MHD simulation of two successive interplanetary disturbances driven by cone-model parameters in IPS-based solar wind



[1] We present the measurement-based MHD simulation model of the interplanetary disturbances; the quiet solar wind is obtained with the MHD-based analysis method for the interplanetary radio scintillation (IPS) measurement data, and the interplanetary disturbance parameters, such as speed, direction and angular size of the expanding coronal mass ejection (CME), are determined from the SOHO LASCO/C3 data with the Cone-model. We chose the two successive interplanetary disturbances resulting from two flare-associated halo CMEs of April 2002. The simulated interplanetary shocks are compared with the nearby-Earth measurement, and the well produced shock arrivals to the Earth implied the ability of the cooperation of the Cone-model, the IPS-analysis and MHD simulation. It is found that the second interplanetary disturbance propagated faster in the rarefaction region of the first event, implying that the multi-event simulation is important to enhance the simulation model.

1. Introduction

[2] Because the dynamics of the solar wind can be well described by the magnetohydrodynamics (MHD) equations, two- and three-dimensional MHD simulation has been widely used to determine the global structure of solar wind and the temporal evolution of the transient phenomena such as the interplanetary disturbance propagation. For the study of the interplanetary disturbance, many MHD simulation studies give the numerical perturbation mimicking the transient event such as coronal mass ejection (CME) to the quiet background solar wind to induce the interplanetary disturbance event [e.g., Odstrcil et al., 2004]. For this model approach, it is important to prepare realistic multi-dimensional background solar wind and the perturbation parameters that well represent the reality. Therefore, it is preferable if the simulated MHD variables are set up using the measurement data.

[3] There are several approaches to obtain the global three-dimensional structure of the quiet background solar wind. One of them is to simulate the trans-Alfvénic solar wind and solar corona starting from the solar surface, or photosphere, on which the observation-based magnetic field can be given as the boundary condition [e.g., Linker et al., 1990; Usmanov and Dryer, 1995]. This approach must be orthodox, however, sophistication of the coronal heating and solar wind acceleration model is required so that the realistic solar wind solution will be obtained. Another approach is to use the interplanetary radio scintillation (IPS) measurement data and analysis methods [e.g., Jackson et al., 1998; Kojima et al., 2001] that can reconstruct the solar wind structures at r ≥ 25Rs. The MHD-version of the IPS tomography analysis [Hayashi et al., 2003] can numerically reconstruct the three-dimensional steady MHD solution of the co-rotating solar wind from the line-of-sight integrated IPS measurement data. Because the solar wind observable by IPS measurement represents the consequence of the solar wind heating and acceleration process, it is a suitable choice to use the IPS-based MHD solution as the background solar wind in which the numerical interplanetary disturbance will propagate.

[4] In order to parameterize the CME structure, the Cone-model was proposed by Zhao et al. [2002] and improved by Xie et al. [2004] as the inversion method to determine the kinematic and geometric parameters of CME from the line-of-sight coronagraph data. This analysis method can determine the direction, the latitudinal and longitudinal angular widths, and the speed of CME by fitting the five parameters of the Cone-model geometry to the observation. They used the LASCO/C3 observation data at 5Rs < r < 23Rs. In addition, the Cone-model can derive the position of CME as a function of time; therefore, the time at which the CME will pass the reference distance can be estimated. The Cone-model in this way can provide the parameters needed to start MHD simulation of interplanetary disturbance.

[5] In this study, we will present the MHD simulation that uses the MHD-version of IPS tomography and the Cone-model. A new feature of this simulation is that both three-dimensional structure of the quiet solar wind and the characteristics of the interplanetary disturbance are determined from the measurements. Therefore, without treating the complex coronal dynamics, the simulation setup can be well prepared. We chose a period, mid-April 2002, during which two halo-CME events occurred. By choosing this period, we can additionally examine how the second event will propagate in the solar wind distributed by the first event.

2. Simulation Model and Data

[6] The simulation model consists of two parts; the first one is carried out to obtain the MHD solution of the quiet solar wind at r > 30Rs, and the other is performed to trace the temporal evolution of the interplanetary disturbances.

[7] In the first part, the three-dimensional steady MHD solution of the super-Alfvénic solar wind is provided from the MHD tomography analysis of IPS measurement. The original MHD tomography analysis method uses the radial-increment method to solve the MHD solution of the super- Alfvénic solar wind, in order to speed up the process. In this study, the time-dependent MHD simulation code identical to that used in the second part is used in the MHD tomography analysis. In the second part, the CME parameters obtained from the Cone-model are given as the numerical perturbations to the numerical steady super-Alfvénic solar wind, and the evolution of the interplanetary disturbance propagation is simulated.

[8] The time-dependent MHD simulation code used in this study is the same one described by Hayashi [2005], though there are two different points. The first one is that the simulation region starts at 30 solar radii so that the IPS velocity data and the Cone-model CME parameters can be used. The fixed boundary condition is used for this super-Alfvénic inner boundary. The other point is that the specific heat ratio is set 1.46, following the analysis of the Helios data by Totten et al. [1995]. The numerical grids are constructed in the spherical coordinate system with the 144, 64 and 128 grids along the radial (from 30 to 250 solar radii), latitudinal and longitudinal directions, respectively.

[9] Figure 1 shows the maps of the radial component of the magnetic field (Br) and plasma velocity (Vr) of the steady and quiet solar wind. To determine the density and temperature of the quiet solar wind at 30 Rs, we used the relation functions N(Vr) and T(Vr) that are deducted from the Helios data and used in the MHD tomography analysis of IPS data [Hayashi et al., 2003]. The magnetic field map is calculated using the solar photospheric magnetic field data at Wilcox Solar Observatory of Stanford University and the potential-field source-surface model [Schatten et al., 1969]. The latitudinal component of magnetic field and plasma flow, Bθ and Vθ, are assumed zero, and the longitudinal component of plasma flow is set to be (−r sin θΩ), where Ω is the solar rotation rate. The longitudinal component of magnetic field Bϕ is set BrVϕ/Vr so that the magnetic field will be parallel to the plasma in the rotating frame. It would be emphasize that the measurement-based parameters Vr and Br are used to determine the other MHD parameters on the inner boundary sphere.

Figure 1.

Maps of MHD variables at (left) r = 30 and (right) 1 AU. The polarity of the radial component of magnetic field Br are shown by the solid contour lines (outward) and the dashed (toward the Sun). Thick dashed lines in all eight plots show the region where Br = 0, which corresponds to the current sheet. The cross in the left plots denotes the approximate center positions of two numerical pulse perturbations, with the gray circle in Figure 1c showing approximate size of the perturbations.

[10] The parameters of the CME are determined through the Cone-model analysis. Because comparisons of the simulated data with the in-situ measurement is essential to check the ability of this simulation model, it is preferable if the simulated CME event directs the Earth and if the events can be separated from others so that the simulated events can be identified in the nearby-Earth measurement data set. We chose the period of mid April of 2002 in which there are two major halo-CME events that followed two flares of 15 and 17 April 2002 and the associated interplanetary shocks arrived at the Earth on 17 and 19 April, respectively. Table 1 tabulates the CME parameters derived with the Cone-model. The two CMEs propagated to almost same direction, and the speed of the second shock was estimated about 900 km/s, 300 km/s faster than the first event.

Table 1. Summary of Simulated Two CME Events and Cone-Model Parameters
 First EventSecond Event
Cone-Model Parameters at 30 Rs
Time, UT04/15, 10:0004/17, 12:00
Speed, km/s600900
Latitude, degN2N8
Longitude (Carr.), deg150154
Spread angle, deg103120
Associated Flare (AR 9906)
Time, UT04/15, 03:0504/17, 07:46
Disc position, degS15 W16S15 W42
IP at Earth, UT04/17, 11:0004/19, 08:00

[11] While the Cone-model can provide the basic kinematic and geometric parameters of the CME, it does not provide the interior structure. In this study, we assumed the spatial distribution and the temporal profile of the CME plasma variables on 30Rs sphere, in a form;

equation image


equation image


equation image

[12] The trigonometric functions, arctan, sin2 and cos2 are used to smoothly connect the background and disturbance parameters. The subscription c denotes the variables obtained from the Cone-model analysis; Vc is the Cone-model velocity of the CME body, tc is the time for the analyzed CME to reach the 30Rs sphere, δc is the spread angle. The angular arc distance δ is counted from the central direction of CME, θc and ϕc. The subscription b denotes the values of the background solar wind obtained from the IPS tomography analysis. The time ta is the total time for one CME to pass through the 30Rs inner boundary sphere. We assumed it is 30 hours for both two CME events, in order to treat the lack of information about the radial size of CME body in a unified manner. The density is determined with the same profile function but the peak value is assumed to be three times as large as the background state, 3 · Nb. The temperature is assumed unchanged during the perturbation.

3. Simulation Results

[13] Figure 2 demonstrates the temporal evolution of the solar wind responses to the first numerical perturbation. Figures 2a and 2d show the quiet solar wind speed on the equatorial and meridional plane, respectively. Figures 2b and 2e show the flow speed and Figures 2c and 2f do the density in the same format at 50 hours after the first perturbation is given. It is notable that the position of the shock front varied depending on the background ambient solar wind structures, and the density enhancements occurred both at the central part of disturbance and at outer parts encountering the slower ambient wind.

Figure 2.

Propagation of disturbance at 30Rsr ≤ 250Rs. The radial component of plasma flow, Vr, and the normalized density, Nr2, are drawn with the fixed contour interval of 50 km/s and 5 AU2 cm−3. The circles in Figures 2b, 2c, 2e, and 2f are drawn for reference, with the radius corresponding to the position of the shock in the slower ambient wind.

[14] Figure 3 shows the simulated (a) flow speed, (b) temperature, (c) density, and (d) Bx component of magnetic field sampled at the position of the Earth, superposed with the measurement data. We used the hourly averaged measurement data of the OMNI database at NSSDC/NASA and plotted with solid lines (0). The four simulation cases are plotted; (1) the numerical quiet solar wind without any perturbation with dotted lines, (2) the two-CME case with dashed line, (3) the case perturbed by only the second event with dash-dotted lines, and (4) the case perturbed by only the first event with the long dash lines. The moments of the start and peak at the simulated shocks are indicated with H-shaped lines.

Figure 3.

Comparison of the simulated MHD variables sampled at the Earth's position with the nearby-Earth measurement. Plots show the temporal variations of the radial component of flow Vr, the plasma temperature T, the plasma density N, and the magnetic field component in Earth-to-Sun direction Bx, respectively. The vertical lines of H-shaped marks depict the moments the simulated variables start to divert from the pre-shock state and reach the peak value.

[15] Because the two plasma velocity data, the quiet solar wind speed from IPS measurement and the CME velocity with the Cone-model analysis, are used, the agreements of the flow speed and arrival time at the Earth are reasonably obtained. The temperature enhancements are reconstructed as well. On the contrary, the simulated density variations, such as a sudden increase and rapid decrease of the first event and a rather broader profile of the second event, were not well reproduced. These discrepancies are thought due to the lack of the information on the density structures of the CME body.

[16] As shown in Figure 3, the second of the simulated two successive shocks arrived to the Earth a few hours earlier than the single-shock simulation case. Because the second shock encountered the lower-density trailing part of the first shock than the undisturbed quiet solar wind, the deceleration the second shock got was smaller and thus the earlier arrival of the second shock was reasonably obtained. The simulated Alfvén speed, ∼∣equation image∣/equation image, sampled at a tailing part of the first event (r = 90Rs, marked with cross in Figure 2) was about 170 km/s, while that of unperturbed wind was about 110 km/s. Such differences affecting the propagation speed of the interplanetary disturbances can be derived by considering two successive events.

[17] In Figure 3a, the two-peak profile of the flow speed is found at the second shock event. This simulated profile is a result of the superposition of the compression region of the shock and the background speed structure that the shock has overridden. We performed an experimental hydrodynamics simulation with the same CME parameters but uniform background solar wind and obtained the compression region with a flat speed profile that is followed by the sudden increase, peak and decrease at the trailing part. The second event propagated in the pre-shock wind that had a flow speed profile increasing with respect to radius (thus, deceasing with respect to time at the Earth), therefore the superposed speed at the second shock had two peaks. In contrast, the first shock did not have two-peak speed profile. This is probably due to a smaller difference of the speed between the shock body and ambient wind; the first shock had the difference of about 200 km/s, 300 km/s smaller than the second event. Though 200 km/s is comparable to the local Alfvén wave speed, we think this difference in speed was not enough for the compression region to be dominant over the spatial variation of the ambient wind.

4. Conclusion

[18] We performed MHD model simulations of the measurement-based interplanetary disturbances; the numerical perturbation is derived from the Cone-model analysis, and the quiet background solar wind is constructed with the IPS data analysis. The arrival times of the interplanetary disturbances to the Earth were well reproduced, and the temporal profiles reasonably resembled the nearby-Earth measurements. These agreements show that the MHD simulation model using the measurement-based parameters well represents the spatial structure of the real solar wind and simulates the temporal evolution of the interplanetary space. The two-CME events are examined, and the differences of the propagation of the second event in the quiet undisturbed solar wind and the solar wind perturbed by the first event are obtained.

[19] The MHD simulation can be extended outward beyond the orbit of the Earth. Figure 4 shows the density of the simulated two interplanetary disturbances at r ≤ 800Rs. At about 2 AU, the faster second interplanetary shock caught up with the first one and merged, then the merged disturbance collided to the existing spiral of the co-rotating interaction regions (CIR). The interaction between the interplanetary shocks and CIRs has been well studied [e.g., Odstrcil and Pizzo, 1999]. This presented model would have an ability to simulate such complex interplanetary collisions in the measurement-based situation.

Figure 4.

Normalized density of simulated disturbance on the solar equatorial plane at 30Rsr ≤ 850Rs.

[20] In this simulation, the kinetic energy v2 dominates over the magnetic B2/ϱ, gravitational GMs/r and thermal energy 2kBT/(γ − 1). This simulated situation helps to obtain the agreements, or resemblances of the speed at the Earth, because the direct input were the speed data obtained from the Cone-model and the IPS analysis. In contrast, as seen in Figures 3c and 3d, the density and the magnetic field structures of the interplanetary shocks were not well reproduced because the input data lacked information on them. To improve the simulation model, it might be preferable if these parameters will be replaced with, for example, the adequate description model of flux loop inside the CME. We expect such information will be available, for example, by considering the plasma confinement in the magnetic field and the three-dimensional plasma density structure reconstructed from the multi-site STEREO mission. The simulation studies that include the models of the initiation of CME and the solar wind heating and acceleration process must be one orthodox approach to give the reasonable three-dimensional model structure of the magnetic loop and the plasma inside the interplanetary shocks and will improve the numerical data input to the presented simulation study. However, many mechanisms of these phenomena are complex and still unsolved. Because the data used in this study represent consequences of these unsolved processes, we think our approach presented in this work can be a framework to better predict and reproduce the interplanetary conditions.


[21] The authors used the data set of the SOHO/LASCO C3 image data and the IPS data of Nagoya University, Japan. The SOHO is an international project between NASA and ESA. We also used the OMNI nearby-Earth measurement data set distributed at NASA/NSSDC. This work is supported in part by the NASA/MDI project under grant NAS5-13261, the NSF/CISM project under grant ATM-0120950, the NASA grant NNGO4B84G, and the DoD/MURI project under grants F005001 and SA3206.