Geoeffectiveness of solar eruptions during the rising phase of solar cycle 24

New Astronomy 51 (2017) 74–85

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Geoeffectiveness of solar eruptions during the rising phase of solar cycle 24 Hema Bisht a, Bimal Pande b,∗, Ramesh Chandra b, Seema Pande a a b

Department of Physics, MBPG College, Haldwani, India Department of Physics, DSB Campus, Kumaun University, Nainital, India

h i g h l i g h t s • • • • •

We have taken 33 halo CME events of the current solar cycle 24 (2009–2013). We analyzed statistically the different parameters responsible for the geoeffectiveness of solar eruptions. Big flares produce high speed CME. The source location of geoeffective halo CME events exhibit N-S asymmetry. Out of these 33 halo CME events, the majority are associated with M class flares.

a r t i c l e

i n f o

Article history: Received 19 June 2015 Revised 10 August 2016 Accepted 21 August 2016 Available online 24 August 2016 Keywords: Dst index CMEs Geomagnetic storms Solar flares

a b s t r a c t This paper presents a statistical analysis of different parameters responsible for the geoeffectiveness of solar eruptions during the rising phase of solar cycle 24. We have selected 33 halo CME events from the beginning of the current solar cycle 24 (2009–2013). The levels of geomagnetic activity are categorized into two groups based on the observed minimum Dst index, i.e., moderate (−100 nT < Dst ≤ −50 nT) and intense (Dst ≤ −100nT). The parameters are represented graphically and analyzed statistically. The Spearman rank correlation coefficient between Dst index and CME speed is 0.02 with a P-value 0.91 (much higher than 0.05) and between Dst index and X-ray flux of flares is 0.13 with a P-value 0.48 (higher than 0.05), which shows that high speed CMEs and big flares are not the effective and significant parameters for geoeffectiveness of these selected halo events. The Spearman rank correlation coefficient between CME speed and X-ray flux is better, i.e., 0.38 and the P-value is equal to 0.03 (less than 0.05), which clearly implies that big flares are responsible for producing high speed CMEs and both parameters share a significant relationship . The source location of geoeffective halo CME events exhibit N-S asymmetry. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Coronal mass ejections or CMEs are the most energetic and largest phenomena linked with the magnetic field and plasma expelled from the Sun’s corona in the heliosphere. Gopalswamy (2006) explained CMEs as large scale magnetized plasma structures that originate from closed magnetic field regions on the Sun. These regions are active regions, filament regions, active region complexes and trans-equatorial interconnecting regions. They are the major solar drivers of space-weather and are responsible for causing a significant impact on the near-Earth space environment in the form of geomagnetic storms (Baidyanath et al., 2010; Chen, 2011; Gopalswamy et al., 2005; Gosling et al., 1991; Joshi et al., 2011; Tsurutani et al., 1988; Webb and Howard, 2012). ∗

Corresponding author: Tel.: +919412044061; Fax: +915942237450. E-mail addresses: [email protected] (H. Bisht), [email protected] (B. Pande). http://dx.doi.org/10.1016/j.newast.2016.08.014 1384-1076/© 2016 Elsevier B.V. All rights reserved.

Coronal mass ejections (CMEs) occurring close to the solar disk center are important from the space-weather point of view. They are likely to affect the Earth magnetosphere and hence are effective for predicting geomagnetic storms (Cid et al., 2012; Gopalswamy, 2006; Sharma et al., 2008). Such Earth-directed CMEs are a major cause of severe geomagnetic storms (Chen, 2011; Cid et al., 2012; Gopalswamy et al., 2005; Gopalswamy, 2006; Gopalswamy et al., 2007, 2010; Gosling et al., 1991; Sharma et al., 2008; Tsurutani et al., 1988; Webb et al., 20 0 0; Webb and Howard, 2012). CMEs aimed at Earth are referred to as halo events (apparent angular width equal to 3600 ) on account of the way they look in coronagraph images. As the expanding cloud of an Earth-directed CME emerges larger and larger, it appears to envelope the Sun, hence forming a halo around it. Thus, the halo CMEs appear as enhancements, encompassing the “occulting disk” of coronagraphs (Gopalswamy, 2009; Howard et al., 1982; Webb and Howard, 2012). These halo CMEs were first

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reported by Howard et al. (1982) on the basis of observations from Solwind on P78-1. Now a day, the images taken by the LASCO C2 and C3 instruments located on the SOHO (Solar and Heliospheric Observatory) spacecraft are put to use to be certain, whether a coronal mass ejection is directed towards Earth or not. The solar magnetic field responsible for controlling all the cyclic changes is engendered and maintained by circulating currents in the convection zone, potentially mixed up by turbulent currents which are produced by the change in rotational speed occurring at the periphery between radiative and convective zones. Variations in the solar wind compress the magnetosphere and produce perturbations known as geomagnetic storms (Kamide and Maltsev, 2009; Nicolson, 1999) A geomagnetic storm is a major component of space weather. According to Gonzalez et al. (1994), a geomagnetic storm is defined as an interval of time during which a sufficiently intense and long lasting interplanetary convection electric field advances through a substantial energization in the magnetosphere-ionosphere system, to an intensified ring current strong enough to surpass some key threshold of the quantifying storm time, Dst index. Dst (Disturbance Storm Time) index are the hourly values of the mean global variation of the low-latitude horizontal (H) component of the geomagnetic field caused by the changing magnetospheric ring current. These hourly values were first published by Sugiura (1964) for the International Geophysical Years. At present, these are assembled by the World Data Center C for Geomagnetism in Kyoto, Japan. The characteristic feature of a geomagnetic storm is a depression in the horizontal component of geomagnetic field enduring more than one to a few days, given by the Dst index (Sugiura, 1964; Kamide and Maltsev, 2009). It is broadly accepted that storms are times with a Dst(min) less than -50nT. Consequently, 20 to 50 storm events occur annually, depending upon solar activity. When the horizontal component of geomagnetic field attains a negative value of about 25– 30 nT, Dst(min) occurs in a range of 20 0–60 0 nT (Kane, 2012). Dst decrease or Dst index attaining a negative value, which is the main manifestation of geomagnetic storms, is caused by the ring current enclosing the Earth. Large negative value of Dst index indicate an increase in the intensity of the ring current. A ring current is an electric current conveyed by charged particles caught in a planet’s magnetosphere. Geomagnetic storm is only an enhancement of this ring current. The capacity of CMEs to cause geomagnetic storms is known as geoeffectiveness, and we measure it regarding a geomagnetic index such as disturbance storm time or Dst index (Gopalswamy, 2006; Gopalswamy et al., 2007; Gonzalez et al., 1994; Loewe and Prolss, 1997; Zhang et al., 2006). Loewe and Prolss (1997) categorized geomagnetic storms into five groups which were based on the minimum value of Dst: weak (−30 nT to −50 nT), moderate (−50 nT to −100 nT), strong (−100 nT to −200 nT), severe (−200 nT to −350 nT), and great (< −350 nT).

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In general, we classify CMEs with Dst (≤ −100 nT) as strongly geoeffective and the other category as moderately geoeffective (−100 nT < Dst ≤ −50 nT). Loewe and Prolss (1997) also calculated the median Dst values for weak, moderate and strong storms as −36 nT, −68 nT and −131 nT respectively. Gopalswamy et al.(2007) studied halo CMEs of solar cycle 23(1996–2005) and found that out of all frontside CMEs, a larger fraction i.e., about 75% of disk halos are most geoeffective, limb halos are moderately geoeffective and backside CMEs are not at all geoeffective. Cid et al. (2012) also found that disk center CMEs are more geoeffective and when the source heliographic longitude moves away from the central meridian the geoeffectiveness decreases. Zhang et al. (2007) studied and explored the origin of all major geomagnetic storms (Dst ≤ –100 nT) happening amid the time period 1996–2005 and found that the associated CMEs showed up as a full halo CMEs in 68% of the cases. They also concluded that in 86% of the cases, the origin of the geoeffective CMEs was situated less than 45° from the central meridian position. As described above, Dst is one of the significant parameter to define geoeffectiveness. All previous studies show that it depends on several parameters of the solar eruptions such as – CME source locations, speed etc. In this paper, we have presented the analysis and results of CME source locations, CME speed, flare class (X-ray flux) and geomagnetic storms Dst index. The aim of the present study is to understand the different parameters (as mentioned above) responsible for the geoeffectiveness of solar eruptions. We have considered 193 halo events from the beginning of the current solar cycle 24 (2009–2013). Since during this rising phase of the solar cycle not much solar activity is observed on the Sun and also the solar cycle 24 is observed to be extremely weak as measured by the sunspot numbers (Gopalswamy et al., 2015), it gives us a better opportunity to understand the association between geoeffectiveness and its source location on the solar surface. We have grouped the levels of geomagnetic activity into two groups on the basis of observed minimum Dst index i.e., moderate (−100 nT < Dst ≤ −50 nT) and intense (≤ −100 nT). We studied the Spearman rank correlation among Dst index, CME speed and X-ray flare class. The significance of the relationship among these is studied with the help of P-value using Chi-square statistic (If Pvalue < 0.05, relationship is taken as significant). We have focused on the characteristics of CMEs with respect to their speed and heliographic longitude.

2. Data sources and analysis 1. We have considered all the 193 halo CMEs observed by SOHO/LASCO from 2009 to 2013. These are extracted from the

Fig. 1. Dst variation on 15 march 2013.

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Fig. 2. Evolution of CME on 15 March 2013.

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2.

3. 4. 5.

SOHO/LASCO catalogue available at http://cdaw.gsfc.nasa.gov/ CME_list/halo/halo.html The other properties of CMEs (CME speed, location and flare class) are also taken from the above-mentioned website. X-ray light curves from the geostationary environmental satellite, active region (AR) NOAA number and locations are taken from http://www.solarmonitor.org The Dst values are taken from the World Data Center in Kyoto. The website is – http://swdcdb.kugi.kyoto-u.ac.jp/dstdir/ Daily movies are from the LASCO CME catalogue: [http://cdaw. gsfc.nasa.gov/CME_list/] Associated flares with halo CMEs are rechecked from Heliophysics Events Knowledgebase available at www.lmsal.com/ hek/index.html

We started our stepwise analysis by extracting the halo CME events available at http://cdaw.gsfc.nasa.gov/CME_list/halo/ halo.html. There are 193 halo CME events during the rising phase of solar cycle 24(2009–2013). In the next step we checked the geoeffectiveness between 1 to 5 days after the CME onset. A time window of 1 to 5 days is taken after the CME onset and the minimum value of Dst index during this time interval is obtained from the WDC-C2 for Geomagnetism, Kyoto, Japan (http:// swdcdb.kugi.kyoto-u.ac.jp/dstdir/). According to the different characteristic properties such as speed, time, source location and heliographic coordinates with an approximation of ± 1 day, we found the Dst value related to the observed CME. We also rechecked the Dst value from SOHO/LASCO CME catalog. We selected only those CMEs for which the Dst values are less than or equal to −50 nT, as

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we categorize an event as geoeffective if its Dst index is less than −50 nT (Gonzalez et al., 1994). For example, let us consider a halo CME event that occurred on 15 March 2013 at 07:12:05 UT (Fig. 1). In the next step we checked the minimum Dst values occurring within 1 to 5 days after the onset of CME which were less than −50 nT. In this case we got minimum Dst index as −132 nT on 17 March 2013 at 21:00 UT. The Dst value was rechecked from SOHO/LASCO CME catalog. Considering first the speed of CME and then the location, time of onset of CME, heliographic region and time of minimum Dst values, we predicted the minimum Dst for this particular CME. We watched the daily movies from SOHO and LASCO, found the active region and then rechecked it from the solar monitor. We also rechecked the associated flares with halo CME Heliophysics Events Knowledgebase available at (www.lmsal.com/hek/index.html). In this case we found that minimum Dst value of −132 nT on 17 March 2013 at 21:00 UT is only associated with this geoeffective CME. Fig. 2 shows the CME observed by SOHO/LASCO on 15 March 2013. The time of the halo CME (width 3600 ) was 07:12:05 UT. The speed was 1063 km/s and the location on solar disk was N11E12. The associated flare was M1.1 (http://cdaw.gsfc.nasa.gov/ CME_list/halo/halo.html). As the distance from Sun to Earth is 149,597,871 km, using speed distance formula, we calculated the time which comes out to be 39.09 hours (more than one and a half days) and using the approximation ± 1 we found the above mentioned Dst value to be most appropriate. Using the above criterion for CMEs selection, we found 33 such halo events. The level of geomagnetic activity is categorized into two groups based on the observed minimum Dst index i.e.,

Table 1 Geoeffective events during Solar cycle 24 [2009–2013]. I. Moderately geoeffective events (−100 nT < Dst ≤ −50 nT) S.no.

CME date

CME time [UT]

Speed [km/s]

Location

Flare class

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

12-02-2010 03-04-2010 24-05-2010 01-08-2010 01-02-2011 06-09-2011 27-10-2011 19-01-2012 10-02-2012 16-02-2012 04-03-2012 10-03-2012 26-03-2012 14-06-2012 08-07-2012 31-08-2012 02-09-2012 17-05-2013 28-06-2013 09-07-2013 29-09-2013 06-10-2013 28-10-2013 07-11-2013 07-11-2013 07-12-2013

13:42:04 10:33:58 14:06:05 13:42:05 23:24:12 23:05:57 12:00:06 14:36:05 20:00:05 6:36:05 11:00:07 18:00:05 23:12:05 14:12:07 14:36:05 20:00:05 4:00:06 9:12:10 2:00:05 15:12:09 22:12:05 14:43:22 15:36:05 0:00:06 15:12:10 7:36:05

509 668 427 850 437 575 570 1120 533 538 1306 1296 1390 987 796 1442 538 1345 1037 449 1179 567 812 1033 411 1085

N26E11 S25E00 N13W31 N20E36 N07E182 N14W18 N33E15 N32E22 N25E05 N10W158 N19E61 N17W24 N17E164 S17E06 S17W178 S25E59 N03W05 N12E57 S18W19 N19E14 N17W29 S16W13 S06E28 S11W97 S13E23 S16W49

M8.3 B7.4 B1.2 C3.2 B4.5 X2.1 B9.0 M3.2 C1.0 B1.0 M2.0 M8.4 C2.7 M1.9 C6.7 C8.1 C2.9 M3.2 C4.4 C2.3 C1.3 C1.1 M4.4 M1.8 M2.4 M1.2

N16W30 N12E42 N35W40 N25E26 S15W01 N06W34 N11E12

M6.0 M3.0 M1.3 X1.3 X1.4 C3.7 M1.1

Storm DST(nT)

Storm date

Storm time

−58 −81 −85 −67 −59 −69 −72 −67 −58 −54 −74 −50 −55 −71 −68 −54 −68 −57 −98 −72 −67 −65 −52 −81 −70 −66

15-02-2010 06-04-2010 29-05-2010 04-08-2010 04-02-2011 09-09-2011 01-11-2011 22-01-2012 15-02-2012 19-02-2012 07-03-2012 12-03-2012 28-03-2012 17-06-2012 09-07-2012 02-09-2012 05-09-2012 18-05-2013 29-06-2013 14-07-2013 02-10-2013 09-10-2013 30-10-2013 09-11-2013 11-11-2013 08-12-2013

23:00 UT 15:00 UT 14:00 UT 05:00 UT 22:00 UT 18:00 UT 16:00 UT 22:00 UT 17:00 UT 05:00 UT 10:00 UT 17:00 UT 05:00 UT 14:00 UT 13:00 UT 24:00 UT 06:00 UT 05:00 UT 07:00 UT 23:00 UT 08:00 UT 02:00 UT 24:00 UT 09:00 UT 08:00 UT 09:00 UT

−107 −101 −132 −131 −127 −119 −132

06-08-2011 26-09-2011 25-10-2011 09-03-2012 15-07-2012 01-10-2012 17-03-2013

04:00 UT 24:00 UT 02:00 UT 09:00 UT 19:00 UT 05:00 UT 21:00 UT

II.Intense geoeffective events (Dst ≤ −100 nT) 1 2 3 4 5 6 7

03-08-2011 24-09-2011 22-10-2011 07-03-2012 12-07-2012 28-09-2012 15-03-2013

14:00:07 19:36:06 1:25:53 1:30:24 16:48:05 0:12:05 7:12:05

610 972 593 1825 885 947 1063

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Fig. 3. Figure taken from LASCO CME catalog showing CME height-time and GOES X-ray flare class.

moderate (−100 nT < Dst ≤ −50 nT) and intense (Dst ≤ −100 nT). The data for the selected CMEs and corresponding Dst values along with the characteristics of CMEs and Dst time is provided in Table 1 (I & II). The Spearman rank correlation coefficient rs among Dst index, CME speed and flare class is calculated by using formula given in Eq. (2.1).

rs = rR1,

R2

=

cov(R1 , R2 )

σR 1 , σR 2

(2.1)

where rR1, R2 is the Pearson correlation coefficient applied to rank variables, cov(R1 , R2 ) is the covariance of the rank variables, σR1 and σR2 are the standard deviations of the rank variables. The ranks of CME speed, storm Dst index and X-ray flux (flare class) are provided in Table 3. The correlation coefficients obtained herein are evaluated using Chi-square statistic. The formula used is provided in Eq. (2.2).

χ 2 = nrs 2

(2.2)

Here, rs is the correlation coefficient; n represents the number of events which are equal to 33 in our case. The value of χ 2 is computed and compared with Chi-square statistic given in the standard table for different levels of significance and different degrees of freedom, hence obtaining the P-value for different correlation coefficients at a significance level of 0.05. The significance of the relationship is studied with the help of obtained P-values i.e., if P-value < 0.05, relationship is taken as significant. Fig. 3 shows the CME height time and the GOES X-ray flare class. The limits of the flare class have been defined as indicated in Table 2.

Table 2 Limits of the flare class. A < 10−7

Watt m−2

B 10−7 –10−6 C 10−6 –10−5 M 10−5 –10−4 X > 10−4 Watt

Watt m−2 Watt m−2 Watt m−2 m−2

3. Results and discussion 3.1. Dst characteristics and CME source location In Fig. 4, we have plotted the Dst indexes during the solar cycle 24. The plot shows that the number of maximum Dst events occurred during the rising phase with an average intensity of −78.39 nT. We observed 78.79% Dst’s having moderate intensity (−100 nT < Dst ≤ −50 nT) and 21.21% having strong intensity (Dst ≤ −100 nT). Thus we conclude that most of the geomagnetic storms which occurred during the rising phase of solar cycle 24 had moderate intensity. All the selected halo CME events, occurring in different heliographic longitudes are compared and it was found that 19 out of 33 events are occurring from the center i.e., heliographic longitude ± 300 . Thus, 57.58% of the source locations of halo CMEs is located at the center, i.e., they are the most geoeffective. The geomagnetic storms corresponding to these central sources were mostly found to be of moderate intensity (−100 nT < Dst ≤ −50 nT). The remaining 42.42% were found at the non-disk center, i.e., source location > ± 300 . In another study, on moving closer to the equator, we found more accurate results for the active regions on the solar disk (Fig. 5). About 36.36% events are occurring at the center, i.e., in the active regions with heliographic longitude ± 200 . Out of 14 events, occurring at non disk center (excluding 19 events occurring at heliographic longitude ± 300 ), 50% events

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Fig. 4. Plot showing Dst index statistics.

Fig. 5. Distribution of source location with number of events.

occurred in the western hemisphere and 50% events occurred in the eastern hemisphere, clearly indicating an equal distribution in the western and eastern hemisphere of the events which occurred at a non-central location. Comparing the source location of geoeffective halo CME events, we found majority of 22 events, about 66.67%, were in the northern hemisphere and a minority of 11 events, about 33.33%, were in the southern hemisphere. This shows the north-south asymmetry in the source location of geoeffective halo CME events.

3.2. Associations between DST index and CME speed The CME speed refers to the radial propagation speed of the upper portion of a CME frontal loop. It is one of the fundamental properties of a coronal mass ejection and is measured from a time series of coronagraphic images with reference to the sky plane. These images show the propagation of CME in the plane perpendicular to the Sun-Earth line. The CME speed is determined with the help of a linear fit to the height time (h-t) plots. The measured sky-plane speed varies from a few kms−1 to 30 0 0 kms−1 approximately (Gopalswamy, 2004).

Fig. 6(a) shows the variation of Dst index with CME speed. The ranks of Dst index and CME speed (given in Table 3) are plotted in Fig. 6(b). The studied 33 events are of non-normal distribution (Figs. 4 and 10). Hence, we analyzed the characteristics of the events by applying non-parametric statistics. The Spearman correlation coefficient (rs ) is a non-parametric measure of how well the two variables or characteristics statistically depend on each other. It is equal to the Pearson correlation coefficient (r) applied to the rank variables (Myers, and Well, 2003). On using the data given in Table 3, we obtained the Spearman correlation coefficient equal to 0.02, positive but a very low value (nearly equal to zero). Hence, for these selected halo CME events, both the parameters are poorly correlated. In order to determine the significance of the relationship between the two, Chi-square statistics is applied. A null hypothesis is made stating ‘There is no significant relationship between the Dst index and CME speed’. For this null hypothesis (rs = 0), Chi-square (χ 2 ) value is calculated using Eq. (2.2). The obtained value is equal to 0.013. As we are dealing with two categories, namely Dst index and CME speed, the degrees of freedom (df) is equal to 1, as

df = N − 1

(2.3)

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Fig. 6. (a) Plot showing the variation of Dst index as a function of CME speed with Spearman correlation coefficient rs = 0.02, χ 2 -value (value of Chi-square statistic) = 0.013 and P-value = 0.91 with level of significance 0.05 (or 5%; here the P-value  0.05); (b) Plot showing the linear fit analysis of ranks (Dst index) as a function of ranks (CME speed); the linear fit is providing value of rs .

where N is the number of categories taken. Using the χ 2 statistic and the df, we calculate the right tailed probability (P-value) of the Chi-squared distribution equal to 0.91. As P-value is much higher than 0.05 (the chosen level of significance), we accept the null hypothesis. Hence, these two parameters are significant differently. These results clearly indicate that CME speed is not an effective parameter responsible for geoeffectiveness of these halo CME events.

The study shows that the CMEs located at the center of the solar disk (± 300 ) have an average speed of 781.7 km/s. The Dst index of these centrally located CMEs is mostly of moderate intensity (−100 nT < Dst ≤ −50 nT). The trend of CME speed and the Dst index is in agreement with the above result i. e. as the heliographic longitude increases the Dst index decreases and the speed of the CMEs increases.

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Table 3 Ranks of CME speed, Storm Dst and X-ray flux for geoeffective events during Solar cycle 24 [2009–2013]. S. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

CME date 12-02-2010 03-04-2010 24-05-2010 01-08-2010 01-02-2011 03-08-2011 06-09-2011 24-09-2011 22-10-2011 27-10-2011 19-01-2012 10-02-2012 16-02-2012 04-03-2012 07-03-2012 10-03-2012 26-03-2012 14-06-2012 08-07-2012 12-07-2012 31-08-2012 02-09-2012 28-09-2012 15-03-2013 17-05-2013 28-06-2013 09-07-2013 29-09-2013 06-10-2013 28-10-2013 07-11-2013 07-11-2013 07-12-2013

CME time[UT] 13:42:04 10:33:58 14:06:05 13:42:05 23:24:12 14:00:07 23:05:57 19:36:06 1:25:53 12:00:06 14:36:05 20:00:05 6:36:05 11:00:07 1:30:24 18:00:05 23:12:05 14:12:07 14:36:05 16:48:05 20:00:05 4:00:06 0:12:05 7:12:05 9:12:10 2:00:05 15:12:09 22:12:05 14:43:22 15:36:05 0:00:06 15:12:10 7:36:05

Speed [km/s] 509 668 427 850 437 610 575 972 593 570 1120 533 538 1306 1825 1296 1390 987 796 885 1442 538 947 1063 1345 1037 449 1179 567 812 1033 411 1085

Ranks CME speed

Storm DST(nT)

5 14 2 17 3 13 11 20 12 10 26 6 7.5 29 33 28 31 21 15 18 32 7.5 19 24 30 23 4 27 9 16 22 1 25

−58 −81 −85 −67 −59 −107 −69 −101 −132 −72 −67 −58 −54 −74 −131 −50 −55 −71 −68 −127 −54 −68 −119 −132 −57 −98 −72 −67 −65 −52 −81 −70 −66

3.3. Associations between flare class and DST index Solar flares are categorized by their energy output measured in watts/square meter (Table 2). Fig. 7(a) shows the scattered plot between the X-ray flux versus Dst index. The ranks of both parameters (given in Table 3) are plotted in Fig. 7(b). The Spearman correlation coefficient (using the rank data given in Table 3) is equal to 0.13, which shows a weak correlation. The significance of the relationship between the flare class and Dst index is examined by applying Chi-square statistics. A null hypothesis is stated as – ‘There is no significant relationship between the Dst index and flare class’. For this null hypothesis (rs = 0), Chi-square (χ 2 ) value is calculated using Eq. (2.2). The obtained value is equal to 0.546. The degrees of freedom (df) is equal to 1 (using Eq. (2.3)) Using the χ 2 statistic and the df, we calculated P-value equal to 0.46. Because 0.46 is greater than 0.05 (the chosen level of significance), we accept the null hypothesis. Hence, flare class and Dst index show low significance. Such a low value of correlation coefficient and high P-value (more than 0.05) indicates that for these selected 33 halo CME events, it is dispensable for a geoeffective halo CME to be associated with a strong flare. Thus, a solar flare class cannot be considered as a significant parameter in predicting the geoeffectiveness of these CMEs. Moreover, according to the data given in Data Table 1, it is found that about 10.53% B class flares, 31.58% C class flares, 42.10% M class flares and 15.79% X class flares are associated with the central source regions, which clearly supports the above result. 3.4. Association between flare class and CME speed Fig. 8 shows a plot between flare class and CME speed. A good correlation is seen as compared to the previous two cases. Fig. 8(a) shows a plot between flare class and CME speed. A good correla-

Ranks storm DST 7.5 23.5 25 13 9 28 17 27 32.5 20.5 13 7.5 3.5 22 31 1 5 19 15.5 30 3.5 15.5 29 32.5 6 26 20.5 13 10 2 23.5 18 11

Flare class

X-ray flux [W/m²]

Ranks x-ray flux

M8.3 B7.4 B1.2 C3.2 B4.5 M6.0 X2.1 M3.0 M1.3 B9.0 M3.2 C1.0 B1.0 M2.0 X1.3 M8.4 C2.7 M1.9 C6.7 X1.4 C8.1 C2.9 C3.7 M1.1 M3.2 C4.4 C2.3 C1.3 C1.1 M4.4 M1.8 M2.4 M1.2

8.3 × 10¯ 7.4 × 10¯7 1.2 × 10¯7 3.2 × 10¯6 4.5 × 10¯7 6.0 × 10¯5 2.1 × 10¯4 3.0 × 10¯5 1.3 × 10¯5 9.0 × 10¯7 3.2 × 10¯5 1.0 × 10¯6 1.0 × 10¯7 2.0 × 10¯5 1.3 × 10¯4 8.4 × 10¯5 2.7 × 10¯6 1.9 × 10¯5 6.7 × 10¯6 1.4 × 10¯4 8.1 × 10¯6 2.9 × 10¯6 3.7 × 10¯6 1.1 × 10¯5 3.2 × 10¯5 4.4 × 10¯6 2.3 × 10¯6 1.3 × 10¯6 1.1 × 10¯6 4.4 × 10¯5 1.8 × 10¯5 2.4 × 10¯5 1.2 × 10¯5

29 4 2 12 3 28 33 24 19 5 25.5 6 1 22 31 30 10 21 15 32 16 11 13 17 25.5 14 9 8 7 27 20 23 18

5

tion is seen as compared to the previous two cases. The ranks of flare class and CME speed are taken from Table 3 and plotted as in Fig. 8(b). The Spearman rank correlation coefficient comes out to be 0.38, positive and a moderate correlation. The significance of this correlation between the two parameters is assessed with the help of Chi- square statistics. The null hypothesis is stated as – ‘There is no significant relationship between flare class and CME speed’. For this null hypothesis (rs = 0), Chi-square (χ 2 ) value is calculated using Eq. (2.2). The obtained value equals to 4.642. The degrees of freedom (df) is equal to 1 (using Eq. (2.3)). Using the χ 2 statistic and the df, we calculated P-value equal to 0.03. Hence, as this P-value (0.03) is lesser than 0.05 (the chosen level of significance), we reject the null hypothesis. Thus, these two parameters, namely, flare class and CME speed show a moderate correlation and are significantly related to each other at 95% significance level. This indicates that the greater the flare is, the greater the CME speed. We found the average speed of B class flares to be 528 km/s, for C class flares it is 884.36 km/s, for M class flares it is 938.71 km/s and for X class flares it is 1095 km/s, which is in agreement with the results. 3.5. Flare characteristics and CME characteristics Fig. 9 represents the flare characteristics during the rising phase of the solar cycle 24. The average X-ray class was M3.0 and the median X-ray flare class was found to be M1.1. During this phase, we found 15.15% B class flares 33.33% C class flares 42.42% M class flares and 9.1% X class flares. The average Dst index corresponding to B class flares was found to be −70.2 nT, for C class flares it is −71.91 nT, for M class flares it is −79.86 nT and X class flares it has an average of −109 nT. Most of the geoeffective halo CME events are associated with M class flares. (Kane, 2012; Gupta, 2015)

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Fig. 7. (a) The scattered plot between flare class (X-ray flux) and Dst index with Spearman correlation coefficient rs = 0.13, χ 2 -value (value of Chi-square statistic) = 0.546 and P-value = 0.46 with level of significance 0.05 (or 5%; here the P-value > 0.05); (b) Plot showing the linear fit analysis of ranks (flare class) as a function of ranks (Dst index); the linear fit is providing value of rs .

Figure 10 represents the speed of the CMEs during this period. The average speed of the CMEs is 872.58 km/s and the median speed is 850 km/s. 4. Summary and conclusions In this paper, we have studied the different parameters of geoeffective events statistically which occurred in the beginning phase

of solar cycle 24. We analyzed 33 halo CME events which have Dst index lower than −50 nT. We summarize our results as follow: A low geomagnetic activity is observed in the rising phase of solar cycle 24 (2009–2013). Neither severe (−200 to −300 nT) nor great (< −350 nT) storms have been observed during this period. In contrast to this, during the maximum of solar cycle the Dst index rose to several hundreds of nT. For example, the biggest solar storm in solar cycle 23 was associated with Dst index −472 nT

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Fig. 8. (a) The scattered plot between flare class and CME speed with Spearman correlation coefficient rs = 0.38, χ 2 -value(value of Chi-square statistic) = 4.642 and Pvalue = 0.03 with level of significance 0.05 (or 5%; here the P-value < 0.05); (b) Plot showing the linear fit analysis of ranks (flare class) as a function of ranks (CME speed); the linear fit is providing value of rs .

(Gopalswamy et al., 2005; Richardson, 2013). Richardson (2013), investigated the geomagnetic activity in the starting four years of solar cycle 24 and found that the geomagnetic storm rates are only comparable to or even below the ones observed during the solar minima in previous solar cycles (17–23). One important conclusion is north-south asymmetry. Majority of 22 out of 33 halo CME events, about 66.67%, were in the northern hemisphere and a minority of 11 events, about 33.33%, were

in the southern hemisphere. Thus, during the selected period of solar cycle 24, most of the halo CME events were dominated in the northern hemisphere. Hence, the study of the source location of geoeffective halo CME events exhibit north-south asymmetry (Bankoti et al., 2010) and gives us one more parameter to understand this asymmetry. Out of 33 halo CME events, more than half are found to be geoeffective. The study of the Dst index of selected events revealed

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Fig. 9. Distribution of GOES X-ray peak flux with number of events.

Fig. 10. Distribution of CME speed with number of events. Table 4 Different statistical parameters for characteristic features. Statistical parameters

rs

SD

χ -square

P-value

0.02 0.13 0.38

9.82 9.73 9.11

0.013 0.546 4.642

0.91 0.46 0.03

Characteristic features DST index with CME speed X-ray flux (flare class) with DST index X-ray flux (flare class) with CME speed

that most of the geomagnetic storms which occurred during the rising phase of solar cycle 24 had moderate intensity. We noticed seven events having Dst index ≤ −100 nT. Out of them, the source region of four events lies in ± 300 . The halo CME events occurring at non disk center showed an equal distribution in the western and eastern hemisphere which is in contradiction to earlier findings (Wang et al., 2002; Zhang et al., 2007). The average and median speed of CMEs is 872.58 km/s and 850 km/s respectively. We also found that 15.15% B class flares, 33.33% C class flares, 42.42% M class flares and 9.1% X class flares were associated with geoeffective events. The average and median X-ray flare class was M3.0 and M1.1 respectively. Hence, out of these 33 events, the majority are associated with M class flares (Kane, 2012; Gupta, 2015).

The Spearman rank correlation coefficient among the parameters Dst index, CME speed and X-ray flare class is obtained and the significance of their relationship is studied by Chi-square statistic (Table 4). The correlation coefficient (rs ) between the Dst index and CME speed is 0.02, χ 2 -value is 0.013 and P-value 0.91 (much greater than 0.05) and between Dst index and X-ray flux of flares, rs = 0.13, χ 2 = 0.546 with a P-value 0.46 (greater than 0.05), which shows that high speed CMEs and big flares are not the effective and significant parameters for geoeffectiveness of these selected halo events. It also indicates that it is not necessary for a geoeffective halo CME to be associated with a strong flare. The correlation coefficient (rs ) between CME speed and X-ray flux is better, i.e., 0.38, χ 2 = 4.642 and the P-value is equal to 0.03 (less than 0.05), which clearly reflects that big flares are

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responsible for producing high speed CMEs and both parameters share a significant relationship. We found the average speed of B class flares to be 528 km/s, for C class flares it is 884.36 km/s, for M class flares it is 938.71 km/s and for X class flares it is 1095 km/s, which is in agreement with the results. Acknowledgement The authors are thankful to the NASA and NRL team for SOHO/LASCO CME catalog. SOHO is a project of international cooperation between ESA and NASA. The Dst index data were provided by the World Data Center for Geomagnetism at Kyoto University. We acknowledge the above data sources. The authors are also thankful to the reviewers whose comments have proved to be of immense help in improving the paper. References Baidyanath, B., Chattopadhyay, T., Biswas, S.N., 2010. An Introduction to Astrophysics, second ed. PHI, pp. 90–92. Bankoti, et al., 2010. North–south asymmetry of different solar activity features during solar cycle 23. New Astron. (Netherlands) 15, 561–568. doi:10.1016/j.newast. 2010.01.005. Chen, P F, 2011. Coronal mass ejections: models and their observational basis. Living Rev. Solar Phys. (Germany) 8, 1–92. Cid, et al., 2012. Can a halo CME from the limb be geoeffective. J. Geophys. Res. (USA) 117, 1–25. doi:10.1029/2012JA017536, A11102. Gopalswamy, N., 2004. A Global Picture of CMEs in the Inner Heliosphere. In: Poletto, G., Suess, S.T. (Eds.). In: The Sun and the Heliosphere as an Integrated System, vol. 317. Astrophysics and Space Science Library, Kluwer, Dordrecht, Boston, pp. 201–251. Gopalswamy, et al., 2005. Solar source of the largest geomagnetic storm of cycle 23. Geophys. Res. Lett. (USA) 32, 1–5. doi:10.1029/2004GL021639, L12S09. Gopalswamy, N, 2006. Coronal mass ejections of solar cycle 23. J. Astrophys. Astr. (India) 27, 243–254. Gopalswamy, et al., 2007. Geoeffectiveness of coronal mass ejections. J. Geophys. Res. (USA) 112, 1–13. doi:10.1029/2006JA012149, A06112. Gopalswamy, N, 2009. Introduction to special section on large geomagnetic storms. J. Geophys. Res. (USA) 114, 1–4. doi:10.1029/20 08JA014026, A0 0A0 0. Gopalswamy, et al., 2010. The catalog of halo coronal mass ejections from SOHO. Sun Geosphere (Bulgaria) 5, 7–16. Gopalswamy, et al., 2015. CMEs during the two activity peaks in cycle 24 and their space weather consequences. Sun Geosphere (Bulgaria) 10/2, 101–108.

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