ZEC Model parameters of Halo CMEs Xuepu Zhao Jan. 18, 2011

1. Observation According to the _22:00 USAF/NOAA Report of Solar and Geophysical Activity, there were two halo CMEs on Aug. 1, One is a partial-halo CME associated with the 07: :11 UT disappearing filament centered near N37W32 and the other is a full-halo CME associated with the 08:26 UT long-duration flare at N13E21 or N20E35 in AR The two halo CMEs may be a chain reaction. Schrijver and Title (see news/science-at-nasa/2010/13dec_globaleruption/) recently suggest that the solar storm is a “global event”, i.e., an eruption of the entire hemisphere of the Sun. This storm contains., flares, tsunamis, CMEs, and all components go off all at once, hundreds of thousands of miles apart.

Was the event one big chain reaction, in which one eruption triggered another? Or did everything go off together caused by global reconfiguration through, say, the loss of equilibrium of global magnetic field ? As shown in Figure 1, the halo CMEs were first seen in LASCO/C3 at 14:18 UT, several hours after the onset of the associated flares and DSF (There was no C2 observation before 14:18 UT). If it is a chain reaction, the _14:18 halo image may be made of partial and full halo CMEs associated with the two near-surface activities. However, If the solar storm is a “global event”, the halo image may be a single halo CME!

Fig 1. Six white-light halo images observed by SOHO/LASCO C3 between 14:18 UT and16:48 Aug. 1, All images show complicated structure, suggesting that it may be a composite event.

2. Identifying elliptic outline of the _14:18 halo CMEs If it is a single event, an elliptic outline may be obtained by selecting 5 points well-distributed around entire edge of the halo image (Cremades, 2005), as shown by the five green dots in the left panel of Figure 2. How to recognize the full- and partial- halo CME from the images in Figure 1? It is a challenge!

Fig 2 The three elliptic outlines obtained based on the five green dots in the three panels. The elliptic outlines in the Left, middle, and right panels are for the case of Single-halo, Full-halo, and Partial-halo CMEs. To find the elliptic outline of the full- and partial-halo CMEs, we tried to select five points located on the well-recognized half of outer edge of halos (see the five green dots in the middle and right panels of Figure 2).

2.1 Five halo parameters obtained based on the three elliptic outlines in Fig. 2 Table 1 Five Halo parameters SAx Say Dse ψ α Single-halo 11.2 Rs 12.3 Rs 1.24 Rs -34° 133° Full-halo 10.4 Rs 13.7 Rs 1.35 Rs -12° -108° Partial-halo 6.8 Rs 10.0 Rs 4.15 Rs -22° -13°

3. ZEC model parameters We calculate six ZEC model parameters using the one-point approach on the basis of the five halo parameters and the position of the associated near surface activity (Zhao, 2008). We first calculate the CME projection angle β and CME propagation direction, using the halo parameter α and flare position (see top panels of Figure 3), then invert the other four model parameters from the halo parameters (see the bottom panels of Fig 3).

Fig 3 Inversion of the 3-D geometrical property of the _14:18 single, full- and partial-halo CMEs using the halo parameters of the single, full and partial halo CMEs and the position of flare and DSF, i.e. N13E21 (left), N20E35(middle), and N37E32 (right column).

3.1 Six ZEC model parameters and CME propagation directio (λ, φ) Table 2 Model parameters & CME propagation direction α β χ ωy ωz Rc λ φ Single-halo 133° 81.3° -37.0° 56.3° 53.9° 8.25 Rs -6.34° -5.96° Full-halo -108° 63.1° -19.0° 77.9° 75.5° 2.99 Rs 25.42° -9.08° Partial-halo -13° 54.7° -35.0° 56.4° 47.8° 7.17 Rs 7.54° 34.58°

3.2 The kinematic property of the full- and partial- halo CMEs The six C3 images in Figure 1 may be used to measure the sky- plane speed, Vs, and sky-plane acceleration, As, at the measured polar angle, mpa, for the single-, full- and partial-halo CMEs. By combining mpa, Vs, As with the inferred model parameters in Table 1, the true radial speed, Vr, and acceleration, Ar, at time, T21.5, when the CME was arriving at 21.5 solar radii (See Table 3). Table 3 Kinematic properties mpa Vs As T21.5 Vr Ar Single-halo 9° 425 km/s :49UT 569 km/s 0.0 Full-halo 9° 425 km/s :20UT 436 km/s 0.0 Partial-halo 253° 464 km/s :58UT 466 km/s 0.0

4. Propagation direction of the full-halo CME observed by STEREO A/B COR1 and COR2 On Aug. 1, 2010 the Earth Ecliptic (HEE) longitudes of the STEREO Ahead and Behind are 78.4° and °, respectively. The Earth-directed halo CME observed by STEREO Ahead and Behind would be east and west limb CMEs. Figures 4 and 5 show limb CMEs observed by COR1 and COR2.

Fig 4 Ahead (left) and Behind (right) COR1 Observation between 08:01 and 10:01 UT Fig 5 Ahead (left) and Behind (right) COR2 Observation between 08:09 and 10:09 UT

Fig 5 shows east and west limb CMEs with angular width greater than 45°. This pair of limb CMEs started after 08:09UT, implies that it is a Earth-directed CME, the same as the SOHO/C3 full halo CME. To see if its propagation direction is in north-east quadrant, we infer its propagation direction on the basis of the measured image-plane longitude α a and α b of the central axis of the limb CMEs (Zhao, 2011), as shown in Figure 6. It is found that the propagation direction of the Earth-directed CME is indeed in the north-east quadrant, i.e., N11E26, qualitatively agreeing with above result (Table 1).

5. Summary 5.1 We tried to find out the elliptic outline of halo CMEs on the basis of the five points selected around a half of and the whole edge of halo CMEs. 5.2 Based on the assumptions of global storm and chain reaction, we calculate the ZEC model parameters from the elliptic outlines in Figure 2.

5.3 The inferred geometrical and kinematical properties for Single-, Full- and Partial-halos (see Table 4) may be used as an input to simulate CME propagation or interaction in the heliosphere, and to see which agrees with in situ observation. Table 4 The time and model parameters at 21.5 Rs T21.5 λ φ ωy ωz χ Vr Single-halo 16:49UT -6.34° -5.96° 56.3° 53.9° km/s Full-halo 18:20UT 25.42° -9.08° 77.9° 75.5° km/s Partial-halo 17:58UT 7.54° 34.58° 56.4° 47.8° -35.0° 466km/s