Cone model for halo CMEs: Application to space weather forecasting

Transcription

1 JOURNAL OF GEOPHYSIAL RESEARH, VOL. 9, A39, doi:.29/23ja226, 24 one model for halo MEs: Application to space weather forecasting Hong Xie, Leon Ofman, and Gareth Lawrence atholic University of America, Washington, D.., USA Received 8 September 23; revised 5 December 23; accepted 4 January 24; published 3 March 24. [] In this study, we present an innovative analytical method to determine the angular wih and propagation orientation of halo oronal Mass Ejections (MEs). The relation of ME actual speed with apparent speed and its components measured at different position angle has been investigated. The present work is based on the cone model proposed by Zhao et al. [22]. We have improved this model by () eliminating the ambiguity via a new analytical approach, (2) using direct measurements of projection onto the plane of the sky (POS), (3) determining the actual radial speeds from projection speeds at different position angles to clarify the uncertainty of projection speeds in previous empirical models. Our analytical approach allows us to use coronagraph data to determine accurately the geometrical features of POS projections, such as major axis, minor axis, and the displacement of the center of its projection, and to determine the angular wih and orientation of a given halo ME. Our approach allows for the first time the determination of the actual ME speed, wih, and source location by using coronagraph data quantitatively and consistently. The method greatly enhances the accuracy of the derived geometrical and kinematical properties of halo MEs, and can be used to optimize Space Weather forecasts. The applied model predications are in good agreement with observations. INDEX TERMS: 753 Solar Physics, Astrophysics, and Astronomy: oronal mass ejections; 239 Interplanetary Physics: Interplanetary shocks; 2 Interplanetary Physics: Ejecta, driver gases, and magnetic clouds; 2447 Ionosphere: Modeling and forecasting; KEYWORDS: coronal mass ejections, space weather, cone model itation: Xie, H., L. Ofman, and G. Lawrence (24), one model for halo MEs: Application to space weather forecasting, J. Geophys. Res., 9, A39, doi:.29/23ja226.. Introduction urrently at Department of Solar Physics, Royal Observatory of elgium, russels. opyright 24 by the American Geophysical Union /4/23JA226 [2] The advent of Solar and Heliospheric Observatory (SOHO) has produced significant enhancements in geomagnetic storm forecasting [rueckner et al., 998; Zhang et al., 23]. One of the most significant advances has been the detection and confirmation of front-side halo ME events, and other likely causes of geomagnetic storms [e.g., Gosling et al., 99; Webb et al., 2]. Halo MEs, first reported by Howard et al. [982], have been interpreted as shell-like coronal mass ejections of dense coronal plasma heading directly toward (front-side halo) or away from (backside halo) the Earth. It is now well established that front-side halo MEs are the major cause for large geomagnetic storms [e.g., rueckner et al., 998; ane et al., 2; Gopalswamy et al., 2; Webb et al., 2; Wang et al., 22; Zhang et al., 23]. [3] Halo MEs and associated solar surface activities can be well correlated through the combination of SOHO/ LASO (Large Angle and Spectrometric oronagraph; rueckner et al., 995; Howard et al., 997; St. yr et al., 2; and EIT (EUV Imaging Telescope; Delaboudiniere et al., 995; nascom.nasa.gov/eit/) observations. The LASO instrument is a set of three coronagraphs (, 2, and 3) that image the solar corona from. to 32 solar radii (note, that is not operational since June 998, and the heliocentric distance covered by 2 and 3 is 2 32 solar radii). EIT images the full solar disk and inner corona in four selected band-passes at 7, 95, 284, and 34 Å. Extreme-ultraviolet (EUV) images of the low corona and solar disk reveal massive MEassociated signatures, including large-scale waves in the inner corona [e.g., Thompson et al., 999], extended regions of dimming [e.g., Sheeley et al., 983; Sterling and Hudson, 997; Webb et al., 2], flares and localized brightening, and post-eruption bright arcades [e.g., Hudson et al., 998; McAllister et al., 996; Weiss et al., 996; Alexander et al., 2; Sterling et al., 2]. The major geomagnetic storms are associated with strong and persistent southward magnetic fields, either in interplanetary magnetic clouds or in the compressed sheath of plasma shocks in solar wind [e.g., othmer and Schwenn, 995; Tsurutani and Gonzalez, 998; Tsurutani, 2]. [4] Halo MEs can now be routinely recorded with LASO due to its large field view and high sensitivity [St. yr et al., 2; Webb, 22]. However, LASO coronagraph images can only detect apparent speeds and wihs of MEs since the images are two-dimensional projections of the white light emission on the plane of the sky (POS). The three-dimensional structure and actual A39 of3

2 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 Figure. Topology of the cone model and transformation of coordinate systems. See color version of this figure in the HTML. speeds of MEs remain unknown due to the projection ambiguity. Schwenn et al. [2] derived a correlation between the radial speeds V rad and lateral expansion speed V exp as V rad =.88V exp, which can be used as an empirical formula when V rad is inaccessible because of the geometry. They also provide an estimation of the ME travel time as T tr = ln(v exp ), with an uncertainty of about 24 hours. [5] Recently, Zhao et al. [22] has proposed a cone model to estimate the geometrical and kinematical properties of three-dimensional halo MEs, based on three assumptions: () MEs move out in nearly constant angular wih in a radial direction through the corona; (2) the source location of a halo ME is in the vicinity of the solar disk center and the area of the associated solar surface active region; (3) ME s bulk velocity is radial and the expansion is isotropic. Previous works have demonstrated that the cone model is a reasonable approximation [e.g., Fisher and Munro, 984; St. yr et al., 2; Webb et al., 2]. [6] This work is an extension of Zhao et al. s [22] model. In their study, the ME s angular wih and propagation orientation were determined iteratively: the initial values of angular wih and central axis angles of the cone are chosen and then adjusted iteratively until the modeled halos best fit with the observed ME halos. This method has two shortcomings: () Visual fitting of the model to the LASO images introduces uncertainty and ambiguity to the results; (2) The iterative technique is computationally time-consuming and inefficient in this case. In the present paper we present an innovative analytical method to determine the relation of cone ME angular wih and orientation to its elliptical POS projection and the relation of ME actual radial speed to projection speeds at different position angles. This analytical method allows us to obtain the ME wih and orientation from geometrical features of elliptical projections, such as major and minor axes, and the displacement of the center of projection, and to determine the ME actual radial speed from projection speeds measured at any arbitrary position angles. Our method has the advantages of consistency, high accuracy, and efficiency. It is the first time that the ME actual speed, wih, and source location can be determined by using coronagraph data quantitatively and consistently and the new method optimizes the determination of geometrical and kinematical properties of halo MEs. These properties are critically important in space weather modeling. [7] The remainder of the paper is organized as follows. Section 2 presents a detailed description of the analytical solution for the cone ME model and investigates the relation of actual radial speeds of halo MEs with POS projection speeds at different azimuthal angles d, and position angles PA. Section 3 examines the validity of the cone model. Section 4 provides an estimate of ME transit times using the actual radial speed. Section 5 considers the occurrence of Earth-directed halo MEs, and suggests possible constraints on geoeffective halo MEs. Finally, the conclusions and a discussion of this study are presented in section one ME Model [8] We begin with a heliocentric coordinate system (x h, y h, z h ) where z h points to Earth (not x h, the normal convention), y h points north, and the x h y h plane defines the plane of the sky. Now consider an apexcentered right cone and coordinate system (x c, y c, z c ), where x c is the cone axis, and the y c z c plane is parallel to the base of the right cone. The orientation of the cone is defined by longitude angle, a (or f), latitude angle q (or l); and angular wih of the cone is defined by 2w, as shown in Figure. Note that (f, l) are the longitude and latitude angles relative to the ecliptic plane, which is normally used in heliospheric studies. We define (a, q), i.e., q the angle between the cone axis and the plane of the sky (POS) and a the angle between the cone axis projection on POS and x h - axis, as the longitude and latitude to POS to determine conveniently the cone model parameters as outlined below. Note that in the cone coordinate system, the orientation of the cone describes the propagation of the ME. [9] The transformation from the heliocentric coordinate system to the cone coordinate system can be carried out in following two steps. [] In step the transformation from (x h, y h, z h )toan intermediate coordinate system (x c, y c, z c ) is carried out, where z c is parallel to z h, and the rotation about z h is through the angle a. Let M be the transformation matrix for step, we have x h y h z h ¼ M A x c y c z c or A x c y c z c ¼ M A x h y h z h ; ðþ A 2of3

3 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 where cos a sin a M ¼ sin a cos a ; M A ¼ cos a sin a sin a cos a : A [] In step 2 the transformation from the (x c, y c, z c ) coordinate system to the cone coordinate system (x c, y c, z c ) is carried out. This transformation requires a single rotation around y c through the angle q; this provides for the tilt of the cone axis with respect to the plane of the sky (POS). Note that in Figure the orange plane is the cross-section plane of the cone model. [2] Assuming the matrix M 2 corresponds to the transformation of step 2, we have x c y c A ¼ M 2 x c y c A or x c y c A ¼ M 2 x c y c A ; ð2þ where z c z c z c z c Figure 2. Elliptical projection of the circular cross section of the cone on the plane of the sky. cos q sin q M 2 ¼ A ; M sin q cos q 2 ¼ cos q sin q A : sin q cos q Therefore the transformation from the heliocentric coordinate system (x h, y h, z h ) to the cone coordination system (x c, y c, z c )is z h y h z h A ¼ M x c y c z c A or x c y c z c A ¼ M x h y h z h A ; where M is the transformation matrix from the heliocentric coordinate system to the cone coordination system given by cos a cos q sin a cos a sin q M ¼ M M 2 ¼ sin a cos q cos a sin a sin q A ; sin q cos q or M ¼ M 2 M ¼ cos a cos q sin a cos q sin q sin a cos a A : cos a sin q sin a sin q cos q ð3þ 2.. Determination of the one Model Parameters [3] In the cone coordinate system (x c, y c, z c ), the cross section of the cone (shown as blue circle in Figure ) at the distance r can be expressed as: x c ¼ r cos w y c ¼ r sin w cos d z c ¼ r sin w sin d; where d =tan (z c /y c ) is the azimuthal angle in the cone cross-section plane. Substituting (4) into (2), we obtain the projection equation of circular cross-section of the cone model in x c y c plane (i.e., the plane of the sky): Let x c ð4þ r cos w cos q 2 y 2 c þ ¼ : ð5þ r sin w sin q r sin w h ¼ r cos w cos q a ¼ r sin w sin q b ¼ r sin w; then Equation (5) can be written as x c h 2 2 þ y c ¼ : ð7þ a b Equation (7) shows the elliptical orbit of the cone with circular cross-section projected on POS. Parameters a, b, ð6þ 3of3

4 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 Figure 3. Dependence of apparent speed V r and its components V xc, V yc, V xh, V yh on azimuthal angle d and position angle PA at fixed actual radial speeds of V r = 55. km s and V r = 39. km s for the (a) 3 November 2 and (b) 4 April 2 events, where V r is apparent speed in POS, V xc (V xh ), V yc (V yh ) are apparent speed components in x c (x h ) and y c (y h ) direction, and V 2 r = V 2 xh + V 2 yh. and h are the minor axis, major axis, and displacement of its center to the origin in the heliocentric system, respectively, as illustrated in Figure 2. [4] We use LASO 2 and 3 images to determine a, b, and h (the detailed descriptions are given in section 3.). Equation (6) can be written as sin q ¼ a b ; q ¼ a sin b tgw ¼ b cos q; w ¼ tg b h h cos q : The conventional longitude f and latitude l are given by l ¼ tg cos q sin a 2 =2 A cos q cos a þðsin qþ 2 f ¼ tg cos q cos a : sin q Therefore the orientation and angular wih of the cone model can be determined analytically by equations (8) and (9). [5] Note that if a = b and h =, then we have cos q =. In this case the solution is degenerate since the solution for angular wih w is not unique. This occurs when the orientation of the cone ME is aligned with the line-ofsight. This case is consistent with Zhao et al. s [22] study. In such cases, the empirical formula (e.g., V rad =.88V exp ð8þ ð9þ [Schwenn et al., 2]) can be used when V rad is inaccessible because of the geometry Determination of the Actual Radial Speed of the one-model ME [6] Using equation (4) and transformation equation (2) we obtain the relation between the actual radial speed of the ME and the projection speeds V xc and V yc as follows: thus or V x c V y c ¼ dx c ¼ dy c ¼ dr ðcos w cos q sin w sin q sin dþ ¼ dr sin w cos d; V x c V r ¼ dr ¼ cos w cos q sin w sin q sin d ; V r ¼ dr ¼ V yc sin w cos d : ðþ ðaþ ðbþ Similarly, using equation (4) and transformation equation (3) we can derive the relation between the ME actual radial speed and the projection speeds V xh and V yh as: V xh V yh ¼ dx h ¼ dy h ¼ dr ðcos w cos q cos a sin w sin a cos d sin q cos a sin w sin dþ ¼ dr ðcos w cos q sin a þ sin w cos a cos d sin q sin a sin w sin dþ; ð2þ 4of3

5 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 thus V r ¼ dr V xh ¼ ðcos w cos q cos a sin w sin a cos d sin q cos a sin w sin dþ ; or ð3aþ V r ¼ dr V yh ¼ ðcos w cos q sin a þ sin w cos a cos d sin q sin a sin w sin dþ : ð3bþ Here V xh, V yh, V xc and V yc are the apparent (projection) speed components along x h, y h, x c and y c axis in POS. Figures 3a and 3b show the dependence of V xh, V yh, V xc, V yc and V r on azimuthal angle d (PA) at fixed actual radial speeds of V r = 55. km s and V r = 39. km s for the event of 4 April 2, and 3 November 2, 2 2 respectively, where V r = V xh + V 2 yh. As shown in equations () and (3), the apparent speed components V xh, V yh, V xc and V yc in POS vary as a function of azimuthal angle d as well as different position angles PA. (PA is defined counter clockwise in degrees from solar north in LASO POS, PA = tan ( x h /y h ). The transformation relation between d and PA is described in section 3.) Apparent speeds V r measured at different PA values in POS vary differently for each given event as shown in Figure Validation of the one Model 3.. Application of the one Model to the 4 April 2 Event [7] In order to validate the application of our model, we use the above method to reproduce the 4 April 2 event. LASO 2 and 3 images show that this event was a full halo ME initiated at 6:32 UT. The Disturbance Storm Time (Dst) equivalent equatorial magnetic disturbance index reached its negative peak (Dst 288 nt; see ftp://ftp.ngdc.noaa.gov/stp/geomagneti_data/ INDIES/DST) on 7 April 2 at : UT, indicting that a major geomagnetic storm has occurred. In EIT images there was a 9.7 flare in active region (AR) 8933 associated with this event at N9W56 at 5:34 UT, showing that this is a halo ME directing toward the Earth (front-side halo ME). [8] Figure 4 shows modeled halo ME (black circles) superposed on LASO 3 images from 4 April 2. Using the SOHO Solar Software library ( lmsal.com/solarsoft/), we measured the parameters a = (22., 23.), a 2 = (384., 392.), b = (28., 424.), b 2 = (423., 69.) from the 8:8 UT image. These values are given in pixels device units where the full window size of 52 pixels corresponds to 3 R s at the poles and equator, and 32 R s toward the corners. Note that for consistency, all analyses in the paper limit the 3 field of view to 3 R s. We then calculated a, b, h, and a (as shown in Figure 2): h a ¼ :5 ða 2x a x Þ 2 i 2 =2; þ a 2y a y h b ¼ :5 ðb 2x b x Þ 2 i 2 =2; þ b 2y b y a ¼ tg a 2y a y =2 a; ; h ¼ a 2 2x a 2x a þ a2 2y x and obtained a = 3.2, b = 63.6, h = 47., and a = 46.. Substituting these parameters into equation (8), we get q = 53.3, and w = Finally from equation (9), we obtain l = 25.7, and f = Figure 4 shows comparison of the applied model (black circles) with the observed images at different times. The results show that our method reproduces the geometric features of the ME images well Identification of ME Actual Radial Speed Using Measurements From Different Position Angles [9] To further test the applicability of the cone model, we calculate the actual radial speed of a ME based on projected speeds at different d(pa) in POS and then compare the results of different measurements in Table. [2] From equations () and (3) it is evident that the actual radial speed of the cone-model ME can be derived from projection speed components V xc and V yc (or V xh and V yh ) respectively. This provides a way to test if the cone model is valid by comparing the results obtained from equation () or (3) at different d(pa). Here azimuthal angle d is defined as d =tan (z c /y c )in the cone coordinates and position angle PA is defined as PA = tan ( x h /y h ) in LASO POS. PA and d has a complex and unique transformation relation for each event. The corresponding transformation relation between PA and d is derived as follows. [2] From equation (3), we have x h ¼ x c cos q cos a y c sin a z c sin q cos a y h ¼ x c cos q sin a þ y c cos a z c sin q sin a: z h ¼ x c sin q þ z c cos q Substituting equation (4) into equation (4), we obtain ð4þ PA ¼ tan x h y h ¼ tg cos q cos actgw= cos d sin a sin q cos atgd : cos q sin actgw= cos d þ cos a sin q sin atgd ð5þ Please note, that the relation of PA to azimuthal angle d varies case by case and depends on three free parameters of the cone, i.e., w, a, and q. 5of3

6 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 Figure 4. omparison of modeled halos (black circles) and LASO images for the 4 April 2 event. [22] Table lists the results from measurements along different PAs (thus different d). The apparent speeds V r are obtained from height-time plots using LASO 2 and 3 data in POS and actual radial speeds V r are determined from equations (a) and (b) respectively, where apparent speed components in the x c - and y c - directions V xc = V r sin(a PA) and V yc = V r cos(a PA). From Table, we can see that the results of actual radial speeds derived from equations (a) and (b) vary by about 56 km s at most, i.e., the estimated error range is about 5%. The total difference for results from different PAs is about km s and the error range is about %. In terms of the spatial and time resolution of SOHO/ 6of3

7 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 Table. omparison of the Derived Actual Radial Speeds From Different PA (d) PA, deg d, deg V a r,kms V xc,kms V yc,kms V b r-xc,kms V c r-yc,kms V r d,kms N/A N/A a V r, apparent speed measured in POS using height-time profile at different PA. b V r-xc, the actual radial speed derived from Equation (a). c V r-yc, the actual radial speed derived from Equation (b). d V r, the average actual speed of V r-xc and V r-yc. LASO, these error ranges are reasonable. Thus the ME cone model that assumes isotropic radial velocity is acceptable and valid. 4. Determination of ME Transit Time [23] ME transit time is a key parameter for Space Weather forecasting. Apparent speeds for MEs determined from sequences of LASO 2 and 3 images have been used in various models (e.g., at NOAA SE space forecasting centers). However, since the ME apparent speed is a projection of the true speed on POS, projection effects will be introduced in the prediction. Using actual speeds derived from the cone model improves the results and corrects for projection effects. It has been shown that ME speeds vary widely, from km s to more than 25 km s [e.g., Sheeley et al., 999; St. yr et al., 2; Gallagher et al., 23]. MEs have been classified into two categories according to the speeds: () gradual (slow) MEs, which have speeds of 4 6 km s, often observed after prominences erupt; and (2) impulsive (fast) MEs with speeds > 5 km s, often associated with flares. Most slower MEs accelerate as they move outward through LASO 2 field of view and then travel with approximately constant speed in LASO 3 field of view, while fast events have been observed to decelerate [e.g., Sheeley et al., 999; Andrews and Howard, 2; Zhang et al., 2]. In this section we use typical examples to illustrate the improvement due to our model: () slow ME: event of 3 November 2 and (2) fast ME: event of 4 April Slow ME: Event of 3 November 2 [24] The first example is a slow halo ME that occurred on 3 November 2 at 8:26 UT. For this event the applied model parameters are: w = 89., a = 63.8, q = The apparent speeds obtained from LASO 2 and 3 coronagraph data indicate that it is a slow ME event. Figures 5a, 5b, and 5c are heighttime plots using first order fit (constant speed), second order fit (constant acceleration), and third order fit (quadratic acceleration), respectively. As shown in Figure 5a, the apparent speed V xc measured at position angle PA = 334 (azimuthal angle d = 27 ) using first order fit is km s. From Equation () we obtain the actual radial speed of the ME as km s. In the 2nd order fitting the apparent speed V xc is 34.2 km s and apparent acceleration is 4.87 m s 2 at 6:42 UT 4 November 2. The derived actual radial speed from equation () is 55. km s and the actual acceleration is 7.87 m s 2, respectively. In 3rd order fitting, the actual radial speed at 6:8 UT is km s with no significant acceleration. Assuming that the ME moves out at constant speed beyond the field of view of 3, using the speed obtained from 2nd order fitting, the estimated ME transit time T = (7: : 8:26) hr + (24 3) 7 5 /55./36 hr = 78 hr, where 7:42 UT is the time that the ME left 3 field of view, 8:26 UT is the ME onset time, and T is defined as the interval between the ME onset time and the interplanetary ME counterpart (IME) arrival time at the WIND spacecraft ( shtml) in near Earth space. IME arrival time can be either indicted by the arrival of IME shock front (SF) or the starting time of IME ejecta (magnetic cloud, M). As shown in Figure 6, the in situ solar wind plot from plasma and magnetic field instruments on the WIND spacecraft ( we can see that the shock front arrived at WIND at : UT 6 November 2 (SF) and IME ejecta (magnetic cloud) arrived at 22: UT 6 November 2 (M). The observed transit times from the Sun to the WIND spacecraft near Earth orbit are (: 8:26) hr = 63.6 hr (SF) and (22: 8:26) hr = 75.6 hr (M). Our model estimated ME transit time using the actual radial speed is much closer to observed transit time 75.6 hr (M) (within the error range of 2.4 hr in this case) than the estimated transit time using apparent speed at PA = 334, which is (7: : 8:26) hr + (24 3) 7 5 /35.3/36 hr = 4.8 hr. Also, the predicted radial speed of the halo ME of 55. km s agrees with to the in situ speed from WIND, where the average speed of the magnetic cloud is around 55 km s (see Figure 6) Fast ME: Event of 4 April 2 [25] Second example is a fast front-side halo ME that occurred at 6:32 UT on 4 April 2. Figures 7a and 7b are height-time plots using first order fit (constant speed), second order fit (constant acceleration). The height-time second order fitting plot gives ME initial apparent speed V rc = 8.3 km s at PA = 39 (d = 273 ) at distance 7.58 R s at 6:43 UTand apparent acceleration of 3.36 m s 2. Applied model parameters for this event are w = 64.3, a = 46., q = From Equation () we obtain the actual initial speed and acceleration of 39. km s and 7of3

8 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 Figure 5. Height-time plots of apparent speeds and accelerations of the 3 November 2 ME using (a) first order fit, (b) second order fit, and (c) third order fit m s 2, respectively. Assuming that the fast ME decelerates at a constant rate when it travels through the Sun- Earth space, the kinematic equation of a ME is S ¼ ut þ :5at 2 ; ð6þ where S is the distance from the Sun to near-earth, u is the ME initial speed, t is the ME travel time, and a is the acceleration. Substituting S = ( ) R s = 26.4 R s, u = 39. km s, a = 3.42 m s 2 at 6:43 UT, we obtained the ME kinematic equation: :73 3 t 2 þ 39:t 26:4 6:96 5 ¼ ; ð7þ which yields the solution of the estimated IME transit time of 47 hr and the estimated IME speed of V IME = 39. at = km s. The observed IME arrival time and speed in Wind data are 6:27 UT, 6 April 2 (where this time is the shock front arrive time, with no obvious M component in this case, nasa.gov/wind/current_listips.htm) and 6 km s, respectively (see Figure 8). Thus the Observed ME transit time 2 24 hr + (6:27 6:32) hr = 47.9 hr. The modeled ME transit time and ME speed are in good agreement with observation. [26] Note that in this event the values for ME transit time of 47.3 hr and speed of 546. km s estimated before 8of3

9 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 Figure 6. Solar wind plot for the major geomagnetic storm on 6 November 2 (Day of year = 3). From top to bottom the panels are plasma velocity, density, and magnetic field components in x, y, and z direction (GSE), respectively. The vertical solid line indicates the time of the IME shock front arrival at the WIND spacecraft in the near Earth space. The two vertical dashed lines indicate the start and end times of the magnetic cloud (IME ejecta). The data are from the WIND experiment. 9of3

10 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 projection effect correction are also within acceptable ranges; and the predicted transit time of 47.3 hr are even closer to the observed travel time. This is due to the fact that the projection speed at PA = 39 is very close to the actual speed (see Figure 3b). Figure 3b shows that for the event of 4 April 2 the apparent speeds measured at PA 276 to 355 are nearly equal to the actual speed. 5. Dependence of the Occurrence of Earth- Directed Halo MEs on the Orientation and Angular Wih [27] Front-side halo MEs are considered the main cause of large geomagnetic storms [e.g., Webb et al., 2; ane et al., 998; Gopalswamy et al., 2; Wang et al., 22]. LASO has detected halo MEs (including partial halo MEs, which are defined as those with spans 4 ) totaling % of all MEs during the ascending and maximum phases of the current solar cycle [Zhao and Webb, 23]. However, not all front-side halo MEs are causing storms (are geoeffective). There are two constraints on the geoeffectiveness of halo MEs: () the MEs have to be able to reach the Earth; (2) the MEs must produce long duration southward magnetic field component in interplanetary medium. [28] The first constraint on geoeffective MEs is related to the ME propagation direction and its actual size, i.e., the orientation and angular wih of the halo ME. Figure shows that the projection of the cross-section of MEs should at least pass the line-of-sight, i.e., z c -axis in the Figure, in order to reach the Earth. That is (x c ) min. From equation (8), we have ðx c Þ min ¼ rsin w sin q þ r cos w cos q; ð8þ where d = 9, thus, sin w sin q þ cos w cos q ¼> tgw cot q; w 9 q: ð9þ Equation (9) gives the constraint relation between half angular wih and cone s central orientation for a ME to encounter the Earth. [29] onstraint relation (9) can be illustrated by using Figure 9. When a ME originates at the solar disk center (D) O, the constraint is equivalent to w b, where b = 9 q is the angle between the cone axis and the line-ofsight. This result agrees with the derivation in Liu et al. s [22] study. If MEs originate from any arbitrary point O near the D, the constraint relation should be modified as follows: w b + D, where D = L/AU (see Figure 9). In this case, the ME may appear as a partial halo in LASO images, and its orientation may not be aligned with the latitude of the solar source surface region. This explains why partial halo MEs can be geoeffective even if solar source regions are located at high latitudes or close to either limb. [3] The second constraint on geoeffective MEs is that there exists southward component in the interplanetary ME (IME, the counterpart of ME in interplanetary space). The orientation of the magnetic field in IME or Figure 7. Height-time plots of apparent speeds and accelerations of the 4 April 2 ME using (a) first order fit and (b) second order fit. magnetic cloud has been found to correlate with the direction of magnetic field and magnetic helicity in ME s source active regions such as pre-eruptive filament or post-eruption coronal arcade [othmer and Schwenn, 994; Zhao and Hoeksema, 998; McAllister and Martin, 2; Yurchyshyn et al., 2]. The study of magnetic structure in halo MEs is beyond the scope of this paper, and future work using MHD models is planned. 6. Summary and Discussion [3] An innovative analytical method has been derived to determine the angular wih and central position angle of a cone model ME. The relationship of apparent speed V r and its components V xh, V yh, V xc and V yc with azimuthal angle d (and corresponding position angle PA) for fixed ME actual radial speed V r has been investigated. The ME transit time was estimated by using actual radial speeds for several cases. Also, possible constraints on Earth-directed of 3

11 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 Figure 8. Solar wind plot for the major geomagnetic storm on 4 April 2 (Day of year = 97). From top to bottom the panels are plasma velocity, density, and magnetic field components in x, y, and z direction (GSE) respectively. The vertical solid line indicates the time of the IME shock front arrival at the WIND spacecraft in the near Earth space. The data are from the WIND experiment. of 3

12 A39 XIE ET AL.: ONE MODEL FOR HALO MES A39 work is supported by the NSF program (ATM-27588) and NASA grant NAG We wish to acknowledge the support of SOHO/LASO team. SOHO is a mission of international cooperation between the European Space Agency and NASA. We acknowledge the use of data from the LASO ME catalog and the WIND spacecraft. The ME catalog is generated and maintained by the enter for Solar Physics and Space Weather, atholic University of America, in cooperation with the Naval Research Laboratory and NASA, and the WIND magnetic field and plasma data are from on-line DA Web site of NASA/GSF. [34] The Editor thanks Volker othmer and Haimin Wang for their assistance in evaluating this paper. Figure 9. Illustration of the constraint relation between angular wih and orientation for a front-side ME to encounter the Earth. halo (full & partial) ME were proposed. We find that the applied model predictions are in good agreement with observations. ompared to previous studies, this method improves the accuracy and efficiency of the modeling. It is the first time that the ME s actual speed, wih, and source location are determined using coronagraph data quantitatively, and consistently. These parameters are critically important in space weather modeling. [32] While the cone model produces significant enhancements in predictions by using the actual speeds of MEs, uncertainties remain. For instance, the accuracy of ME transit time prediction relies on the accuracy of ME actual speeds and accelerations, which are derived from apparent speeds and accelerations. urrently, apparent speeds and accelerations of MEs can only be measured within 3 R s (field of view of LASO/3). We know little about them beyond 3 R s. 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