The dayside magnetopause in the spring of 2004: A case study and a statistical report A. Blăgău (1, 2), B. Klecker (1), G. Paschmann (1), M. Scholer (1), S. Haaland (1, 3), O. Marghitu (2, 1), I. Dandouras (4), L. M. Kistler (5) and E. A. Lucek (6) (1) Max-Planck-Institut für extraterrestrische Physik, Garching, Germany (2) Institute for Space Sciences, Bucharest, Romania (3) Department of Physics, University of Bergen, Norway (4) CESR-CNRS, Toulouse, France (5) Space Science Center, University of New Hampshire, Durham, USA (6) Imperial College, London, UK

Aim: To present a case of magnetopause crossing and to show the results we obtained when applying various methods for determining its geometry and motion A statistical report about the reconnection occurrence on the dayside MP

Methods for magnetopause normal and velocity determination Minimum variance analysis (MVA) of the magnetic field (Sonnerup, B. and Scheible, M, ISSI) Report, 1998 Timing analysis from the four Cluster satellites (Haaland, S. et. al. AnGeo, 22, 4, 2004) Minimum variance analysis of the current density (Haaland, S. et. al. GRL, 31, 10, 2004) Because the MP possesses a good deHoffmann-Teller frame, we compared the normal component of the deH-T velocity with the velocity obtained from the timing analysis ( Khrabrov, A. and Sonnerup, B., ISSI Report, 1998) gives n, no V gives n and V gives n, no V no n, gives the velocity of the discontinuity as a whole

Single satellite method Assumes the MP is a planar, 1-D discontinuity Finds the direction in space along which the magnetic variation has a minimum and associates it with the MP normal Sometimes the simple, un-constrained MVA gives false results (Bn unreasonable large) It is better to do both constrained (by imposing Bn=0) and unconstrained MVA and to compare the results Minimum variance analysis (MVA) of the magnetic field (Sonnerup, B. and Scheible, M, ISSI) Report, 1998 Timing analysis from the four Cluster satellites (Haaland, S. et. al. AnGeo, 22, 4, 2004) Minimum variance analysis of the current density (Haaland, S. et. al. GRL, 31, 10, 2004) Because the MP possesses a good deHoffmann-Teller frame, we compared the normal component of the deH-T velocity with the velocity obtained from the timing analysis ( Khrabrov, A. and Sonnerup, B., ISSI Report, 1998) Methods for magnetopause normal and velocity determination

Relies on all 4 spacecraft measurements and on the assumption that the MP is locally planar We have the task of determining the orientation and velocity of a plane that moves over the Cluster configuration. For solving it the 4 crossing times and the satellites position at the time of crossing are sufficient For assigning the 4 moments of time we fitted the magnetic data corresponding to the transition and pick representative points of the fit (e.g. central points). In addition, from the duration of the transition we compute the discontinuity thickness. We could assume that the velocity of the discontinuity is constant or that it has a constant thickness. Minimum variance analysis (MVA) of the magnetic field (Sonnerup, B. and Scheible, M, ISSI) Report, 1998 Timing analysis from the four Cluster satellites (Haaland, S. et. al. AnGeo, 22, 4, 2004) Minimum variance analysis of the current density (Haaland, S. et. al. GRL, 31, 10, 2004) Because the MP possesses a good deHoffmann-Teller frame, we compared the normal component of the deH-T velocity with the velocity obtained from the timing analysis ( Khrabrov, A. and Sonnerup, B., ISSI Report, 1998) Methods for magnetopause normal and velocity determination

Multi-spacecraft method The current density is first obtained from the curlometer technique (by using Ampere’s law) A constrained MVA analysis is performed on the current density (relies on Jn=0 assumption) Appropriate when the spacecraft separation is small compared with the scale-length of the discontinuity. Minimum variance analysis (MVA) of the magnetic field (Sonnerup, B. and Scheible, M, ISSI) Report, 1998 Timing analysis from the four Cluster satellites (Haaland, S. et. al. AnGeo, 22, 4, 2004) Minimum variance analysis of the current density (Haaland, S. et. al. GRL, 31, 10, 2004) Because the MP possesses a good deHoffmann-Teller frame, we compared the normal component of the deH-T velocity with the velocity obtained from the timing analysis ( Khrabrov, A. and Sonnerup, B., ISSI Report, 1998) Methods for magnetopause normal and velocity determination

Single-spacecraft method Search for the existence of a reference system in which the convection electric field is zero (search whether the data corresponding to a discontinuity could be interpreted as produced by time-stationary structure, without an intrinsic electric field, that moves across the spacecraft) Minimum variance analysis (MVA) of the magnetic field (Sonnerup, B. and Scheible, M, ISSI) Report, 1998 Timing analysis from the four Cluster satellites (Haaland, S. et. al. AnGeo, 22, 4, 2004) Minimum variance analysis of the current density (Haaland, S. et. al. GRL, 31, 10, 2004) Because the MP possesses a good deHoffmann-Teller frame, we compared the normal component of the deH-T velocity with the velocity obtained from the timing analysis ( Khrabrov, A. and Sonnerup, B., ISSI Report, 1998) Methods for magnetopause normal and velocity determination

Cluster trajectory and configuration at Cluster orbit in GSE Crossing in the dayside northern hemisphere Separation distance around 100 km (ideal for curlometer) The sequence of crossings is Cluster1, 4, 3 and 2 Cluster constellation projected on MP plane and in a plane containing the MP normal (at 21:51:30)

Cluster1 data sets from HIA (ions) and FGM (magnetic field) Particularly interesting is the step- like variation seen in magnetic field max. var. component, density, temperature and pressure We have a complex transition, with a two-step boundary layer followed by the magnetopause crossing

Particularly interesting is the step- like variation seen in magnetic field max. var. component, density, temperature and pressure We have a complex transition, with a two-step boundary layer followed by the magnetopause crossing The total pressure (magnetic + plasma) is in approx. equilibrium in the boundary layers but not at the magnetopause The limits of the inner and outer boundary layer show a well-defined magnetic rotation, allowing us to determine the orientation, velocity and thickness for all layers Cluster1 data sets from HIA (ions) and FGM (magnetic field)

Timing analysis for the magnetopause interval Fitting function: superposition of two displaced tanh functions Magnetopause definition: the interval where most of the magnetic change occurs (approx. 76% of the total jump) From fit we obtained the central time T_middle (to be used for timing) and dT (for thickness calculation) Cluster1 magnetic field, maximum variance component

Timing analysis for the magnetopause interval The results for the normals obtained by various methods are shown in polar plot The center represents a reference direction in space, which we took as the average over the 4 normals from the constrained analysis on B We have 8 normals from constrained and unconstrained MVA on B (2 for each satellite), 2 from timing analysis and 1 from MVA for J The Walen test for this crossing failed so we think the constrained MVA of B are the better normals. If we neglect the un-constrained normals, the remaining ones are within a cone of approx. 5 deg.

Timing analysis for outer boundary layer margin Fitting function: difference of two displaced tanh (to account for the overshot) In this case the constrained and un-constrained normals are well separated The timing analysis and the MVA on J allow us to decide what are the correct normals: i.e. the constrained ones. We have a tangential discontinuity between inner and outer boundary layer Another argument for this: the origin of the plot corresponds to MP direction

Timing analysis for inner boundary layer margin Fitting function: difference of two displaced tanh (to account for the overshot) In this case the normals are more spread in direction, possible because we have a small, low-shear transition The uncertainties are higher but still within approx. 12 deg. The origin of the plot is different by approx. 12 deg (MP normal direction in the violet square)

Results for velocities and thicknesses (timing analysis) For each discontinuity we obtained a velocity and a thickness (shown in km and gyro- radius) In the plateau regions the thicknesses were computed by using averaged velocity

Results from deH-T analysis For each discontinuity we obtained a velocity and a thickness (shown in km and gyro- radius) In the plateau regions the thicknesses were computed by using averaged velocity For the MP we identified a good deHT reference frame (cc and slope of ) The deHT velocity perpendicular to the MP is in good agreement with the one from timing If we search for an accelerated deHT frame we obtain an inward acceleration, consistent with our timing velocities at MP and outer boundary layer Fit between the convection electric field E i =V i X B i and the V dHT X Bi

Conclusions In the case we studied, the various methods for finding the MP orientation are in good agreement Particularly good agreement was obtained from constrained MVA on B and MVA on J (not a surprise, considering the small separation distance between the satellites and the thickness of our discontinuities) One should be careful when applying un-constrained MVA The important finding is that between the inner and outer boundary layers we have a tangential discontinuity, which explains why the two do not mix

Statistical study Period covered: Crossing in the northern hemisphere, at approx. local noon DeHT succesful when cc > 0.95