ACE/Wind Multispacecraft Analysis of the Magnetic Correlation in the Solar Wind

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Proceedings of the 30th International Cosmic Ray Conference ID 937 Rogelio Caballero, Juan Carlos D’Olivo, Gustavo Medina-Tanco, Lukas Nellen, Federico A. Sánchez, José F. Valdés-Galicia (eds.) Universidad Nacional Autónoma de México, Mexico City, Mexico, 2008 Vol. 1 (SH), pages 625–628

30TH INTERNATIONAL COSMIC RAY CONFERENCE

ACE/Wind multispacecraft analysis of the magnetic correlation in the solar wind

1 2 3 2 2 4 S. DASSO , W.H. MATTHAEUS ,J.M.WEYGAND , P. CHUYCHAI , L.J. MILANO , C.W. SMITH , 3 M.G. KIVELSON 1Instituto de Astronom´ıayF´ısica del Espacio (IAFE) and Departamento de F´ısica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Argentina. 2Bartol Res. Institute, Department of Physics and Astronomy, University of Delaware, Newark, Delaware, USA. 3IGPP, UCLA, Los Angeles, California, USA. 4Institute of Earth, Oceans and Space, University of New Hampshire, New Hampshire, USA. [email protected]

Abstract: The propagation of galactic and solar cosmic rays in the solar wind (SW) can be strongly influenced by the SW fluctuations properties. Magnetohydrodynamic scale fluctuations in the solar wind are usually highly anisotropic, and have also been found to exhibit different properties in regions of high and low solar wind speed. Previous studies analyzed the anisotropy properties of the solar wind magnetic fluctuations at scales of the order of (105 106) km (inertial range) using two times – single point measurements (assuming the Taylor frozen-in− hypothesis), and found that the fluctuations in the fast solar wind tend to reside in wave vectors with their parallel component (to the mean magnetic field) larger than the perpendicular one, while the fluctuations in the slow wind present the opossite trend. In the present study we compare the magnetic autocorrelation function in the solar wind obtained with two times – single point observations (from a single spacecraft) with the same quantity obtained from single time – two points measurements (from simultaneous observations of two spacecraft, observing the pure spatial structures). We preliminarily compare also previous results of the anisotropy of the solar wind fluctuations, obtained from a single spacecraft, with our new multispacecraft analysis using combining observations from the ACE and Wind spacecraft.

Introduction more readily perpendicular to B0 than those parallel to it. Theories of scattering of energetic solar particles in Of the various descriptions of anisotropic wave the heliosphere [1] and solar modulation of galac- and turbulence properties of the solar wind, the tic cosmic rays [2] require knowledge of turbu- so-called ’Maltese cross’ [6] illustrates level con- lence parameters to express particle diffusion co- tours of the magnetic self correlation which are efficients. seen to have a cross-like pattern when plotted in In particular, several theories (as the quasi-linear a 2D plane where one of the axes is parallel to the theory [3]) need the correlation of the turbu- magnetic field. There is a lobe along each axis. A lent magnetic fields as an input that describe the suggestive but oversimplified interpretation is the cosmic-rays transport presence of two components or populations: slab- k It is known that the presence of a uniform ’direct like fluctuations (with wavevectors, , mainly par- current’ (constant in space and time) magnetic field allel to the mean field: k// >> k ) and quasi-2D- like fluctuations (having k mainly⊥ perpendicular to (B0) in a turbulent MHD system develops spectral B0: k >> k//). anisotropies for isotropic initial conditions (e.g., ⊥ [4, 5]): high wavenumbers components develop Unidirectionally propagating Alfven´ waves correspond to values of the normalized cross helicity

625 MAGNETIC CORRELATION IN THE SOLAR WIND

0.8

0.6

0.4

Rb(r)/Rb(0) 0.2

−0.2

0 500 1000 1500 separation distance, r [R ] E

Figure 1: Comparison of Rb from ACE-SSC (solid line), Wind-SSC (dotted line), and ACE/Wind-TSC (asterisk).

(σc) equal to +1 or -1, depending of the sense of Recently a few studies on the spatial dependence of the propagation, while high levels of turbulence are the magnetic correlation function in the solar wind usually accompanied by a value of σc close to zero from two spacecraft (TSC, using two-point/single- (see, e.g., [7], and references therein). From an time) were done [10, 11, 12] using data from the analysis of 5 years of solar wind data (one minute Cluster fleet. However, detailed comparison be- of time cadence) measured by the spacecraft ACE tween the previous studies (using the single space- on the Sun-Earth line at 1AU, [8] shown that σc craft) and the new approach (using TSC) have not is roughly isotropic in the inertial range, a result been done yet. plausible with similar levels of turbulence for the In the present work we present a comparison of ’slab-like’ population and for the ’quasi-2D-like’ magnetic correlation functions in the solar wind one. Using the same sample of solar wind data, 5 6 obtained from a SSC with those obtained from [9] found that at scales of the order of (10 − 10 ) TSC. We also present some preliminary results km (i.e., the inertial range) the fluctuations in the from the analysis of the anisotropy of the mag- fast solar wind present a trend to having a more netic fluctuations at the inertial range scales (∼ 5 6 abundant population with k// >> k than with − ⊥ 10 10 km), using TSC. k >> k//, while the fluctuations in the slow wind⊥ present the opposite trend (more abundant population with k >> k//). Data analysis, results, and conclusions ⊥ All these previous studies are based on single spacecraft (SSC, using two-times/one-point) ob- We analyze observations of the magnetic field servations. Because the solar wind speed is much measured by the Advanced Composition Explorer larger than the local Alfven/sound´ speeds, the spa- (ACE) and Wind spacecraft, using the same sam- tial correlation function can be measured in the di- ples (intervals of one day of duration, with a time rection of the flow direction (i.e., the solar wind cadence of one minute) than those used by [10]. fluctuations are convected in the reference frame Thus, we analyze here solar wind observations that of the spacecraft in a short time compared with the correspond to a distance of ∼ 1 AU from the Sun characteristic time scale of the dynamical variation and on the ecliptic plane. of the fluctuations). Our main goal is to compute, from two-points and single time observations, the spatial correla-

626 30TH INTERNATIONAL COSMIC RAY CONFERENCE

0.8 θ ε [0,25] (o)

0.6 θ ε [40,50] (∆)

0.4 θ ε [65,90] (*) Rb(r)/Rb(0) 0.2

0 0 50 100 150 200 250 300 350 separation distance, r [R ] E

Figure 2: Observations of Rb from ACE/Wind-TSC for fast solar wind for different angular channels between the spatial lag direction and B0. Exponential fit is included to each angular channel (dashed line for θ1ǫ[0◦, 25◦], dotted line for θ2ǫ[40◦, 50◦], and solid line for θ3ǫ[65◦, 90◦]). tion function of the form Figure 1 shows the comparison of Rb using ACE- SSC (solid line), Wind-SSC (dotted line), and Rb(r) =< b(0,t) · b(r,t) > (1) both ACE/Wind-TSC (asterisk). The mean value of the two SSC observations (RbACE SSC and Note that Equation 1 is the trace of the usual two- − RbACE SSC ) at a separation of 199RE (the sep- points correlation tensor for the magnetic field, aration− between ACE and Wind) resulted 0.16, where spatial and temporal translation symme- while Rb = 0.23; that means b ACE/Wind TSC tries were assumed. represents the fluctuating that the TSC-SSC ratio,− at spatial separations of magnetic field, and we will study the variance- 6 ∼ 10 km, is RbTSC /RbSSC ∼ 1.3. normalized correlation, In order to analyze the anisotropy of Rb from TSC, Rbnorm(r) = Rb(r)/ < b · b > , (2) which allow us to cover spatial lag directions inde- pendently from the angle between B0 and the solar with Rbnorm(0) = 1, as done in [8, 9, 10]. For wind flow direction, we split the full set of ana- simplicity of notation, we omit the “norm” label lyzed intervals according with three angular chan- hereafter. The SSC correlations were computed as nels for the angle (θ) between the direction of described in [8, 9], while the TSC correlations as the spatial lag, given by the relative positions be- described in [10]. tween ACE and Wind, and the mean magnetic field B 0 0 0 0 In this preliminary work we compare values for ( 0): 0 ≤ θ1 < 25 , 40 ≤ θ2 < 50 , and 0 ≤ 0 Rb obtained from SSC and TSC for the interval 65 θ3 < 90 . (selected from all intervals analyzed in [10]) hav- Because from SSC in previous studies there were ing the minimum angle (α) between the spatial lag only a few intervals for fast solar wind and for ex- direction for TSC (given by the relative position treme angles θ ∼ 0◦ and θ ∼ 90◦, in this first stage between ACE and Wind) and the Sun-Earth line; of the study we select only fast solar wind intervals thus, the spatial correlation from TSC corresponds (VSW > 470 km/sec). Figure 2 shows the normal- to the same direction of the intrinsec spatial lag ized Rb, only from TSC for fast solar wind and given by SSC. This interval corresponds to the full for different angular channels: symbol o is used to day of Oct 4, 1999, and it corresponds to α = 3◦. represent θ1 (spatial lag parallel to the mean field The separation distance between ACE and Wind is B0), symbol ∆ to represent θ2 (spatial lag at in- 6 B 199RE ∼ 10 km (RE = 6378km, is the Earth termediate angles respect to 0), and symbol ∗ to radius). represent θ3 (spatial lag perpendicular to B0). It is

627 MAGNETIC CORRELATION IN THE SOLAR WIND possible to observe that Rb for θ1 is significantly (1981) 825. lower than the values obtained for the other two di- [5] J. V. Shebalin, W. H. Matthaeus, D. Mont- rections, a result consistent with a fast solar wind gomery, Anisotropy in MHD turbulence due having a more important population of ’slab-like’ to a mean magnetic field, J. Plasma Phys. 29 fluctuations than ’quasi-2D-like’ ones. (1983) 525. We also compute the correlation lengths (λc) (com- [6] W. H. Matthaeus, M. L. Goldstein, D. A. puted as in [8, 9]) for Rb, considering each of the Roberts, Evidence for the presence of quasi- c 5 angular channels. We obtained λ1 = 4.8 × 10 km two-dimensional nearly incompressible fluc- c 5 tuations in the solar wind, J. Geophys. Res. (θ ∼ 0◦), λ2 = 7.7 × 10 km (θ ∼ 45◦), and c 5 95 (1990) 20673–20683. λ3 = 8.0 × 10 km (θ ∼ 90◦). Thus, our result is consistent with the correlation scale obtained pre- [7] C.-Y. Tu, E. Marsch, MHD structures, waves viously for the mixed solar wind (all angular chan- and turbulence in the solar wind: obser- nels and all speeds) by [10] (λc ∼ 106km). vations and theories, Dordrecht: Kluwer, —c1995, 1995. We presented here an analysis that compares Rb [8] L. J. Milano, S. Dasso, W. H. Matthaeus, from SSC and TSC, and using only TSC we ana- C. Smith, Spectral distribution of the cross lyzed the anisotropy of the fast solar wind fluctu- helicity in the solar wind, Phys. Rev. Lett. 93 ations. For the analyzed sample we found that, at (2004) 155005. separations of ∼ 106 km, the magnetic correlation [9] S. Dasso, L. J. Milano, W. H. Matthaeus, function computed from SSC is ∼ 30% smaller C. W. Smith, Anisotropy in Fast and Slow than when it is computed from TSC. This is pos- Solar Wind Fluctuations, Astrophys. J. 635 sibly a consequence of time evolution during the (2005) L181–L184. SSC observations. In the second case, we resist [10] W. H. Matthaeus, S. Dasso, J. M. Weygand, to the temptation of drawing any major conclusion L. J. Milano, C. W. Smith, M. G. Kivelson, concerning anisotropy because we beleive that it Spatial Correlation of Solar-Wind Turbulence is necessary to make an analysis of more samples, from Two-Point Measurements, Physical Re- ranging a larger angular set of bins. We plan to view Letters 95 (23) (2005) 231101. extend our research and present complete results [11] K. T. Osman, T. S. Horbury, Multispace- elsewhere. In the meantime, we believe that on- craft Measurement of Anisotropic Correla- going studies of this type will contribute to better tion Functions in Solar Wind Turbulence, As- understanding of the solar wind fluctuations and its trophys. J. 654 (2007) L103–L106. influence on the cosmic rays propagation in the he- [12] J. M. Weygand, W. Matthaeus, S. Dasso, liosphere. M. G. Kivelson, W. R. J., Taylor scale and effective magnetic reynolds number deter- References mination from plasma sheet and solar wind magnetic field fluctuations, J. Geophys. Res. [1] W. Droge,¨ Particle Scattering by Magnetic (2007) submitted. Fields, Space Science Reviews 93 (2000) 121–151. [2] S. Parhi, J. W. Bieber, W. H. Matthaeus, R. A. Burger, Sensitivity of cosmic ray modulation to the correlation length, Geophys. Rev. Lett. 29 (2002) 99–1. [3] J. R. Jokipii, Cosmic-Ray Propagation. I. Charged Particles in a Random Magnetic Field, Astrophys. J. 146 (1966) 480. [4] D. C. Montgomery, L. Turner, Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field, Phys. Fluids 24

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