the opposite direction along B. This well justifies warnings (e.g., Roberts et al. 1987; Marsch 1991) that the results of statistical analyses do not necessarily imply that discrete sunward-propagating Alfvénic fluctuations or RDs are common in the pristine solar wind at 1 AU.

Zoom In Zoom Out Reset image size

Finally, the fact that fluctuations in the field component that defines the underlying field direction are always relative to a base value rather than to an average value suggests that conclusions derived from statistical analyses of solar wind data, including those based on determinations of the underlying field direction itself, that assume the fluctuations in all field components are relative to average values, should be re-examined.

J.G. thanks A. Balogh, J. Borovsky, T. Horbury, B. Matthaeus, M. Neugebauer, C. Smith, and M. Velli, for a number of stimulating conversations on one or more of the topics of this paper, C. Smith for use of the magnetometer data, and M. Desai for providing energetic particle observations. This work has been supported by NASA grant NNG06GC27G and the SWEPAM portion of the NASA/ACE program.