Annales Geophysicae (2004) 22: 4273–4290 SRef-ID: 1432-0576/ag/2004-22-4273 © European Geosciences Union 2004
Annales Geophysicae
Plasma depletion layer: its dependence on solar wind conditions and the Earth dipole tilt Y. L. Wang1 , J. Raeder2 , and C.T. Russell3 1 Los
Alamos National Laboratory, Los Alamos, USA of New Hampshire, Durham, USA 3 University of California, Los Angeles, USA 2 University
Received: 26 November 2003 – Revised: 25 September 2004 – Accepted: 3 October 2004 – Published: 22 December 2004
Abstract. The plasma depletion layer (PDL) is a layer on the sunward side of the magnetopause with lower plasma density and higher magnetic field compared to their corresponding upstream magnetosheath values. It is believed that the PDL is controlled jointly by conditions in the solar wind plasma and the interplanetary magnetic field (IMF). In this study, we extend our former model PDL studies by systematically investigating the dependence of the PDL and the slow mode front on solar wind conditions using global MHD simulations. We first point out the difficulties for the depletion factor method and the plasma β method for defining the outer boundary of the plasma depletion layer. We propose to use the N/B ratio to define the PDL outer boundary, which can give the best description of flux tube depletion. We find a strong dependence of the magnetosheath environment on the solar wind magnetosonic Mach number. A difference between the stagnation point and the magnetopause derived from the open-closed magnetic field boundary is found. We also find a strong and complex dependence of the PDL and the slow mode front on the IMF Bz . A density structure right inside the subsolar magnetopause for higher IMF Bz might be responsible for some of this dependence. Both the IMF tilt and clock angles are found to have little influence on the magnetosheath and the PDL structures. However, the IMF geometry has a much stronger influence on the slow mode fronts in the magnetosheath. Finally, the Earth dipole tilt is found to play a minor role for the magnetosheath geometry and the PDL along the Sun-Earth line. A complex slow mode front geometry is found for cases with different Earth dipole tilts. Comparisons between our results with those from some former studies are conducted, and consistencies and inconsistencies are found. Key words. Magnetospheric physics (magnetosheath, solar wind-magnetosphere interactions) – Space plasma physics (numerical simulation studies)
Correspondence to: Y. L. Wang (
[email protected])
1
Introduction
The plasma depletion layer (PDL) is a layer on the sunward side of the magnetopause with lower plasma density and higher magnetic field compared to their corresponding upstream magnetosheath values. As an important layer between the solar wind and the Earth’s magnetosphere, the PDL has been found in some former studies to be controlled by the conditions in the solar wind (e.g. Farrugia et al., 1997; Siscoe et al., 2002; Wang et al., 2003, 2004b). In this paper we present a systematic study of the properties of the PDL for different solar wind conditions using global MHD simulations. Denton and Lyon (2000) have studied the effects of pressure anisotropy on the magnetosheath structure using a 2-D MHD model with anisotropic pressure and a flux surface magnetopause. They found that the exact form of the parallel pressure gradient force may not be crucial for the global dynamics of the PDL, except that the anisotropy leads to a larger bow shock standoff distance compared to the isotropic case. Their results also imply that the effects of pressure anisotropy may be even less for a 3-D system than for a 2-D system. Thus, our use of the isotropic MHD code appears to be appropriate. Farrugia et al. (1997) studied three examples of lowlatitude ISEE 2 passes through the dayside magnetosheath near noon on 3 December 1979, 5 October 1979, and 11 November 1979, and they found that the properties of the plasma depletion layer depend on the solar wind Alfv´en Mach number. Siscoe et al. (2002) summarized four important MHD effects in the magnetopause boundary layer and the magnetosheath that cannot be produced by gasdynamic models, including the PDL. They found a clear dependence of the PDL thickness on the IMF clock angle based on their global model results. Wang et al. (2003) compared their global MHD model results, using IMP 8 and ACE solar wind plasma and IMF observations as a driver, with Wind in-situ observations for two PDL events on 12 January 1996 and 1 January 1999. They found good visual consistency between PDL observations and their model results. Meanwhile, the
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Table 1. Model input parameters for different model runs in this PDL dependence study. Model input parameters (in GSE) Vx (km/s) Vy (km/s) Vz (km/s) Bx (nT) By (nT) Bz (nT) N (cm−3 ) Tp =Te (eV) IMF tilt angle (◦ ) IMF clock angle (◦ ) Earth dipole tilt angle (◦ )
Values −450, −600, −750 0 0 0, 7, 14 0 2, 7, 14, 21 6 10 0, 45, 63 0, 15, 30, 45 0, 15, 30
average model departures, which are defined as the average separations between model results and observations, were found to be generally smaller than the standard deviations of observations in their study. They concluded that an MHD description can produce the plasma depletion features in the magnetosheath. Furthermore, they showed that the PDL is stable for stable solar wind conditions and small magnetosheath variations observed by single spacecraft were temporal, rather than spatial, variations during these two events. Wang et al. (2004b) went further to address the role of the slow mode waves for the formation of the PDL, and they confirmed the existence of the slow mode front in the magnetosheath for certain, but not all, stable solar wind conditions. Their results showed a clear dependence of the slow mode front on the IMF Bz . Although they concluded that the slow mode waves have little effect on the magnetosheath flow and field structures, including the plasma depletion layer, they did not exclude the possibility of a much larger role of such waves for the formation of the PDL for more turbulent magnetosheath conditions. Until now, however, still no systematic study has been conducted for the dependence of the PDL on various solar wind parameters. Experimentally this is very difficult because of the scarcity of observations. This is mostly because satellites that have their apogee or perigee near the magnetopause distance, for example, Geotail, do not traverse the PDL, but rather skim along the magnetopause. From such measurements it is generally not even possible to determine if one has observed the PDL. On the other hand, satellites that traverse the magnetosheath rapidly provide data that allow one to identify the PDL. However, such orbits, for example, those of Wind, provide magnetosheath traverses at a much lower rate. Further, Wind’s orbit is controlled and it penetrates the magnetosheath far from the subsolar point where the most important physics of the PDL occurs. Together with the requirement of concurrent observations of stable solar wind conditions, northward IMF preferred, leads to very few PDL observations.
An alternate approach is to use models to investigate and document the dependence of the PDL on solar wind conditions. Such an approach would be similar to the one taken by Spreiter et al. (1966) for the basic properties of the magnetosheath. Spreiter’s model has proven extremely useful for many subsequent studies. However, his model is gasdynamic and thus does not include the plasma depletion layer. It is an approximation to the real magnetosheath environment because of its lack of the magnetic force and the use of a rigid magnetopause. Contemporary demands require a more thorough verification and understanding of the results from Spreiter’s model. With the introduction of MHD and a self-consistent model, significantly more free parameters enter the problem compared to a study based on a gasdynamic model. At a minimum, the IMF strength and orientation need to be considered in addition to the gasdynamic parameters. In this paper, we first introduce the parameters for the model runs that we have conducted for this study. Then we discuss the definition of the PDL outer boundary, which itself is a challenge for the PDL study. After that, we show the dependence of the PDL on the solar wind magnetosonic Mach number, the IMF Bz , and the IMF tilt and clock angles. Because of the special role of the slow mode waves in both observational and theoretical studies of the PDL formation (Zwan and Wolf, 1976; Song et al., 1990a, 1992; Southwood and Kivelson, 1992, 1995), we also address the dependence of the slow mode front on solar wind conditions. The results can help us better understand the wave environment in the magnetosheath, especially during turbulent solar wind conditions when the slow mode waves could play a much more important role to control the flow and field in the magnetosheath. Since the Earth dipole tilt also affects the coupling between the Earth’s magnetosphere and the solar wind, we also address the dependence of the PDL and the slow mode front on it, which has seldom been done before. Finally, we summarize the results in this study.
2
Model runs
The Raeder global geospace model is used in this study. This model solves resistive MHD equations with isotropic pressure in a large, three-dimensional volume surrounding the Earth, such that the entire interaction region between the solar wind and the magnetosphere, as well as the ionosphere, is included (Raeder, 2003). Specifically, the simulation domain comprises the bow shock, the magnetopause, and the magnetotail up to several hundred RE from the Earth. The NOAA Coupled Thermosphere Ionosphere Model (CTIM) is included to handle the coupling between the magnetosphere and the ionosphere (Fuller-Rowell et al., 1996; Raeder et al., 2001b). In this study, however, we only use uniform ionosphere conductivity of 5 Siemens because the ionosphere is likely to have little influence on the magnetosheath flows. In order to study the dependence of the PDL on solar wind conditions and the Earth dipole tilt, we make a series of global model runs with a solar wind density of N=6 cm−3 ,
Y. L. Wang et al.: Plasma depletion layer: dependence on solar wind conditions and Earth dipole tilt
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Fig. 1. The utility of the N/B ratio to mark the outer boundary of the plasma depletion layer. Shown here are the global model results with the baseline solar wind conditions as input. The left panels show the results in the GSE z=0 plane, and the right panels show the results in the GSE y=0 plane. The N/B values are shown as the background on the top panels, and the plasma density values are shown as the background on the bottom panels. The open-closed magnetic field boundary is shown as a red zigzag curve in each of the panels. The flow lines are shown as white smooth curves in the left panels, and magnetic field lines are shown as white smooth curves in the right panels.
an interplanetary magnetic field B=(0, 0, 7) nT, a solar wind velocity V =(−450, 0, 0) km/s, and a solar wind temperature of Tp =Te =10 eV as the baseline solar wind conditions. The input parameters for the model runs in this study are shown in Table 1. Those values in Table 1 that have only a single number are not varied in the parameter tests. In each parameter test, the global geospace model is run for three hours in physical time, which is sufficient for the model to overcome its start-up effects. The results shown in this paper are obtained at the final time of each run, which reflect stable subsolar magnetopause and magnetosheath configurations.
3 The definition of the PDL boundary The plasma depletion layer is not a very well-defined structure in the magnetosheath. Although it is more or less sharply bounded by the magnetopause on the downstream side, it usually has no sharp boundary on the upstream side but a rather gradual change in the magnetic field magnitude and the plasma density. Defining the upstream boundary is therefore difficult and any method must be to some extent arbitrary. Currently, there are two most commonly used methods to define the PDL outer boundary: the depletion factor method and the plasma β method. In the depletion factor method, the depletion factor, λ, is defined as the ratio between the plasma density just after the bow shock and that on the mag-
netopause. This method was first introduced by Zwan and Wolf (1976) and it has been used in some other PDL studies (e.g. Siscoe et al., 2002; Song and Russell, 2002). Zwan and Wolf (1976) found λ to be 3–4 at the stagnation point and they defined the thickness of the depletion layer to be the distance from the stagnation point to the half post-bow shock density point (λ=2). The PDLs with λ larger than 2 have been observed (e.g. Crooker et al., 1979; Paschmann et al., 1993; Phan et al., 1994; Wang et al., 2003). However, most numerical model studies obtained smaller λ values (e.g. Wu, 1992; Lyon, 1994). Siscoe et al. (2002) obtained a λ of ∼10, which is not only much higher than most other numerical model results, but also much larger than the usually observed λ values. Later in this paper, we show that λ is controlled by solar wind conditions. The plasma β method has also been used by some authors (e.g. Farrugia et al., 1997) to define the PDL outer boundary. The plasma β is defined as the ratio between the plasma pressure and the magnetic pressure, which reveals the relative contribution of the plasma and magnetic field in controlling plasma motion. When β1, plasma is more important. Usually from the bow shock to the magnetopause, the β value decreases and the magnetic field is playing a more and more important role in controlling plasma motion. It is convenient to use a particular β value to define the PDL outer edge. Farrugia et al. (1997) believed that this definition captures the physical meaning of the plasma depletion layer in which the magnetic force dominates over the plasma pressure force. Usually β=1 was used to define the
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PDL outer boundary. However, sometimes they used β=0.5 for a more restrictive definition. The depletion factor method defines the PDL outer boundary in a more descriptive way, and the plasma β method defines the PDL outer boundary in a more physical way. Although these two methods are very easy to use in practice, they have major difficulties. For the depletion factor method, it misses the earlier drop of the plasma density in the magnetosheath, which includes important physics that distinguishes the PDL from the other part of the magnetosheath. For the plasma β method, it assumes that the plasma β is the controlling factor of the PDL. However, this assertion lacks sound observational and theoretical support. To be specific, if the solar wind Mach number is low, β
