CORRELATIONS OF PLASMA DENSITY AND
MAGNETIC FIELD STRENGTH IN THE HELIOSHEATH
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Gutynska, O., J. Šafránková, Z. Němeček, and J. D. Richardson.
“CORRELATIONS OF PLASMA DENSITY AND MAGNETIC FIELD
STRENGTH IN THE HELIOSHEATH.” The Astrophysical Journal
722, no. 2 (October 5, 2010): L228–L232. © 2010 The American
Astronomical Society
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http://dx.doi.org/10.1088/2041-8205/722/2/l228
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IOP Publishing
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Final published version
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http://hdl.handle.net/1721.1/95817
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CORRELATIONS OF PLASMA DENSITY AND MAGNETIC FIELD STRENGTH IN THE HELIOSHEATH
O. Gutynska1, J. ˇSafr ´ankov ´a1, Z. N ˇeme ˇcek1, and J. D. Richardson2
1Charles University, Faculty of Mathematics and Physics, V Holeˇsoviˇck´ach 2, 180 00 Prague 8, Czech Republic;jana.safrankova@mff.cuni.cz 2Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
Received 2010 July 28; accepted 2010 September 20; published 2010 October 5
ABSTRACT
The crossing of the termination shock (TS) by Voyager 2 in 2007 at 84 AU allows a comparison of fluctuations in different heliosheath regions. The Letter concentrates on MHD waves that exhibit a significant correlation between the magnetic field strength and plasma density. The correlations between both quantities were computed on 2 hr time intervals in the frequency range of 1× 10−4 to 4× 10−3 Hz. We separate the data into two regions with different magnetic field behavior; the post-TS region with many crossings of the current sheet and the unipolar region where the magnetic field direction remains nearly constant. We find that typical correlation coefficients in these regions are about 0.55–0.65, larger than in Earth’s magnetosheath. The largest correlations occur when the spectrum of magnetic field fluctuations is dominated by low frequencies.
Key words: magnetic fields – Sun: heliosphere – waves
1. INTRODUCTION
Voyager 2 (V2) crossed the termination shock (TS) at least
five times from 2007 day of year (DOY) 242–245 (Burlaga et al.
2008; Decker et al.2008; Richardson et al.2008; Stone et al.
2008) and is now in the heliosheath, the region of fluctuating, dynamic, shocked solar wind between the TS and heliopause. The TS was a relatively weak, quasi-perpendicular shock with a shock strength of about 2 (Richardson et al. 2008; Burlaga et al.2008). The solar wind plasma was slowed, compressed, and heated at the TS. According to Richardson et al. (2008), the flow remained supersonic (super-Alfv´enic) with respect to the thermal ions downstream of the TS. Most of the solar wind energy is transferred to the pickup ions or other energetic particles both upstream of and at the TS. The heliosheath boundaries move in response to a large merged interaction region (MIR; Burlaga et al.1985) driven shocks and due to solar cycle changes in the solar wind pressure, but these motions are small compared to the size of the heliosheath.
Burlaga et al. (2009) analyze high-resolution measurements of the magnetic field, B and find that V2 (similarly to Voyager 1) observed compressible “turbulence” in the heliosheath. Large-amplitude fluctuations of B occur at small scales (i.e., on scales of tens of minutes to tens of days) with very complex profiles. These include “kinetic-scale” features that are characterized by a series of depressions/enhancements in the field strength such as isolated magnetic holes and humps, and their trains (Burlaga et al.2006). Avinash & Zank (2007) have shown that these structures can be considered as solitons propagating with an arbitrary angle to the ambient magnetic field. The turbulence also includes “micro-scale” features (>100 proton gyroradii) that can be described by magnetohydrodynamic (MHD) theory. The small-scale fluctuations (both kinetic-scale and micro-scale fluctuations) may be mirror mode disturbances generated by temperature anisotropies generated at the TS (Liu et al.2007).
Burlaga & Ness (2009) described two regions behind the TS with different magnetic field behavior: (1) “the post-TS region” from 2007 DOY 245 to 301, where the magnetic field strength fluctuates about 0.09 nT but with large jumps in B on timescales of minutes to several hours, and the magnetic field direction fluctuates in a complicated way during intervals of several hours and (2) “the unipolar region” from 2008 DOY 2
to 76, a region with a nearly constant magnetic field azimuthal angle and with an elevation angle near zero. The magnetic field strength fluctuated around a linear trend. The unipolar region was caused by an excursion of the heliospheric current sheet past the latitude of V2 (Burlaga & Ness2009). Their analysis of both regions indicates that fluctuations on scales less than 1 day were significant in both the post-TS and unipolar regions. These magnetic fluctuations, characterized by a series of depressions in the field magnitude, are similar to those observed downstream of quasi-perpendicular interplanetary and planetary bow shocks which have been identified as mirror mode structures (e.g., Bavassano Cattaneo et al.1998).
On its path from 1 AU, V2 observed different types of correlations between the plasma speed, density, and magnetic field strength. Using 25 day averages, Richardson et al. (2003) looked at the correlations between the plasma speed, density, and the magnetic field magnitude. They found that the correlation between the density and magnetic field decreases with distance from 0.6 near Earth to about zero at 30 AU but was as high as 0.64 in the 2002 data at 67 AU. A numerical model (Wang & Richardson2001) was used to propagate the solar wind observed at Earth to the position of V2. The one-dimensional MHD model includes the effect of pickup ions (Wang & Richardson2001) and shows a high correlation between B and N throughout the heliosphere near solar maximum, but the high value probably results from the one-dimensional nature of the model which forces B and N changes to occur synchronously.
In this Letter, we used the Burlaga & Ness (2009) definition of heliosheath regions and performed a study of correlation properties of fluctuations of the plasma density, N, and magnetic field strength, B, measured by V2 in both the post-TS and unipolar regions. The purpose of the study is to find the dominant wave modes in the heliosheath and to deduce possible sources of these waves. Among many types of fluctuations observed in these regions, we concentrate on MHD waves that exhibit significant correlation between the plasma density and magnetic field strength.
2. DATA SET AND METHODOLOGY
The Voyager plasma experiment registers solar wind protons simultaneously in three Earthward-pointing Faraday cups over L228
No. 2, 2010 CORRELATIONS IN THE HELIOSHEATH L229 Voyager 2 250 300 350 400 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 B, nT 24 hr avg n o i g e R r a l o p i n U n o i g e R S T t s o P (a) 250 300 350 400 0.000 0.001 0.002 0.003 0.004 0.005 N, cm -3 7 hr avg (b) 250 300 350 400 0 100 200 300 az (c) 250 300 350 400
DOY from Jan. 1, 2007 -40 -20 0 20 40 60 el (d)
Figure 1.Overview of the V2 observations in the post-TS and unipolar regions. (a) Daily averages of the magnetic field strength, (b) 7 hr averages of the plasma density, daily averages of the magnetic field azimuthal (c) and elevation (d) angles.
an energy range of 10–5950 eV with a time resolution of 192 s (Bridge et al. 1977). When possible, the three spectra are fit with convected isotropic Maxwellian distributions to determine the proton velocity, density, and temperature. Data quality often does not allow this fitting procedure. For this study, we use moment densities obtained by integrating over the plasma distribution which allows us to use all the spectra and thus gives better time resolution.
The Voyager magnetometer measures the magnetic field with two sensors mounted on a boom, one at the end of the boom and the other closer to the spacecraft (Behannon et al.1977). We use 48 s averages of the magnetic field strength. The proton density is linearly interpolated to obtain the same time resolution as that of magnetic field measurements. The data are only available when the spacecraft is tracked by the Deep Space Network. Thus, the final data set consists of intervals of 8–14 hr in duration that repeat each day. This feature allows us either to study fast fluctuations within these intervals or to average the parameters over the whole interval and to investigate fluctuations with periods of several days and longer. However, the number of days that V2 spent in the heliosheath is still insufficient for the latter investigation.
An overview of the observations is presented in Figure 1
which shows daily averages of the magnetic field strength (a), 7 hr averages of the plasma density (b), and daily averages of the magnetic field azimuthal (c) and elevation angles (d) measured by V2. For this correlation analysis, we divide the data into two time subintervals: (1) from 2007 DOY 245 to 301—the post-TS region (38 intervals) and (2) from 2008 DOY 2 to 76—the unipolar region (55 intervals). The magnetic field
and proton density behave differently; neither correlation nor anti-correlation is seen on the scale of the figure. Nevertheless, enhanced levels of magnetic field fluctuations often correspond to enhanced levels of density fluctuations which suggests that the fluctuations may be associated with MHD waves. We try to identify these waves with our correlation analysis.
Taking into account the above constraints, we investigate only fluctuations with periods from ≈4 minutes (limited by the temporal resolution) to ≈2 hr (limited by the duration of the continuous intervals of data). For each of these intervals, we compute a cross-correlation coefficient using a subinterval of proton density measurements in the center of the time interval and a time lag with respect to the magnetic field measurements within a range of±3 hr. Both signals were pre-processed by applying a bandpass filter 1× 10−4to 4× 10−3Hz.
3. RESULTS AND DISCUSSION
Figure2shows an example of the magnetic field and plasma density profiles measured in one≈10 hr time interval on DOY 277 of 2007 in the post-TS region. The duration of the data we correlate is 120 minutes. The bottom panel shows the auto-correlation coefficients of the magnetic field (blue line), as well as the proton density (red line) and their cross-correlation coefficients (black line). The auto-correlation does not decrease to zero for large time lags, which suggests the presence of coherent periodic components. The same is true for the profile of the density auto-correlation but the periodicity is different. The cross-correlation techniques allow us to filter from the whole spectrum of fluctuations those in which B and N behave a
Voyager 2 277.7 277.8 277.9 278.0 0.0 0.1 0.2 0.3 0.4 B, nT
48 sec av Post-TS Region
(a) 277.7 277.8 277.9 278.0 DOY, 2007 0.000 0.001 0.002 0.003 0.004 N, cm -3
180 sec av Post-TS Region
(b) -200 -100 0 100 200 Lag [min] -1.0 -0.5 0.0 0.5 1.0 cor B x N (c)
Figure 2.Example of measured and computed profiles through one≈10 hr time interval on DOY 277 of 2007: (a) the magnetic field, (b) the plasma density, and (c) the computed cross-correlation coefficient between the magnetic field and plasma density (black line) and the auto-correlation coefficients of the magnetic field (blue) and the proton density (red). The light dashed lines distinguish one half of the period of the dominant MHD wave.
coherent way. The dashed line distinguishes the maximum and minimum of the cross-correlation coefficient, which are +0.7 and−0.7, respectively. In this particular case, the difference of the corresponding lags (≈230 minutes) is approximately equal to a half of the period of the dominant MHD wave. However, the cross-correlation profile suggests the presence of a wave with a much shorter period, about 55 minutes. The presence of two (or more) waves can explain why the typical value of the cross-correlation coefficient for zero lag was found to be arbitrary (close to zero in Figure2), whereas MHD theory predicts that
B and N would change in phase or anti-phase for fast and slow
waves, respectively.
The theory of correlation functions assumes unlimited time intervals (numbers of points), but our time intervals are rather short. To test whether our results are significant or arise from the errors caused by the use of a limited number of points, we generated 1000 pairs of random sequences and processed them using the same method as for the real signals. The comparison is shown in Figure 3. The black squares show the average maximum (top) or minimum (bottom) correlations computed using different data subintervals within the post-TS region (38 intervals). The black bars show the standard deviations. The green squares show the correlations for the unipolar region (55 intervals) and the red for the random signals. The magnetic field and plasma density exhibit a statistically significant correlation. The mean correlation coefficient decreases nearly linearly with the duration of the subinterval and approaches the random
0 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 max cor N x B Post TS region Unipolar region Artif signal 0 100 200 300 400 500 600 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 min cor n x B Post TS region Unipolar region Artif signal 0 100 200 300 400 500 600 length [min]
Figure 3.Averaged profiles of maxima and minima of correlation coefficients in both regions computed using subintervals with different durations. For comparison, the correlation coefficients derived from a random sequence of two signals are also shown (red points).
-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 Correlation coefficient 0 5 10 15 20 Number of events Post TS Unipolar R cor N x B (0 lag)
Figure 4.Distributions of maximum and minimum correlation coefficients in the post-TS (black) and unipolar (green) regions. The red histogram shows the distribution of correlations coefficients for zero lag in both regions.
sequence level for subintervals of≈600 minute long. This result indicates that the coherent features persist for about 10 hr in the analyzed frequency range.
The same features were found in both regions, but the correlation is slightly higher in the unipolar region. Since the MHD fluctuations are generated either at the TS or locally in the heliosheath near the TS, the small increase of the correlation at larger distances from the TS suggests that the incoherent fluctuations are gradually damped as they are convected from the source through the post-TS region to the unipolar region.
Figure4presents histograms of the maxima (positive values) and minima (negative values) of correlation coefficients between
N and B in both regions. The distributions are nearly identical,
No. 2, 2010 CORRELATIONS IN THE HELIOSHEATH L231 0 50 100 150 200 250 -9 -8 -7 -6 -5 -4 PSD [nT 2 /Hz] (a) 0 50 100 150 200 250 Period [min] 0.2 0.4 0.6 0.8 1.0 max cor N x B Post-TS region Unipolar region chi2= 0.21 chi2= 0.074 (b)
Figure 5. (a) Typical spectrum of magnetic field fluctuations (the dashed line indicates the period of a dominant wave). (b) Maxima of the correlation coefficient plotted vs. the period of the dominant wave. The standard deviations are shown at the top of the figure.
panel of Figure2 is typical. The most frequent values of the coefficients are around 0.6 and are slightly higher in the unipolar region. These values are surprisingly large; Gutynska et al. (2009) reported that correlation coefficients of 0.4 were typical in the Earth’s magnetosheath. The distribution of correlations for zero lag (red line in Figure4) is very broad and centered around zero. This suggests that there is no preferred wave mode in the heliosheath, whereas Gutynska et al. (2009) found slow or mirror mode to be more frequent in the magnetosheath.
Figure 5(a) shows a typical spectrum of magnetic field fluctuations, and the dashed line indicates the period of a dominant wave. The correlation coefficient plotted versus this period in each interval is given in Figure5(b). The correlation coefficient increases with the wave period. This trend is more pronounced in the unipolar region, which has a larger number of intervals with low frequencies. The larger correlations observed in the unipolar region (see Figure 4) may result from the damping of higher-frequency waves as they convect through the heliosheath, leaving more low-frequency waves (which have higher correlations) in the unipolar region. We note that the longest periods correspond to the duration of the intervals. Heliosheath fluctuations could have longer periods but the available data do not allow them to be identified.
Variations of the magnetic field magnitude are not accom-panied with correlated changes of its direction. It is clear in the unipolar region where the field direction is almost constant (Figure1) on any timescale, and we have found the same be-havior in the post-TS region. This supports the interpretation of the fluctuations as trains of solitons (Avinash & Zank2007); on
the other hand, such solitons would exhibit an anti-correlation between the density and field strength which is not the case (Figure4).
One-point measurements are insufficient for a reliable deter-mination of the wave mode. If the mirror mode waves in the heliosheath (Liu et al.2007) and in Earth’s magnetosheath be-hind of the quasi-perpendicular bow shock (e.g., Schwartz et al.
1996; T´atrallyay et al. 2008) were similar, the typical wave-length would be of the order of 106km. Since the mean Alfv´en velocity is about 50 km s−1and mean flow speed≈150 km s−1 in the heliosheath, the wavelength of other modes would be of the same order. Such waves cannot propagate (or be convected) through planetary magnetosheaths (Hubert et al.1998), thus a comparison of these apparently similar environments is difficult.
4. CONCLUSION
We analyzed MHD fluctuations in two regions of the he-liosheath and found:
1. Strong fluctuations in the frequency range of 1×10−4to 4× 10−3Hz with correlated changes of the magnetic field and density which were identified in both regions.
2. The cross-correlation coefficient of these quantities is≈0.6 in both regions, significantly larger than the value of 0.4 in Earth’s magnetosheath and is slightly larger in the unipolar region that is located farther from the TS.
3. Typical periods of the fluctuations range from 50 to 220 minutes.
4. The value of the cross-correlation coefficient increases with the period of the dominant wave in the frequency spectrum. 5. Larger values of cross-correlation coefficients observed in the unipolar region are consistent with a larger portion of long-period fluctuations.
Above observations suggest that the heliosheath fluctuations are generated at the TS. The waves of higher frequencies are gradually damped, and lower frequencies prevail at larger distances from the TS.
The present work was partly supported by the Czech Grant Agency under Contracts 205/09/0170, 205/07/0694, and 202/ 08/H057, and partly by the Research Plan MSM 0021620860 that is financed by the Ministry of Education of the Czech Republic. O.G. is thankful for support from Grant ME09056 and GAUK 163810. J.D.R. was supported by the NASA through the Voyager project and grant NNX08AC04G.
Facility: Voyager II
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