Magnetospheric modes and solar wind energy coupling efficiency

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1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009ja014737, 2010 Magnetospheric modes and solar wind energy coupling efficiency T. I. Pulkkinen, 1 M. Palmroth, 1 H. E. J. Koskinen, 1,2 T. V. Laitinen, 3 C. C. Goodrich, 4 V. G. Merkin, 4 and J. G. Lyon 5 Received 6 August 2009; revised 21 September 2009; accepted 23 October 2009; published 6 March [1] Using observations and two different global MHD simulations, we demonstrate that the solar wind speed controls the magnetospheric response such that the higher the speed, the more dynamic and irregular is the magnetospheric response. For similar level of driving solar wind electric field, the magnetospheric modes can be organized in terms of speed: Low speed produces steady convection events, intermediate speeds result in periodic sawtooth oscillations, and high speeds drive large geomagnetic storms. We show that the control parameter of energy transfer and coupling is the electric field along the large scale X line. We demonstrate using global MHD simulations that for slowly varying interplanetary magnetic field (IMF), the reconnection line is tilted approximately by an angle /2, where is the IMF clock angle. Then, for clock angles away from northward, the magnetospheric energy entry and response scale with the electric field along the reconnection line (E PAR ), rather than the traditionally used E Y. If we define the energy coupling efficiency as response/e PAR, we can show it to be independent of the IMF clock angle and only weakly dependent on the solar wind dynamic pressure. These results demonstrate the ability of the localized reconnection line to control the energy input through the entire magnetopause. Citation: Pulkkinen, T. I., M. Palmroth, H. E. J. Koskinen, T. V. Laitinen, C. C. Goodrich, V. G. Merkin, and J. G. Lyon (2010), Magnetospheric modes and solar wind energy coupling efficiency, J. Geophys. Res., 115,, doi: /2009ja Introduction [2] The solar wind magnetosphere interaction is a complex set of processes driven by (variations of) the solar wind plasma parameters and the interplanetary magnetic field (IMF). The magnetospheric activity that follows has been empirically categorized to several distinct event classes, and efforts have been made to identify the drivers that are associated with each activity type. As a rule of thumb, substorms follow a period of southward IMF longer than about 30 min, and a magnetic storm is caused by southward IMF duration longer than about 3 h [Gonzalez et al., 1994]. [3] Earlier work on coupling functions have clearly identified the role of southward IMF and solar wind speed in driving magnetospheric activity. The most often used coupling functions are the Y component of the solar wind electric field E Y =( V B) Y [Burton et al., 1975] and the epsilon parameter defined as =(4p/m 0 )l 2 0 VB 2 sin 4 (/2), where the 1 Finnish Meteorological Institute, Helsinki, Finland. 2 Department of Physics, University of Helsinki, Helsinki, Finland. 3 Swedish Institute for Space Physics, Uppsala, Sweden. 4 Center for Space Physics, Boston University, Boston, Massachusetts, USA. 5 Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire, USA. Copyright 2010 by the American Geophysical Union /10/2009JA014737$09.00 IMF clock angle is given by =tan 1 (B Y /B Z )andl 0 =7R E is an empirical scaling parameter [Akasofu, 1981]. While the former can be related to the electric field inside the convecting and reconnecting magnetosphere [Dungey, 1961], the latter is essentially the Poynting flux incident at the magnetopause. More recently, several more complex coupling functions involving V, B, and have been devised using correlation analysis techniques [e.g., Newell et al., 2007, and references therein]. These works have led to a firm association of the energy transfer with the magnetic reconnection process [e.g., Siscoe et al., 2001]. [4] In the large scale, global MHD simulations can be used to trace the temporal evolution of the fields and plasmas in the magnetosphere. However, the real magnetosphere is a much more complex system than that represented by ideal MHD simulations; major limitations of the simulations arise from the MHD approximation of the plasma physics, incomplete resolution both in some parts of the magnetosphere and in the ionosphere, simplified description of the ionospheric physics, and highly simplified description of the magnetosphere ionosphere coupling. Both the plasma physics description and grid resolution issues limit the ability of MHD simulations to describe the details of the reconnection process within the diffusion region itself, but comparisons of simulation runs of actual events with proxy indices and in situ measurements show quite comparable temporal behavior in the observations and in the simulation [Palmroth et al., 2004]. Therefore, we assume that the temporal evolution and the characteristic behavior of the energy transfer and 1of9

2 Figure 1. Superposed epoch analysis of storm time substorms, sawtooth oscillations, and steady magnetospheric convection events. (left) Comparisons of storm time substorms with sawtooth events and (right) comparisons of sawtooth events with SMC events. (top to bottom) The solar wind electric field E Y in mv/m, the AL index in nt, and the solar wind speed in km/s. Note that the two sets of sawtooth events in Figure 1 (left) and Figure 1 (right) are not the same, as the events were chosen to have similar driving E Y with the comparison data set. Each data set consists of about 25 events. For details, see Pulkkinen et al. [2007a] and Partamies et al. [2009]. dissipation processes driven by reconnection can be quite well reproduced in the simulation magnetosphere. [5] In this paper, we use observations and two global MHD simulations to further examine the role of solar wind speed in determining the mode of the magnetosphere and the role of reconnection in the energy transfer process in a quantitative way. Section 2 discusses observations and global MHD simulation results on the changing response of the magnetosphere when individual solar wind driver parameters are changed. Section 3 discusses reconnection at the magnetopause and the role of the reconnection rate in determining the coupling efficiency. Section 4 examines the coupling efficiency between the solar wind and ionospheric parameters. Section 5 concludes with discussion. 2. Solar Wind Speed and Magnetospheric Modes [6] Recently, Pulkkinen et al. [2007a] and Partamies et al. [2009] examined the role of solar wind speed in driving geomagnetic activity. Using superposed epoch analysis techniques on a set of storm time substorms, sawtooth oscillations, and steady magnetospheric convection (SMC) events, they concluded that the solar wind speed is the distinguishing factor in the driver characteristics. Figure 1 shows a composite using four subsets of those data. Figure 1 (left) shows a comparison between a subset of storm time substorms and sawtooth events, selected such that the driving electric field (E Y ) is almost the same for both sets of events. Figure 1 (right), in a similar manner, shows a comparison between a subset of sawtooth events (different from the one in Figure 1 (left)) and SMC events, again selected to yield a similar driving electric field. [7] Figure 1 showing E Y, the negative of the AL index, and the solar wind speed summarizes the key findings: First, there is an ordering of ionospheric activity with the storm time substorms causing the largest ionospheric electrojets, and the SMC events causing the smallest response in AL. Second, there is an ordering with the solar wind speed, with the storm time substorms being associated with highest solar wind speed and the SMC events associated with the lowest solar wind speed. For similar levels of E Y driving, storm time substorms are driven by higher speed and less negative IMF B Z, while the periodic sawtooth activity is associated with lower speed and more negative IMF B Z. On the other hand, comparison of sawtooth events and SMC events with similar E Y drivers shows that the sawtooth events are associated with higher speed and less negative IMF B Z, while the SMC events are produced during low solar wind speeds, which can carry quite intense southward IMF B Z. E Y here is computed in the GSM coordinates, which are used throughout the paper. [8] Goodrich et al. [2007] and Pulkkinen et al. [2007b] tested the role of solar wind parameters on the resulting activity using the Lyons Fedder Mobarry (LFM) global MHD simulation [Lyon et al., 2004]. The LFM code solves the ideal MHD equations in a box that extends from 30 R E in the sunward direction to 300R E tailward of the Earth, and ±100R E in the perpendicular dimensions. Highest spatial resolution in the code is obtained in the inner magnetosphere, plasma sheet, and boundaries where the gradients can be expected to be largest. The upstream boundary uses solar wind and IMF values as boundary conditions, while supersonic outflow conditions are applied at the other boundaries. [9] In this paper we expand their study of a steady convection event on 3 4 February Figure 2 shows the solar wind parameters used to drive the simulation runs. The simulation was run using the observed solar wind parameters that led to a period of steady convection lasting for about 12 h during which no substorms or geostationary orbit injections were observed (SMC run, shown in black). The B run uses otherwise the observed parameters, but the IMF B Z was increased by 50% (blue). For the V run the solar wind speed was increased by 50% (red). Both of these changes to the original conditions lead to a 50% increase of the driving solar wind E Y, while only the V run causes a change in dynamic pressure. New in this paper is the N run, where the solar wind density was increased by 50% (green); this increases the dynamic pressure but leaves the electric field unchanged. The simulation setup for each run is identical to that described by Goodrich et al. [2007]. [10] Simulations that provide plasma and field parameters throughout the magnetosphere allow us to quantitatively analyze the magnetospheric response. Here we quantify the magnetotail plasma sheet activity level by two parameters: earthward transport of mass and electromagnetic energy flux (Poynting flux) through a given Y Z plane, which we use as an indicator of the global convection intensity. The spatial variances of these quantities computed over the entire closed 2of9

3 events, although the simulation does not reveal such coherent inner magnetosphere behavior in this case. [13] A new result in this paper is that similar flow structuring is seen also in the N run when the density is enhanced. In this case the original SMC run and the N run have equal E Y drivers, while especially the mass flux is enhanced in the N run, and the variances in both mass and electromagnetic energy fluxes are much larger in the N run than in the original SMC run. Thus, one would expect SMC events to be characterized both by low solar wind speed and low dynamic pressure. Figure 2. Solar wind and IMF parameters used as input for LFM global MHD simulation. (top to bottom) IMF B Y and B Z in nt, solar wind speed in km/s, density in cm 3,and pressure in npa. The SMC run is shown in black, the B run (increased B Z ) is shown in blue, the V run (increased V) is shown in red, and the N run (increased N) is shown in green. All other parameters during the simulation runs were the same for each run. 3. X Line Orientation and Energy Transfer Efficiency [14] Laitinen et al. [2006, 2007] used the GUMICS 4 global MHD simulation [Janhunen, 1996] to examine the properties of the large scale X line and energy conversion at the magnetopause. The energy conversion is evaluated using the quantity (r S)dl, where S is the Poynting vector across the magnetopause and the integration extends over the thickness of the magnetopause. This quantity then gives the energy conversion per unit area of the magnetopause. plasma sheet cross section in turn characterize the spatial structuring of the flows: Laminar flows (flow speed the same throughout the plasma sheet cross section) produce low spatial variances, while highly structured bursts lead to high spatial variances [Pulkkinen et al., 2007b]. Figure 3 shows the mass and electromagnetic energy fluxes and their variances for the four runs through a plane X = 15R E, which remains earthward of the large scale tail reconnection line at all times, while still away from the quasi dipolar region. [11] Figure 3 clearly shows that making the IMF B Z more negative stabilizes the tail instead of making it more active. The mass flux slightly decreases, while the electromagnetic energy flux is almost unchanged. The variances in both quantities decrease, which indicates that the magnetotail is in a state where a large scale reconnection region feeds rather steady earthward flows (see Goodrich et al. [2007] for more details about the tail behavior). On the other hand, increasing either the solar wind speed or density increases the flux levels and structures the flows to localized bursts. This is seen both as increased level of average mass and electromagnetic energy flux transport and, especially, much larger spatial variances over the plasma sheet cross section. [12] The simulation results reveal a similar ordering to the observations shown in Figure 1: Comparing the B run and V run, which have equal E Y drivers, it is clear that the first leads to a stable, laminar convection resembling SMCs, while the latter leads to bursty behavior that could be interpreted as being quasi periodic substorm activity resembling sawtooth Figure 3. (top) Earthward mass flux and (bottom) Poynting flux through a plane at X = 15R E. The black lines show averages over the entire closed field line plasma sheet cut plane, while the colored shadings show the spatial variances over the closed plasma sheet cut plane. 3of9

4 Figure 4. (top) IMF B Y and B Z and solar wind dynamic pressure for (left) the IMF rotation runs and (right) solar wind speed, density, and pressure for the pressure runs. (bottom) Reconnection power (negative values of r S), flux generation power (positive values of r S), and total energy flux all in units of W over the magnetopause surface (see text and Pulkkinen et al. [2008] for more details). (left) Runs with B = 5 nt are shown with thin lines, runs with B = 10 nt are shown with thick dotted lines, runs with P = 2 npa are shown in blue, and runs with P = 8 npa are shown in red. (right) The run with variable speed is shown in red, and the run with variable density is shown in blue. [15] The GUMICS 4 simulation solves the ideal MHD equations in a fully conservative form in a simulation box extending from 32 R E upstream of the Earth to 224 R E in the tailward direction and ±64 R E in the directions perpendicular to the Sun Earth line. The MHD grid is adaptive in a sense that the grid is automatically refined to a minimum cell size of 0.25 R E whenever the code detects large spatial gradients. Furthermore, the code uses subcycling in order to save computation time, i.e., the time step varies dynamically with the local travel time of the fast magnetosonic wave across the grid cell. Solar wind density, temperature, velocity, and magnetic field are given as boundary conditions along the sunward boundary while supersonic outflow conditions are applied on the other boundaries of the simulation box. [16] In the IMF rotation runs (Figure 4, left), the clock angle rotated over a period of 6 h a full 360. The field magnitude was constant at two different values, 5 nt (thin lines) and 10 nt (thick lines). The solar wind dynamic pressure was constant at two different values, 2 npa (blue) and 8 npa (red); the solar wind speeds were 400 km/s and 600 km/s, respectively. In the pressure runs (Figure 4, right), the solar wind dynamic pressure was first linearly increased and later decreased over a period of 4 h. Two runs are shown. In the first the pressure change was caused by increasing the solar wind speed while keeping the density constant (shown red). In the second run the solar wind speed was held constant while the density increased (shown blue). In these runs, the IMF was southward with clock angle constant at For more details of the simulation runs, see Pulkkinen et al. [2008]. [17] Figure 4 (bottom) shows the surface integrals over the dayside magnetopause of the Poynting vector divergence. Negative and positive values of the Poynting vector divergence were integrated separately and termed reconnection and flux generation powers, respectively. The negative values of the Poynting vector divergence define areas where magnetic energy is transformed to plasma energy, while the positive values of Poynting vector divergence give surface locations where magnetic flux is being generated [Laitinen et al., 2007]. Figure 4 (bottom) shows the energy flux through the boundary obtained by direct integration of the normal component of the total energy flux vector through the simulation magnetopause earthward of X = 30 R E [Palmroth et al., 2003, 2006]. 4of9

5 Figure 5. Magnetopause projection in the Y Z plane as viewed from the sunward direction. The black crosses indicate the X line orientation for different IMF clock angle directions given above each plot. The circular outline depicts the magnetopause boundary at the terminator. The arrows indicate the directions of the interplanetary magnetic and electric fields. (Modified from Laitinen et al. [2007].) [18] The IMF rotation runs show that the IMF clock angle modulates strongly the energy transfer process; highest energy transfer occurs for due southward IMF. On the other hand, both rotation runs and pressure runs show the strong role played by the solar wind dynamic pressure: in the IMF rotation runs, the high pressure runs result in much larger energy transfer, and in the pressure runs, the increasing pressure much enhances the energy transfer. It is also clear that the solar wind density has a lesser role, and especially the reconnection power is quite independent of the solar wind density. However, because the magnetic flux generation typically occurring tailward of the cusps does increase for higher densities, the total energy flux through the boundary is also density dependent [Pulkkinen et al., 2008]. [19] Figure 5 shows the magnetopause X line, defined here as a region having field lines with different topologies occurring close together [Laitinen et al., 2007]. Figure 5 shows the X line for different IMF orientations ranging from due northward through dusk to southward and through dawn back to northward in a projection looking at the magnetopause surface from the sunward direction. The arrows in Figure 5 indicate the directions of the magnetic and electric fields in the undisturbed solar wind. For due southward IMF, the X line extends over the equatorial magnetopause. For other directions of the IMF, the X line becomes highly tilted such that it is almost north south oriented for due northward IMF. Caution must be used when interpreting the plot showing the due northward IMF, as at that time subsolar reconnection is very weak and the existence of a single X line across the entire subsolar surface is questionable. It can be shown that the X line is tilted at an angle roughly equal to /2. [20] In classical Petschek reconnection, the reconnection rate is quantified by the electric field along the X line [e.g., Vasyliunas, 1975]. Assuming the geometry presented above, the electric field along the X line is given by E PAR = Esin(/2). We demonstrate the role of E PAR as a control parameter by showing in Figure 6 the energy transfer quantities (reconnection power, flux generation power, and energy flux transfer) scaled by E PAR as functions of IMF clock angle and solar wind dynamic pressure. It is clear that apart from near northward orientations, the reconnection power, flux generation power, and energy flux transfer all scale with E PAR, leaving their ratio almost independent of the IMF clock angle. Furthermore, the reconnection power and energy flux transfer scaled by E PAR are almost independent of the solar wind dynamic pressure, while the magnetic flux generation scaled by E PAR is higher for higher solar wind pressures. Thus, a general conclusion is that the electric field parallel to the large scale X line controls the energy transfer efficiency through the magnetopause. [21] If we define energy transfer efficiency as energy flux/ E PAR, the results above show that the energy transfer efficiency is independent of the IMF clock angle, and only weakly dependent on the solar wind pressure. This indicates that proportionally the same amount of energy gets into the magnetosphere for all IMF orientations (away from near northward). We note that the pressure dependence of the energy transfer efficiency is similar for both pressure runs, regardless of whether the pressure increase was created by increasing the density or solar wind speed. 4. X Line Orientation and Ionospheric Energy Coupling Efficiency 4.1. MHD Testing [22] In order to test the result presented above, we use both the LFM global simulation results and observations of magnetic cloud events to examine the energy coupling efficiency. We assume that for relatively steady and slowly varying IMF conditions, the large scale X line orientation is given by /2, similar to that obtained in the IMF rotation runs. This allows us to use the IMF clock angle to determine the orientation of the X line and the parallel electric field, and thus the coupling efficiency. In this case, we evaluate the energy coupling efficiency by evaluating ionospheric parameters scaled by E PAR. [23] For the LFM simulations presented in section 2, we have evaluated the Joule heat, the field aligned currents, and the polar cap potential in the northern hemisphere (Figure 7). Figure 7 (bottom) shows the same quantities scaled by E PAR and plotted as a function of the IMF clock angle. While the scatter is larger due to the fact that the simulation was run using real (rather than idealized) solar wind parameters and 5of9

6 Figure 6. Coupling efficiency dependence on IMF clock angle and solar wind dynamic pressure: Reconnection power (positive values of r S), flux generation power (negative values of r S), and total energy flux have been scaled by E PAR (the solar wind electric field parallel to the X line at the magnetopause) and are plotted (left) as functions of IMF clock angle for the IMF rotation runs and (right) as functions of the solar wind dynamic pressure for the pressure runs. The colors and symbol sizes are similar to those in Figure 4. thus produces more small scale variations, the basic conclusion is the same as for the GUMICS 4 simulation: For each of the four runs having different values of the IMF B Z, solar wind speed and density, the scaling produces relatively constant results that are independent of the IMF clock angle Observational Testing [24] For observational evidence, we use a set of 10 magnetic clouds to examine interaction of slowly varying solar wind and IMF with the magnetosphere [Huttunen and Koskinen, 2004]. Figure 8 (top) shows the solar wind speed, IMF clock angle, and the AE index during the cloud events. The times have been shifted to zero epoch at the cloud arrival at the magnetopause. The periods shown with dotted colors indicate the duration of the cloud proper; each event is shown with a different color. The solar wind speeds during these events ranged from above 300 to above 600 km/s, and the large scale rotations of the IMF clock angle occurred both from north to south and from south to north. The AE indices indicate strong ionospheric activity driven by the clouds. [25] Figure 8 (bottom) shows the energy coupling efficiency defined as AE/E PAR as a function of IMF clock angle and solar wind dynamic pressure. Similarly to the simulation results, the coupling efficiencies, regardless of IMF magnitude, orientation, or solar wind speed values, are relatively independent of the IMF clock angle or the dynamic pressure. 5. Discussion and Conclusions [26] Our study has used observations and two independent global MHD simulations to reach three main conclusions: [27] 1. The solar wind speed is a key factor in determining the magnetotail dynamic mode. The tail convection is laminar and less intense for drivers with slow speed, while it is stronger and more structured for drivers with higher speed. These differences remain true even if the driver intensity otherwise would be the same. For magnetospheric morphology, this means ordering of events from SMC to sawtooth to storms as the solar wind speed increases from low to moderate to high. [28] 2. For slowly varying IMF conditions, the large scale X line at the magnetopause is oriented at an angle roughly /2, where is the IMF clock angle. Therefore, the reconnection rate is determined by the electric field along the X line, E PAR = Esin(/2). [29] 3. For IMF clock angles away from northward direction, the amount of energy entry is controlled by the electric field parallel to the large scale X line (E PAR = Esin(/2)) Energy transfer rate per E PAR is independent of the IMF clock angle and only weakly dependent on the solar wind dynamic pressure. Similar clock angle independence is found for the ionospheric response calculated as AE/E PAR. This result indicates that the (small scale) reconnection process controls the amount of energy entry over the entire magnetopause surface. [30] Already the early theoretical works on reconnection recognized that the reconnection efficiency would be dependent on the IMF clock angle [Petschek, 1966]. Sonnerup [1974] derives this angular dependence using a geometrical argumentation that the reconnection line should always be perpendicular to the vector connecting the magnetic field vectors in the magnetospheric and magnetosheath sides. For purely southward IMF, this leads to an X line in the equatorial plane, but for other clock angles, the tilting of the X line depends on the clock angle and the ratio of the field magnitudes outside and inside the magnetopause. In the special case of equal field magnitudes in both sides, the X line orientation 6of9

7 subsolar magnetopause is geometrically not possible. In the simulations, energy transfer is present at all IMF orientations; as the IMF rotates, the energy transfer locations smoothly change from the subsolar magnetopause to the cusp region in the tail. This apparently causes the much less steep reduction in energy transfer in the simulation as compared to that predicted by the reconnection efficiency at the subsolar magnetopause (sin(/2) in the simulation instead of sin 2 (/2) in Sonnerup s formulation). [32] Recently, attention has been paid to the drivers of the various magnetospheric modes. Huttunen et al. [2002] point out that the ring current enhancement (as measured by Dst) and auroral activity (as measured by Kp) are different for steady and rapidly varying solar wind: Highly variable CME sheath regions drive higher auroral activity, while the slowly varying CME ejecta drive high ring current intensification and lesser auroral activity. Tanskanen et al. [2005] demonstrate that substorm activity is statistically dependent on the solar wind speed: During solar cycle phase with frequent interplanetary high speed streams the observed substorms were 30% more intense and transferred twice as much magnetic energy to the auroral ionosphere than the substorms that occurred during periods of few or no high speed streams. Figure 7. (top) Ionospheric response during the SMC runs: Joule heat, field aligned current, and polar cap potential in the northern hemisphere for the four runs shown in Figure 2. (bottom) Energy coupling efficiency as a function of IMF clock angle: Joule heat, field aligned current, and polar cap potential scaled by E PAR computed in the undisturbed solar wind. is given by sin(/2), consistent with our result. However, for all other field ratios the X line tilt is larger in the simulation than that predicted by the geometrical argumentation. This is most likely caused by the fact that the global configuration responds to conditions at all magnetopause locations rather than only to those near the subsolar point. As the magnetospheric field is roughly 70 nt, field ratio of unity would assume about 20 nt IMF magnitude often found during magnetic clouds, while field ratio of 0.25 is representative of typical conditions with IMF magnitude of about 5 nt. [31] Sonnerup [1974] obtain a formulation for the electric field parallel to the X line that is proportional to sin 2 (/2) by assuming that the inflow is limited by the Alfvén speed perpendicular to the X line. This again holds for the special case of field ratio of unity (i.e., under conditions typically found during magnetic storms). For smaller magnetosheath field values, the angular dependence is much steeper and E PAR goes to zero between 45 (field ratio of 0.75) and 80 (field ratio of 0.25). As Sonnerup s consideration only treats the subsolar X line, it is not able to represent processes during northward IMF periods, when reconnection at the Figure 8. (top) Selected magnetic cloud events: Solar wind speed, IMF clock angle, and AE index. Each event is shown with a different color indicated during the cloud proper. (bottom) Energy coupling efficiency AE/E PAR as a function of clock angle and solar wind dynamic pressure. 7of9

8 Both of these results support our conclusion of the solar wind speed influence on the magnetospheric mode. [33] Henderson et al. [2006], among others, note that the solar wind speed seems to be in the intermediate range during sawtooth intervals. While Pulkkinen et al. [2007a] and Partamies et al. [2009] arrive at a similar conclusion, and further point out the role of the solar wind speed in determining the type of activity, they were unable to set limiting solar wind parameter values that would categorize the different modes. Lavraud and Borovsky [2008] suggest that sawtooth oscillations are associated with low Alfvén Mach number solar wind. This is consistent with Figure 1 (left), which gives a lower Mach number (M A = V/V A ) for sawtooth oscillations than other storm time activations. The MHD simulation results in Figure 3 lend further support to the role of the solar wind speed (and density) influence on the structuring of the magnetotail flows: increasing the solar wind density or speed led to a much more variable magnetotail, while increasing the IMF B Z led to stable, laminar flows in the tail [see also Goodrich et al., 2007]. [34] In this paper we demonstrate that if the reconnection rate is estimated by E PAR instead of E Y, the energy transfer efficiency becomes independent of the IMF clock angle, and to large extent also of the solar wind dynamic pressure. This result holds for two different MHD simulations as well as a small statistics of magnetic cloud events. When the IMF is due southward, E Y and E PAR are the same, and thus E Y controls the energy entry. For other IMF directions away from 180, E Y and E PAR are different. Using E PAR as the coupling function gives a similar dependence on the clock angle as the " parameter, which in earlier studies has also been identified as a successful control parameter of the energy entry [Akasofu, 1981]. However, E PAR highlights the importance of the reconnection process controlling the energy entry process rather than the amount of Poynting flux incident at the magnetopause. [35] It is interesting to note that the magnetotail mode and the energy coupling are not identical in their dependence on the solar wind driver. This is best demonstrated in the LFM simulations of the SMC runs, where the solar wind speed and density enhancement clearly changed the mode of the magnetotail, while enhancement of B Z did not. However, in all cases, the ionospheric response still scales with E PAR independent of IMF clock angle or dynamic pressure. Changes in the magnetospheric mode may be related to the creation of larger wave activity along the magnetopause for higher solar wind speed and/or dynamic pressure [Collado Vega et al., 2007]. [36] Acknowledgments. Part of the research has received funding from the European Research Council under the European Community s Seventh Framework Programme (FP7/ )/ERC starting grant agreement QuESpace. The work of M.P. is supported by the Academy of Finland. [37] Zuyin Pu thanks the reviewers for their assistance in evaluating this paper. References Akasofu, S. I. (1981), Energy coupling between the solar wind and the magnetosphere, Space Sci. Rev., 28, Burton, R. K., R. L. McPherron, and C. T. Russell (1975), An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 80, Collado Vega, Y. M., R. L. Kessel, X. Shao, and R. A. Boller (2007), MHD flow visualization of magnetopause boundary region vortices observed during high speed streams, J. Geophys. 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9 Tanskanen, E. I., J. A. Slavin, A. J. Tanskanen, A. Viljanen, T. I. Pulkkinen, H. E. J. Koskinen, A. Pulkkinen, and J. Eastwood (2005), Magnetospheric substorms are strongly modulated by interplanetary high speed streams, Geophys. Res. Lett., 32, L16104, doi: /2005gl Vasyliunas, V. M. (1975), Theoretical models of magnetic field line merging I, Rev. Geophys., 13, 303. C. C. Goodrich and V. G. Merkin, Center for Space Physics, Boston University, 725 Commonwealth Ave., Boston, MA 02215, USA. H. E. J. Koskinen, Department of Physics, University of Helsinki, PO Box 64, FIN Helsinki, Finland. T. V. Laitinen, Swedish Institute for Space Physics, SE Uppsala, Sweden. J. G. Lyon, Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA. M. Palmroth and T. I. Pulkkinen, Finnish Meteorological Institute, PO Box 503, FIN Helsinki, Finland. 9of9