Vol 17, No 12 (2017) / Le

Dependence of large SEP events with different energies on the associated flares and CMEs

Dependence of large SEP events with different energies on the associated flares and CMEs

Le Gui-Ming1, 2, , Zhang Xue-Feng2

Key Laboratory of Space Weather, National Center for Space Weather, China Meteorological Administration, Beijing 100081, China
School of Computer Science, Anhui University of Technology, Maanshan 243032, China

† Corresponding author. E-mail: legm@cma.gov.cn


Abstract: Abstract

To investigate the dependence of large gradual solar energetic particle (SEP) events on the associated flares and coronal mass ejections (CMEs), the correlation coefficients (CCs) between peak intensities of (I 10), (I 30) and (I 50) protons and soft X-ray (SXR) emission of associated flares and the speeds of associated CMEs in the three longitudinal areas W0–W39, W40–W70 (hereafter the well connected region) and W71–W90 have been calculated. Classical correlation analysis shows that CCs between SXR emission and peak intensities of SEP events always reach their largest value in the well connected region and then decline dramatically in the longitudinal area outside the well connected region, suggesting that they may contribute to the production of SEPs in large SEP events. Both classical and partial correlation analyses show that SXR fluence is a better parameter describing the relationship between flares and SEP events. For large SEP events with source location in the well connected region, the CCs between SXR fluence and I 10, I 30 and I 50 are 0.58±0.12, 0.80±0.06 and 0.83±0.06 respectively, while the CCs between CME speed and I 10, I 30 and I 50 are 0.56±0.12, 0.52±0.13 and 0.48±0.13 respectively. The partial correlation analyses show that in the well connected region, both CME shock and SXR fluence can significantly affect I 10, but SXR peak flux makes no additional contribution. For protons with source location in the well connected region, only SXR fluence can significantly affect I 30, and the CME shock makes a small contribution to I 30, but SXR peak flux makes no additional contribution. For protons with source location in the well connected region, only SXR fluence can significantly affect I 50, but both CME shock and SXR peak flux make no additional contribution. We conclude that these findings provide statistical evidence that for SEP events with source locations in the well connected region, a CME shock is only an effective accelerator for protons. However, flares are not only effective accelerators for protons, but also for protons, and protons may be mainly accelerated by concurrent flares.

Keywords: Sun: coronal mass ejections (CMEs);Sun: flares;(Sun:) particle emission



1 Introduction

There are two kinds of solar energetic particle (SEP) events, named impulsive and gradual SEP events respectively. The former is accompanied by an impulsive flare, while the latter is accompanied by both a gradual flare and a fast coronal mass ejection (CME), and the intensity-time profile of solar proton events (SPEs) can be used to predict the geoeffectiveness of the CMEs associated with SPEs (Le et al. 2016 ). Nobody doubts that the solar source of an impulsive SEP event is associated with an impulsive flare. However, when a gradual SEP event happens, whether the concurrent flare contributes to the SEP event is still an open question. There are two points of view on the solar source of gradual SEP events. The first one is that only CME-driven shocks contribute to gradual SEP events (e.g. Reames 1999 ; Tylka et al. 2005 ). The second one is that the solar source of a gradual SEP event may be both concurrent flare and shock driven by the associated CME (e.g., Kallenrode 2003 ; Trottet et al. 2015 ). Cane et al. ( 2007 ) suggested that solar flares and CMEs are likely to coexist and the evolution of any event depends on the relative importance of the processes. This is also consistent with the statement (Firoz et al. 2012 ) that type III and type II bursts are successive evolutions and it is difficult to separate them. Andriopoulou et al. ( 2011 ) suggested that it difficult to determine which the dominant acceleration mechanism is in each ground level enhancement (GLE) case. Investigation of the properties of SEPs inferred from their associated radio emission suggests that a clear-cut distinction between flare-related and CME-related SEP events is difficult to establish (Kouloumvakos et al. 2015 ). Some cases and statistical studies (e.g. Miroshnichenko et al. 2005 ; Aurass et al. 2006 ; Le et al. 2006 ; Simnett 2006 ; Li et al. 2007a , b , 2009 ; Bazilevskaya 2009 ; Masson et al. 2009 ; Grechnev et al. 2008 ; Pérez-Peraza et al. 2009 ; Aschwanden 2012 ; Le et al. 2013 ; Klein et al. 2014 ) have shown that relativistic solar protons (RSPs) may be accelerated by concurrent flares. Some statistical investigations have also been devoted to studying the relationship between peak intensities of SEP events and parameters of the associated solar flares and CMEs (e.g. Dierckxsens et al. 2015 ; Grechnev et al. 2015 ; Trottet et al. 2015 ). However, longitudinal dependence of peak intensities of SEP events on associated flares has not been investigated in the literature (Dierckxsens et al. 2015 ; Grechnev et al. 2015 ; Trottet et al. 2015 ). The longitudinal dependence of peak intensities of SPEs on soft X-ray (SXR) peak flux has been investigated by Park et al. ( 2010 ). However, the longitudinal area was divided into E90–E30, E30–W30 and W30–W90 and only the correlation coefficients (CCs) between peak intensities of SPEs and flare intensities in these three longitudinal areas have been calculated. It is evident that Park et al. ( 2010 ) did not calculate the CC between SXR peak flux and peak intensities of SPEs in the well connected region (W40–W70), and the relationship between SXR fluence and peak intensities of SPEs was not investigated in their paper.

It has been accepted that SEPs accelerated by a CME-driven shock can be observed in a very large longitudinal area, but flare-accelerated particles can only be observed in a small longitudinal area, especially in the longitudinal area well connected with the source location of an associated SEP event. When a solar flare is an eruptive flare, the accompanying CME will open the magnetic field over the associated active region (AR), leading to the flare-accelerated particles escaping from the AR and then entering interplanetary space. Because the magnetic field lines over an AR are very complicated and SEPs can not only propagate along the magnetic field lines, but can also propagate along the direction perpendicular to the magnetic field lines (Bieber et al. 2004 ; Qin 2007 ; Qin et al. 2013 ; Qin & Zhang 2014 ; Qin & Wang 2015 ), flare-accelerated particles can not only can be observed in the longitudinal area well connected with the SEP source region, but also can be observed in the longitudinal area outside the well connected region. However, the largest flux of flare-accelerated particles can only be observed in the longitudinal area well connected with the SEP source location. When a large gradual SEP event happens, if a lot of satellites can be used to observe the SEP flux at every magnetic field line, then it is easy to check whether the SEP flux is longitudinally dependent and reaches its largest flux in the longitudinal area well connected with the SEP source location, which can be used to judge whether associated flares contribute to the production of SEPs in a large gradual SEP event. However, there has not been this kind of SEP data. Statistical correlation analysis can also be used to judge whether flares contribute to the production of SEPs. If flares really contribute to the production of SEPs in large gradual SEP events, then flares should have a good correlation with the peak intensities of SEP events in the well connected region, but flares should have poor correlation with the peak intensities of SEP events in the longitudinal area outside the well connected region. Classical and partial correlation analyses for the relationship between the peak intensities of protons and parameters of associated flares and CMEs in the well connected region and in the longitudinal area outside the well connected region have been investigated. The results suggest that, for SEP events with source location in the well connected region, protons may be mainly accelerated by concurrent flares (Le et al. 2017 ).

In this paper, the relationship between the parameters of flares and CMEs and the peak intensities of protons with different energies lower than 100 MeV in the well connected region and in the longitudinal area outside the well connected region will be investigated. This is the motivation of the paper. Data sources and definitions are presented in Section 2. The associated classical correlation analysis is presented in Section 3. Section 4 describes the related partial correlation analysis. Section 5 is the summary and discussion, and conclusions are presented in the final section.

2 Data Sources and Definitions

A large gradual SEP event, or an SPE, is defined as the proton peak flux (particle flux unit, particle cm−2 sr−1 s−1) in the channel as measured by the Geostationary Operational Environmental Satellite (GOES) spacecraft during an SEP event accompanied by both a fast CME and a long duration SXR flare. When a large gradual SEP event happens, the flux of protons with different energies, such as , and protons and even higher energy protons may increase at almost the same time, however, the peak fluxes of protons with different energies are different.

The time integral of SXR flux for a flare, fluence (Φ x ), is defined as

where f(t) is the SXR flux, and and are the start and end times of the SXR flare, respectively. Equation (1) indicates that SXR flux, from which the background has been subtracted, is integrated over the flare start to end times. The flare start, peak and end times have been defined by SEC/NOAA. The flare end time was defined as the time when SXR flux decayed to a middle point between SXR peak flux and background SXR flux (Kubo & Akioka 2004 ). Φ x is related to the total energy released by the associated flare (Kubo & Akioka 2004 ; Chen et al. 2016 ), indicating that Φ x is a better parameter for describing the properties of SXR emission than SXR peak flux, and SXR fluence has a better correlation with peak flux of 15–40 MeV protons than SXR peak flux (Trottet et al. 2015 ).

The SXR flare start, peak and end times, and the SXR fluence, are obtained from (ftp://ftp.ngdc.noaa.gov/STP/space-weather/solar-data/). The peak intensity of , and protons observed by GOES during solar cycle 23 were obtained from the website (http://spidr.ngdc.noaa.gov/spidr/). It can be noticed that the proton data observed by GOES have been removed from the website (http://spidr.ngdc.noaa.gov/spidr/). For SPEs that occurred during solar cycle 23, the source location, CME speed and flare intensity for each SPE can be directly copied from the paper Cane et al. ( 2010 ). The CME speed associated with SPE that occurred on 2005 January 20 used in the paper is 3242 km s−1 (Gopalswamy et al. 2005 ). The SPEs that occurred during solar cycle 24 are available from (http://umbra.nascom.nasa.gov/sdb/goes/particle/). The linear speed of a CME, , can be obtained from the CME catalog (Yashiro et al. 2004 , http://cdaw.gsfc.nasa.gov/CME_list/) of Solar and Heliospheric Observatory/Large Angle Spectroscopic Coronagraph (SOHO/LASCO; Brueckner et al. 1995 ).

The source location that is magnetically well connected with the Earth should be located in the west hemisphere of the Sun. Seventy-nine SPEs with source locations in the west hemisphere that occurred during 1997–2014 were selected and are listed in Table 1.

No. Year yyyy Date mm/dd Time hh:mm Location (SXR peak flux) (erg cm−2) (km s−1) I 10 (pfu) I 30 (pfu) I 50 (pfu)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
1 1997 11/04 05:55 S14W33 X2.1 5.60E–02 785 72 20.3 9.98
2 1997 11/06 11:50 S18W63 X9.4 3.60E–01 1556 490 189 115
3 1998 04/20 10:00 S43W90 M1.4 6.10E–02 1863 1700 384 103
4 1998 05/02 13:35 S15W15 X1.1 6.70E–02 938 150 48 24.3
5 1998 05/06 08:00 S11W65 X2.7 2.10E–01 1099 210 47.5 19.3
6 1998 11/05 19:00 N26W18 M8.4 1.10E–01 1118 11 0.94 0.328
7 1999 06/04 07:03 N17W69 M3.9 2.40E–02 2230 64 3.7 0.93
8 2000 04/04 15:41 N16W66 C9.7 2.30E–02 1188 55 0.99 0.321
9 2000 06/10 17:02 N22W38 M5.2 7.30E–02 1230 46 4.22 1.57
10 2000 07/14 10:24 N22W07 X5.7 7.50E–01 1674 24000 5680 1670
11 2000 07/22 11:34 N34W56 M3.7 7.00E–02 1230 17 4.22 1.57
12 2000 09/12 12:17 S17W09 M1.0 4.50E–02 1550 320 9.91 1.95
13 2000 11/08 23:28 N10W75 M7.4 2.10E–01 1738 14800 4440 1880
14 2000 11/24 14:55 N22W07 X2.3 1.60E–01 1245 100 14.7 4.98
15 2001 01/28 16:00 S04W59 M1.5 3.00E–02 916 49 6.03 1.89
16 2001 03/29 10:15 N14W12 X1.7 2.20E–01 942 35 3.93 1.15
17 2001 04/02 21:51 N18W82 X20 1.50E+00 2505 110 217 53.5
18 2001 04/10 05:26 S23W09 X2.3 3.00E–01 2411 355 14.4 3.69
19 2001 04/12 10:28 S19W42 X2.0 3.00E–01 1184 50 13.9 5.75
20 2001 04/15 13:50 S20W85 14.4 6.10E–01 1199 951 357 275
21 2001 04/26 13:12 N17W31 M7.8 9.20E–02 1006 57 0.5 0.298
22 2001 09/15 11:28 S21W49 M1.5 3.70E–02 478 11 1.26 0.45
23 2001 10/19 16:30 N15W29 X1.6 1.6E–01 901 11 2.59 1.03
24 2001 11/04 16:20 N06W18 X1.0 2.20E–01 1810 31700 1070 266
25 2001 11/22 22:30 S15W34 M9.9 3.10E–01 1437 18900 857 162
26 2001 12/26 05:40 N08W54 M7.1 3.40E–01 1446 779 331 180
27 2002 01/14 06:27 S28W83 M4.4 3.40E–01 1492 15 1.69 0.53
28 2002 02/20 06:12 N12W72 M5.1 2.20E–02 952 13 1.51 0.5
29 2002 03/15 23:10 S08W03 M2.2 1.30E–01 957 13 0.61 0.215
30 2002 03/18 02:31 S09W46 M1.0 4.50E–02 989 53 2.48 0.579
31 2002 03/22 11:14 S09W90 M1.6 4.90E–02 1750 16 0.45 0.162
32 2002 04/17 8:24 S14W34 M2.6 1.50E–01 1240 24 1.51 0.367
33 2002 04/21 01:51 S14W84 X1.5 6.00E–01 2393 2520 649 208
34 2002 05/22 03:54 S19W56 C5.0 2.50E–02 1557 820 10.2 1.15
35 2002 07/15 20:08 N19W01 M1.8 4.30E–02 1300 234 4.27 0.92
36 2002 08/14 02:12 N09W54 M2.3 6.00E–02 1309 26 0.77 0.36
37 2002 08/22 01:57 S07W62 M5.4 3.30E–02 998 36 12.6 5.98
38 2002 08/24 01:12 S08W81 X3.1 4.60E–01 1913 317 123 76.2
39 2002 11/9 13:23 S12W29 M4.6 4.80E–02 1838 404 12 1.46
40 2003 05/28 00:27 S07W17 X3.6 2.80E–01 1366 121 4.84 3.72
41 2003 05/31 02:24 S07W65 M9.3 8.50E–02 1835 27 6.79 2.92
42 2003 10/26 18:19 N02W38 X1.2 5.10E–01 1537 466 42.6 10.4
43 2003 10/29 20:49 S15W02 X10 8.70E–01 2029 3300 869 360
44 2003 11/02 17:15 S20W56 X8.3 9.10E–01 2598 1570 476 155
45 2003 11/04 19:29 S19W83 X28.0 2.30E+00 2657 353 59.3 15.3
46 2003 11/20 07:47 N01W08 M9.6 6.00E–02 669 13 0.82 0.26
47 2003 12/2 09:48 S13W65 C7.2 5.10E–03 1393 86 2.28 0.39
48 2004 04/11 04:19 S14W47 C9.6 1.30E–02 1645 35 1.04 0.4
49 2004 07/25 15:14 N08W33 M1.1 6.50E–02 1333 2086 29.1 1.86
50 2004 11/07 16:06 N09W17 X2.0 2.00E–01 1759 495 33.2 4.93
51 2004 11/10 02:13 N09W49 X2.5 1.60E–01 2000 300 49.5 13.2
52 2005 01/15 23:02 N15W05 X2.6 6.30E–01 2861 300 1.93 0.83
53 2005 01/17 09:52 N15W25 X3.8 8.40E–01 2547 400 1330 387
54 2005 01/20 07:01 N14W61 X7.1 1.30E+00 3242 1680 1550 1150
55 2005 07/13 14:49 N10W80 M5.0 2.00E–01 1423 10 1.16 0.32
56 2005 07/14 10:55 N10W89 X1.2 3.90E–01 2115 110 14.2 2.63
57 2005 08/22 17:27 S12W60 M5.6 1.70E–01 2378 330 27.2 4.8
58 2006 12/13 02:40 S06W24 X3.4 5.10E–01 1774 698 372 239
59 2006 12/14 22:15 S05W31 X1.5 1.20E–01 1042 215 42.3 13.5
60 2010 08/14 10:05 N17W52 C4.4 9.90E–03 1205 14 1.69 0.63
61 2011 03/07 20:12 N24W59 M3.7 1.20E–01 2125 50 4.66 0.82
62 2011 06/07 06:41 S21W64 M2.5 4.40E–02 1255 72 24.5 12.8
63 2011 08/04 03:57 N15W49 M9.3 5.40E–02 1315 96 20.2 7.79
64 2011 08/09 08:05 N17W83 X6.9 1.90E–01 1610 26 15.4 8.65
65 2011 11/26 07:10 N08W49 C1.2 5.30E–03 933 80 2.91 0.56
66 2012 01/23 03:59 N28W36 M8.7 2.00E–01 2175 6310 422 73
67 2012 01/27 18:37 N27W71 X1.7 3.20E–01 2508 796 136 43.5
68 2012 03/13 17:41 N18W62 M7.9 2.40E–01 1884 469 71.8 21.2
69 2012 05/17 01:47 N12W89 M5.1 9.90E–02 1582 255 124 78.3
70 2012 07/06 23:08 S18W50 X1.1 4.30E–02 1828 25 5.11 2.06
71 2012 07/12 16:49 S16W09 X1.4 4.60E–01 885 96 3.49 0.96
72 2012 07/17 17:15 S17W75 C9.9 2.10E–01 958 136 14.6 4.67
73 2012 09/27 23:57 N08W41 C3.7 9.40E–03 1035 28 3.24 0.6
74 2013 05/22 13:32 N15W70 M5.0 1.40E–01 1466 1660 125 22.9
75 2013 09/29 23:37 N15W40 C1.3 1.10E–02 1179 182 8.81 1.54
76 2014 01/07 18:32 S15W11 X1.2 2.50E+00 1830 1033 185 42.6
77 2014 02/20 07:55 S15W67 M3.0 6.30E–02 948 22 6.67 3.59
78 2014 04/18 13:03 S16W41 M7.3 1.10E–01 1208 58 5.77 2.44
79 2014 09/10 17:45 N16W06 X1.6 3.80E–01 1425 126 7.89 3.19

Table 1 The Parameters of Flares and CMEs Associated with Large Gradual SEP Events during 1997–2014

In the table, SPEs are numbered in Col. (1), the year and date of the events in Cols. (2) and (3) respectively, the time when SXR flux reached its peak value in Col. (4), the location of the flare site in Col. (5), SXR peak flux, , in Col. (6), SXR fluence in Col. (7), the linear speed of the CME in Col. (8), the peak intensity of protons, I 10, in Col. (9), the peak intensity of protons, I 30, in Col. (10), and the peak intensity of protons, I 50, in Col. (11). The CME speed associated with the SPE that occurred on 2005 January 20 estimated by Gopalswamy et al. ( 2005 ) is 3242 km s−1, which will be used in the paper.

3 Classical Correlation Analysis and Results

Because our sample only comprises 79 SPEs, we also use the bootstrap method (Wall & Jenkins 2012 ) to estimate the statistical uncertainty of CCs, which was used by Trottet et al. ( 2015 ). The CCs were calculated for N pairs of values chosen at random within the set of N observations. This procedure was repeated 5000 times.

3.1 Correlation between SEPs and SXR Peak Flux

The source locations well connected with the Earth are mainly distributed in the longitudinal area ranging from W40 to W70, which can be seen from figure 2.3 in the paper Reames ( 1999 ). The CCs between peak intensities of SEP events and SXR peak flux in three longitudinal areas: W0–W39, W40–W70 and W71–W90 have been derived and are shown in Figure 1 for protons, Figure 2 for and Figure 3 for protons.

Fig. 1 Scatter (log-log) plots of I 10 versus in the three longitudinal areas.
Fig. 2 Scatter (log-log) plots of I 30 versus in the three longitudinal areas.
Fig. 3 Scatter (log-log) plots of I 50 versus in the three longitudinal areas.

We can see from Figure 1 that the CCs between I 10 and in the three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.24±0.17, 0.43±0.15 and 0.26±0.24 respectively. It is obvious that the CC between I 10 and SXR peak flux is longitudinally dependent. The largest CC is only 0.43±0.15 in the well connected region, suggesting that I 10 has only a weak correlation with in the well connected region.

We can see from Figure 2 that the CCs between I 30 and SXR peak flux in the three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.43±0.15, 0.71±0.09 and 0.35±0.22 respectively. It is evident that the CC between I 30 and SXR peak flux is highly longitudinally dependent, and the CC between I 30 and reaches its largest value in the well connected region and then declines dramatically in the longitudinal area outside the well connected region.

Figure 3 shows that the CCs between I 50 and in the three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.54±0.13, 0.77±0.07 and 0.36±0.22 respectively. The CC between I 50 and is highly longitudinally dependent, and the CC between I 50 and reaches its largest value in the well connected region and then declines dramatically in the longitudinal area outside the well connected region.

3.2 Correlation between SEPs and SXR Fluence

To check whether the CCs between SXR fluence and the peak flux of SEP events are longitudinally dependent, and compare the CC between SXR fluence and peak intensities of SEP events with the one between SXR peak flux and peak intensities of SEP events, the CCs between SXR fluence and peak intensities of SEP events have been derived and are shown in Figure 4 for , Figure 5 for and Figure 6 for protons.

Fig. 4 Scatter (log-log) plots of I 10 versus Φ x in the three longitudinal areas.
Fig. 5 Scatter (log-log) plots of I 30 versus Φ x in the three longitudinal areas.
Fig. 6 Scatter (log-log) plots of I 50 versus Φ x in the three longitudinal areas.

We can see from Figure 4 that the CCs between I 10 and Φ x in the three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.43±0.15, 0.58±0.12 and 0.39±0.22 respectively. Although the correlation between Φ x and I 10 is moderate in the well connected region, the CC between Φ x and I 10 is still highly longitudinally dependent. It evident that Φ x has a closer association with I 10 than with .

We can see from Figure 5 that the CCs between I 30 and Φ x in three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.50±0.14, 0.80±0.06 and 0.37±0.22 respectively. It is evident that the CC between I 30 and Φ x is highly longitudinally dependent, and I 30 has a good correlation with Φ x in the well connected region. The CC between Φ x and I 30 is larger than that between and I 30 in the well connected region, suggesting that Φ x has a closer association with I 30 than . The CC between I 30 and Φ x is larger than the one between I 10 and Φ x in the well connected region, suggesting that I 30 has a closer association with Φ x than I 10.

Figure 6 shows that the CCs between I 50 and Φ x in the three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.54±0.13, 0.83±0.06 and 0.13±0.28 respectively. It is evident that the CC between I 50 and Φ x is highly longitudinally dependent. The CC between I 50 and Φ x is larger than the one between I 50 and in the well connected region, suggesting that I 50 has closer association with Φ x than . The CC between I 50 and Φ x is larger than the one between I 30 and Φ x in the well connected region, suggesting that I 50 has a closer association with Φ x than I 30.

3.3 Correlation between Peak Intensities of SEP Events and CME Speeds

The CCs between the speeds of CMEs and the peak intensities of SEP events with different energies in three longitudinal areas W0–W39, W40–W70 and W71–W90 have been derived and are shown in Figure 7 for protons, Figure 8 for protons and Figure 9 for protons.

Fig. 7 Scatter (log-log) plots of I 10 versus in the three longitudinal areas.
Fig. 8 Scatter (log-log) plots of I 30 versus in the three longitudinal areas.
Fig. 9 Scatter (log-log) plots of I 50 versus in the three longitudinal areas.

We can see from Figure 7 that CCs between I 10 and in the three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.67±0.10, 0.56±0.12 and 0.45±0.21 respectively. The CC between and I 10 is slightly longitudinally dependent and the CC reaches its largest value in the longitudinal area W0–W39.

We can see from Figure 8 that CC between I 30 and in the three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.54±0.10, 0.53±0.13 and 0.40±0.21 respectively. The CC in the longitudinal area W0–W39 is almost the same as the CC in the longitudinal area W40–W70.

Figure 9 shows that CCs between I 50 and in the three longitudinal areas W0–W39, W40–W70 and W71–W90 are 0.50±0.14, 0.48±0.14 and 0.34±0.23 respectively. The difference between the CC in the longitudinal area W0–W39 and the CC in the longitudinal area W40–W70 is only 0.02, which can be ignored.

4 Partial Correlation Analysis

Partial correlation between two variables is considered by nullifying the effects of the third (or fourth, or more) variable upon the variables being considered, which has been used by Trottet et al. ( 2015 ) to analyze the correlation between peak intensities of 15–40 MeV protons and the parameters of the associated solar activities. To investigate how CME speed, SXR peak flux and SXR fluence independently affect the peak intensities of , and MeV protons in the well connected region, the partial CCs between the peak intensities of , and protons and the parameters of associated solar activities, together with statistical uncertainties from the bootstrap method, will be calculated. We use CC (X, Y) to indicate the partial CC between parameters X and Y.

4.1 Partial Correlation Analysis for Protons

For SEP events with a source location in the well connected region, CC , ), CC , ) and CC , ) are 0.46±0.15, and respectively, suggesting that for the SEP events with source location in the well connected region, both CME speed and SXR fluence can significantly affect the peak intensities of protons, but SXR peak flux makes no additional contribution.

4.2 Partial Correlation Analysis for Protons

For SEP events with source location in the well connected region, CC , ), CC , ) and CC , ) are , and respectively. It is evident that Φ x has much better correlation with peak intensity of protons than , suggesting that for SEP events with source location in the well connected region, only Φ x can significantly affect the peak intensities of protons, while CME shock just makes a small contribution to the peak intensities of protons, and makes no additional contribution the peak intensities of protons.

4.3 Partial Correlation Analysis for Protons

For SEP events with source location in the well connected region, , ), CC , ) and , ) are 0.11±0.19, and respectively, suggesting that for the SEP events with source location in the well connected region, only SXR fluence can significantly affect the peak intensities of protons, but both SXR peak flux and CME speed make no additional contribution to the peak intensities of protons.

5 Summary and Discussion

If the source locations of SEP events are not well connected with the Earth, the GOES spacecraft is located in a poor position to observe the particles accelerated by concurrent flares. However, if the source locations of SEP events are well connected with the Earth, the GOES spacecraft is located in a good position to observe flare-accelerated particles. This suggests that if flares really contribute to the production of SEPs in large gradual SEP events, then the CC between flares and the peak intensities of SEP events should be longitudinally dependent, and the CC between flares and SEPs should reach its largest value in the well connected region and decline dramatically in the longitudinal area outside the well connected region. The results of the paper suggest that flares really contribute to production of , and protons.

By comparing Figure 1 with Figure 7, we can find that the CC between speeds of CMEs and I 10 is always larger than the CC between SXR peak flux and I 10 in the same longitudinal area, suggesting that for protons, CME speed is more important than flare intensity, which is consistent with the result obtained in the paper Park et al. ( 2012 ).

For , and protons with source location in the well connected region, classical correlation analyses show that the CC between SXR fluence and peak intensities of SEPs is always larger than that between SXR peak flux and peak intensities of SEPs, suggesting that SXR fluence always has a closer association with the peak intensities of SEP events than SXR peak flux, namely that SXR fluence is a more important parameter describing the relationship between SXR emission and SEP events than SXR peak flux.

For protons, the combination of classical correlation and partial correlation analyses shows that in the well connected region, both flare and CME shock are effective accelerators for protons. For protons, the combination of classical correlation and partial correlation analyses shows that in the well connected region, protons can be accelerated by both concurrent flares and CME shocks. However, protons may be mainly accelerated by concurrent flares. For protons, the combination of classical correlation and partial correlation analyses shows that in the well connected region, protons may be only accelerated by concurrent flares.

The outstanding property of flare-accelerated particles is that the flux of particles accelerated by flares is highly longitudinal or the CC between flares and the peak intensities of SEP events is highly dependent on heliolongitude. If we do not divide the SEP events into three longitudinal regions shown in the paper, the longitudinal dependence of SEP events on the associated flares cannot be found, which has been proved by Le et al. ( 2017 ). It can be noticed that the well connected region may not be exactly in the longitudinal area ranging from W40 to W70. The CCs between flares and peak intensities of SEP should be calculated in many more longitudinal areas to precisely look for the well connected region if the number of samples of large SEP events is large enough.

It can be noticed that the flares, in some cases, are not accompanied by SEP events if the flares are not accompanied by CMEs. Klein et al. ( 2010 ) suggested that flare-accelerated particles might be trapped in the flare site if radio emissions at decimeter and longer wavelengths are absent. In other words, the flare is confined. If the solar flare is eruptive, an associated CME can open quite a large amount of magnetic field lines over the AR so that flare-accelerated particles can escape from the AR and then propagate into interplanetary space.

6 Conclusions

Classical correlation analysis shows that in the well connected region, higher energy protons have a closer association with concurrent flares, while lower energy protons have a better correlation with the speeds of associated CMEs, suggesting that flares are effective accelerators for higher energy protons, while CME shocks are effective accelerators for lower energy protons.

The combination of classical correlation analysis and partial correlation analysis suggests that for SEP events with source location in the well connected region, a CME shock is only an effective accelerator for protons. However, flares are not only effective accelerators for protons, but also for protons, and protons may be mainly accelerated by concurrent flares.

Statistical results are usually given for the majority of cases. The results of the paper do not rule out the possibility that for SEP events with source locations in a well connected region, a shock driven by an associated CME may play a key role in the production of protons and even for higher energy protons. The discussion of shock geometry and intensity, and whether this kind of shock is well connected with the Earth, is beyond the scope of this paper.


References

Andriopoulou M. Mavromichalaki H. Plainaki C. Belov A. Eroshenko E. 2011 Sol. Phys. 269 155
Aschwanden M. J. 2012 Space Sci. Rev. 171 3
Aurass H. Mann G. Rausche G. Warmuth A. 2006 A&A 457 681
Bazilevskaya G. A. 2009 Advances in Space Research 43 530
Bieber J. W. Matthaeus W. H. Shalchi A. Qin G. 2004 Geophys. Res. Lett. 31 L10805
Brueckner G. E. Howard R. A. Koomen M. J. et al. 1995 Sol. Phys. 162 357
Cane H. V. Richardson I. G. von Rosenvinge T. T. 2007 Space Sci. Rev. 130 301
Cane H. V. Richardson I. G. von Rosenvinge T. T. 2010 Journal of Geophysical Research (Space Physics) 115 A08101
Chen Y. Le G. Lu Y. et al. 2016 Ap&SS 361 40
Dierckxsens M. Tziotziou K. Dalla S. et al. 2015 Sol. Phys. 290 841
Firoz K. A. Gan W. Q. Moon Y.-J. Li C. 2012 ApJ 758 119
Gopalswamy N. Xie H. Yashiro S. Usoskin I. 2005 International Cosmic Ray Conference 1 169
Grechnev V. V. Kurt V. G. Chertok I. M. et al. 2008 Sol. Phys. 252 149
Grechnev V. V. Kiselev V. I. Meshalkina N. S. Chertok I. M. 2015 Sol. Phys. 290 2827
Kallenrode M.-B. 2003 Journal of Physics G Nuclear Physics 29 965
Klein K.-L. Trottet G. Klassen A. 2010 Sol. Phys. 263 185
Klein K.-L. Masson S. Bouratzis C. et al. 2014 A&A 572 A4
Kouloumvakos A. Nindos A. Valtonen E. et al. 2015 A&A 580 A80
Kubo Y. Akioka M. 2004 Space Weather 2 S01002
Le G.-M. Tang Y.-H. Han Y.-B. 2006 ChJAA (Chin. J. Astron. Astrophys.) 6 751
Le G.-M. Li P. Yang H.-G. et al. 2013 RAA (Research in Astronomy and Astrophysics) 13 1219
Le G.-M. Li C. Tang Y.-H. et al. 2016 RAA (Research in Astronomy and Astrophysics) 16 14
Le G.-M. Li C. Zhang X.-F. 2017 RAA (Research in Astronomy and Astrophysics) 17 073
Li C. Tang Y. H. Dai Y. Fang C. Vial J.-C. 2007a A&A 472 283
Li C. Tang Y. H. Dai Y. Zong W. G. Fang C. 2007b A&A 461 1115
Li C. Dai Y. Vial J.-C. et al. 2009 A&A 503 1013
Masson S. Klein K.-L. Bütikofer R. et al. 2009 Sol. Phys. 257 305
Miroshnichenko L. I. Klein K.-L. Trottet G. et al. 2005 Journal of Geophysical Research (Space Physics) 110 A11S90
Park J. Moon Y.-J. Lee D. H. Youn S. 2010 Journal of Geophysical Research (Space Physics) 115 A10105
Park J. Moon Y.-J. Gopalswamy N. 2012 Journal of Geophysical Research (Space Physics) 117 A08108
Pérez-Peraza J. Vashenyuk E. V. Miroshnichenko L. I. Balabin Y. V. Gallegos-Cruz A. 2009 ApJ 695 865
Qin G. 2007 ApJ 656 217
Qin G. Wang Y. Zhang M. Dalla S. 2013 ApJ 766 74
Qin G. Zhang L.-H. 2014 ApJ 787 12
Qin G. Wang Y. 2015 ApJ 809 177
Reames D. V. 1999 Space Sci. Rev. 90 413
Simnett G. M. 2006 A&A 445 715
Trottet G. Samwel S. Klein K.-L. Dudok de Wit T. Miteva R. 2015 Sol. Phys. 290 819
Tylka A. J. Cohen C. M. S. Dietrich W. F. et al. 2005 ApJ 625 474
Wall J. V. Jenkins C. R. 2012 Practical Statistics for Astronomers Cambridge Cambridge Univ. Press
Yashiro S. Gopalswamy N. Michalek G. et al. 2004 Journal of Geophysical Research (Space Physics) 109 A07105
Cite this article: Le Gui-Ming, Zhang Xue-Feng. Dependence of large SEP events with different energies on the associated flares and CMEs. Res. Astron. Astrophys. 2017; 12:123.

Refbacks

  • There are currently no refbacks.