A comprehensive ~ 25 MeV solar proton event list has been published in Richardson et al. (2014) and has since been kept up to date to include more recent events (Richardson, 2024). In this list, SEP proton events are identified in the cross-calibrated data sets of SOHO/COSTEP EPHIN and STEREO A and STEREO B HET. The process of identification excludes proton enhancements that are associated with the arrival of disturbances such as shocks at the s/c. Remote-sensing observations are used to identify the source location of the particle event. The process is explained in detail in Richardson et al. (2014).
This study identifies a subset of events from the list. We require that detecting s/c are separated by > 130ᵒ in longitude at 1 AU, and that SOHO is one of the s/c detecting the particle event. Valid periods are for combinations of SOHO and STEREO A: 5 Feb. 2013–12 Aug. 2017; of SOHO and STEREO B: 21 Dec. 2012 – Oct. 2014 (i.e., loss of STEREO B); and of all three s/c: 16 Dec. 2009–8 Apr. 2012. This reduces the event selection to 52 events.
Energy dispersion analysis focuses on the proton spectrograms of SOHO/COSTEP EPHIN, using three energy ranges: ~4–5 MeV, ~ 9–11 MeV and ~ 40–53 MeV. Figure 1 shows an example of the determination of the proton onset times for the particle event of 22 Sep. 2014. It is preceded by the onset of a Type-III radio burst identified in Wind/WAVES data at 0615UT, which is marked by a red vertical line in the electron and proton spectrograms. The electron spectrogram is displayed in energy (250 keV – 9 MeV) vs time, whereas the proton spectrogram is displayed in 1/v vs time. The time range of Fig. 1 starts two hours before the radio burst onset and covers 24 hours total. The time-intensity diagrams at bottom display the intensities of the adjacent energy bins of the proton spectrogram (top two, 8th and 9th from top, bottom two). The determination of the onset time and error is performed through onset interval fitting of the log value of the intensities. Any intervals without particle counts are filled with the average pre-event proton intensity value that is determined during the two hours preceding the type-III radio burst onset. The onset time is then determined by locating the intersection of each energy bin with the pre-event background value. The average time determines the onset time, and the spread from onset determines the error.
SOHO’s magnetic connection longitude difference from the SEP source longitude is determined by using the solar wind speed measured around the time of the type-III radio burst onset. It is assumed that the inherent uncertainty of this method, which assumes constant speed from the Sun to 1 AU, including non-radial fields in the solar corona, as well as uncertainty in the source longitude (which may be extended and not a point source) to be ~ 15ᵒ, but could be larger.
Theoretical minimum delays from field-aligned propagation from the Sun to 1 AU related to these energy intervals are listed in Table 2, for three common solar wind speed ranges, assuming a Parker spiral and that particles of each energy are injected onto the field line simultaneously. [Place Table 2 here]
Of the 52 wide-spread events listed in Table 1, 30 originate from inside the Solar Radiation Hemisphere (SRH), which is defined in Posner et al. (2021) as the hemisphere of the Sun that is centered around W60, spanning from E30 to W150. 22 events originate from outside the SRH. One of the events, No. 36, carries a caveat, as it is listed with a source at E58, but there is near-simultaneous sympathetic solar activity in the well-connected western hemisphere of the Sun that may have caused the small SEP event observed at SOHO. Given the ambiguity, we omit this event from further consideration, reducing the total number of events analyzed to 51 and those from outside the SRH to 21. Figure 2 shows histograms of proton intensities at SOHO distinguished by their origin within (top) or outside (bottom) the solar radiation hemisphere. There is a clear ordering of high local intensity from SEP events that originate from inside the SRH. These events have small magnetic connection distances from the source of the solar activity, in particular when compared to SEPs originating outside the SRH.
Table 1
lists data products of all 52 events in chronological order. Events in which the EPHIN instrument is pointed perpendicular to the nominal magnetic field are indicated by an asterisk. The table contains the source locations, durations of energy dispersion, including the event discussed above (No. 48 in the table), and times of identified type-III and electron event onsets. Missing onset times are indicated by N/A. The presence or absence of type-II radio bursts is also provided. [Place Table 1 here]
Ev. No.
|
Date/Time Type-III Onset [UT]/p int. max.
|
Source Long./ Conn. Dist. [o]
|
e- Onset [UT]/ Type-II?
|
p+
45MeV Onset [UT]
|
P + 10MeV Onset [UT]
|
p+
4.5 MeV Onset [UT]
|
Dur. 45 MeV – 4.5 MeV
|
Dur. 45 MeV – 10 MeV
|
Dur. 10 MeV – 4.5 MeV
|
1*
|
2009 Dec.22 04:55 0.0005
|
W40 30.8
|
05:38
N
|
N/A(a)
|
N/A(a)
|
N/A(a)
|
N/A(a)
|
N/A(a)
|
N/A(a)
|
2
|
2010 Aug. 14 10:03 0.2
|
W54 3.1
|
10:18
N
|
10:35 ± 0.5
|
11:03 ± 15
|
11:53 ± 1
|
78 ± 1.5
|
28 ± 15.5
|
50
± 16
|
3
|
2010 Aug. 18 05:39 0.03
|
W100 -32.7
|
06:02
Y
|
N/A(b)
|
07:35 ± 1
|
08:23 ± 6
|
N/A(b)
|
N/A(b)
|
48
± 7
|
4
|
2010 Aug. 31
20:52 0.005
|
W145 -71.0
|
21:16
Y
|
N/A(b)
|
23:53 ± 4
|
01:28 ± 4
|
N/A(b)
|
N/A(b)
|
95
± 8
|
5
|
2010 Sep. 08 23:29 0.003
|
W92
-21.8
|
23:42
Y
|
N/A(b)
|
01:04 ± 0.5
|
02:08 ± 1
|
N/A(b)
|
N/A(b)
|
64 ± 1.5
|
6
|
2011 Mar. 21 02:20 0.11
|
W138 -68.8
|
03:00
Y
|
03:29 ± 2
|
04:24 ± 17
|
04:52 ± 2
|
83
± 4
|
55
± 19
|
28
± 19
|
7*
|
2011 Jun. 04 22:04 0.04
|
W165 -116.8
|
22:24
Y
|
N/A(c)
|
N/A(c)
|
N/A(c)
|
N/A(c)
|
N/A(c)
|
N/A(c)
|
8
|
2011 Aug. 04 03:51 1.1
|
W36 35.2
|
04:24
Y
|
05:09 ± 5
|
05:45 ± 6
|
06:35 ± 10
|
86
± 15
|
36
± 11
|
50
± 16
|
9
|
2011 Sep. 06 22:22 0.1
|
W18 42.6
|
22:58
Y
|
23:52 ± 0.5
|
01:21 ± 5
|
01:58 ± 17
|
126 ± 17.5
|
89 ± 5.5
|
37
± 22
|
10*
|
2011 Nov. 03 22:24 0.04
|
E152
-134.7
|
23:00
Y
|
23:30 ± 3
|
00:25 ± 7
|
01:26 ± 18
|
116 ± 21
|
55
± 10
|
61
± 25
|
11*
|
2011 Nov. 26 07:11 0.3
|
W48 12.6
|
07:24
Y
|
N/A(c)
|
N/A(c)
|
N/A(c)
|
N/A(c)
|
N/A(c)
|
N/A(c)
|
12
|
2012 Jan. 23 03:40 20.
|
W21 33.3
|
04:00
Y
|
04:33 ± 0.5
|
05:38 ± 3
|
06:16 ± 0.5
|
103
± 1
|
65 ± 3.5
|
48 ± 3.5
|
13*
|
2012 May 17 01:33 0.6
|
W76
-7.8
|
01:56
Y
|
03:07 ± 6
|
04:52 ± 8
|
06:24 ± 30
|
197 ± 36
|
105 ± 14
|
92
± 38
|
14*
|
2012 May 26 20:48 0.03
|
W116 -47.8
|
21:06
Y
|
21:52 ± 4
|
22:43 ± 4
|
23:45 ± 3
|
113
± 7
|
51
± 8
|
62
± 7
|
15
|
2012 Jul. 23 02:12 0.2
|
W140 -84.2
|
05:20
Y
|
06:05 ± 3
|
N/A(c,d)
|
N/A(c,d)
|
N/A(c,d)
|
N/A(c,d)
|
N/A(c,d)
|
16
|
2012 Aug. 31 19:50 0.04
|
E42 121.2
|
20:40
Y
|
N/A(b)
|
22:42 ± 7
|
00:10 ± 43
|
N/A(b)
|
N/A(b)
|
88
± 50
|
17
|
2012 Sep. 20 14:57 0.003
|
E158
-152.9
|
22:00
Y
|
N/A(a)
|
N/A(a)
|
N/A(a)
|
N/A(a)
|
N/A(a)
|
N/A(a)
|
18
|
2013 Feb. 26 10:08 0.01
|
W131 -54.2
|
11:20
Y
|
N/A(b)
|
12:20 ± 14
|
N/A(d)
|
N/A(b,d)
|
N/A(b)
|
N/A(d)
|
19
|
2013 Mar. 05 03:43 0.006
|
E141
-150.8
|
07:30
Y
|
N/A(a,d)
|
N/A(a,d)
|
N/A(a,d)
|
N/A(a,d)
|
N/A(a,d)
|
N/A(a,d)
|
20*
|
2013 Apr. 11 06:56 2.
|
E12 71.9
|
07:42
Y
|
08:10 ± 7
|
08:58 ± 14
|
10:50 ± 4
|
160 ± 11
|
48
± 21
|
112 ± 18
|
21*
|
2013 Apr. 21 07:30 0.02
|
W124 -36.3
|
08:10
N
|
N/A(b)
|
N/A(d)
|
N/A(d)
|
N/A(b,d)
|
N/A(b,d)
|
N/A(d)
|
22*
|
2013 Apr. 24 21:38 0.01
|
W175 -115.8
|
22:12
N
|
22:43 ± 19
|
23:38 ± 61
|
N/A(d)
|
55
± 80
|
N/A(d)
|
N/A(d)
|
23*
|
2013 May 13 15:56 0.01
|
E95 162.3
|
17:36
Y
|
17:59 ± 72
|
21:57 ± 15
|
02:39 ± 2
|
520 ± 74
|
238 ± 87
|
282 ± 23
|
24*
|
2013 May 22 13:10 20.
|
W70
-15.2
|
13:42
Y
|
14:03 ± 19
|
14:40 ± 7
|
15:11 ± 3
|
68
± 22
|
37
± 26
|
31
± 10
|
25*
|
2013 Jun. 21 02:55 0.06
|
E73 124.2
|
06:00
Y
|
N/A(b)
|
12:07 ± 5
|
15:31 ± 5
|
N/A(b)
|
N/A(b)
|
324 ± 10
|
26
|
2013 Jul. 22 06:32 0.001
|
W172 -105.6
|
08:06
N
|
08:48 ± 18
|
10:36 ± 2
|
11:36 ± 84
|
168 ± 102
|
108 ± 20
|
60
± 86
|
27
|
2013 Aug. 19 23:13 0.01
|
W174 115.5
|
01:00 (+ 1d) Y
|
N/A(b)
|
N/A(b,d)
|
N/A(d)
|
N/A(b,d)
|
N/A(b,d)
|
N/A(b,d)
|
28
|
2013 Sep. 29 21:55 0.5
|
W25 66.6
|
22:22
Y
|
22:36 ± 15
|
23:36 ± 3
|
00:18 ± 17
|
102 ± 32
|
60
± 18
|
42
± 20
|
29*
|
2013 Oct. 11 07:14 0.002
|
E96 159.0
|
14:00
Y
|
N/A(a,d)
|
N/A(a,d)
|
N/A(a,d)
|
N/A(a,d)
|
N/A(a,d)
|
N/A(a,d)
|
30*
|
2013 Nov. 02 04:32 0.02
|
W127 -52.6
|
06:00
N
|
0702 ± 10
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
31*
|
2013 Nov. 19 10:24 0.04
|
W69
-4.4
|
10:40
Y
|
11:27 ± 5
|
12:18 ± 1
|
12:47 ± 0.5
|
80
± 1
|
51 ± 1.5
|
29 ± 1.5
|
32*
|
2013 Dec. 14 06:25 0.002
|
E144
-154.6
|
09:00
N
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
33*
|
2013 Dec. 26 02:54 0.03
|
E161
-109.6
|
04:30
N
|
N/A(b)
|
05:57 ± 1
|
06:56 ± 3
|
N/A(b)
|
N/A(b)
|
59
± 4
|
34*
|
2014 Jan. 06 07:48 0.6
|
W110 -45.6
|
08:25(e)
Y
|
N/A(e)
|
09:31 ± 9
|
10:47 ± 3
|
N/A(e)
|
N/A(e)
|
76
± 12
|
35
|
2014 Jan. 07 18:07 2.2
|
W11 56.3
|
19:00
Y
|
19:32 ± 4
|
20:30 ± 9
|
21:23 ± 34
|
111 ± 38
|
58
± 13
|
53
±43
|
36
|
2014 Jan. 30 16:03 0.002
|
E58(e) 125.3
|
16:50
N
|
N/A(b)
|
17:54 ± 9
|
18:42 ± 1
|
N/A(b)
|
N/A(b)
|
48
± 10
|
37
|
2014 Feb. 14 0822 0.003
|
W147 -75.8
|
09:40
N
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
38
|
2014 Feb. 18 01:20 0.004
|
E45 115.1
|
03:50
Y
|
N/A(b)
|
N/A(d)
|
N/A(d)
|
N/A(b,d)
|
N/A(b,d)
|
N/A(d)
|
39
|
2014 Feb. 21 15:44 0.001
|
E120 172.3
|
20:00
N
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
40
|
2014 Feb. 25 00:47 0.3
|
E82 139.1
|
02:02
Y
|
03:26 ± 10
|
07:45 ± 7
|
13:12 ± 6
|
586 ± 16
|
259 ± 17
|
327 ± 13
|
41*
|
2014 Mar. 28 23:22 0.001
|
W23 34.3
|
00:02 (+ 1d) Y
|
N/A(b)
|
02:23 ± 9
|
02:39 ± 0.5
|
N/A(b)
|
N/A(b)
|
16 ± 9.5
|
42*
|
2014 Mar. 29 17:46 0.03
|
W32 26.2
|
18:06
Y
|
18:42 ± 2.5
|
19:24 ± 5
|
19:42 ± 31
|
60 ± 33.5
|
42 ± 7.5
|
18
± 36
|
43*
|
2014 Apr. 02 13:28 0.001
|
E53 116.0
|
19:00
Y
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
44*
|
2014 May 09 02:22 0.003
|
W110 -43.6
|
03:50
Y
|
N/A(b)
|
04:39 ± 1
|
05:50 ± 5
|
N/A(b)
|
N/A(b)
|
71
± 6
|
45
|
2014 Jul. 08 16:12 0.0005
|
E56 131.6
|
16:58
N
|
17:12 ± 1
|
18:41 ± 4
|
19:24 ± 9
|
132 ± 10
|
89
± 5
|
43
± 13
|
46
|
2014 Sep. 01 11:03 0.02
|
E108 168.6
|
14:40
Y
|
21:23 ± 53
|
01:34 ± 22
|
06:18 ± 40
|
535 ± 93
|
251 ± 75
|
284 ± 62
|
47
|
2014 Sep. 10 17:30 0.4
|
E02 68.4
|
18:45
Y
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
48
|
2014 Sep. 22 06:15 0.03
|
W149 -91.1
|
06:48
Y
|
07:22 ± 2
|
08:18 ± 1
|
09:02 ± 4
|
100
± 6
|
56
± 3
|
44
± 5
|
49*
|
2014 Sep. 24 20:50 0.003
|
W179 -123.2
|
23:00
Y
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
50*
|
2015 Oct. 29 02:19 0.2
|
W95
-13.1
|
02:36
N
|
03:02 ± 12
|
03:49 ± 12
|
04:28 ± 13
|
86
± 25
|
47
± 24
|
39
± 25
|
51*
|
2015 Nov. 09 12:06 0.04
|
E39 84.9
|
14:50
Y
|
15:50 ± 17
|
19:21 ± 5
|
20:50 ± 5
|
300 ± 22
|
211 ± 22
|
89
± 10
|
52
|
2017 Jul. 23 05:01 0.01
|
W148 -105.3
|
07:40
Y
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
N/A(d)
|
Table 2
The table lists the expected delay durations between arrivals of protons of the energy ranges listed on the left, for various typical solar wind speeds. The distance to the Sun along the Parker spiral is also provided. The minimum delays are included in Figs. 4 and 6 as horizontal lines.
Proton Energy
Interval
|
Delay Duration
300km/s Vsw
|
Delay Duration
400 km/s Vsw
|
Delay Duration
500 km/s Vsw
|
45 MeV – 4.5 MeV
|
72.9 min
|
67.5 min
|
65.3 min
|
45 MeV – 10 MeV
|
37.8 min
|
35.0 min
|
33.8 min
|
10 MeV – 4.5 MeV
|
35.1 min
|
32.5 min
|
31.5 min
|
Ideal Parker Spiral Length
|
1.26 AU
|
1.16 AU
|
1.12 AU
|
80% of the SRH SEP events are accompanied by type-II radio burst activity observed by the STEREO and/or Wind spacecraft (e.g., https://cdaw.gsfc.nasa.gov/CME_list/radio/waves_type2.html). The existence of a type-II is indicative of a CME-driven shock accelerating electrons. CMEs of our sample with type-IIs are on average faster (1,300km/s) and wider (335ᵒ) than non-type-II producing CMEs (894km/s, 305ᵒ). Non-SRH SEP events are accompanied by solar type-II radio bursts only at a rate of 71%. While the statistical sample is small, it is surprising that we observe any SEPs without accompanying type-II from the non-SRH in view of the literature (e.g., Rouillard et al., 2012) requiring broad CME shocks to reach observers that are not well connected to the source location.
80% of SRH SEP events show clear signatures of proton energy dispersion in the 4.5–45 MeV range at SOHO. (Note that this and the type-II-distribution originating in the SRH are overlapping but non-identical.) A much lower percentage of non-SRH SEP events has clearly recognizable proton energy dispersion: 52%. This is not surprising given the much lower relative maximum intensities, which are reflected in correspondingly lower intensity ramps near the onset. If an elevated pre-event particle intensity is present locally, the onset energy dispersion of weaker-appearing events would have a lower signal-to-noise level and would be more difficult to recognize. This affects non-SRH events disproportionately. There are clear examples, events Nos. 46 and 23, that reveal onset dispersion despite the inferred magnetic connection distance exceeding 160ᵒ in longitude. Recognition of energy dispersion requires a combination of clean observations and quiet pre-event conditions. Under favorable circumstance, it appears likely that SEP events from anywhere on the Sun can create energy dispersion patterns of protons anywhere at 1 AU.
The durations between the arrivals of 4.5 MeV and 45 MeV protons range from about one hour to almost 10 hours. In the literature, onset dispersion signatures are being used to infer particle release time, and the length of the magnetic field line connecting the observer with the Sun (see, e.g., Klein & Posner, 2005; Dresing et al., 2024). It is important to recognize that these two inferences require proton cross-field diffusion to be extremely low. Our statistical analysis of a large ensemble of wide-spread SEP events tests whether this assumption is generally valid. There are two (extreme) possibilities:
a) No cross-field transport of protons. In this scenario, protons can only reach the observer if a direct magnetic field line connection to the accelerating source is established. As the extended source, notably a CME-driven shock, expands into the heliosphere, it can intercept the magnetic field line that connects Earth/SOHO with the Sun. This may occur at a significant distance from the Sun, therefore shortening the magnetic field line length between the acceleration source and the 1 AU observer. From a statistical analysis one would expect shorter durations of proton energy dispersion with increasing magnetic connection distance from the SEP source. This is equivalent to a racetrack in which the arrival time is clocked between a faster and a slower car. If the racetrack is shortened, the time delay between the two arrivals is shortened proportionately. If one assumes a wide CME spanning up to 180ᵒ in longitude, the intercept of a shock with the Parker spiral would rise to a significant distance from the Sun rather quickly.
b) Particles reach regions far away from any magnetic connection to an acceleration region at the Sun via cross-field transport. This may encompass pitch angle scattering or transport across the average field by processes such as field-line random walk while within the same magnetic sector. Limiting ourselves to particle scattering, one would expect the diffusive transport away from the best-connected field line to proceed quickly. With increasing connection distance, however, the particle intensity gradient would decrease, and the process slows down, as protons become increasingly likely to be scattered back towards their longitude of origin. The diffusion process would increase the effective path length of particles, but not necessarily along existing field lines. Assuming comparable cross-field diffusion coefficients across the energy range of EPHIN for protons, the effective path length increase would be equivalent to the lengthening of the “racetrack”, increasing the duration between fast- and slow-moving particles arriving at SOHO, and resulting in longer durations of proton energy dispersion.
The recent example of 12 July 2012, discussed under assumption (a), is presented in Fig. 3 by Wijsen et al. (2022), using a EUHFORIA simulation (Pomoell & Poedts, 2018). The SEP event is not included in Table 1 as it was detected by SOHO and STEREO B when the s/c were less than 130ᵒ apart. The authors discuss the onset of the SEP event and find that “[i]n the simulation, this observer (hereafter Earth) connects with the shock front about ~ 30 h after the CME insertion (i.e., on 13 July, around 22:00 UT). However, the observed onset of the SEP event suggests that Earth had likely a direct magnetic field connection to the shock wave shortly after the CME eruption (i.e., on 12 July around 17:00 UT).” The following discussion in the paper considers an even wider shock, and the possibility that the magnetic field was more radial, but not the possibility that the acceleration may have occurred near the SEP origin and that the particles reached the observer predominantly through cross-field diffusion.
A related question is whether or how SEP onsets with energy dispersion can be detected from events originating in excess of.~90ᵒ from the observer. A magnetic connection to a CME shock outside 1 AU (e.g., Reames, Barbier and Ng, 1996) is not a possibility, as the onset times consistently stay within one day of the solar event, and CMEs that reach 1 AU within this time have not been observed. Reports of CMEs extending beyond 180ᵒ exist. But even in this case, the average field line length connecting the observer to the overly wide CME shock would not increase, no matter what the magnetic connection distance from the SEP source is. Thus, the onset dispersion durations of well-connected events would set the upper limit for all events assuming possibility (a).
Linear fits to three energy ranges in Fig. 4 have a positive slope, meaning that the average duration of the energy dispersion increases with increasing magnetic connection distance. As discussed above, the sample of events with recognizable energy dispersion at large magnetic connection distances is rather limited. However, the observed events are clear cases.
Figure 5 shows representative examples of proton energy dispersion in a “Solar Energetic Particle Clock” organization, which displays electron and ion spectrograms over each of the 12 clock sectors of their source longitude with respect to Earth at the 6 o’clock position. Events in the Solar Radiation Hemisphere cover sectors 3–6 and split sectors 2 and 7 with events outside the Solar Radiation Hemisphere. Long-duration energy dispersion events are present in sectors 7, 9, and 10, which refer to the events No. 51, No. 40, and No. 46 in Table 1.
Richardson et al. (2014) have shown that onset time delays for electrons and for protons each at a different single energy show a positive correlation with magnetic connection distance. This tendency was also previously discussed by Kallenrode (1993). Figures 15 and 16 of Richardson et al. (2014) show that the delay can be matched by assuming a fixed duration for streaming along the field to 1 AU for each species if combined with the expansion of an inciter at the solar surface. To match, the inciter must have a higher speed for relativistic electrons than for the 25 MeV protons they analyzed. While this set of observations already hints towards an interpretation that particle speed dependent cross-field particle diffusion away from the source location is the likely cause for the onset delays, as recently also shown in the simulations of Strauss et al. (2023), the option of having different acceleration regions for protons and electrons driven by an expanding CME shock cannot be ruled out. Based on the observations above, we can add that the onset delays for a single species at different energies bolsters the case for the role of speed-dependent particle cross-field diffusion. In addition, an explanation of our observations by scatter-free travel from the accelerating source would require a slow exciter speed for low-energy protons and a high exciter speed for higher-energy protons, and it would require the exciter to remain at solar surface height. This seems unlikely.
We also note that longer-duration proton energy dispersion coincides with longer average delays between type-III and electron onsets for the same events. This is discernible from the color coding of the events shown in Fig. 4. Figure 6 contains the same information as Fig. 4 but switches the way magnetic connection distance and electron onset delay are displayed. The correlation of proton energy dispersion with electron delay is visible here. It is, moreover, important to highlight that all long-duration proton energy dispersion events also have long delays of electron onsets over type-III radio bursts. These two independent observations can be separated in time by > 12 hours (event No. 40. This poses a challenge to view (a) in that a direct magnetic connection to far-away accelerator inside-1-AU needs to be maintained for a long time.
We also note that there are a few events for which a comparatively small delay between type-III onset and electron onset suggests a shorter magnetic connection distance than listed. A possibility is that the source longitude for the protons detected at Earth is ambiguous and different from that listed. One such event is listed as No. 10. This has been widely discussed because of the unusually rapid particle arrival at both STEREOs and at Earth following an eruption behind the east limb associated with a CME which was directly observed by STEREO B (Richardson et al., 2014; Gomez-Herrero et al., 2015; Zhao & Zhang, 2018). While these authors have concluded that this single eruption gave rise to the widespread SEP event, we note that Park et al. (2013), and Prise et al. (2014 have proposed that a separate source gave rise to the SEP event at Earth. However, Gomez-Herrero et al. (2015) argue on several grounds that this view is not correct. Since the poorly connected source region is likely to be correct for this event, this suggests that other factors may influence particle propagation beyond the two scenarios considered here.