### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Observation of the 6–12 January 1997 Halo-CME
- 3. Background Solar Wind
- 4. Numerical Simulation of CMEs Propagation
- 5. Results and Discussion
- 6. Conclusion
- Acknowledgments
- References

[1] A three-dimensional time-dependent, numerical magnetohydrodynamic (MHD) model is used to investigate the propagation of coronal mass ejections (CMEs) in the nonhomogenous background solar wind flow. On the basis of the observations of the solar magnetic field and K-coronal brightness, the self-consistent structure on the source surface of 2.5 Rs is established with the help of MHD equations. Using the self-consistent source surface structures as initial-boundary conditions, we develop a three-dimensional MHD regional combination numerical model code to obtain the background solar wind from the source surface of 2.5 Rs to the Earth’s orbit (215 Rs) and beyond. This model considers solar rotation and volumetric heating. Time-dependent variations of the pressure and velocity configured from a CME model at the inner boundary are applied to generate transient structures. The dynamical interaction of a CME with the background solar wind flow between 2.5 and 215 Rs (1 AU) is then investigated. We have chosen the well-defined halo-CME event of 6–12 January 1997 as a test case. Because detailed observations of this disturbance at 1 AU (by WIND spacecraft) are available, this event gives us an excellent opportunity to verify our MHD methodology and to learn about the physical processes of the Sun-Earth connection. In this study, we find that this three-dimensional MHD model, with the self-consistent structures on the source surface as input, provides a relatively satisfactory comparison with the WIND spacecraft observations.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Observation of the 6–12 January 1997 Halo-CME
- 3. Background Solar Wind
- 4. Numerical Simulation of CMEs Propagation
- 5. Results and Discussion
- 6. Conclusion
- Acknowledgments
- References

[2] Space weather research is of growing importance to the scientific community and can affect human activities. Interplanetary coronal mass ejections (ICMEs, including their shocks) and vast structures of plasma and magnetic fields that are expelled from the Sun outward through the heliosphere are now known to be a key causal link between solar eruptions and major interplanetary and geomagnetic disturbances [*Dryer*, 1994]. In order to realistically reflect the properties of three-dimensional CME propagation, the numerical research of three-dimensional background solar wind has become one of key problems that have to be solved for modeling space weather events.

[3] CMEs and their interplanetary consequences (ICMEs) represent different aspects of the same phenomenon responsible for large geomagnetic storms [*Gosling*, 1990]. Because of the great complexity, each aspect has typically been investigated separately. This approach is useful for revealing the basic underlying physics; however, a complete picture requires a comprehensive model of all of the processes considered together. Successful merging of two-dimensional and three-dimensional magnetohydrodynamic (MHD) coronal and heliospheric models has been reviewed and performed by *Dryer* [1974, 1975, 1982, 1994], *Dryer* [1998], *Usmanov and Dryer* [1995], *Wu et al.* [1997, 1999], *Odstrcil et al.* [2002a, 2004a], and *Manchester et al.* [2005]. The coronal simulation conducted by *Odstrcil et al.* [2002a] started from an initial potential magnetic field and spherically symmetric Parker solar wind. The plasma density and the temperature at the boundary were given as constants, and the radial velocity was determined at each time step by solving the gas characteristic equations. In the work by *Odstrcil et al.* [2002b], the coronal model, whose domain extends from the photosphere up to 30 Rs, was based on the three-dimensional resistive MHD equations that were solved by a semi-implicit finite difference scheme using staggered values, while the heliospheric model, whose domain extends from 30 to 275 Rs, was based on the three-dimensional ideal MHD equations that were solved by an explicit finite difference Total Variation Diminishing/Lax-Friedrichs (TVD/LF) scheme using cell-centered values. The output from the coronal model consisted of a temporal sequence of MHD flow parameters, which were used as a boundary condition for the heliospheric model. An alternative procedure that included a three-dimensional kinematic approach for shock arrival prediction procedures was described by *Fry et al.* [2001, 2003].

[4] *Usmanov et al.* [2000] also used a global axisymmetric MHD solar wind model with WKB Alfvén waves, which were simulated by combining a time relaxation numerical technique in the two-dimensional solar corona region (1–22 Rs) with a marching-along-radius method in the outer region (22 Rs-10 AU). In the coronal region, they assumed the initial state of the magnetic field as a dipole, and the hydrodynamic variables were given by a Parker-type solution of the one-dimensional HD equations [*Parker*, 1963]. Once a steady state solution in the inner region was obtained, a slice of the solution at the interface between the two regions interface (22 Rs) was used as the inner boundary condition to start integration throughout the outer region [*Usmanov*, 1993; *Usmanov and Dryer*, 1995; *Usmanov et al.*, 2000]. Their global steady state axisymmetric MHD model successfully reproduced quantitatively the observations made by Ulysses during its first fast latitude traversal in 1994–1995 [*Usmanov and Dryer*, 1995; *Usmanov et al.*, 2000].

[5] The large-scale structure of solar wind observed by Ulysses near solar minimum was also simulated by*Feng et al.* [2005] by using the three-dimensional numerical MHD model. Their model combined the TVD Lax-Friedrich scheme and MacCormack II scheme and divided the computational domain into two regions as follows: one from 1 to 22 Rs and the other from 18 Rs to 1 AU. On the basis of the observations of the solar photospheric magnetic field and an addition of the volumetric heating [*Suess et al.*, 1996; *Wang et al.*, 1998] to MHD equations, the large-scale bimodal solar wind (i.e., fast and slow wind) structure mentioned above was reproduced by using the three-dimensional MHD model, and their numerical results were roughly consistent with Ulysses’ observations. Their simulation showed that the initial magnetic field topology and the addition of volume heating could govern the bimodal structure of solar wind observed by Ulysses and also demonstrated that the three-dimensional MHD numerical model used by them was efficient in modeling the large-scale solar wind structure.

[6] *Riley et al.* [2001; see also *Linker et al.*, 1999] proposed an empirically driven global MHD model of the solar corona and inner heliosphere. They used the output of the coronal solution directly to provide the inner boundary condition of the heliospheric model. In modeling the solar corona they specified at the lower boundary the radial component of the magnetic field *B*_{r} based on the observed line-of-sight measurements of the photospheric magnetic field. Uniform characteristic values were used for the plasma density and temperature. Initial estimates of the field and plasma parameters were found from a potential field model and a Parker transonic solar wind solution [*Parker*, 1963], respectively. Their results showed that the simulations reproduced the overall large-scale features of the observations during the “whole Sun month” (August/September 1996), although the specified lower boundary conditions were very approximate.

[7] The self-consistent, time-dependent initial and boundary conditions with solar rotation, on the basis of observation results, will play a very important role in three-dimensional background solar wind numerical model, and the work devoted to this aspect is still at its initial stage. In this paper, on the basis of the observation of the solar magnetic field and K-coronal brightness, the self-consistent structures on the source surface are established with the help of MHD equations at 2.5 Rs according to the global distribution of coronal mass output’s flux *F*_{m} (density *ρ* × speed *v*) by *Wei et al.* [2003]. By using the self-consistent source surface structures as initial and boundary conditions, we have successfully developed a three-dimensional magnetohydrodynamic (MHD) regional combination numerical model [*Feng et al.*, 2005] of background solar wind, from the source surface of 2.5 Rs to near the Earth’s orbit (215 Rs) and beyond. This model includes solar rotation and volumetric heating. Once a steady state solar wind is produced, we use a CME model as input into the inner boundary of 2.5 Rs. The dynamical interaction of a CME with the background solar wind flow between 2.5 and 215 Rs (1 AU) is investigated. Observations of the 6–12 January 1997 Sun-Earth connection event are used as a test for our numerical simulation. A brief description of the observations is given in section 2. The three-dimensional MHD regional combination numerical model of background solar wind, which includes self-consistent initial and boundary conditions, is described in section 3. The three-dimensional numerical simulation of CMEs is given in section 4. Numerical results and comparisons with the observations are presented in section 5. Finally, the concluding remarks are given in section 6.

### 2. Observation of the 6–12 January 1997 Halo-CME

- Top of page
- Abstract
- 1. Introduction
- 2. Observation of the 6–12 January 1997 Halo-CME
- 3. Background Solar Wind
- 4. Numerical Simulation of CMEs Propagation
- 5. Results and Discussion
- 6. Conclusion
- Acknowledgments
- References

[8] Many CMEs observed near the solar limb maintain angular widths that are nearly constant as a function of height [*Webb et al.*, 1997] and propagate almost radially beyond the first few solar radii [*Plunkett et al.*, 1997]. On the basis of these properties of limb CMEs, the empirical cone descriptive assumption for halo-CMEs was developed by *Zhao et al.* [2002] with free parameters that characterize the angular width of the cone and the orientation of the central axis of the cone. The free parameters can be determined by matching the cross section of the cone at a specified radial distance projected on the sky plane with the observed bright ring of the halo-CME at a specified time. The cone model was also used in the numerical simulation by *Odstrcil et al.* [2004b, 2005]. The reader is reminded that the approach of *Zhao et al.* [2002] is an empirical one, whereas the present model is a physics-based three-dimensional MHD one that starts “cone-like” but expands because of the anisotropic wave dynamics.

[10] The CME was observed first in the C2 coronagraph on 6 January 1997 at 17:34 UT and later in the C3 coronagraph before 19:50 UT [*Webb et al.*, 1998] and appeared as a partial arc moving at ∼20°S and ∼3°W of the central meridian [*Michalek et al.*, 2003]. These observations were followed on 10 and 11 January 1997 by a well-observed magnetic cloud that passed the WIND spacecraft located in the solar wind upstream of Earth [*Burlaga et al.*, 1998]. According to *Webb et al.* [1998], it was halo-like and the traveltime to Earth was about 85 hours which was right for a CME with a typical speed of 450 km/s. It had a large angular span bigger than 140°, greatly exceeding those of most CMEs. Measurements of the expansion speed of the front by a height/time diagram yield a speed of about 100–150 km/s [*Wu et al.*, 2002]. As reported by *Wu et al.* [1999] the source of this CME event is related to the disappearance of a filament located at ∼20°S and ∼4°W of the central meridian according to ground-based *H*-*α* observation.

[11] The central axis of the CME model pointed to 20°S, 03°W while its half angular width is about 52.5° [*Michalek et al.*, 2003]. We assume that the leading edge of the CME reached a radial height of 2.5 Rs with a speed of 160 km/s. This speed is almost consistent with the projection-corrected speed by using SOHO observations and the formula derived by *Hundhausen et al.* [1994].

### 4. Numerical Simulation of CMEs Propagation

- Top of page
- Abstract
- 1. Introduction
- 2. Observation of the 6–12 January 1997 Halo-CME
- 3. Background Solar Wind
- 4. Numerical Simulation of CMEs Propagation
- 5. Results and Discussion
- 6. Conclusion
- Acknowledgments
- References

[31] The CME is introduced near the inner boundary of 2.5 Rs at the location where the disappearance of a filament occurred (i.e., ∼20°S and 3°W) as a time-dependent pulse. This pulse consists of pressure and momentum pulses to simulate the effects of the disappearance of a filament, as done for mimicking flare input by *Han et al.* [1988], *Smith and Dryer* [1990], *Odstrcil et al.* [1996a, 1996b], *Odstrcil and Pizzo* [1999], and *Groth et al.* [2000] in the two-dimensional and three-dimensional MHD context. Up to now, the approximate solar observations to use for “mimicking” solar flare/filament and CME imitation are challenging problems.

[32] Once a steady state solar wind is obtained, we input a filament disappearance-induced CME into the inner boundary. We model a CME as follows:

where

[33] Here *ξ* and *ξ*_{0} are, respectively, the angles relative to the central axis of the CME and the initial angular width radius of the CME (here *ξ*_{0} = 52.5°). The axis of the initial simulated CME is at 20°S, 03°W (i.e., *θ* = −20°, *ϕ* = 183°) to conform to the location of the filament disappearance (see section 2). Also, *t* = 0 hour in the simulation is taken to be at 17:34 UT on 6 January 1997, when the CME is first observed in the C2 coronagraph of SOHO/LASCO. *τ*_{1} and *τ*_{2} are, respectively, the ramp-up and ramp-down times (linear transition between the background and constant perturbation values), and *τ*_{m} is the duration of the perturbation at maximum value. This form of input-perturbation enhances a spherical wedge of solar surface since it has no latitudinal dependence. *V*_{max}, *ρ*_{max}, and *T*_{max} represent, respectively, the amplitude of the perturbation of the radial velocity, density, and temperature.

[34] This perturbation will be started by the following relation:

where *v*_{r0}, *ρ*_{0}, and *T*_{0} are the background values of the radial velocity, density, and temperature.

[35] In our simulation of the January 1997 event, we use the following values: perturbation ramp duration *τ*_{1} = *τ*_{2} = 0.5 hour; the perturbation duration at maximum value *τ*_{m} = 1 hour and maximum values of the radial velocity, density, and temperature are *V*_{max} = 160 km/s, *ρ*_{max} = 9 × 10^{7} cm^{−3}, *T*_{max} = 1.5 × 10^{6} K.

### 5. Results and Discussion

- Top of page
- Abstract
- 1. Introduction
- 2. Observation of the 6–12 January 1997 Halo-CME
- 3. Background Solar Wind
- 4. Numerical Simulation of CMEs Propagation
- 5. Results and Discussion
- 6. Conclusion
- Acknowledgments
- References

[36] Figures 8a and 8b show the positions of CME fronts at *ϕ* = 180° and at *θ* = 0°, *θ* = 20°, and *θ* = 45° in the corona and heliosphere. From this figure we can clearly see the evolution of the CME propagation at three different latitudes of the Northern Hemisphere. In particular, they show that, at the equator or almost along the current sheet, the CME propagates faster at the equator than at other locations. This behavior is consistent with the observational result that the transient disturbances caused by solar activities would deflect toward the heliospheric current sheet as they travel to the Earth [*Wei and Dryer*, 1991; *Feng and Zhao*, 2006]. During the period of this event, the heliospheric current sheet lies almost on the solar equator. Note that the characteristics of the CME propagation show nonuniform acceleration and deceleration.

[37] The relative density ((*ρ* − *ρ*_{0})/*ρ*_{0}), where *ρ* is the total density and *ρ*_{0} the density of the background wind, is shown in Figure 9 at six consecutive times (pairs of plots, Figures 9a–9f). Each pair shows the projection in the meridional plane (left panel) and equatorial plane (right panel). The radial scales on Figures 9 and 9b are from 2.5 to 22 Rs and from 2.5 to 215 Rs in Figures 9c to 9f. The meridional directions are *ϕ* = 180° in the left panels of Figures 9a, 9b, and 9c, *ϕ* = 150° in left panel of Figure 9d, and *ϕ* = 135° in the left panels of Figures 9e and 9f.

[38] Figure 10 shows the evolution of the velocity-distance profile in the direction *θ* = 0° and the meridional directions selected for each panel in Figure 9. Figures 9a–9f and 10a–10f separately show the CME interaction with the background solar wind flow at 2 hours, 5 hours, 20 hours, 40 hours, 60 hours, and 80 hours after its launch from the inner boundary of 2.5 Rs. Note that the density maxima of Figure 9 and the slope changes in all trajectories of Figure 10 are consistent with the location of the ICME’s shock front in Figure 8. Note also that the sharp shock (Figure 9a) decays rapidly with both time and heliographic longitudinal position.

[39] Note that the CME was centered at *θ* = −20°, *ϕ* = 183°. We notice from Figure 9, that the initially elliptical ejecta becomes circular and then develops into a “pancake” structure both in the meridional plane and equatorial plane. This structural development is a consequence of the combined effects of (1) kinematic expansion, as the ejecta moves into an ever larger spherical volume, (2) dynamic evolution, as the ejecta plows into slower ambient solar wind ahead, and (3) radial flow collision, lateral material expansion, and interactions with the background velocity and density structures [*Odstrcil et al.*, 1996a, 1996b; *Odstrcil and Pizzo*, 1999; *Dryer et al.*, 2001, 2004; *Riley et al.*, 2004].

[40] From Figure 10, we can see how ICME propagation influences the bulk velocity. At 2 hours, influenced by the CME which was introduced near the inner boundary of 2.5 Rs as a time-dependent pulse, the plasma velocity at ∼6 Rs sharply increased to ∼500 km/s, which is significantly greater than the background solar wind speed at this location (see Figure 5). After 5 hours, when the ICME has reached ∼17 Rs, the bulk speed is ∼550 km/s, while the radial background solar wind speed at this location is ∼380 km/s. Gradually, through these interactions, the bulk velocity will finally return to its background speed of ∼550 km/s shown in Figures 10a and 10b. At 20, 40, 60, and 80 hours, as the solar wind speed increases while the influence of the ICME decays, the slope changes in these curves from Figures 10c to 10f become less sharp. We can still find the peak of the ICME, within our computational domain, in these three panels, ∼50, ∼90, and ∼130 Rs at 20, 40, and 60 hours, respectively; the ICME location is much more clearly seen in the density plots of Figure 9. At 80 hours, the CME front has propagated out beyond the Earth’s orbit, and the bulk velocity increases to ∼640 km/s at this location.

[41] Figure 11 shows the comparison of the computed plasma and field parameters at 215 Rs in Figure 11b with the observed magnetic cloud of January 1997 shown in Figure 11a. This figure clearly indicates a qualitative resemblance (magnetic field maximum of |*B*|, *B*_{x}, *B*_{y}, *B*_{z}, field rotation, low temperature, and increasing |*B*|, *B*_{x}, *B*_{y}, *B*_{z}, density, velocity). One of the reasons why quantitative agreement is not expected is that the present model, like many others already mentioned, is only a single-fluid model. More importantly, there exist other two extremely important and still unsolved reasons as pointed out by *Dryer* [1998] and now recognized by many other modelers [*Fry et al.*, 2001; *Odstrcil et al.*, 2004a, 2004b]. These two reasons are as follows: (1) uncertainty of the initial realistic solar wind and IMF background conditions and (2) uncertainty of the appropriate solar observations to use for “mimicking” solar flare filament and CME initiation input pulse conditions. In the ambient pre-CME state, the simulated velocity is ∼550 km/s shown in Figures 7c and 10 and, at the ICME maximum, it is ∼650 km/s shown in Figure 11. In fact, these values are a little higher than the observation. The reason for this may be from our volumetric heating. The heating process is unclear up to now. The choice of such heating may give some favorable results but not all. It is usually believed [*Wu et al.*, 2006] that IP shock travels faster in fast solar wind, which may be another plausible reason for our high-speed ICME. To some extent, our establishment of using more observational data such as magnetic fields and the density by constraining the model is to try to avoid the uncertainty of the initial realistic solar wind. But, the approximate solar observations to use for “mimicking” solar flare/filament and CME imitation are challenging problems. It can be believed that more solar and interplanetary observations will clarify these uncertainties.

[42] By examining the computed total, *x* coordinate, *y* coordinate, *z* coordinate magnetic field profile, density profile, temperature profile, and velocity profile results given in Figure 11b we notice that the fast-mode shock arrived at 1 AU and ∼82 hours after the initiation of the CME, since we use 17:34 UT on 6 January 1997 as the onset time (vertical dotted line in Figure 11a) (see section 2). These computed results are quite in accord with the interplanetary shock observed by the WIND spacecraft located in the solar wind upstream of Earth at 01:04 UT on 10 January 1997 (vertical dashed line in Figure 11a) and also with the magnetic cloud that passed the WIND spacecraft at 04:00 UT on 10 January 1997 (vertical solid line in Figure 11a) [*Cane and Richardson*, 2003]. We believe that the lack of a sharp shock jump in the simulated physical parameters is a consequence of the two reasons mentioned above. From the computed *B*_{z} field shown in Figure 11b, we find that the field turns southward at ∼69 hours and then northward at ∼78 hours. This magnetic field south-north rotations are mainly due to passing through the helical field of the CME mentioned by *Wu et al.* [1999]. By examining simultaneously the computed density, temperature, and velocity profiles shown in Figure 11b, we can see that the largest density enhancement (in the first part of day 11) can be identified with the plasma compressed in the helmet dome and the additional plasma swept up by the system in the undisturbed corona during the initial CME propagation. This plasma is hot, as seen in the temperature profile (Figure 11b), because this represents the shocked, compressed plasma. These results is also in agreement with those of the asymmetric (2.5D) MHD model given by *Wu et al.* [1999]. We again stress again that our one-fluid (proton) model can not account for the high temperature in a magnetic cloud and the anticorrelation between the electron temperature and density. The fact that our results (neglecting an initial flux rope configuration at the Sun) appear to be in accord with some of the results given by *Wu et al.* [1999], who used an initial flux rope to simulate CME initiation processes due to the filament eruption for this 6–11 January 1997 simulation exercise. The difference and similarity between the present study and the work of *Wu et al.* [1999] require further investigation. For example, it is possible that the IMF can move in a variety of ways behind a shock wave as demonstrated in two dimensions by *Dryer et al.* [1984, p. 205], via the classical circular IMF hodogram, and in three dimensions by *Wu et al.* [1996]. One must, therefore, question the need for extensive considerations of flux ropes as a major part of most ICMEs. In fact, it has been demonstrated [*Richardson and Cane*, 2005] that only 15% of all ICMEs intercepted at Earth have the features of a flux rope (magnetic cloud).

### 6. Conclusion

- Top of page
- Abstract
- 1. Introduction
- 2. Observation of the 6–12 January 1997 Halo-CME
- 3. Background Solar Wind
- 4. Numerical Simulation of CMEs Propagation
- 5. Results and Discussion
- 6. Conclusion
- Acknowledgments
- References

[43] We have used a three-dimensional time-dependent, numerical MHD model based on a code by *Feng et al.* [2005] to investigate large-scale background solar wind structures and the propagation of a specific ICME and its shock wave in a nonuniform background solar wind flow derived from observed magnetic field and density at the source surface.

[44] To establish the self-consistent structures on the source surface of 2.5 Rs for background solar wind, we have used the observational data of the solar magnetic field, K-coronal brightness (density) (Figure 2), and the first principle of MHD. By using the self-consistent source surface structures as initial and boundary conditions, we have successfully developed a three-dimensional MHD regional combination numerical model of the background solar wind whose domain extends from source surface of 2.5 Rs to near the Earth’s orbit (215 Rs) with consideration of solar rotation and volumetric heating. The three-dimensional MHD equations are solved by combining a time relaxation numerical technique in the corona with a marching-along-radius method in the heliosphere as used by *Feng et al.* [2005]. The ratio of specific heats is given as *γ* = 1.05 at the coronal model and *γ* = 1.2 at the heliospheric model. Our numerical results of background solar wind (Figures 3, 4, 5, 6, and 7) show that (1) we have reproduced a typical Archimedes’ spiral lines of magnetic field topology in the equatorial plane by including the solar rotation, (2) the configurations of both corona and heliosphere consist of a dense and slow flow near the current sheet (the range of latitude is about ±25°), as well as high-speed wind in high latitude, and (3) the absolute value of the radial magnetic field remains almost constant outside of the current sheet, independent of latitude, which is consistent with Ulysses observations.

[45] We then investigated the dynamical interaction of a CME with the background solar wind flow between 2.5 and 215 Rs. The CME is introduced at the inner boundary of 2.5 Rs as a time-dependent pulse to mimic the effects of a filament eruption. We chose the well-defined halo-CME event of 6–12 January 1997 for our first test because of all the data available from the SOHO/LASCO and WIND spacecraft. The numerical results of the CME propagation are shown in Figures 8, 9 and 10. The density peaks of Figure 9 and the slope changes in all curves of Figure 10 are consistent with the location of the CME front in Figure 8. Figures 8, 9, and 10 also show that, (1) at the equator, the CME propagates faster than that at other location, (2) the initially elliptical ejecta becomes circular and then develops into a “pancake” structure, (3) the CME propagation is influenced by the bulk velocity.

[46] When the ejecta reached 1 AU, its physical parameters (Figure 11) resembled qualitatively the observations of the magnetic cloud recorded by the WIND spacecraft [*Burlaga et al.*, 1998]. This demonstrates that a CME, initiated by CME model, may evolve into an interplanetary ejecta or magnetic cloud. However, the fact that our model did not incorporate a modeled flux rope configuration (as was done by *Wu et al.* [1999]) suggests, as discussed above, that it may not be necessary to use such assumptions in three-dimensional MHD simulations to explain the flux rope-type hodogram discussed by *Burlaga et al.* [1998, and references therein]. In front of the ejecta, the density enhancement exhibited the characteristics of the observed CME to some degree; however, further studies should consider other forms of the input pulse to mimic the CME as well as the form of nonuniform background solar wind in three dimensions.

[47] In summary, in this study, we find that this three-dimensional MHD model, with the self-consistent structures on the source surface as input, provides a relatively satisfactory comparison with the observations. While this model still needs improvement, there exist many other factors that should be studied, such as, heating and acceleration mechanism of solar wind and better understanding of CME initiation.