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WDS'12 Proceedings of Contributed Papers, Part II, 169–175, 2012. ISBN 978-80-7378-225-2 © MATFYZPRESS

Statistical Study of the Solar Velocity Modification Upstream of the ’s : THEMIS Observations

J. Urbar, K. Jelinek, L. Prech, J. Safrankova, and Z. Nemecek Charles University Prague, Faculty of Mathematics and , Prague, Czech Republic.

Abstract. In our statistical study of the solar wind propagation from L1 to the Earth’s bow shock, we use multi-point observations from the THEMIS-ARTEMIS mission and compare them with a WIND solar wind monitor with motivation to estimate different factors influencing evolution of solar wind . We have found a systematic deceleration of the average solar wind with a decreasing distance to the bow shock that is controlled by the level of fluctuations and by the flux of reflected and accelerated particles. We can conclude that the reflected particles not only excite of large amplitudes but also modify mean values of quantities measured in an unperturbed solar wind.

Introduction The Parker´s theory predicts that the solar wind (SW hereafter) speed is nearly constant above some distance from the . This prediction was confirmed by Voyager observations throughout the whole , where SW deceleration attributed to interstellar pickup was confirmed only over 30 AU by Richardson et al. (1995), and Wang et al. (2000). In this view, the observation in the L1 Lagrangian point would serve as a good proxy of SW parameters impinging the Earth . The studies of the SW-magnetosphere interaction thus often rely on these observations propagated toward the Earth using various techniques. The present spacecraft configuration with two monitors near L1 and a fleet of the spacecraft orbiting in front of the bow shock (BS hereafter) brings a great opportunity to test the propagation techniques as well as the assumption on a negligible SW evolution. The interplanetary parameters used for the study of solar-terrestrial relationships are usually the SW speed, the SW , the total interplanetary magnetic field (IMF), and its Bz component. Both hourly and daily values of these parameters have usually been employed to be associated with parameters defining terrestrial effects that are related to the Space . The average and magnetic field correlation coefficients of the structures measured by the spacecraft in different distances (ISEE 1, ISEE 3, IMP 8, and Wind) from the Earth range from about 0.6 to 0.7 during quiet periods and increase substantially during the geomagnetic storms (Paularena et al., 1998). However, the Earth’s foreshock (FS hereafter) significantly degrades the correlation when one or both spacecraft are within 30 Earth radii (RE hereafter) of Earth during quiet periods, and this degradation extends beyond 50 RE during geoeffective periods (Jurac and Richardson, 2001). The FS region is typically observed upstream of the Earth’s quasi-parallel BS, and is characterized by enhanced ULF fluctuations. These fluctuations are created due to the interaction of the SW plasma flow with the ions reflected at the BS (e.g., Greenstadt, 1976, Gosling et al., 1978). As a result, fast magnetosonic waves are generated with an in-phase relationship between ion flux and magnetic field magnitude fluctuations (e.g., Zastenker et al., 1999). The deceleration of the SW in the FS has been observed by many authors more than the 30 years ago. For example, Bame et al. (1980) have reported that this deceleration is of an average of 7–10 km/s and it is correlated with the ‘diffuse’ but not with the ‘reflected’ ion population. They have suggested that the SW deceleration is a result of momentum transfer between the backstreaming ions and the SW ions through -particle interaction. Bonifazi et al. (1980, 1983) have noted that the magnitude of the deceleration of the SW depends on its bulk speed. Zhang et al. (1995) found that the SW speed decreases in front of the quasi-parallel BS and this deceleration is seen to have a maximum near the BS and falls when the distance from the BS reaches 5 RE. Upstream SW ion velocity deceleration and associated density changes may result in pressure disturbances which could significantly affect the surface (Fairfield et al., 1990). Moreover, since IMF is highly

169 URBAR ET AL.: SOLAR WIND STATISTICS UPSTREAM OF THE EARTH’S BOW SHOCK variable in direction, the configuration of the FS is a subject to changes; the FS moves and the pressure distribution along the magnetopause moves accordingly. Later, similar results of the SW deceleration were reported both from statistical and case studies based on closely separated Cluster spacecraft by Cao et al. (2009) and Fu et al. (2009). However, as Kis et al. (2007) noted, it is confusing if these processes are based on observations of a single spacecraft or several spacecraft which are relatively close to each other compared with the dimensions of the FS, because observed ions have a completely different origin. We performed a statistical study to test the hypothesis whether and which way are the SW parameters modified in different distances from the BS. We have found a significant (≈7%) deceleration of the SW close to the BS that extends up to 30 RE from the Earth.

Data analysis Our statistical study uses medians of 1-minute ratios of the velocity from THEMIS and WIND (propagated to the respective THEMIS position). The WIND plasma velocity from the SWE instrument (Ogilvie et al., 1995) measured around L1 (≈ 200 RE from the Earth) is shifted to the THEMIS locations by the two-step propagation routine of Safrankova et al. (2005) where aberrated data take into account the Earth orbital motion, but the perpendicular components of the SW velocity are omitted. The intervals of THEMIS measurements in the SW were exactly identified for years 2007 till 2009 using BS crossings identified by a visual inspection of magnetic field and plasma parameter plots, adding to the Jelinek et al. (2009) database of THEMIS BS crossings. THB and THC data from years 2010–2011, when operating close to the (ARTEMIS) was not identified visually, but the data were used as in SW only when probe was located geometrically safely (see Fig. 2) upstream the Earth BS and out of a lunar wake. In order to avoid possible problems with an exact identification of the quasiparallel BS crossings, we have discarded any moment calculated from measurements 30 s after outbound or prior to inbound crossings. In order to evaluate the influence of magnetic field fluctuations, we computed a 1-minute standard deviation of IMF fluctuations from the FGM instrument data (Auster et al., 2008). The THEMIS velocity is taken from ESA ground processed level-2 full distribution PEIF moments (McFadden et al., 2008) with a nominal time resolution of 6.4 minutes where only data with the best quality flag 0 are used. Due to ongoing THEMIS intercalibration efforts and the fact that moment computations also include weighting factors to correct for energy and angle efficiency variations in the sensors, it was possible to merge data provided by a whole THEMIS fleet independently on a specific spacecraft just according to its position and measurement mode (solar wind (SWM) / magnetospheric (MSM)) as it is confirmed in Fig. 1. However, the distribution of the velocity ratios was rather broad. Extreme values of this ratio can be attributed to errors in the data or in their processing. For this reason, we have limited our analysis to velocity ratios from 0.1 to 1.9.

b

Figure 1. Occurrences of 1-min velocity ratios THEMIS/WIND, where THB (line) and THC (dotted line) operate in the magnetospheric (grey) and in the solar wind (black) modes in the SW plasma during 2007–2011 (left), and the measurements with spacecraft separations of <3 RE only (right).

170 URBAR ET AL.: SOLAR WIND STATISTICS UPSTREAM OF THE EARTH’S BOW SHOCK

The figure shows a good intercalibration of velocity measurements between THEMIS-B (THB) and THEMIS-C (THC) in both the magnetospheric (MSM) and solar wind (SWM) modes during all 2007–2011 (a) and in measurements only during spacecraft separations of <3 RE (b). However, it is clearly demonstrated that these two instrument modes should not be mixed as noted in McFadden et al. (2008). In the presented study, we therefore quantify how well can ESA in MSM resolve the SW beam (using a wider energy sweep and a broader angular aperture than the width of the SW stream). The difference between Wind and THEMIS velocities measured in SWM is ≈ 2% but it is as large as ≈ 5% in MSM (Fig. 1). We will use these values as starting point for the discussion of the SW deceleration as those differences are attributable to the intercalibration of the devices (in spec. modes). In the orbital plots (Fig. 2), there is already seen the difference between moments determined from 3D ion distributions measured in particular ESA modes, but also spatial effects that can be probably attributed to the FS. THEMIS ZGSE coordinates ranged [–4, 0.5] during 2007, reaching on THB [–9, 3] and THC [–6, 1] in 2008, during 2009 manoeuvres shortly [–40, 13] on THB and [–12, 7] on THC, then converging to the Lunar orbit with [–6, 6] RE. In the MSM part of Fig. 2, high ZGSE data are apparent. We processed and present data measured in both MSM and SWM separately in following figures, where the diamonds stand for SWM, MSM are shown as crosses. The parametric x-axis is equally binned over a specific range with point’s x-component representing data median in that range, while the y-axis represents a respective median of the VTHEMIS/VWIND velocity ratios. We have analyzed different possibilities of the description of the THEMIS locations (e.g., radial distance from the Earth or from the model BS) but we found that the distance measured along the magnetic field line from THEMIS to the intersection of this line with the model BS (Formisano et al., 1979) provides the best organization of the data. We tried to use either propagated IMF from Wind or the local THEMIS measurements and found that both methods give similar results and thus, all relevant figures use the local magnetic field. Fig. 3a shows the VTHEMIS/VWIND ratio as a function of the distance of THEMIS to the BS along the IMF line. The actual ion deceleration on top of calibration offset seems to be reaching ≈ 3% when the instrument was in MSM and ≈ 2% in SWM. The deceleration is observable up to ≈ 30 RE along the IMF lines from the BS in both modes. Due to the used method, only data measured at points that were connected to the BS via IMF line are shown in Fig. 3a. The rest of the data is shown in Fig. 3b as a function of the radial distance from the model BS and one can note that the effect of deceleration is negligible (if any) in this part of the dataset.

Magnetospheric mode (MSM) Solar wind mode (SWM)

Figure 2. Orbital plot of THEMIS/WIND velocity ratios measured upstream of the bow shock, in the ESA MSM (left) and SWM (right). THB&THC coverage 2007–2011, THA, THE&THD of 2007 only.

171 URBAR ET AL.: SOLAR WIND STATISTICS UPSTREAM OF THE EARTH’S BOW SHOCK

Fig. 4a clearly shows that large fluxes of 5 keV energetic particles coincide with the large (≈ 5%) deceleration in both modes for the slow SW (<450 km/s). For the faster SW, there is already considerable contamination of energy fluxes in the 5 keV channel by nuclei, but it is the only channel available for both ESA modes at energies above the SW beam plasma. Fig. 4b demonstrates also that the IMF fluctuations (computed as 1-min standard deviation of the magnetic field) order the data rather well, but the deceleration is much weaker in SWM. Fig. 5a shows the dependence of deceleration on the angle between the BS normal and IMF direction (ϑBN hereafter) determined at intersection of the local magnetic field with the model BS for all events connected to the BS, whereas an Fig. 5b uses only our visually identified FS events on THB and THC during 2009 based not only on fluctuations of IMF, but also on enhanced fluxes of energetic particles. We have checked and extended the database of FS intervals by Hsieh et al. (2011) for this plot. The SW ion deceleration is less pronounced in the MSM for 2009 FS as THB and THC reached greater apogee. Fig. 6a shows the deceleration dependence on the radial distance from the model BS using our identified FS intervals. Lower bars demonstrate medians of standard deviations of IMF fluctuations, where the actual values are depicted as 1/10 of median, added to 0.88. No deceleration for remaining periods of the relatively pristine SW (Fig. 6b) was found even when the level of magnetic field fluctuations was relatively high. Therefore, the energy lost by the SW seems to accelerate reflected particles. The deceleration is observable even at ≈ 20 RE radially from the BS in both modes.

Solar wind mode (SWM) Solar wind mode (SWM)

Magnetospheric mode (MSM) Magnetospheric mode (MSM)

a b

Figure 3. Dependence of the velocity ratio VTHEMIS/VWIND on the distance from the BS along the IMF lines connected to the BS (a), on the radial distance from the BS when IMF unconnected to the BS (b).

a b

Figure 4. Velocity ratio (deceleration) dependence on the energy flux of 5 keV ions with the SW speed limited to 450 km/s. (a). Deceleration dependence on the IMF fluctuations using all SW data during 2007–2011 (b).

172 URBAR ET AL.: SOLAR WIND STATISTICS UPSTREAM OF THE EARTH’S BOW SHOCK

a b

Figure 5. The deceleration dependence on ϑBN determined at an intersection of the local magnetic field with the model BS during 2007–11 (a) and for 2009 foreshock periods only (b).

a b

Figure 6. The deceleration dependence on the radial distance from the model BS for the 2009 foreshock (a), and quiet SW periods (b). The lower bars show a level of associated IMF fluctuations.

a b

Figure 7. ESA 2D ion energy fluxes show distribution of plasma populations with resolved velocity components on THB (a) and THC (b). The vertical bars illustrate VX equivalent of 300 km/s, direction of the thick clock lines (coming from the center) represents the velocity components resolved.

173 URBAR ET AL.: SOLAR WIND STATISTICS UPSTREAM OF THE EARTH’S BOW SHOCK

Discussion and Conclusions We performed a statistical study to test whether and which way is the SW ion velocity measured by THEMIS modified in different locations relative to the BS. The study compares velocity measured by THEMIS in the SW with the velocity measured by Wind and lagged on propagation time for time intervals during 2007–2001 that represent almost 400,000 minutes of simultaneous observations. We can note an excellent intercalibration of the THEMIS spacecraft that allows us to merge the data from all THEMIS spacecraft. On the other hand, we found significant differences between velocities determined in MSM and SWM of THEMIS measurements and we processed data from these two modes separately. The difference between Wind and THEMIS velocities measured in SWM is ≈ 2% but it is as large as ≈ 5% in MSM (Fig. 1). These differences would be probably attributed to the intercalibration of the devices and modes and we will use these values as starting point for the discussion of the SW deceleration. Although it was suggested by Cao et al. (2009) that the deceleration is limited to ≈ 5 RE from the BS, we found the deceleration detectable at 30 RE along the IMF lines from the BS in the FS region and radially almost at 20 RE from the BS regardless of the instrument mode. Large magnetic field fluctuations coincide with a large deceleration (Fig. 4b) but we don’t observe direct proportionality (Fig. 6) as Cao et al., (2009) did. The fluctuation level itself (quantified as medians of standard deviations of magnetic field fluctuations computed on a 1-minute interval) cannot explain the observed deceleration of the SW, therefore the deceleration needs to be connected with the presence of the reflected and accelerated particles in the ambient medium as Fig. 4a confirms. Fig. 6b shows data with computed ϑBN ≈ 90° which should not be present for visually identified FS intervals, but as they also show a negligible deceleration, it just demonstrates its origin in intermittent pristine SW conditions during prevailing FS intervals. However, the plasma in front of the BS is strongly non-Maxwellian and the moments of the distribution are not sufficient for its description. The interpretation of our conclusions thus should be considered in this view, while using moments which take into account not only the SW population. Fig. 7 shows for closely-spaced spacecraft THC (a) and THB (b) calculated ESA velocities (represented as a direction of the thick clock lines coming from the center). A significant portion of reflected and accelerated particles influences the resulting velocity considerably on THC (a) relative to THB (b), but 2D spectrograms also reveal that the THC’s main population is decelerated: A peak of the SW beam distribution is located in the higher energy channel on THB compared to THC (see the vertical line in Fig. 7). To study detailed phenomena of complex magnetospheric plasma physics, multiple particle populations must be identified and characterized, therefore only angular sectors of the SW beam should be taken into account if deceleration of the SW beam itself is being studied. ESA plasma moment computations include weighting factors to correct for energy and angle efficiency variations in the sensors, but for resolving the actual SW bulk we should integrate moments only over SW surrounding angular bins omitting the population of reflected particles. We conclude that our study revealed a preconditioning of the SW bulk velocity in front of the BS that is not only of wave-particle origin, but probably also mediated by the direct interaction with reflected particles. It is yet to be answered if MHD waves or kinetic processes play a more important role, but since a full particle description of the SW–magnetosphere interaction is far ahead, we need MHD models (one or more fluids, isotropic or anisotropic) and as such models use plasma moments, efforts finding proper ways of plasma moment determination and application should be still useful. A further effort will be devoted to the study of an evolution of the distribution function and to transformation of the energy lost due to deceleration to thermal and magnetic energies because about one half of the dayside magnetopause is behind the FS under an average IMF orientation. The question that would be answered is whether our view on the SW-magnetopause interaction should incorporate that or it is not important where the transformation of the dynamic pressure to the thermal one occurs.

Acknowledgements. The authors acknowledge the NASA contract NAS5-02099 and V. Angelopoulos for use of data from the THEMIS mission. Specifically, C. W. Carlson and J. P. McFadden for use of ESA data and K. H. Glassmeier, U. Auster and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy

174 URBAR ET AL.: SOLAR WIND STATISTICS UPSTREAM OF THE EARTH’S BOW SHOCK and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC 0302. The present work was partly supported by the Czech Grant Agency under Contracts 205/09/0170 and 205/09/0112, and partly by the Research Plan MSM 0021620860 that is financed by the Ministry of Education of the Czech Republic. The provision of 2009 foreshock interval database by Wen-Chieh Hsieh for testing FS influence on THB and THC measurements is acknowledged as well as the incredible comments of professor Vitek.

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