Solar wind plasma correlations between IMP 8, INTERBALL- 1, and WIND

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL 103, NO A7, PAGES 14,601-14,617, JULY 1, 1998 Solar wind plasma correlations between IMP 8, INTERBALL- 1, and WIND K I Paularena, 1 G N Zastenker, 2 A J Lazarus, 1 and P A Dalin 2 Abstract Solar wind plasma flux correlations between data from three spacecraft (IMP 8, WIND, and INTERBALL-I) were analyzed for approximately 4 months during late 1995 and mid 1996 (near solar minimum) in order to investigate the local homogeneity of the solar wind The data were split into 6-hour segments, resulting in a total of 397 segments where data from at least one pair of spacecraft could be correlated The results show that the average flux correlation was 07 over distances ranging from 0 to 220 Rz in the radial direction and up to 80 Rz perpendicular to the Earth-Sun line 43% of the segment studied had correlation coefficients of at least 08, while only 19% of the segments had correlation coefficients less than 05 The additional lags, after performing radial advection shifts at the plasma bulk speed, cluster near zero (71% of the best correlations occur with lags under 10 min), implying that the advection shift is a good approximation of the propagation time for the structures being correlated There appeared to be no dependence of the correlation on spacecraft separation in either XGSE or YGSE The best organizers of the flux correlation ppe r to be the vmue of the flux nd the standard deviations of the flux nd the density 1 Introduction intervals, showed that the worst correlations occur when With the launch of the INTERBALL-1 tail probe in interplanetary magnetic field (IMF) variances are small August 1995, there is an unusual opportunity to examand the spacecraft are separated over distances perpenine solar wind correlations from three spacecraft with dicular to the Earth-Sun line (the X6sz axis) of greater orbital distances ranging from Earth's bow shock out than 90 RE [Craaker et al, 1982] King [1986], using to the L1 point The WIND spacecraft, launched in several 4-week intervals of 5-min-averaged IMP 8 and November 1994, has a complex petal-shaped orbit which ISEE 3 plasma data, found a 70% probability that the carries it out to ~200 Re upstream of Earth, while the agreement between solar wind speeds would be within orbit of IMP 8, launched in October 1973, covers an 18 km/s, while the agreement between measure densiarea with near-circular cross-section ~35 Rz in radius ties was within 30% Thus, while it is commonly ex- The INTERBALL-1 tail probe's orbit is a series of el- pected that plasma correlations are higher than the lipses oriented nearly perpendicular to the ecliptic plane magnetic field correlations, detailed studies of plasma and precessing about the Z6sz axis Data from simcorrelations at several scales are needed to help understand the short-scale evolution and behavior of nearilar Faraday cup instruments on each spacecraft allow Earth solar wind for good comparisons of plasma flux with reduced concern about differential instrument response (see, for ex- Additionally, recent interest in space weather, with ample, the discussions in section of Vasyliunas an emphasis on geomagnetic forecasting using L1 so- [1971] and of Lazarus and Paularena [1998]) lar wind monitors, as well as the necessity for inter- Correlations of 64-s averaged magnetic field parame- calibrating plasma data from the newer WIND and ters for 3-hour intervals from ISEE I and 3 have shown INTERBALL-1 spacecraft with the long duration (24- that the correlation coefficients are fairly low, with half year) IMP 8 data set, have made the cross correlation of the correlations having values of less than 073 [Rus- of solar wind plasma parameters an important task sell et al, 1980] A study of 64-s-averaged magnetic Clearly, even if the impact on Earth's magnetosphere field data from the same spacecraft pair, using 2-hour of a change in solar wind plasma parameters is wellunderstood, the reliability of any forecast depends on I Center for Space Research, Massachusetts Institute of the accuracy of the input data used Reliance on L1 Technology, Cambridge monitors to supply plasma parameters for input to mag- 2Space'Research Institute, Russian Academy of Sciences, netospheric response models thus requires that L1 solar Moscow wind conditions accurately representhe solar wind im- Copyright 1998 by the American Geophysical Union Paper number 982A /98/98JA pinging on Earth's bow shock As the Russell et al [1980] and Craaker et at [1982] magnetic field studies show, this assumption may be only partially valid Thus one purpose of this study and of other solar wind 14,601

2 14,602 PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND : ' IMP - lo 5 o!, : : -I 15h r= (b) t WIND ",o- ß " '?""';'%";': ß ' ß :! ;,,, - 0J j r 0g ::: :: :,, j ::: : - NTEBALL : Hour (UT), June 6 (DOY 158), Additional Lag (s) Figure 1 An example of good flux correlation between all three spacecraft Data shown are from June 6 (DOY 158) 1996 (a) IMP 8 and INTERBALL-1 data (b) IMP 8 and WIND data (c) INTERBALL-1 and WIND data (d) Correlations as a function of lag for all three pairs correlation studies [eg, Richardson et al, [1998] is to strument performs integral measurements As a result, exploit the multipoint measurements provided by some the fluxes from both IMP 8 and WIND are calculated by of the International Solar-Terrestrial Physics (ISTP) taking the product of plasma bulk speed and number spacecraft suite to determine the spatial homogeneity density, while for INTERBALL-1 the bulk speed and of solar wind plasma number density are calculated from examination of the 2 Data Sets shape of the integral energy measurement Although speed is generally the most accurate plasma parameter, this study uses flux in order to avoid possible prob- Data sets from three spacecraft are correlated in this study In all cases, the data are plasma number flux values derived from similar Faraday cup instruments The IMP 8 instrument is described by Bellomo and Mavretic lems with speed values calculated using data from the INTERBALL-1 integral instrument Additionally, examining flux correlations allows variations in both speed and density, perhaps better correlated with some mag- [1978], the WIND instrument by Ogilvie et al [1995], netospheric effects than either parameter alone (eg, and the INTERBALL-1 VDP instrument by afrdnkovd the fairly good prediction level for the bow shock posiet al [1997] One major difference between the three instruments is that both the IMP 8 and WIND Faraday cup experiments provide measurements of current as a function of energy/charge, while the INTERBALL-1 intion seen by Fairfield [1971])to be considered together Since density variations are of far greater relative magnitude than speed fluctuations, the flux variations are driven primarily by density changes

3 PAULARENA ET AL: SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND 14,603 2O 10 IJJ D ( : El : -2O -30 5o June 6 ' ß April $ June 7 : : : : ' i ' : : : I : IMP INT WIND O E] A I : : I : I 2o hi 10 td O Xcsr (Rr) Figure 2 Positions of the three spacecraft during the time periods shown in Figures i (June 6; open points), 3 (April 3; solid points), and 4 (June 7; half-filled points) IMP 8 is represented by circles, INTERBALL-1 by squares, and WIND by triangles (a) The Y positions plotted against X (b) The Z positions plotted against X Data from 4 months (August and September 1995 and April and June 1996) are examined in this paper These months were chosen since they provide good INTERBALL-1 solar wind coverage and also cover a fairly wide separation in both XasE and in time (N B The Geocentric Solar Ecliptic (GSE) coordinate system is used throughout this paper; this system has X sunward, Z toward the ecliptic north pole, and Y completing a right-handed system) An attempt was made to exclude foreshock regions from the INTER- BALL data set, since the relatively low orbital distance caused the spacecraft to be in the foreshock during some parts of the months studied Because the sampling rate for IMP 8 data is so much longer than that for the INTERBALL-1 data, it was difficult to be sure when IMP 8 was in the foreshock, and thus IMP 8 data were not edited to remove any foreshock regions However, this should not have a very large impact on the results, since the statistics for the overall correla- tion values and for those with INTERBALL foreshock data were essentially the same In order to provide the largest number of correlations possible and to look for geometric effects, the data were compared in three separate pairs: IMP/WIND, INTERBALL/IMP, and IN- TERBALL/WIND The process of calculating the cross correlations is discussed below 3 Method For each spacecraft pair, a base data set was chosen The base data set was the IMP 8 data set for the IMP/WIND pair and the INTERBALL-1 data set for the other two pairs The time resolution of the data used was the finest available for IMP 8 and WIND, approximately i min and 90 s, respectively, and 64-s- average data for INTERBALL-1 (the underlying resolution is I s) The base data set was split into four approximately 6-hour periods along the time bound-

4 14,604 PAULARENA ET AL- SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND IF (b) %: ::" :;, WIND r = 092 " ß L' ß, ' "";P,,q, '?"',: ' "":,, 8 4 -? : ' ß I M P ; ß ß : ß - :;: : i '" \ il, : ': *,,* ß 1 : ::: : : : : C r = f'"' ):, ::,:, :L WIND : :,,, 0o,o s, i i, Hour (UT), April 3 (DOY 94), Additionol Log (s) Figure 3 A period where the flux data show a great deal of agreement but the structures appear to be complex in geometry Data shown are from April 3 (DO¾ 94) 1996 (a) IMP 8 and INTERBALL-1 data (b) IMP 8 and WIND data (c) INTERBALL-1 and WIND data (d) Correlations as a function of lag for all three pairs aries at 6, 12, 18, and 24 hours of each UT day Each of these periods is considered to be a data segment Although six hours is the desirable base segment length, shorter segments were occasionally used in the correlations with INTERBALL-1 data For each pair, the nonbase data set was extended by an hour on each end of the segment, if data were available, in order to allow for maximal data coverage even after advection time shifting and correlation lagging As the IMP 8 data spans often contain tracking gaps and it is necessary to ensure that sufficient data are available for meaningful correlations to be calculated, limits were placed on the allowable minimum coverage for the correlations using IMP 8 data as the base data set The criterion we chose was that 5 of the 6 hours in each segment had to contain at least 10 data points (ap- proximately one-sixth of the maximum number of data points per hour), while the remaining hour could have no data points About 50% of the available segments met this criterion First, an advection offset was made to the nonbase data set by dividing the difference in X position between the two spacecraft by the average speed (during the segment) observed by one of the spacecraft of the pair Because INTERBALL-1 does not routinely produce speed information, as discussed above, the IMP 8 or WIND speeds were used to calculate the advection shift for correlations with INTERBALL-1 For the IMP/WIND correlations, the WIND speed was used since WIND was generally upstream (sunward) of IMP 8 It is important to note that the advection offset used here was constant for each segment This technique was chosen to minimize time regressions, due to abrupt speed increases, which can occur when per-

5 , PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND 14,605 40,35, ' 35?- 25 ',-r D c 30 : 25 :;,y,: 20 Y,:\,:', :: 15 INTERBALL 1o W,ND Hour (UT), June 7 (DOY 159), 1996 o 08 c 06 o "-' 04 o 02 o Additionol Log (s) Figure 4 A period showing poor to good correlations Data shown are from June 7 (DOY 159) 1996 (a) IMP S and INTERBALL-1 data (b) IMP S and WIND data (c) INTERBALL- 1 and WIND data (d) Correlations as a function of lag for all three pairs; linestyles are the same as in Figures i and 3 The advection shifts used were: 159 s (IMP/INTERBALL); 2368 s (IMP/WIND); 2307 s (INTERBALL/WIND) forming a point-by-point advection shift However, this choice of advection-offset calculation tends to emphasize the correlation of static features; ie, those that do not change much in temporal length over the propagation distance As the segment length is over six times as large as the largest average advection offset, this choice is probably of minimal impact Next, the nonbase data set was lagged relative to the base data set, linearly interpolated to the times of the base data set observation points, and the linear Pear- son correlation coefficient [Neter et al, 1988] was calculated This process was repeated for a total of 81 different lags, 60 s apart, from-2400 to 2400 s The sign of the lag is defined using the convention that the lag is negative when shifting the nonbase data to earlier times (ie, a lag of-20 min shifts a measurement time of 1800 UT to 1740 UT) The physical sense of this negative lag is that the correlated feature in data from the spacecraft which is closest on average to Earth occurs later in time than the same feature in the advection-shifted data from the spacecraft which is usually farther from Earth That is, the feature arrived earlier in time than expected The maximum correlation coefficient and the lag at that point were obtained for each data pair, as was the correlation coefficient as a function of lag For each segment pair the averages, standard deviations, and ranges of several plasma parameters were calculated, as were the average positions in X, Y, Z, and R = x/'ay2 -F AZ 2 These parameter values were used to examine their effect on the value of the cor- relation coefficients obtained In order to present the behavior of the correlation coefficient as a function of

6 14,606 PAULARENA ET AL: SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND Median: 077 Mean: 071 Standard Deviation: 022 Total Number of Points' 397 E 10 c 37% IMP-INTERBALL-WIND Flux Correlation Coefficient Figure 5 A histogram showing the percentage of segments having the flux correlation within bins 005 wide Shaded areas show the percentage of segments having correlations below 05 or above 08, for reference to the Crooker et al [1982] results Rounding results in the total being slightly less than 100% the positional and plasma parameter values, the data plotted using the advection shifts and additional lags were binned based on these parameters and the average that together yield the highest correlation coefficients correlation coefficient within each bin was calculated When examining these figures, it is important to remember that the correlation coefficients were calculated 4 Results after one data set in each pair had been interpolated to 41 Individual Cases the base data set This process can result in a higher correlation coefficient being obtained than is immediately obvious from visual examination The bottom panels in each example show the correlation coefficients obtained for each spacecraft pair as a function of additional lag Before discussing the results of the statistical study, it is instructive to examine some examples of both good and poor correlations Figure I shows an example where the correlations between all three spacecraft pairs were excellent The positions of the three spacecraft during this and the following two time periods are shown in Figure 2 (filling of points represents date; shapes represent the different spacecraft) Each data figure shows the IMP/INTERBALL, IMP/WIND, and IN- TERBALL/WIND flux data in the top three panels Figure la shows the correlation between IMP 8 and INTERBALL, the closest spacecraft pair during this time period Fine details, such as the series of flux enhancements between 0200 and 0400 UT, and the larger-scale structure on which they are superposed match very well in time duration and relative ampli-

7 PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND 14, Median: < 0005 s Mean: -157 s Standard Deviation: 809 s Total Number of Pts:, c- c- 15 c IMP-INTERBALL-WlND Additionel Leg (s) Figure 6, A histogram showing the percentage of segments whose maximum correlations were associated with additional lags falling within the plotted bins tude Given the nature of the linear cross-correlation calculation, only relative changes are important- the absolute value does not matter This feature of the correlation is especially important since, as Figtires lb and lc show, the average flux levels measured by the WIND instrument and the IMP 8 and INTERBALL- 1 instruments have a systematic offset However, this offset is not what causes the somewhat lower correlation coefficients seen in the figure; the lower correlations are caused by differences such as those in the small structure near 0210 UT, where IMP and INTER- BALL observe a shorter flux enhancement, followed by a longer flux decrease, than does WIND As Figure 2 shows, WIND is much further upstream than, and on the opposite side of the Earth-Sun line from, the IMP and INTERBALL spacecraft It may be that, unlike the other flux structures seen during this segment, this particular feature either evolved as it propagated earthward, or was of limited spatial extent As is common in most cases where excellent correlations were obtained, the shapes of the coefficients as a function of lag (Figure ld) show single peaks from which the sides fall off rather steeply The fact that all three additional lags are near zero implies that the flux structures are aligned nearly perpendicular to the Earth-Sun line and propagating nearly radially Figure 3 shows a similar case, except that here the best correlation occurs between INTERBALL and WIND (Figure 3c), even though their X separation is,-55 Rr, while IMP and INTERBALL are only about i RE apart in X Here the different Y positions are the likely explanation (Figure 2; square points), especially given the 0 s lag between INTERBALL and WIND In fact, the nonzero lag between IMP and INTERBALL implies that, unlike the example shown in Figure 1, the flux structures being correlated here are not aligned perpendicular to the Earth-Sun line It is important to note that the opposite signs of the IMP/INTERBALL

8 14,608 PAULARENA ET AL- SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND x O,,, I, i, i I, I I I, [ I I, ß, i! i i i ß - Total Number of Pts' '597' j O 10 ' 1-,,, i,,, i,, I 1' [ - i ß Average X Separation Between Spacecraft Pair (RE) Figure 7 Flux correlation as a function of average X separation between the spacecraft pairs (a) The average flux correlation for bins in X separation of 10 Rr width (b) The number of points in each bin in Figure 7a and IMP/WIND lags are due to the sign convention acter of the data produces high correlation coefficients used; in both cases the structures arrive at IMP later This is discussed in more detail in the Discussion and than expected Clearly, given the timing of arrival at Summary section the three spacecraft in the suite, the geometry of the In contrast, Figure 4 shows a segment where a similar correlated structures is complex Nevertheless, as the general character is present, but where details of that small spike in flux on the side of the large flux drop character cause correlations ranging from good (085 near 1450 UT shows, the three spacecraft are all ob- for IMP/INTERBALL; Figure 4a) to poor (048 for serving very similar solar wind plasma While it is clear INTERBALL/WIND; Figure 4c) Even in Figure 4a in Figures 3a and 3b that the structures after 1500 UT it is apparent that smaller features are not as wellare often poorly correlated, the IMP/INTERBALL and correlated as in Figures i and 3 (note the much smaller IMP/WIND correlation coefficients are still quite large flux range here, however) Both Figure 4b, with its indespite these differences, showing that the general char- termediate correlation coefficient (069), and Figure 4c

9 - PAULARENA ET AL: SOLAR WIND CORRELATIONS- IMP $, INTERBALL, WIND 14, t- 06 x O 10,,, i,!, i, Totol Number of Points' 597 ' : -L -, m, Average Y Separation Between Spacecraft Pair (RE) Figure 8 Flux correlation as a function of average Y separation between the spacecraft pairs (a) The average flux correlation for bins in Y separation of 5 Rz width (b) The number of points in each bin in Figure 8a show many areas of disagreement between the space- in Figure 4b and after 2310 UT in Figure 4c) From craft pairs, both in terms of flux magnitude and of struc- Figure 2 (triangular points) it is possible to surmise tural character Here, while it is obvious that the time that the correlation of this segment is, unlike the preseries plots do not track well, the low maximum corre- vious example, somewhat a function of the relative X lation values and multiplicity of local peaks at various positions of the spacecraft pairs However, the intermelags in Figure 4d show that even the interpolated data diate correlation between IMP and WIND is difficult are not in very close agreement This lack of a strong to understand, especially given that the AX, Ay, and single maximum for each correlation series is common in low-intermediate correlation segments It is clear that AZ for IMP/INTERBALL are only approximately 10, 4, and 9 RE, respectively Perhaps the structure is of the instruments are seeing solar wind plasma which, extremely limited spatial extent in Z while grossly similar from one location to another, is The segmentshown in Figures 3 and 4 appear to very different in detail and even at medium scales (espe- demonstrate a relationship between the correlation coefcially note the very different behaviors before 1900 UT ficient and spacecraft separation such that smaller sep-

10 14,610 PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND 1O,7 04 g 02 ß - 60 Totoil Number of Points' 597 o n 40 o a 20 z 0 - I - -, i I, I, I I, I, I I, Average Z Separation Between Spacecraft Pair (Rz) Figure 9 Flux correlation as a function of average Z separation between the spacecraft pairs (a) The average flux correlation for bins in Z separation of 5 Rz width (b) The number of points in each bin in Figure 9a arations yield higher correlations, but this trend does not hold for the example shown in Figure 1 The IMP/WIND and INTERBALL/WIND correlations in Figure i are equally excellent despite the larger AY for IMP/WIND As is shown below, a statistical study of these data shows no evidence that the correlation coefficients are organized by spacecraft separation in any direction 42 Statistical Study While it is interesting and important to examine each set of data, the main focus of this paper is the presentation of a larger sample of data, chosen only for the I existence of data from the three spacecraft during the general period covered While the number of available points is thus somewhat small to provide truly robust statistics, these data can nevertheless give insight into the general behavior of solar wind plasma from near Earth to near L1 Figures 5 and 6 show the distribution of results from this study as a function of the flux correlation coefficient and lag, respectively These figures include all results from this study, regardless of correlational value and spacecraft location Each figure is labeled with the mean, median, and standard deviation of the distribution as well as the total number of points (segments)

11 PAULARENA ET AL: SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND 14, t x O O 10 0 ; : Number of Points: 397 "- L Totel [ o Avg /,(y2 + Z2) Seporotion Between Spacecraft (Rr) Figure!0, Flux correlation as a function of average R for the spacecraft pairs (where R - x/ay2 + AZ ) (a) The average flux correlation for bins in average R of 5 R width (b) The number of points in each bin in Figure 10a -'- O n Figure 5 it is clear that whil e the average corre- BALL/WIND correlations from June 1996, the average lation of flux is fairly high (averaging 07 for all three correlation value was 059, with a median of 061, in spacecraft pairs), a significant portion of the population contrast to the 067 average and 072 median for the has rather poor, even quite poor correlations In fact, correlation coefficients of the corresponding 6-hour segonly 43% of the segmentshowed correlations of 08 or ments higher, a somewhat surprising result given the usual ex- 421 Dependence on spacecraft separation pectation of fairly homogeneous plasma and the results Most lags shown on Figure 6 cluster near zero, implying of King [1986] However, the distribution of plasma cor- that the features being correlated propagate between relations still shows better correlations than the mag- spacecraft in a time approximately equal to the advecnetic field correlation results of Crooker et al [1982], tion shift, much as seen in Figure 1 The large spread of which had only 25% of the 2-hour periods showing cor- additional lags shown on Figure 6 is partially explained relations above 08, and 25% below 05 (in contrasto by periods when correlations are low: the maximum the 19% seen in this study) This difference in correla- value of the correlation coefficient is not necessarily a tion may be partially due to the longer segment length true maximum but can be just a mathematical peak chosen for this study; work done on plasma correlations when the underlying data are, in fact, uncorrelated using 2-hour segmentshows a lower average flux cor- However, a few large lags (over 1000 s) are associated relation In fact, for hour segments of INTER- with times when correlations are good (> 08), and ap-

12 - 14,612 PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND x E 80 ß ß ß, ß - - i ß ß ß i - - ß i ß ß ß I ß - i ß - i '- r Total Number of Points' 397-' O -!!!!:i;:!: ß i - i,, Average IMP or INTERBALL Solar Wind Flux (108/cm2-s) Figure 11 Flux correlation as a function of average solar wind flux observed by either IMP 8 (for IMP 8/INTERSALL and IMP 8/WIND correlations) WIND (for WIND/INTERBALL correlations) (a) The average flux correlation for bins in flux of 1 x l0 s cm -2 s - width (b) The number of points in each bin in Figure 11a The percentage of segments in bins having average correlation of > 08 are shown in the shaded area pear to be valid Stream structures arriving obliquely may (such as in Figure 3) cause these laige lags With the limited Y separations available in the data sets studied here, it is difficult to investigate alignment orientations since slow speeds and small separations may cause large lags This issue has been extensively investigated for two far-larger data sets (IMP/ISEE 3 and IMP/WIND [Richardson and Paularena, 1998]), with the result that the plasma features being correlated appear to be aligned approximately half-way between the good correlations (and thus poor or good predictability) can be expected An obvious possibility, especially given the results of Crooker et al [1982], is that the value of the correlation coefficient is related to the po- sitions of the two spacecraft whose data are being compared Four figures show the correlations observed for each spacecraft pair as a function of separations in X (Figure 7), ¾ (Figure S), Z (Figure ), and the value of R = ;/AY 2 + AZ a (Figure 10) With the exception of R, the separations are calculated as signed differences magnetic field direction and the perpendicular to the in order to maximize the likelihood of discerning any Earth-Sun line underlying geometrical trend The convention used was In order for plasma correlation values to be useful, to always subtract the position of the spacecraft which both to help understand the underlying physics and for is closest, on average, to Earth from the position of the space weather modeling efforts, it is important to find spacecraft which is usually farther away This means some controlling factor which indicates when poor or that the signed positional differences are calculated by

13 ß PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND 14,61: ' ' ' I ' ' ' I ' ' ' i ' ' ' I, 070 ' f ' 1 x , Total Number of Points',397 loo 5o I Stondord Deviotion of IMP or INTERBALL Flux (108/cm2-s) Figure 12 Flux correlation as a function of the absolute standard deviation of solar wind flux observed by either IMP 8 (for IMP 8/INTERBALL and IMP 8/WIND correlations) or WIND (for WlND/INTERBALL correlations) (a) The average flux correlation for bins in standard deviation of flux of 025 x 10 s cm - s -1 width (b) The number of points in each bin in Figure 12a The percentage of segments in bins having average correlation of 08 are shown in the shaded area subtracting IMP and INTERBALL coordinates from WIND coordinates, and INTERBALL coordinates from those of IMP sible conclusion is that this result is unlike the strong dependence on Y separation seen in the magnetic field correlations between ISEE 1 and ISEE 3, it is important to note that the maximum separation achieved for the current study was only 80 Rz, with separations of over In these figures and those that follow, histograms of the average maximum correlation coefficient are plotted in the upper panels, with the width of each bar defining 40 Rz comprising less than 12% of the segments; this the width of the bin in the abscissa parameter The is thus far less than the over 100 Rz separation in the error bars are the standard error of the mean, which is Crooker at al [1982] study Additionally, the X sepagiven by r/, where r is the standardeviation of ration was as great as of Crooker at al [1982] for only the points in each bin, and N is the number of points one small part of the data segments analyzed here It is in the bin Bins with only one point have no error bars possible that a dependence on either X or Y separation The bottom panels show the number of points in each will emerge when data from larger distances are anabin for reference lyzed However, the results of King, [1986] showed no It seems clear from Figures 7-10 that no obvious pat- dependence of hourly-average correlations on Y separatern emerges Fairly high average correlations are ob- tion for comparisons of ISEE 3 and IMP 8 plasma data, served at all spacecraft separations Although one pos- so perhaps this lack of dependence is a real characteris-

14 14,614 PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND x loo 80 Totol Number of Points' o Relative Stc]ndord Deviation of IMP or INTERBALL Flux Figure 13 Flux correlation as a function of the relative standard deviation of solar wind flux observed by either IMP 8 (for IMP 8/INTERBALL and IMP 8/WIND correlations) WIND (for WIND/INTERBALL correlations) (a) The average flux correlation for bins in standard deviation of flux of 005 width (b) The number of points in each bin in Figure 13a The percentage of segments in bins having average correlation of 08 are shown in the shaded area tic of the plasma data and will not change when more widely-separated segments are studied The patterns for Z separation will probably not change a great deal since the maximal values possible given the spacecraft orbits do not much exceed those of the data subsets presented here 422 Dependence on plasma parameters As spacecraft positions do not appear to be very good predictors of flux correlation for the data analyzed here, the influence of various plasma parameters was investigated Figures show the flux correlations as functions of some characteristics of the flux, speed, and density (using only speed and density values from IMP 8 and WIND, as discussed above) Note that the range of the correlation coef cient axes is now 03-10, rather than 0-10 as for Figures 7-10 As Figure 11 shows, the average value of the flux provides an indication of the degree of correlation, with higher average correlations associated with higher fluxes The standard deviation of flux segments (Figure 12) also shows a marked organization: periods with higher standard deviations of flux generally have high flux correlations This appears to be qualitatively parallel to the increase in correlation seen by Crooker et al [1982] for larger magnetic field variance The average values of the density and bulk speed, as well as their ranges (the differences between their maximum and minimum values during the segment), were also investigated as potential organizing factors for the correlation coef cients The results show only that as the average density increases, so does the average correlation coef cient (an expected result, given Figure 11), and that the opposite is true for speed (again, expected given the general anticorrelation of speed and density)

15 = -,, PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND 14, ' I ' I ', ' ' ' i ' ' i ' 090 ',, - t- t :: " ß!I x ø1-8 i i i i i i i i ' - L Totol Number of Points', Standard Deviation of IMP or WINDensity (#/cm 3) Figure 14 Flux correlation as a function of the absolute standard deviation of solar win density observed by either IMP 8 (for IMP 8/INTERBALL and IMP 8/WIND correlations) WIND (for WlND/INTERBALL correlations) (a) The average flux correlation for bins in standard deviation of density of 05 cm -3 width (b) The number of points each bin in Figure 14a The percentage of segments in bins having average correlation of > 08 are shown in the shaded area There is no apparent consistent relationship between solute) standar deviation, and is the average value of flux correlation and speed or density range Figtires showing these histograms are not presented here The standard deviation of flux shown in Figure 11 is the "absolute" standard deviation, meaning that pethe abscissa parameter over the segment period While there are too few points at high relative standard deviation to be sure of the trend beyond 04, it seems clear that this measure of variability also acts to organize the riods with an average flux of 10 x 10 s cm -2 s -1 and flux correlations, with higher variability of the time sevariations of i x l0 s cm -2 s -t (ie, AF/F ~ 01) are ries (relative to the mean) yielding higher correlation mixed in with periods having an average flux 10 times less but the same level of variability (ie, AF/F ~ 1) This is the cause of some of the high-standard deviation coefficients In order to search for the fundamental plasma characteristic driving the correlation behavior pattern, Figoutliers- large changes during periods of high flux In ures show the observed correlation coefficients as an attempt to separate these effects; that is, to look not at the values of the changes but at their magnia function of the (absolute) standard deviations in speed and density, respectively Figure 14 shows that better tudes relative to the background level, Figure 13 shows flux correlations are obtained when there is a higher the correlation coefficients plotted against the "relative" standard deviation, trr = tr/, where tr is the usual (abstandard deviation in the observed density This result is expected in view of the fact that density variations

16 -- 14,616 PAULARENA ET AL' SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND o 070 o ',,,,,,,,,I,,,,,,,,I,,,,,,,1,,,,,,,,I,,,,,,,,I,,,,,,,,,,,,,,,,',,,,, 150 Totol Number of Points', O I Stondord Devietion of IMP or WIND Speed (km/s) Figure 15 Flux correlation as a function of the absolute standard deviation of solar wind speed observed by either IM? S (for IM? 8/INTERBALL and IMP 8/WIND correlations) or WIND (for WlND/INTERBALL correlations) (a) The average flux correlation for bins in standard deviation of speed of 5 km/s width (b) The number of points in each bin in Figure 15a account for a large fraction of any flux variations (the 5 Discussion and Summary relative standard deviation of the density varies between Correlations of plasma flux between three spacecraft 003 and 204, compared to that of the speed, which pairs (IMP/INTERBALL, IMP/WIND, and INTERvaries only between 0007 and 017) Nevertheless, it is BALL/WIND) show that the average correlation for important to examine the correlation as a function of hour segments is 07 The value of the linspeed variability in case there is an unexpected relation- ear correlation coefficient appears to increase with inship Figure 15 shows that there is no real trend in the creasing flux, so that all bins with fluxes greater than behavior of flux correlations and standard deviations in 5 x 108 cm -: s - (33% of the segments) show an average speed, implying that the observed organization of better correlation above 08 In similar fashion to the increase correlations with higher flux standard deviations occurs of correlation with increasing magnetic field variance because the correlation is strongly associated with the [Crooker et al, 1982], the correlation increases with invariability in density This result is especially important creasing standard deviation of the flux, which is driven since density is a difficult plasma parameter to measure by increases in the standard deviation of the density and accurately (see the discussion of Lazarus and Paularena not by that of the speed Comparisons of the absolute [1998 and references therein]), while speed is generally and relative standard deviations show that the highest fairly straightforward for all instruments correlations are associated with flux changes that are

17 PAULARENA ET AL: SOLAR WIND CORRELATIONS- IMP 8, INTERBALL, WIND 14,617 both large both in value and relative to the average flux, although there is a slight trend for a higher proportion of high correlations () 08) with absolute standard deviation bins above 075 x 10 s cm -: s -1 (39% of the seg- ments) This effect may be due to the mathematical nature of the linear Pearson correlation coefficient, which results in an emphasis on the correlation of large-scale structures: Segments containing large flux jumps yield and WIND data analyses were supported by NASA contracts NAGS-584 (IMP) and NAGS-2839 (WIND) to MIT higher calculated correlation coefficients than segments The editor thanks Joseph King for his assistance in evalwith a low range of fluxes but with the same degree of uating this paper fine-scale agreement Various methods for highlighting the underlying physical meaning of the plasma corre- References lations are currently under investigation Additionally, the data must be examined for structure-specifi correlation behavior, so that defined structures such as coro- nal mass ejections (if present in this solar minimum data set) or other stable features are grouped together For the data sets compared here, correlation values do not appear to be dependent on spacecraft distances, in particular showing no organization for X or Y separations of up to 220 and 80 RE, respectively While this is in marked contrast to the results of Craaker et a! [1982], it may be partially a function of the limited number of segments with the largest spacecraft separations Also, as with the higher average correlation coe cients (as discussed previously), it may be that larger structures show a different dependence on separation, so that a study of plasma correlations for 2-hour segments would yield a different result Nevertheless, it will be interesting to see if including more data at the farthest distances (above 100 RE) changes the dependence of correlation on AX, since the present lack of dependence is also in contrast to the results of Richardson eta! [1998], which used 6-hour segments Their results show a dependence on AX for IMP 8 and ISEE 3 correlations when the X separation was greater than 150 RE If the lack of X dependence seen in Figure 7 continues to hold when more long-separation data are included, it may be that solar cycle affects distant correlations, such that structures observed nearer solar maximum (IMP 8 and ISEE 3) have smaller scale lengths than those seen near solar minimum (the present study) Because several of the results of this plasma correlation study are in contrast to the earlier magnetic field correlation work of both Russell eta! [1980] and Craaker at al [1982], it is important to understand what other differences may exist between magnetic field and plasma correlations Magnetic field correlation work between data from IMP 8 and WIND is still in an early stage [Collier et al, 1997], and no correlation work has yet been done with the INTERBALL-1 magnetic field data Thus segment-by-segment comparisons of plasma and magnetic field correlations have not yet been made Future work will include such comparisons, as well as an investigation of any relationships between plasma correlation and magnetic field behavior Acknowledgments The authors thank R D Nouralieva for her invaluable assistance with data reduction, and J D Richardson for many helpful discussions This work was partially supported by NASA contract NAG (IN- TERBALL Guest Investigator) to MIT, by the NSF space weather program under grant ATM , and was made possible in part by Award RPI-246 of the US Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF) to MIT and IKI, as well as by RFBR to IKI The IMP 8 Bellomo, A, and Mavretic, A, Description of the MIT plasma experiment on IMP 7/8, Rep CSR TR-78-œ, 51 pp, Cent for Space Res, Mass Inst of Technol, Cambridge, 1978 Collier, M R, J A Slavin, R P Lepping, D Fairfield, and A Szabo, ISTP observations of magnetotail compressions caused by solar wind pressure discontinuities: WIND and IMP-8, Eos Trans A GU, 78, S277, 1997 Crooker, N U, G L Siscoe, C T Russell, and E J Smith, Factors controlling degree of correlation between ISEE 1 and ISEE 3 interplanetary magnetic field measurements, J Geophys Res, 87, , 1982 Fairfield, D H, Average and unusual locations of the Earth's magnetopause and bow shock, J Geophys Res, 76, , 1971 King, J H, Solar wind parameters and magnetospheric coupling studies, in Solar Wind-Magnetosphere Coupling, edited by Y Kamide and J A Slavin, pp , Terra Sci, Tokyo, 1986 Lazarus, A J, and K I Paularena, A comparison of solar wind parameters from experiments on the IMP 8 and Wind spacecraft, in Geophysical Monograph Series edited by J E Borovsky, R F Pfaff, and D T Young, AGU, Washington, D C, in press, 1998 Neter, J, W Wasserman, and G A Whitmore, Applied Statistics 3rd ed, 1006 pp, Allyn and Bacon, Boston, Mass, 1988 Ogilvie, K W, et al, SWE, a comprehensive plasma instrument for the Wind spacecraft, Space Sci Rev, 71, 41-54, 1995 Richardson, J D, F Dashevskiy, and K I Paularena, Solar wind plasma correlations between L1 and Earth, J Geophys Res, in press, 1998 Richardson, J D, and K I Paularena, The orientation of plasma structure in the solar wind, Geophys Res Left, in press, 1998 Russell, C T, G L Siscoe, and E J Smith, Comparison of ISEE-1 and -3 interplanetary magnetic field observations, Geophys Res Left, 7, , 1980 SafrJxtkov, J, et al, Small scale observations of magnetopause motion: Preliminary results of the INTERBALL project, Ann Geophys, 15, , 1997 Vasyliunas, V M, Deep space plasma measurements, in Methods oj Experimental Physics, vol 9B, edited by R H Lovberg and H R Griem, pp 49-88, Academic, San Diego, Calif, 1971 P A Dalin and G Zastenker, Space Research Institute, Russian Academy of Sciences, 84/32 Profsoyuznaya, Moscow, Russia ( gzastenk@arcikirssiru) A J Lazarus and K I Paularena, Center for Space Research, Massachusetts Institute of Technology, Room , Cambridge, MA ( kip@spacemitedu) (Received November 14, 1997; revised February 4, 1998; accepted February 17, 1998)