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Keywords:

  • solar wind–magnetosphere coupling;
  • substorms;
  • convection

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. GUMICS-4 Global MHD Simulation
  5. 3. Statistical Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[1] We show that the dependence of magnetospheric activity on the driving solar wind electric field is qualitatively different for northward and southward IMF conditions. For southward IMF, the AE-index is driven by the solar wind electric field, but for a given EY, AE is higher when the solar wind speed is higher. For northward IMF, AE does not scale with the electric field, but is lowest for low solar wind speed and small IMF clock-angles. These results are explained by a quantitative analysis of the amount of energy that enters the magnetosphere using the GUMICS-4 global MHD simulation.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. GUMICS-4 Global MHD Simulation
  5. 3. Statistical Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[2] The dependence of geomagnetic activity on the solar wind and interplanetary magnetic field (IMF) parameters has been widely studied and several coupling parameters have been suggested and used in the literature. Most of these involve the solar wind electric field (E = −V × B, where V is the solar wind velocity and B the IMF vector) and some function of the IMF clock angle θ = tan−1(BY/BZ). The clock-angle dependence, often in the form of ε = 107l02VB2 sin4 θ/2 (where l0 = 7 RE is a scaling parameter), brings an improvement over the pure EY component in that it recognizes the energy input into the system even when BZ is northward if there is a sufficiently large IMF BY present [e.g., Akasofu, 1981]. Most statistical studies have found that for northward IMF, there is no significant correlation between the activity parameters and the driver intensity [Newell et al., 2006; Lyatsky et al., 2007].

[3] In this paper we return to the question of the amount of energy input and the level of magnetospheric activity as a function of the driving solar wind speed and IMF for northward IMF conditions. We show that different combinations of the parameters yielding the same values for the solar wind electric field can produce different levels of activity. These results are used to discuss the roles of the various parameters in the energy coupling between the solar wind and the magnetosphere.

2. GUMICS-4 Global MHD Simulation

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. GUMICS-4 Global MHD Simulation
  5. 3. Statistical Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[4] GUMICS-4 is a global magnetohydrodynamic (MHD) simulation [Janhunen, 1996] that solves the ideal MHD equations in a region from 32 RE upstream of the Earth to −224 RE tailward of the Earth and ±64 RE in the directions perpendicular to the Sun-Earth line. Solar wind density, temperature, velocity, and the IMF components are given as input at the sunward edge of the simulation box, outflow conditions are applied at the other boundaries. The MHD regime is coupled to an electrostatic ionospheric simulation, which solves the ionospheric potential using precipitation and field-aligned currents from the MHD simulation, and returns the potential as a boundary condition for the inner boundary of the magnetospheric part at 3.7 RE. More details of the simulation setup can be found in work by Janhunen [1996] and Palmroth et al. [2003].

[5] Laitinen et al. [2007] report on two sets of runs that they used to examine magnetopause reconnection and energy transfer efficiency dependence on the driving IMF and solar wind. They performed four “pressure runs”, where the pressure was changed from 1 to 10 nPa by either increasing the solar wind speed or by increasing the solar wind density, for constant northward and southward IMF separately (B = 10 nT, θ = 22.5 and 157.5°, respectively). In the “IMF rotation runs” the IMF clock angle was rotated full 360 degrees over a period of six hours using two values of solar wind dynamic pressure (2 and 8 nPa) and two values of the IMF magnitude (5 and 10 nT). They found that the reconnection power (characterized as the integral of the Poynting flux divergence over the entire dayside magnetopause and magnetopause thickness of ±1.5 RE) decreases for increasingly negative EY for the IMF rotation runs while it increases for increasingly negative EY for the pressure runs (see Laitinen et al. [2007] for more details on the Poynting flux divergence and reconnection at the magnetopause; we only note that the Poynting flux divergence is a robust measure not sensitive to details of the grid structure).

[6] Figure 1 shows another representation of the result discussed above. The left plot shows the amount of energy input through the magnetopause as a function of the solar wind electric field for the two runs where the pressure enhancement was obtained by increasing the solar wind speed. The energy input is evaluated through direct integration of the total energy flux vector normal component at the magnetopause [Palmroth et al., 2003]. The energy is mostly in the form of Poynting flux, mechanical energy transfer is under 10% of the total energy. The right plot shows the same quantities for the four IMF rotation runs. For southward IMF (positive EY) both sets of runs result in a roughly linear dependence of the energy input on the driving electric field. On the other hand, the behavior for northward IMF (negative EY) is opposite for the two sets of runs: When the velocity is changed, the energy input increases for increasing speed (and −EY). During the IMF rotations, the energy input decreases when BZ (and −EY) increase. Thus, the northward IMF behavior seems to depend on how the change in EY occurs.

image

Figure 1. Energy input through the magnetopause as a function of the driving solar wind EY in the GUMICS-4 global MHD simulation. The left plot shows two runs with changing solar wind speed and the right plot shows four runs with rotating IMF clock angle while other parameters were held constant (see text). The electric field EY = −VBZ has a sign convention that produces positive EY for southward BZ and negative EY values for northward BZ.

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[7] These results led us to re-examine statistical data of the driver – response relationship to demonstrate that the simulation results can indeed be recovered using observational data analysis.

3. Statistical Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. GUMICS-4 Global MHD Simulation
  5. 3. Statistical Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[8] The OMNI 2 database consists of solar wind and IMF measurements tagged with magnetospheric activity parameters from years 1963 to 2006 at 1-hour resolution. All solar wind and IMF measurements have been propagated from the spacecraft location to the bow shock nose. The data are freely available from http://omniweb.gsfc.nasa.gov/.

[9] Figure 2 shows the dependence of the AE index on the solar wind speed and IMF BZ in a color coded format. The data set consists of all those for which both solar wind and magnetic index information was available. The color coding shows the median value of AE in the given solar wind speed – IMF BZ bin (using mean values produces identical results). The positive IMF values are shown in the top plot and the negative IMF values in the bottom plot, with different scales for the AE index. The entire data set contains 118000 measurements; bins with no data are marked white. The bottom plot reproduces the expected result: The AE-variations roughly follow the constant-EY curves (shown white) with largest activity obtained for large speed and large negative IMF BZ. However, note that for constant EY, the activity is larger for higher speed and less negative BZ than for lower speed and more negative BZ.

image

Figure 2. The AE index color coded as function of solar wind speed and IMF BZ for (top) positive IMF BZ values and (bottom) negative IMF BZ values. Note that the AE-scales are different in the two plots. The black lines show contours of constant EY in both plots. The thin contour line indicates regions with more than 20 data points.

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[10] The top plot of Figure 2 shows the result of interest for this study: For positive IMF values the activity does not follow the constant EY curves: For any given EY value, smaller speed and higher IMF BZ leads to lower activity than higher speed and lower IMF BZ. For all values of IMF BZ, the activity gets larger for higher solar wind speeds. These results are consistent with the energy input EY dependence from the GUMICS-4 simulations for the velocity change runs shown in the left plot of Figure 1. However, for a given solar wind speed, the plot does not give an indication of changing activity as the IMF BZ changes.

[11] The top plot of Figure 3 shows, in a format similar to Figure 2, the AE-index dependence on the solar wind speed and IMF clock angle. In order to highlight the low activity values, the values below 120 nT have been replotted with a gray scale. The bottom plot shows the solar wind electric field color-coded on the same plane.

image

Figure 3. (top) AE index and (bottom) EY color coded as function of solar wind speed and IMF clock angle θ. The lowest values for the AE-index are plotted in gray scale to highlight changes in that region.

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[12] The color scale in the top plot shows the expected result: The activity is largest when the clock angle is around 180° (due southward field) and large solar wind speed. These are the most favorable conditions for driving magnetic storms and geomagnetic activity. The gray-scale and color-coded results show that for any given solar wind speed value, the activity is lowest for clock angles near 0° and largest for clock angles near 180°. This is the result obtained with the GUMICS-4 IMF rotation simulations shown in the right plot of Figure 1, where the electric field change is obtained by rotating the IMF clock angle while keeping the IMF magnitude constant.

[13] The bottom plot of Figure 3 shows the solar wind electric field dependence on the solar wind speed and IMF clock angle. Comparison of this plot and the activity plot above demonstrates that for northward IMF (clock angles below 90° and above 270°), the AE index has no direct correlation with the electric field, as the two color plots have very different shapes in that region. For high solar wind speeds, even almost purely northward fields produce quite large magnetospheric activity, as seen by the widening of the bell-curve in the top plot. On the other hand, for low solar wind speeds, the magnetosphere is very quiet for due northward IMF, even though the electric field is much less negative than it is for the high-speed case.

4. Discussion and Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. GUMICS-4 Global MHD Simulation
  5. 3. Statistical Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[14] Our study has two main results: First, the magnetospheric activity dependence on the solar wind and IMF parameters is qualitatively and quantitatively different for northward and southward IMF conditions. Secondly, we can explain the northward IMF results by quantitative evaluation of the amount of energy input into the magnetosphere using our global GUMICS-4 MHD simulation.

[15] In the OMNI data set, during southward IMF the activity scales roughly with the solar wind electric field. However, there is a deviation from pure EY-dependence such that large speed and low BZ magnitude drive larger activity than low speed with higher BZ magnitude, even if the EY for both cases is the same. The same result can be obtained for the ε-parameter by using B2sin4(θ/2) instead of BZ(not shown). The results shown here use the AE index as a global measure – using Kp, which is a good indicator of magnetospheric convection [Thomsen, 2004], yields identical results (not shown). In conclusion, the solar wind speed is a more efficient activity driver than (southward) IMF.

[16] For the northward IMF conditions, the activity increases for increasing solar wind speed regardless of the IMF clock angle or BZ-value. On the other hand, the activity shows little or no variability as IMF BZ changes if the speed is held constant, while there is a clear dependence on the clock angle with weakest activity for purely northward IMF. This suggests that the IMF orientation is more important than its magnitude. Taken together, during northward IMF, the magnetospheric activity is not a simple function of the driving EY.

[17] For southward IMF, global MHD simulation results using the GUMICS-4 code show that the energy input into the magnetosphere is almost linearly dependent on the driving solar wind EY [Palmroth et al., 2003; Laitinen et al., 2007]. The energy input increases linearly when the solar wind EY is increased both when the EY is increased by rotating the IMF clock angle and when the increase is associated with an increase in the solar wind speed. This result is qualitatively consistent with the OMNI data set.

[18] During northward IMF, the simulation shows opposite behavior for increasingly negative EY associated with larger solar wind speed and more northward direction of the IMF. The energy input is weakest for small solar wind speed and purely northward IMF. These results are also consistent with the OMNI data set analysis results.

[19] The agreement of the simulation results of energy input into the magnetosphere and the statistical observational results for both southward and northward IMF demonstrates two things: (1) The energy input through the magnetopause into the magnetosphere is the most important parameter controlling the level of magnetospheric activity. (2) The amount of energy input is most dependent on the magnitude of the solar wind speed, then the IMF orientation, and least dependent on the IMF magnitude. The results highlight the importance of the solar wind speed in driving magnetospheric activity and point out that the qualitatively different response during southward and northward IMF orientation needs to be accounted for in statistical analyses.

[20] Laitinen et al. [2007] examine the reconnection power (∇ · S < 0) and dynamo power (∇ · S > 0) at the magnetopause surface separately. They show that while the solar wind speed has an effect on both, changes in the solar wind density only affect the dynamo power, while the reconnection power remains unchanged. Note that this result concerns the total integrals over the surface; changing density changes the size of the magnetopause and the reconnection power surface density in a way that maintains the integral constant. Thus, the effects caused by pressure on the energy transfer processes also depend on whether the pressure change is caused by a change in the solar wind density or in the speed, and the solar wind speed is more effective in changing the energy transfer rate.

[21] During southward IMF, the electric field maps along open field lines to an ionospheric potential. During northward IMF, the open field lines are created by lobe reconnection and map to the ionospheric reverse cells during four-cell convection patterns. These different responses may be associated with the differences in the energy transfer properties. However, it is still an open question whether the reconnection process itself is different at the dayside and behind the cusps, or whether the coupling to the ionosphere is different. While the observational results provide no clear answer to this, the simulation results hint that the reconnection and energy transfer processes are indeed different in their dependence on the solar wind driver. This is clearly an area that warrants further study.

[22] Newell et al. [2007] examine various coupling functions for a variety of magnetospheric activity parameters and arrive at a best-fit function averaged for all parameters of the form V2B sin4(θ/2)2/3, which they interpret to be the rate magnetic flux is opened at the magnetopause. All functions of such form merge positive BZ values with those with small B or small V (i.e., all weak driving cases), and therefore it is impossible to separate the different factors. However, that function may reflect the observations better in that the solar wind speed appears squared while the magnetic field is only linear, consistent with our conclusion that V is a stronger driver than BZ.

[23] The results in this paper provide an explanation of the different functional behavior of the activity on the driving solar wind parameters. Simultaneously, the good agreement of the observations with the simulation results improves our confidence in the capability of global MHD simulations to represent the energy transfer and dissipation processes in the magnetosphere. The multiple parameters and processes involved in the energy transfer highlight the complexity of the coupling and the importance of examining each of the effects individually.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. GUMICS-4 Global MHD Simulation
  5. 3. Statistical Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References

[24] We acknowledge the Space Physics Data Facility (SPDF) and the National Space Science Data Center (NSSDC) for producing and providing the OMNI 2 data set.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. GUMICS-4 Global MHD Simulation
  5. 3. Statistical Results
  6. 4. Discussion and Conclusions
  7. Acknowledgments
  8. References