STAGNATED OUTFLOW OF O +5 IONS IN THE SOURCE REGION OF THE SLOW SOLAR WIND AT SOLAR MINIMUM

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1 The Astrophysical Journal, 602: , 2004 February 10 # The American Astronomical Society. All rights reserved. Printed in U.S.A. STAGNATED OUTFLOW OF O +5 IONS IN THE SOURCE REGION OF THE SLOW SOLAR WIND AT SOLAR MINIMUM Y. Chen, 1,2 R. Esser, 1,3 L. Strachan, 1 and Y. Hu 2 Received 2003 September 2; accepted 2003 October 24 ABSTRACT Using recent coordinated UVCS and LASCO measurements by Strachan and coworkers to constrain the heating parameters of a one-dimensional single-fluid minor ion model, we calculate the outflow velocity profile of O +5 ions in the flow tube overlying the helmet streamer, which has been supposed to be the source region of the slow solar wind at least during solar minimum. The background solar wind parameters and the flow tube geometry are taken from a recent two-dimensional magnetohydrodynamic solar wind model. We show that in this slow-wind source region the O +5 outflow speed varies nonmonotonically with increasing heliocentric distance. There is a local minimum of the outflow speed near the streamer cusp point (about 3 R ), which is below the current observational sensitivity. This type of ion outflow in the slow solar wind is termed stagnated outflow in this paper. We also show that the observed effective temperature in the perpendicular direction (to the magnetic field) and the outflow speed of the O +5 ions can be used to put limits on their parallel thermal temperature. Subject headings: solar wind Sun: corona 1. INTRODUCTION It has been suggested by many authors that the slow wind originates in the streamer belt at least during solar minimum (Feldman et al. 1981; Gosling et al. 1981). This is supported by recent observations (e.g., Woo & Martin 1997; Sheeley et al. 1997; Habbal et al. 1997). The observations with the Ultraviolet Coronagraph Spectrometer (UVCS; Kohl et al. 1995) by Raymond et al. (1997) show that the elemental abundances in the streamer legs closely correspond to those measured in situ in the slow solar wind. These observations suggest that the slow solar wind might originate in the open field regions surrounding the closed field regions of the coronal streamer at least during solar minimum. The physical parameters, as well as the driving mechanism(s), in this slow-wind source region are still not well determined observationally. There are several theoretical solar wind models that show that the proton outflow velocity varies nonmonotonically with increasing heliocentric distance in the vicinity of the streamer cusp point in the slow solar wind (Cuperman, Ofman, & Dryer 1990; Wang 1994; Vásquez, van Ballegooijen, & Raymond 1999; Suess & Nerney 2002; Hu et al. 2003). This type of ion outflow in the slow solar wind is termed stagnated outflow in this paper. Hu et al. (2003) developed a two-dimensional solar wind model, showing that the stagnated proton outflow near the cusp point is closely related to the special slow-wind flow tube geometry (the expansion factor increases rapidly in the inner corona and then decreases beyond the streamer cusp point; see also Wang 1994; Bravo & Stewart 1997; Chen & Hu 2001, 2002). In the above theoretical studies only electrons and protons are considered while minor ions are neglected. The minor ions are much heavier and thus suffer a much stronger sunward gravitational force, and the preferential heating processes that are observed to heat the ions even more than mass proportional in 1 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138; yachen@cfa.harvard.edu. 2 University of Science and Technology of China, China Center for Astrophysics, 96 Jinzai Lu, Hefei, Anhui , China. 3 University of Tromsø, Astrophysics Group, Tromsø NO-9037, Norway. the fast wind might also exist in the slow wind (Strachan et al. 2002; Frazin, Cranmer, & Kohl 2003); therefore, it is not easy to guess the velocity profiles of the minor ions in the slow-wind source region. This article is aimed at addressing this issue, i.e., constructing a model for the minor ions and describing their dynamics in the slow-wind source region. Recent coordinated measurements with UVCS (Kohl et al. 1995) and the Large Angle and Spectrometric Coronagraph Experiment (LASCO; Brueckner et al. 1995) show a sharp transition from no measurable outflow of the O +5 ions to significant flow of about 50 km s 1 between3.6and4.1r along the streamer axis (see Strachan et al. 2002). These observations also show that the O +5 perpendicular effective temperature is about 10 MK hotter than the protons. To make use of these new observational constraints, we focus in this paper on the behavior of O +5 ions. In x 2wedescribeour theoretical model including the main assumptions, background solar wind parameters and the magnetic field topology, and the one-dimensional flow tube model of minor ions. In x 3 we describe our numerical results and analyses. The conclusions and discussion including the limitations of the current model are presented in x THEORETICAL MODEL 2.1. Main Assumptions The model is described in a general way because it can also be applied to minor ions other than O +5. A number of simplifying assumptions have been made: (1) We are mainly interested in the ion behavior in the inner solar wind; therefore, we assume that the ions flow along the magnetic field lines. (2) Since the number densities of minor ions are negligible compared with those of the protons, the presence of minor ions has no observable impact on the background electron-proton solar wind plasma, as well as the magnetic field topology; thus, they can be treated as test particles. These two assumptions allow us to treat the expansion of the ions as a one-dimensional flow tube problem. (3) Only one species of minor ions is considered for simplicity. In other words, the effect of ionization and recombination processes is neglected. (4) The minor ion-to- 415

2 416 CHEN ET AL. Vol. 602 proton density ratio at the coronal base is set to be This value yields reasonable O +5 abundance consistent with the value measured in situ in the fast solar wind, which is about 0.6% of the O +6 abundance (Wimmer-Schweingruber et al. 1998). Please note that the absolute value of this quantity is not important to the minor ion dynamics. We also assume that the minor ions and protons are isothermal at the coronal base as a result of the strong collisional coupling there. Our calculation of the heating timescale and the Coulomb collisional timescale between protons and minor ions presented in x 3.1 justifies this assumption. (5) The processes that heat the ions are still not completely identified. The heating of the ions is therefore described by the exponential ad hoc heating rates (e.g., Withbroe 1988). The parameters of the heating function, i.e., the damping length and the heating rate, are selected in a way so that the calculated parameters are basically consistent with currently available measurements. In other words, they are constrained by the related observations. (6) Only one temperature is used to describe the minor ions. We now know that the fast-wind minor ions are strongly anisotropic (Kohl et al. 1998; Cranmer et al. 1999), but in the case of the slow wind, the measured perpendicular effective temperature of O +5 ions between 3 and 5 R is about 10 MK, much lower than that of the fast-wind O +5 ions (Strachan et al. 2002). The background particle density in this type of wind is higher, which means stronger collisional coupling; therefore, the minor ion anisotropy in the slow wind is much weaker than that in the fast wind. We investigate this assumption in x 3.2 in more detail using freely prescribed parallel and perpendicular temperatures The Background Solar Wind Model As mentioned above, the minor ions are treated as test particles flowing in a solar wind background. The background model is required to be able to yield reasonable electronproton solar wind parameters (-particles are not included in this study) and magnetic field topology especially in the slowwind region. We choose the model by Hu et al. (2003) to provide our background parameters since their model obtained the fast and slow solar winds together with the magnetic field topology in a self-consistent way and achieved solutions in good agreement with observational constraints. The corona magnetic field topology obtained by them is given in Figure 1. The dotted line represents the current sheet (above the cusp point) and the boundary between the closed and open magnetic field regions. The heliospheric latitude is 0 at the equator and 90 at the pole. The electron-proton velocity is parallel to the magnetic field; therefore, the flow tube coincides with the magnetic field line. According to their calculation, the flows from the tubes rooted at heliospheric latitudes from 90 to 36 correspond to the fast wind while the ones from 30 to 36 correspond to slow and intermediate wind. We single out two flow tubes (or magnetic flux tubes) representing the typical solution for the fast ( f ) and slow (s) solar wind, respectively. The two flow tubes are rooted at the heliospheric latitude 32 and 89, respectively. The heavy solid lines in Figure 1 represent the flow tube s. Figure 2 shows the flow tube expansion factors (A/r 2 ) and the angles between the magnetic field and the radial direction () fortubesf (dashed line) ands (solid line), respectively. It can be seen that the flow tube geometries of the fast and slow winds are quite different. The expansion factor of the fast wind increases Fig. 1. Two-dimensional magnetic field topology of the background electron-proton solar wind. The dotted curve depicts the equatorial current sheet and the streamer border. The cusp point is located at 3.0 R. The heavy solid lines represent the slow-wind flow tube s (taken from Hu et al. 2003). monotonically outward from the coronal base, while that of the slow wind increases first in the inner corona below the cusp point and then decreases farther out. This is due to the slow wind flowing around the vicinity of the streamer cusp point where the neutral point of the magnetic field is situated. The fast-wind tube is almost radial, while the slow-wind tube is nonradial. The electron-proton solar wind parameters (densities, velocities, and temperatures) are presented, along with those for the O +5 ions, in x One-Fluid Flow Tube Model of Minor Ions The one-dimensional single-fluid equations (mass, momentum, and energy conservation laws) for the minor ions can be written as þ ðn iv i AÞ¼0; m i ¼ i iv i n Z e n m i GM 1 X m i r 2 þ n i l¼e; p þ v i þ 2T i cos 3A 2Q i 3n i k B 2 n i X 2 3n i k B X l¼e; p K il l¼e; K il ðv l v i Þf ð ðv iaþ T l T i K il exp il 2 m i þ m l m l m i þ m l ðv l v i Þ 2 f ð il Þ¼0; where n, v, andt are the number density, velocity, and temperature along the flow tube, respectively. The subscript i denotes the minor ion species with charge Z i (in units of the electron charge e) andmassm i, while the subscript e ( p) means the parameters for electrons (protons). M, G, and k B are the Sun s mass, the gravitational constant, and Boltzmann s constant. The angle between the magnetic field and the radial direction,, is given in Figure 2b. The total mass density is ¼ i þ p with i ¼ n i m i and p ¼ n p m p,the proton and electron pressures are p i ¼ n i k B T i and p e ¼ n e k B T e, and p w ¼ v 2 =2istheAlfvén wave pressure. The thermal ð1þ ð2þ ð3þ

3 No. 1, 2004 STAGNATED OUTFLOW OF O +5 IONS 417 Fig. 2. (a) Flow tube expansion factors A/r 2 and (b) angles between the radial direction and the magnetic field lines for the fast ( f ) and slow (s; Fig.1,heavy solid lines) wind tubes, respectively. pressure gradient force in equation (2) can be expanded as follows: i n ¼ i k BT i n : The ad hoc heating rate for the minor ions is taken to be Q i ¼ n i Q i0 exp R r ; ð5þ i where Q i0 and i are adjustable parameters of the model. The two parameters are assumed to depend on the individual flow tube and are set to be Q i0ð f Þ ¼ 1: ergs s 1 ; Q i0ðsþ ¼ 0: ergs s 1 ; ð4þ ð6þ ð7þ ið f Þ ¼ 5R ; iðsþ ¼ 2R ; ð8þ where f and s represent the fast and slow wind, respectively. As mentioned above, these parameters are chosen to reproduce ion parameters consistent with currently available measurements on the perpendicular effective temperature of O +5 ions. Please refer to Hu, Esser, & Habbal (2000) for definitions of the terms associated with Coulomb collisions. 3. RESULTS As mentioned above, this study focuses on the properties of O +5 ions in the slow solar wind. The solution for the fast solar wind O +5 ions is also presented, mainly for the purpose of comparison. The first part of this section describes the numerical results for O +5 ions with isotropic temperature, and the case with a freely prescribed thermal anisotropy is presented in the second part The Solution for O +5 Ions and Analyses With the flow tube geometry (the cross section area A and the angles between the magnetic field and the radial direction ) and the electron-proton solar wind parameters along the tube given by the background model, equations (1) (3) are solved by a fully implicit numerical scheme (Hu, Esser, & Habbal 1997). For both tubes f and s, the calculated density, velocity, and temperature profiles for the O +5 ions, as well as those for the protons, are shown in Figure 3. The parameters for the O +5 ions in tubes f and s are presented as solid and dotted lines, respectively, while those for the protons are shown as dot-dashed and dashed lines, respectively. The observational results reported by Strachan et al. (2002) for the electron number density, the O +5 outflow speed, and perpendicular effective temperature are shown as error bars in Figures 3a, 3b, and3c, respectively. The observed perpendicular effective temperature of the protons is also shown in Figure 3c ( plus signs). Only the observations beyond 3 R are shown here since the data below that distance are inside the closed field region and do not apply to the slow solar wind. The modeled effective temperatures for both the O +5 ions and protons, defined by T i;ea ¼ T i þ m i v 2 ; ð9þ 2k B are plotted as long-dashed lines to compare directly with the observations. Figure 3 shows that our modeling results are basically in agreement with the measurements. From Figure 3a it can be seen that the O +5 density in tube s has a hump that corresponds to the dip in the velocity profile shown in Figure 3b between2.2andabout4r. The deceleration of the O +5 ions starts closer to the Sun than that of the protons (at about 2.4 R ). From the coronal base to about 2.2 R, the velocity of O +5 ions follows that of the protons, and then it starts to decrease from 41 km s 1 to the minimum value at about 2.9 R near the streamer cusp point. The minimum velocity is 8 km s 1, well below the current observational sensitivity (20 km s 1 ). After the minimum, the O +5 velocity increases again and reaches about 94 km s 1 at 6 R.The maximum velocity ratio between protons and O +5 ions is 6.2 at 2.7 R, with v p ¼ 56 km s 1 and v o ¼ 9kms 1.From1to 6 R the O +5 ions are slower than the protons in the slow solar wind. However, the velocity difference is within or close to the observational errors and thus not measurable. In the fast solar wind the O +5 ions become faster than the protons at about 1.8 R. It is interesting to note that there is also a dip in the O +5 velocity profile in the fast solar wind although it is much smaller and closer to the coronal base than that in the slow wind. This is consistent with some previous calculations on the minor ions for the fast solar wind (Hu et al. 2000; Chen, Esser, & Hu 2002, 2003). Since the ion deceleration is caused by the negative sum of forces, we present the force balance analysis for the fast and slow winds in Figures 4a and 4b, respectively. Please see the

4 418 CHEN ET AL. Vol. 602 the electric field force due to the electron thermal motion is a smaller contribution. In this stage, the O +5 ions must be slower than the protons so that they can gain momentum through collisions and flow out into interplanetary space (see also Hu et al. 2000). (2) The stagnated flow stage: with decreasing electron and proton densities, the collisional frequencies between these background particles and O +5 ions decrease rapidly. As a result, the sum of the forces becomes negative and the O +5 ions are decelerated. From Figure 4b the strongest sunward (negative) force is the gravitational force. In addition, the thermal pressure gradient force is now negative. Because of the heat deposition, the O +5 ion temperature increases from 1 to about 10 MK in the slow wind and from 1 to about 100 MK in the fast wind; these steep temperature increases correspond to a sunward thermal pressure gradient force that contributes to the formation of the stagnated outflow. Furthermore, after the deceleration starts, the hump of the ion number density begins to form. This positive density gradient makes the sunward thermal pressure gradient force more negative (see eq. [4]). The maximum velocity difference between protons and O +5 ions is 51 km s 1 at 2.5 R for the slow wind and 21 km s 1 at 1.5 R for the fast wind, respectively. These local maxima of the differential velocity account for the humps of the Coulomb collisional forces as seen from the solid lines in Figures 4a and 4b. As mentioned above, the dip in the velocity profile is much smaller in the fast wind than that of the slow wind although the temperature increase in the fast wind is much larger than in the slow wind. This is because the ion velocity profile is determined by the combination of the Fig. 3. Numerical solution for the O +5 ions in the fast ( f ) and slow (s) wind: (a) number density,(b) velocity, and(c) temperature. The long-dashed lines in (c) represent the modeled effective temperatures as defined by eq. (9). The parameters for the protons are also plotted. The observational results for (a) the electron number density, (b) theo +5 outflow speed, and (c) the perpendicular effective temperatures of O +5 ions (error bars) and protons ( plus signs) along a streamer axis beyond 3 R are taken from Strachan et al. (2002). right-hand side of equation (2) for the expressions of these forces. To avoid crowdedness, only the gravity (long-dashed lines), the electric field force (dotted lines), the inertial force (dashed lines), the thermal pressure gradient force (dot-dashed lines), and the Coulomb collisonal force between protons and O +5 ions (solid lines) are given. The other two forces, the wave pressure gradient force and the collisional force between electrons and O +5 ions, contribute relatively little and are, therefore, not shown in the figure. From Figures 3 and 4 it can be seen that the acceleration process of O +5 ions in the source region of the slow solar wind can be divided into three stages: (1) The acceleration by the background solar wind plasma: the outward force balancing the gravitational force is mainly the Coulomb collisional force between protons and O +5 ions, and Fig. 4. Force balance analyses of the O +5 ions flowing in (a) flow tube f and (b) flow tube s. The following forces are plotted: gravity (long-dashed lines), electric field force (dotted lines), inertial force (dashed lines), thermal pressure gradient force (dot-dashed lines), and Coulomb collisional force between protons and O +5 ions (solid lines).

5 No. 1, 2004 STAGNATED OUTFLOW OF O +5 IONS 419 Fig. 5. Comparison of the heating timescale ( h ) and the collisonal timescale ( c )inthe(a) fastand(b) slow solar winds forces, and the thermal pressure gradient force corresponding to the temperature gradient is only a small contribution and not a decisive factor. (3) In this stage at larger distances, the acceleration is mainly due to the thermal pressure gradient force. With increasing heliocentric distance the flow tube continues its expansion and the particle number densities continue to decrease, and also the sharp rise of the O +5 temperature stops. These factors make the thermal pressure gradient force positive, which is now more important than the collisional force, and the outflow speed of the O +5 ions increases again, mainly as a result of the thermal pressure gradient force. To justify our assumption of the isothermal particles at the coronal base, we calculate the heating timescale ( h )andthe collisonal coupling timescale ( c ), which are shown in Figure 5 and given as follows: h ¼ 3 2 n i k B T i Q i ; ð10þ c ¼ n iðm i þ m p Þ : ð11þ 2K ip exp ip 2 From Figure 5 we have in the inner corona c T h.theheat deposited into the O +5 ions is therefore transferred to the protons through Coulomb collisions. The protons and O +5 ions have to be isothermal as a result of the strong collisions there. When the relative difference between the two timescales is small enough, e.g., when the quantity defined by jð h c Þ= c j is less than, for instance, 20% at about 1.4 R for the fast wind and 2.1 R for the slow wind, then the temperatures can be differentiated significantly by the heating and the O +5 temperature can go up rapidly The Effect of Thermal Anisotropy To investigate the possible effect of thermal anisotropy on the stagnated outflow of O +5 ions in the flow tube s, we simply assume that the ion velocity distribution function is gyrotropic along the magnetic field and can be represented by a parallel (to the magnetic field) and a perpendicular temperature (T ik and T i? ). The related anisotropic thermal pressure gradient force is written as ð1=n i ik =@r ð 1=ni AÞ ð@a=@rþ ð p ik p i? Þ. This force is used to replace the isotropic thermal pressure gradient force term ð1=n i Þ ð@p i =@rþ in equation (2). We prescribe the parallel temperature as follows: T ik ¼ max T p ; T i? ; ð12þ a where T i? is taken from the temperature profile plotted in Figure 3 (dotted line) for the isotropic O +5 ions and a is an adjustable parameter. If a ¼ 1, we have T ik ¼ T i? corresponding to the case discussed above. Since the observational analyses by Frazin et al. (2003) suggest that T ik < T i?,we increase a to evaluate the effect of possible thermal anisotropy on the outflow velocity profile. Figure 6 shows the O +5 velocity profile with a ¼ 1:5. It is characterized by a minimum speed of 2 km s 1, which is slower than that for the case with a ¼ 1. However, if a is larger than 1.5, as a result of the reduced thermal pressure gradient force, the minimum velocity will be smaller and the velocity profile beyond 4 R will be unable to fit the measurements. Thus, from a theoretical point of view, the observed perpendicular effective temperature and the outflow speed of O +5 ions can be used to put limits on their parallel thermal temperature. 4. DISCUSSION AND CONCLUSIONS Using a fluid model for one species of minor ions with the flow tube geometry and the background electron-proton solar Fig. 6. Impact of the ion thermal anisotropy on the O +5 outflow velocity with T ik determined by eq. (12), where a ¼ 1:5 andt i? is set to be the value shown in Fig. 3c for flow tube s.

6 420 CHEN ET AL. Vol. 602 wind parameters given by a two-dimensional hydromagnetic coronal model, the dynamics of the O +5 ions in both the fast and slow winds is studied. The emphasis has been put on the behavior of the O +5 ions in the slow-wind source region, i.e., in the flow tube overlying the coronal streamer. The coordinated UVCS and LASCO measurements on the O +5 ions by Strachan et al. (2002) have been used to limit the adjustable heating parameters. We show that in this source region of the slow wind the O +5 outflow velocity varies nonmonotonically with increasing heliocentric distance. There is a local minimum of the velocity profiles near the streamer cusp point (about 3 R ). The minimum speed is below the current observational limit. We find that the acceleration process of O +5 ions in this region can be divided into three stages: (1) From the coronal base to about 2.2 R :theo +5 ions are accelerated mainly by the background solar wind plasma through the Coulomb collisional coupling with protons and the electric field caused by the electron thermal motion. (2) The stagnated flow stage: the O +5 ions are decelerated as the antisunward Coulomb collisional forces become weaker than the sum of the gravity and the sunward thermal pressure gradient force. The sunward thermal pressure gradient force is caused by the steep rise of the O +5 thermal temperature, as well as the local increase of their number density with increasing heliocentric distance due to the deceleration. (3) The acceleration farther out: the O +5 ions are mainly accelerated by the thermal pressure gradient force, which changes direction from sunward to antisunward as a result of the decrease of the O +5 number density. In this stage, the Coulomb collisional forces are basically negligible. It is interesting to point out that a similar but much smaller velocity dip also occurs in the fast wind, which is consistent with previous calculations (e.g., Chen, Esser, & Hu 2003). It is also shown that with the gyrotropic assumption of the ion velocity distribution functions the parallel temperature of O +5 ions in the inner corona is constrained by their observed perpendicular effective temperature and outflow speed. With the same heating function as the one used for O +5 ions, we also calculate the velocity profiles for several other species of minor ions, e.g., C +5,O +6,Mg +9,andSi +10.Wefindthat,as expected, similar velocity dips also exist for each species of these minor ions. Because of the lack of knowledge of the heating processes in the corona and solar wind, a selfconsistent study on their dynamics is currently impossible. The outflow velocity of minor ions also affects their expansion timescale, exp ¼ n 1 ; ð13þ v i and thus could be important to the freezing-in process of minor ions in the slow solar wind (e.g., Esser & Edgar 2000). This study on the dynamics of minor ions in the slow wind can help us understand better the UVCS observations. The velocity profiles along the streamer axis given by Strachan et al. (2002) show that there exists a sharp transition from no measurable outflow to significant outflow in the region between 3.6 and 4.1 R. As mentioned in the text, their results below the cusp point are inside the closed field region and do not apply to the slow solar wind, which is supposed to originate from the flow tube overlying the closed field region (see the heavy solid curve in Fig. 1). According to our calculation, the ion outflow just above the cusp cannot be observed with current instruments. A sharp transition from insignificant to measurable outflows can thus be due either to transition from closed to open field regions or to a stagnated flow. One should be very careful in using the measured sharp transition of the velocity profiles in the streamer region to determine the cusp point location and the open/closed field boundary, as suggested by Strachan et al (2002). Because of the lack of direct measurements on the coronal magnetic field, there is no observational constraint on the flow tube geometry in the source region of the slow solar wind. To make the problem tractable, we treated the O +5 ions as test particles and fixed the electron and proton parameters and the flow tube geometry, which are obtained from a twodimensional solar wind model. With this approach it is impossible to evaluate the impact of varying the background solar wind parameters and flow tube geometry on the ion properties. It has been suggested by many authors that the flow tube geometry is critical to the proton properties in the slow wind (e.g., Wang & Sheeley 1990; Chen & Hu 2001, 2002; Suess & Nerney 2002; Hu et al. 2003). In particular, it may account for the formation of the stagnated outflow of protons (Hu et al. 2003). However, its contribution to the minor ion stagnated outflow is still unclear since the minor ions are much heavier than protons and may not require a nonmonotonic flow tube expansion factor to get stagnated. This point is also implied by our result that the local minimum of the O +5 velocity is present in both the fast and slow winds while for the protons such velocity dip is only present in the slow wind. On the other hand, the solar wind heating and acceleration mechanism(s) may be closely associated with the magnetic field topology. Therefore, to investigate the effect of the flow tube geometry on the minor ion properties, a multifluid solar wind model driven by some physical mechanisms such as ion-cyclotron resonance instead of artificial heat deposition should be constructed. Finally, our study on the minor ion dynamics is based on the assumption that the minor ions flow along the magnetic field lines. Thus, we did not take into account the ion diffusion across the magnetic field lines due to the ion inertia (L. Ofman 2003, private communication). To address this issue, one should establish a twodimensional, multifluid solar wind model such as that constructed by Ofman (2000). We thank the anonymous referee for his/her valuable comments on the paper, which helped to clarify the manuscript. Y. Chen would also like to thank Leon Ofman, Xing Li, and Jun Lin for valuable suggestions. This work was supported by NASA grants NAG and NAG Y. 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