1. The Occurrence and Speed of CMEs Related to Magnetic Helicity Injection in Their Source Regions Sung-Hong Park Solar and Space Weather Research Group Korea Astronomy and Space Science Institute 2011 1 st APSP Meeting # Major Results 1. Importance of long-term evolution of magnetic helicity injection in source regions prior to CMEs 2. Two groups of CMEs classified by two characteristic helicity evolution patterns 3. Fairly good correlation between CME speed and helicity injection rate

2. 2011-03-241st APSPM 1. Introduction - Coronal Mass Ejections (CMEs) are the transient ejections into interplanetary space of as much as a few billion tons of plasma and embedded magnetic fields from the solar corona. - Most of CMEs occur in active regions where intense magnetic fields exist in the solar atmosphere, from the photosphere to the corona. In addition, it is generally thought that CME-productive active regions have complex and non-potential magnetic structures. 1.1 CMEs in Solar Active Regions Hinode/FG/Stokes-VSOHO/LASCO+EIT Active Region NOAA 10930 2006-12-13 Halo CMELine-of-sight Magnetic Field 2

3. 2011-03-241st APSPM 1.2 Why Study Magnetic Helicity? - Magnetic helicity is a useful parameter to represent the non-potentiality of a magnetic field system. - Many of observations and simulations of solar eruptions indicate that the eruptions are associated with twisted magnetic field configuration. - Therefore, magnetic helicity can be considered as a parameter to study the energy buildup and instability leading to solar eruptions. An eruptive prominence on 2010 March 30 (courtesy of SDO Team). 1.3 Main Objective of This Study - Magnetic helicity injected through the photospheric surface of CME-productive active regions is studied to find its relationship with (1) the gradual inflation of an active region coronal arcade building up to a CME and (2) the occurrence and speed of CMEs, which not only help to understand physical processes of energy build-up and onset of CMEs, but also provide a useful tool to carry out CME predictions. 3

4. 2011-03-241st APSPM 2.1 Magnetic Helicity - Magnetic helicity is a measure of how much magnetic field lines in a flux tube are twisted around the tube axis (twists), how much the tube axis is kinked (kinks), and how much flux tubes are interlinked with each other in a magnetic field system (inter-linkages). - Mathematically, magnetic helicity, H, inside a volume, V, of a magnetic field system is defined by: where A is the vector potential of magnetic field, B (i.e., B= ▽ × A). 2. Calculation of Magnetic Helicity in Active Regions P : potential field having the same normal component as B on S cor A p : vector potential for P - Relative magnetic helicity in a coronal volume V cor (Berger & Field 1984; Finn & Antonsen 1985): a gauge-invariant formula 4

5. 2011-03-241st APSPM 2.2 Magnetic Helicity Injection through a Photospheric Surface where v represents the plasma velocity, and subscripts n and t denote the normal component and the transverse component to S, respectively. A p is a specific vector potential satisfying: - Berger & Field (1984) derived the change rate of magnetic helicity, H r, in an open volume through a boundary surface, S : ∙ - Démoulin & Berger (2003): Field line footpoint velocity : Potential Field : Coulomb Gauge : Vanishing Normal Component 5

6. 2011-03-241st APSPM 2.3 Practical Method for Calculating - Chae (2001) developed a practically useful method for calculating using v LCT, the velocity of the apparent motion of field lines determined by the technique of local correlation tracking (LCT), instead of using u: HrHr ∙ with the integrand called magnetic helicity flux density (magnetic helicity per unit area per unit time). where t 0 and t are the start and end time of the magnetogram data set under investigation, respectively. - After is determined as a function of time, the amount of helicity accumulation, Δ H r, is calculated by integrating with respect to time: HrHr ∙ HrHr ∙ HrHr ∙ 6

7. 2011-03-241st APSPM 3.1 Gradual Inflation of a Coronal Arcade Building up to a CME (Liu, R., Liu, C., Park, S., Wang, H. 2010, ApJ, 723, 229) 3. Results Slow Rising of Coronal Arcade on 2006 July 4 7

8. 2011-03-241st APSPM -The time-height profile of the coronal arcade is similar to the short-term (several hours) profile of helicity injection in the active region where the coronal arcade is anchored. -One remarkable thing is that there was a significant and continuous helicity injection for 2 days before the measurement time of the gradual inflation of the arcade, but magnetic flux changes very little in the active region. Slow Rising of Coronal Arcade on 2006 July 4 8

9. 2011-03-241st APSPM 3.2 Two CME Groups by Helicity Injection Patterns By calculating helicity injection rate in 28 active regions producing 46 CMEs, it is found that 46 CMEs can be categorized into two different groups by the two characteristic evolution patterns of helicity injection in their source regions. ※ Group A - 30 CMEs - a pattern of continuous helicity injection followed by no (or a little) injection for a while ※ Group B - 16 CMEs - a pattern of significant helicity injection followed by its sign reversal 9

10. 2011-03-241st APSPM 3.2.1 Monotonically Increasing Phase of Helicity in Group A 10

11. 2011-03-241st APSPM 3.2.1 Monotonically Increasing Phase of Helicity in Group A (Cont.) The same helicity variation pattern is shown in the other cases of Group A. 11

12. 2011-03-241st APSPM - Fan & Gibson (2004) Hood & Priest (1981) studied the stability of line-tied, uniformly twisted, force-free cylindrical flux tubes and found that the tubes become kink-unstable when the number of rotations that each field line winds about the axis between the line-tied ends exceeds 1.25. Fan & Gibson (2004) performed isothermal MHD simulations of the three-dimensional evolution of the coronal magnetic field as an arched, twisted magnetic flux tube emerges gradually into a pre-existing coronal arcade, under the condition of low β-plasma and high electric conductivity. 3.2.1 Monotonically Increasing Phase of Helicity in Group A (Cont.) 12

13. 2011-03-241st APSPM 3.2.2 Helicity Reversal Phase of 16 CMEs in Group B A trigger by reconnection-favorable emerging flux (Chen & Shibata 2000) - CMEs are triggered by the localized reconnection between the reconnection- favorable emerging flux and pre-existing coronal field. - Observational supports (Feymann & Martin 1995; Wang et al. 2004; Jing et al. 2004) 13

14. 2011-03-241st APSPM 3.2.3 Comparison Between Group A and Group B - The CME speed of Group B is much faster than that of Group A. There is also a significant difference in the CME acceleration between Group A and Group B. - Furthermore, the CMEs in Group A tend to be single events, while those in Group B mainly consist of successive events. - These differences may indicate different pre-CME conditions and trigger mechanisms for the two groups. CMEs in Group A seem to be associated with the kink instability. CMEs in Group B might be involved with the emergence of opposite sense of helicity into an existing helicity system, and perhaps an interaction between two helicity systems may be responsible for the CMEs in Group B. 14

15. 2011-03-241st APSPM 3.3 Correlation of Helicity Injection Rate with the Speed of CMEs - The 30 CMEs in Group A were used for the study of helicity injection related to the CME speed. - The solid line indicates the least-squares linear fits to the data points. The correlation coefficient (CC) of the linear fits is also given in the panel. - There is a fairly good correlation (CC=0.71) between | | and the CME speed.. 15

16. 2011-03-241st APSPM - A coronal arcade in AR 10898 is examined. The gradual inflation of the arcade sustains for hours at ~5 km/s, and it is temporally associated with helicity injection. - The CMEs under investigation can be categorized into two different groups by the two characteristic evolution patterns: (1) a monotonically increasing phase with one sign of helicity (Group A, 30 CMEs in 23 active regions) and (2) a phase of significant helicity injection followed by its sign reversal (Group B, 16 CMEs in 5 active regions). - It is suspected that these two groups may have different preconditions and trigger mechanisms. CMEs in Group A seem to be associated with kink instability. CMEs in Group B seem to be involved with emergence of the helicity in the opposite sign into an existing helicity system. - A fairly good correlation (CC=0.71) between the average helicity injection rate and the speed of 30 CMEs in Group A is found. 4. Summary and Conclusion 16

17. 2011-03-241st APSPM References Berger, M. A. and Field, G. B.: 1984, Journal of Fluid Mechanics 147, 133 Chae, J.: 2001, Astrophys. J. Lett. 560, L95 Chen, P. F. and Shibata, K.: 2000, Astrophys. J. 545, 524 Démoulin, P. and Berger, M. A.: 2003, Sol. Phys. 215, 203 Fan, Y. and Gibson, S. E.: 2004, Astrophys. J. 609, 1123 Feynman, J. & Martin, S. F. 1995, J. Geophys. Res., 100, 3355. Finn, J. M. and Antonsen, T. M.: 1985, Comments Plasma Phys. Controlled Fusion 9, 111 Hood, A. W. and Priest, E. R.: 1981, Geophysical and Astrophysical Fluid Dynamics 17, 297 Jing, J., Yurchyshyn, V. B., Yang, G., Xu, Y., & Wang, H. 2004, Astrophys. J., 614, 1054. Wang, J., Zhou, G., & Zhang, J. 2004, Astrophys. J., 615, 1021 Acknowledgments New Jersey Institute of Technology Seoul National University Dr. Haimin Wang Dr. Jongchul Chae Dr. Jeongwoo Lee Dr. Rui Liu KASI/Solar and Space Weather Research Group Dr. Young-Deuk Park Dr. Kyung-Suk Cho Dr. Yeon-Han Kim Dr. Su-Chan Bong 17

18. 2011-03-241st APSPM is the heliocentric angle of the point of interest 2006-12-10 04:51:30 UT 2006-12-10 06:27:30 UT 2006-12-10 08:03:30 UT 2006-12-10 05:39:30 UT 2006-12-10 07:15:30 UT Averaged Local Correlation Tacking (LCT) -Window size = 10” -Window function: top-hat profile -Correlation criterion: above 0.9 -B z criterion: above 5 G Fast Fourier Transform GAGA × (-2B n ) v LCT ApAp × BnBn 18

19. 2011-03-241st APSPM ※ List of CMEs in Group A 19

20. 2011-03-241st APSPM ※ Parameterization of the long-term evolution of helicity injection rate a, b, c, d, & e = constants 1. CME speed 2. CME occurrence time 20