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A Coronal Mass Ejection (CME) is an ejection of energetic plasma with magnetic field from the Sun. In traversing the Sun-Earth distance, the kinematics of the CME is immensely important for the prediction of space weather. The objective of the present work is to study the propagation properties of six major geo-effective CMEs and their associated interplanetary shocks which were observed during solar cycle 24. These reported CME events produced intense geo-magnetic storms (Dst > 140 nT). The six CME events have a broad range of initial linear speeds ~600 - 2700 km/sec in the LASCO/SOHO field of view, comparing two slow CMEs (speed ~579 km/sec and 719 km/sec), three moderate speed CMEs (speed ~1366, 1571, 1008 km/sec), and one fast CME (speed ~2684 km/sec). The actual arrival time of the reported events is compared with the arrival time calculated using the Empirical Shock Arrival model (ESA model). For acceleration estimation, we utilize three different acceleration-speed equations reported in the previous literatures for different acceleration cessation distance (ACD). In addition, we compared the transit time estimated using the second-order speed of CMEs with observed transit time. We also compared the observed transit time with transit time obtained from various shock arrival model. From our present study, we found the importance of acceleration cessation distance for CME propagation in interplanetary space and better acceleration speed for transit time calculation than other equations for CME forecasting.

Coronal Mass Ejection is the most energetic process of solar atmosphere. The CME can be defined as an ejection of plasma with magnetic field from the Sun to the interplanetary space. And its effect on Earth’s environment and space weather. Kinematics of CMEs in space depends upon the initial seed additionally affected by ambient solar wind conditions [

We studied the set of six major geo-effective CME events observed by SOHO/ LASCO during the solar cycle 24. The six CME events generated geo-magnetic storms of high intensity Dst > 140 nT. These selected CMEs events are associated with C, M and X class X-ray flares. The detail of selected CMEs, associated flare and geo-magnetic storms are listed in

CME | Speed (km/s) | Flare | IP Shock | ||||
---|---|---|---|---|---|---|---|

Date/Time | T_{Rise} T_{Peak} T_{End} | Intensity | Location | Date/Time | Dst | IP Shock TT | |

22-10-2011 10:25 | 1005 | 15:14 15:29 15:20 | M1.3 | N29W91 | 24-10-2011 18:31 | −147 | 63.17 |

07-03-2012 00:24 | 2684 | 00:02 00:40 00:24 | X5.4 | N17E15 | 08-03-2012 11:03 | −145 | 33.4 |

15-03-2015 01:48 | 719 | 01:15 03:20 02:13 | C1.3 | S19W25 | 17-03-2015 04:45 | −223 | 50.95 |

21-06-2015 02:36 | 1366 | 01:02 02:00 01:42 | M2.0 | N12E16 | 22-06-2015 18:33 | −204 | 39.59 |

16-12-2015 09:24 | 579 | 08:34 09:23 09:03 | C6.6 | S13W04 | 19-12-2015 16:16 | −155 | 78.86 |

06-09-2017 12:24 | 1571 | 11:53 12:10 12:02 | X9.3 | S09W42 | 07-09-2017 22:38 | −142 | 34.23 |

http://www.lesia.obspm.fr/cesra/highlights/highlight07-5.html. The geomagnetic storms details are obtained from: http://wdc.kugi.kyoto.u.ac.jp/Dst_realtime/index.html. And Omni web from: https://omniweb.gsfc.nasa.gov/form/dx1.html. X-ray solar flare data (start time, peak time, last time and intensity) obtained from: https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/. The arrival time of CMEs and their associated interplanetary shocks/ICME are determined from the time difference between the first detection (appearance) time of a CME in C2 coronagraph on-board at SOHO/LASCO and IP shock/ ICME arrival time in ACE/Wind, identified by variation in solar plasma parameters (density, temperature, velocity, etc.) and magnetic field strength at 1 AU.

Gopalswamy et al., 2001 and Kim et al., 2007 described a procedure to estimate transit time of CME at 1 AU [_{1} + T_{2} where T_{1} is the time of travel up to the acceleration cessation distance d_{1} up to 1 AU (in Equation (1)) and T_{2} is travel time for reaming distance d_{2} at the constant speed (in Equation (2)). For estimating acceleration, we are using three different equations (Equations (3)-(5)) given by Gopalswamy 2001, Michalek et al. 2004. To obtain the effective interplanetary acceleration from the linear initial speed of CMEs and arrival time with three acceleration cessation distances (ACD = 0.7 AU, 0.6 AU and 0.5 AU) and then CME travels the remaining distance (0.3 AU, 0.4 AU and 0.5 AU) with constant speed respectively. Therefore, it is good for study to compare the calculated travel time of these CMEs with the observed travel time. The transit time equations for T_{1} and T_{2} are given by Gopalswamy et al., 2001 are the following:

T 1 = − u + ( u 2 + 2 a d 1 ) a (1)

T 2 = d 2 ( u 2 + 2 a d 1 ) (2)

where u is the linear speed and a is the acceleration at interplanetary medium. We calculate interplanetary acceleration of selected CMEs using with different following equations,

Gopalswamy et al. (2001) a = 2.193 − ( 0.0054 ∗ u ) (3)

Michalek et al. (2004) a = 4.11 − ( 0.0063 ∗ u ) (4)

Michalek et al. (2004) a = 3.35 − ( 0.007 ∗ u ) (5)

In the equations above, u is the initial speed of CME. Now we compare the transit times calculated using these above equations with the actual transit time of reported CME events.

As we have three equation for calculating transit time, so firstly we calculate Transit time using Equations (1) and (2) with acceleration speed Equation (3) given by Gopalswamy et al.; 2001 at different acceleration cessation distances (0.7 AU, 0.6 AU and 0.5 AU). The graphical representation of transit time for various ACD 0.7 AU, 0.6 AU and 0.5 AU against CME speed is plotted in Figures 1(a)-(c) respectively. For comparison, we also plotted transit time profiles estimated by using ESA model for three different acceleration cessation distances. The differences between estimated transit time for various acceleration cessation distances and actual arrival time are reported in

No. of Event | ∆T_{IP} _{Shock} Using Equation (3) | ∆T_{IP} _{Shock} Using Equation (4) | ∆T_{IP} _{Shock} Using Equation (5) | ||||||
---|---|---|---|---|---|---|---|---|---|

0.7 AU | 0.6 AU | 0.5 AU | 0.7 AU | 0.6 AU | 0.5 AU | 0.7 AU | 0.6 AU | 0.5 AU | |

1 | 0.76 | 7.57 | 10.324 | 4.77 | 13.84 | 22.186 | 12.033 | 1.51 | 6.323 |

2 | 15.29 | 15.49 | 15.792 | 15.18 | 15.39 | 15.72 | 14.41 | 14.75 | 15.19 |

3 | −31.75 | −27.22 | −23.44 | −17.03 | 1.529 | −36.51 | −31.54 | −27.39 | −23.34 |

4 | −0.38 | 0.893 | −0.38 | 0.791 | 2.568 | 1.733 | −4.484 | −2.09 | 0.18 |

5 | 48.46 | 46.33 | 45.21 | 50.3 | 47.651 | 42.88 | 40.46 | 46.349 | 43.68 |

6 | 0.61 | 1.48 | 6.4 | 1.51 | 3.64 | 3.07 | −2.42 | −0.83 | 0.79 |

calculated by using Equations (4) and (5) respectively. On the other hand acceleration-speed Equation (5) gives the approximately nearly consistent transit time value with the actual transit time (approximately 0.8 - 15 hr) 6th except event 3rd and 5th events. From the table, we can see that Equation (3) produced the minimum error (∆T_{IP} _{Shock} = 0.6 - 10 hr) for three CME events (1st, 4th and 6th). We get the actual arrival time values of IP shock from Equation (3) for event 1st, 2nd, 4th and 6th but the deviation is more for other two events (event 3rd and 5th), this is may be due to the their slow linear speed (719 km/sec and 579 km/sec respectively).

In this section of observation, we obtained the arrival time using second-order speed of CMEs instead of linear speed reported in the LASCO/SOHO catalogue. So here we are estimating transit time from Equation (3) by using two different second-order speed: 1) at 20 solar radius and 2) at final distance at different acceleration cessation distance (0.7 AU) using ESA model with acceleration-speed Equation (3). In

using second order speed at 20 solar radius and at final distance respectively. The transit time error (within ±11 hr) for the last four events, while the transit time error (~0.2 - 7 hr) for last three events using second-order speed at a final distance. It seems from the investigation above that the speed at final speed gives the arrival time nearly consistent with the actual arrival time.

In this section, we compare the actual arrival time with transit time obtained by other models (_{0}), CME speed at r_{0} (v_{0}), asymptotic solar wind and drag parameter. The DBM tool is accessible in the website http://oh.geof.unizg.hr/index.php/en/spaceweather-tools. After putting all the values for reported CMEs, we have got the transit times at 1 AU. We have taken average ambient solar wind speed as 500 km/sec, which is the average speed of plasma flow recorded by in-situ instrument. Schwenn et al. (2005) proposed a relationship between the arrival time and linear speed of CMEs as:

T r r = 203 − 20.77 ∗ ln ( V CME )

where T_{rr} is arrival time and V_{CME} is linear speed of CME. In this case of arrival time of interplanetary shock, minimum transit time error is given by DBM model for four events (less than 6 hr).

No. of Event | Second-Order Speed (at Final Distance) | Second-Order Speed (at 20 Solar Radii) | ||||
---|---|---|---|---|---|---|

0.7 AU | 0.6 AU | 0.5 AU | 0.7 AU | 0.6 AU | 0.5 AU | |

1 | 26.73 | 26.67 | 26.75 | 23.64 | 23.58 | 23.67 |

2 | 15.71 | 15.67 | 15.70 | 17.19 | 17.16 | 17.18 |

3 | −18.44 | −18.56 | −18.42 | −11.33 | −11.43 | −11.28 |

4 | −0.27 | −0.34 | −0.25 | 2.60 | 2.54 | 2.62 |

5 | −0.95 | −1.12 | −0.98 | −7.51 | −7.71 | −7.60 |

6 | 7.29 | 7.23 | 7.28 | 7.30 | 7.25 | 7.30 |

∆T _{IP Shock} (in Hours) | ||
---|---|---|

Schwenn Model | Drag Based Model | Constant Speed Model |

3.75 | 15.7 | 21.71 |

−5.61 | 5.14 | 17.87 |

−15.42 | −6.47 | −7 |

−15.99 | −0.79 | 5.12 |

7.99 | 12.44 | 6.89 |

−15.91 | −3.34 | 7.7 |

For the present study, we presented the estimation of arrival time of six major coronal mass ejections which produced intense geo-magnetic storms more than Dst > 140 nT observed during solar cycle 24. The reported CME events have different linear speed such as ~579 - 2684 km/sec. The interplanetary acceleration values, calculated from the speed of CME using various acceleration-speed equations, are utilized in the ESA model. All the plots regarding transit time of CMEs at 1 AU obtained by using ESA model for three different acceleration cessation distance (0.5 AU, 0.6AU and 0.7AU). Study demonstrated that each event acts differently in the interplanetary space. The CME propagation is also governed by the speed of CME, interplanetary acceleration/deceleration and acceleration cessation distances. Summarizing the above study and analysis, it is seen that the result of all comparison of arrival times for reported six CME, the arrival time (transit time) error is minimum for the acceleration Equation (3) for ESA model. In addition, the transit time are compared with various models (constant speed model, Schwenn Model and Drag Based Model). Especially, the minimum arrival time error is obtained for Drag Based Model (DBM) for the acceleration-speed Equation (4) for ESA model. Presented study also shown that the linear speed provide minimum transit time error, instead of second order speed at final distances or at 20 solar radii.

We are grateful to Solar Geo-physical Data team, Kyoto and OMNI data team for their open data source policy. Authors are thankful to SOHO/LASCO CME catalogue (generated and maintained by CDAW data centre by NASA). We thank Prof. Bhuwan Joshi, USO, Physical Research Laboratory, Ahmedabad, and Pro. Hari Om Vats, scientist, Physical Research Laboratory, Ahmedabad India for his great support to us.

The authors declare no conflicts of interest regarding the publication of this paper.

Soni, S.L., Singh, P.R., Nigam, B., Gupta, R.S. and Shrivastava, P.K. (2019) The Analysis of Interplanetary Shocks Associated with Six Major Geo-Effective Coronal Mass Ejections during Solar Cycle 24. International Journal of Astronomy and Astrophysics, 9, 191-199. https://doi.org/10.4236/ijaa.2019.93014