Solar Longitude Distribution of High-energy Proton Flares: Fluences and Spectra

The distribution of the longitudes of solar flares associated with the high-energy proton events called ground level events (GLEs) can be approximated by a Gaussian with a peak at ∼W60, with a full range from ∼E90 to ∼W150. The longitudes of flares associated with the top third (24 of 72) of GLEs in terms of their >430 MeV fluences (F430) are primarily distributed over E20–W100 with a skew toward disk center. This 120° span in longitude is comparable to the latitudinal spans of powerful coronal mass ejections (CMEs) from limb flares. Only 5 of 24 strong GLEs are located within the W40–80 zone of good magnetic connection to Earth. GLEs with hard spectra, i.e., a spectral index SI30/200(= log(F30/F200)) < 1.5, also tend to avoid W40–80 source regions. Three-fourths of such events (16 of 21) arise in flares outside this range. The above tendencies favor a CME-driven shock source over a flare-resident acceleration process for high-energy solar protons. GLE spectra show a trend, with broad scatter, from hard spectra for events originating in eruptive flares beyond the west limb to soft spectra for GLEs with sources near central meridian. This behavior can be explained in terms of: (1) dominant near-Sun quasi-perpendicular shock acceleration of protons for far western (>W100) GLEs; (2) quasi-parallel shock acceleration for well-connected (W40–80) GLEs, and (3) proton acceleration/trapping at CME-driven bow shocks from central meridian (E20–W20) that strike the Earth.


Introduction
The high-energy proton events monitored by the worldwide network of ground-based neutron monitors (NMs; Simpson et al. 1953;Bieber & Evenson 1995;Mavromichalaki et al. 2011) are termed ground level events (GLEs). The effective energy threshold for GLEs is 1 GV in rigidity (430 MeV in energy; Mishev et al. 2013). GLEs were first detected in 1942 by ionization chambers (Lange & Forbush 1942;Forbush 1946). To date, 72 GLEs have been observed. 4 Until recently, the principal measure of GLE strength was the largest percentage increase above background observed at any sea-level station (e.g., McCracken et al. 2012;Poluianov et al. 2017). This intensity measure is not ideal because it depends on event timing relative to the location of a changing network of monitors. Because of the lack of a well-defined parameter for GLE strength, distributions of the solar longitudes of GLE-associated flares typically include all GLEs, regardless of size, resulting in a broad Gaussian centered at ∼W60 (e.g., Figure 1 in Smart & Shea 1996), near the nominal ∼W55 footpoint (based on the Sun's rotation rate and the average speed of the solar wind) of the magnetic field-line connecting to Earth. Data now exist to examine the solar longitude distribution of GLEs in greater detail. Tylka & Dietrich (2009) undertook a systematic evaluation of NM and space-based data to construct spectra for all GLEs that were sufficiently large. This work was recently updated and more thoroughly documented by Raukunen et al. (2018) to provide a homogeneous database of GLEs, permitting the determination of proton fluences at all energies.
In this study we use this database to examine where the strongest (and weakest) GLEs in terms of >430 MeV fluence (F 430 ) originate on the Sun. We also examine the variation of GLE spectra, as characterized by log (F 30 /F 200 ), with source longitude. Our analysis is presented in Section 2 and results are discussed in Section 3. Table 1 gives the dates, solar flare coordinates, proton fluences (F 30 , F 200 , and F 430 ), and the spectral index SI 30/200 (=log (F 30/ F 200 )) determined from the spectral parameters given in Raukunen et al. (2018) for 59 of the 72 GLEs. The Raukunen et al. analysis did not consider the first four GLEs (all observed before the neutron monitor era), the most recent GLE on 2017 September 10, and eight other GLEs for which the proton fluences were considered too small to make reliable spectral fits. In our fluence analysis, we divided GLEs into the top third (24 GLEs), middle third, and bottom third in terms of their >430 MeV fluence. We assigned GLE Nos. 1-4 to the top third. Because of their less sensitive mode of observation, the first four GLEs are considered to be among the largest observed (Duggal 1979;Smart & Shea 1991;Shea & Smart 2019). We took the eight events not analyzed by Raukunen et al. (2018) to be among the smallest third. Quoting from their paper, "...eight [GLEs] had too small fluences for the [spectral fits] to be reliable." Based on comparison with other GLEs on the Oulu website, we assigned GLE No. 72 (Mishev et al. 2018) to the middle third of events. For six of the GLEs (No. 42: 1989

Analysis
Figures 1(a), (b) contain histograms of F 430 for the GLEs with the 24 highest and 24 lowest rank order fluences, respectively. The highest-fluence events show a broad distribution from E20 to W100 that is skewed toward disk center, similar to the distribution Smart et al. (2006) obtained for >30 MeV protons. The GLE numbers are given in the histograms, with the two-component (P + ESP) events in red. It is likely that GLE Nos. 1 and 3 were also in this category.  (2006), Gopalswamy et al. (2012Gopalswamy et al. ( , 2013Gopalswamy et al. ( , 2018. Removal of the ESP component for the six events for which we have data would change the classification for GLE No. 42, dropping it out of the top third. This event was unusual in that while the other five events were all located within 20°of disk center, the 1989 September GLE is associated with an eruptive flare located at W100. The histogram in Figure 1(b) shows a broad distribution centered at ∼W60 for the solar locations of the third of GLEs from 1942 to 2017 with the lowest F 430 values. Figure 2 shows that the broad peak in the distribution for all GLEs in the overarching histogram is primarily due to the concentration of small GLEs in the W20-100 range. Figure 3 is a plot of the proton spectral index log (F 30 /F 200 ) versus solar flare longitude (Kovaltsov et al. 2014;Asvestari et al. 2017) for the 59 GLEs from 1956 to 2012 analyzed by Raukunen et al. (2018). These GLEs span a total longitude range of ∼240°, from E88 to W154. The events are colorcoded by their F 430 fluence ranking as follows: top third (magenta), middle third (black), and bottom third (green). The dashed horizontal line bounds hard spectrum events with log (F 30 /F 200 ) values <1.5, and the two dashed vertical gray lines mark the zone of favorable magnetic connection from W40 to 80. The solid line is an ordinary least-squares fit to the scatter showing spectral hardening (reduction of log (F 30 /F 200 )) as one moves westward from solar disk center. In particular, all eight far west GLEs, i.e., those originating at >W100, have spectral indices 1.5 (c.f., Figure 10 in Van Hollebeke et al. 1975 at lower energies). The hardest spectra events tend to avoid the W40-80 zone of good magnetic connection. Of the 21 GLEs with log (F 30 /F 200 )<1.5, only 5 originated from W40 to 80, with 11 associated with flares located >W80.
The median GLE SI 30/200 value increases from ∼1.35 for >W100 events to ∼1.65 for events from the W40-80 zone of good magnetic connection to ∼1.95 for GLEs from central meridian (E20-W20). The 13 central meridian GLEs in Table 1 are strongly associated with "fast transit" CMEs, i.e., CMEs with intervals from eruptive flare onset to a geomagnetic storm sudden commencement (SC; shock arrival) at Earth of 20 hr (Cliver et al. 1990a(Cliver et al. , 1990b, or 30 hr interval (Gopalswamy et al. 2005) as used here. Table 2(a) gives the dates, flare onset times, transit time interval, F 430 size rank (in thirds), SI 30/200 value, ESP occurrence (yes/no), and references for the E20-W20 events in Table 1. Only four of the Table 2(a) events have transit times longer than 30 hr (range from 32 to 38.1 hr). At least 7 of the 12 soft-spectrum GLEs (SI 30/200 1.7) from E20-W20 longitudes are associated with shocks at Earth. In addition to the five such events for which Raukunen et al. (2018) computed a separate ESP spectrum, the 1972 August 4 (Pomerantz & Duggal 1974) and 2003 October 29 (Gopalswamy et al. 2005, their Table 3 and Figure 9) had shock-related >30 MeV proton enhancements at Earth. Pomerantz & Duggal (1974)    60% of the total. In all five cases, the ESP contribution to F 30 was dominant by factors of ∼2-3 or more. In contrast, only three of the eight far western (>W100) GLEs in Table 1 had confirmed associated SCs and the delay from the flare for these three events ranged from ∼50 to 80 hr (Table 2(b)). Effects on the >30 MeV proton time profile at the time of shock arrival at Earth for these events were weak or absent.

Discussion
After an extended debate (e.g., Reames 2015), it is generally accepted that large solar proton events are primarily due to diffusive shock acceleration (DSA; Desai & Giacalone 2016) at shocks driven by coronal mass ejections (CMEs) rather than to a flare-resident process. If there is a remaining area of uncertainty, it is for the highest-energy proton events (McCracken et al. 2008;Klein et al. 2014;Cliver 2016;Klein & Dalla 2017). The comprehensive characterization of GLEs by Raukunen et al. (2018) following the work of Tylka & Dietrich (2009) permits further investigation of this question.
The distribution of source longitudes for the highest-fluence GLES in Figure 1(a) argues against a picture in which highenergy protons are accelerated locally in a solar flare. In such a picture, one would expect the strongest GLEs to be preferentially produced near W60 with proton fluences falling Notes. a Onset times are based on the principal source (first reference listed) for each event and are variously based on Hα, radio, soft X-ray, and CME observations. b Interval between flare onset time and sudden commencement unless otherwise noted.  Ellison et al. (1961) and Obayashi (1962) report a large amplitude SC at ∼10:22 UT on November 13 that is not included in Mayaudʼs (1973) list. e Modulation of the >30 MeV proton time profile is not clearly related to the SC. f All onset times from Cliver et al. (1982) and Cliver (2006). g References: (1) SC from Švestka & Simon (1975), no SC reported by Mayaud (1973)  off with distance from this location. Instead, the distribution in Figure 1(a) is skewed toward disk center with only 5 of 24 such GLEs originating from W40 to 80. The broad distribution of source longitudes in Figure 1(a), with the bulk of large GLEs having sources from ∼E20 to W100, corresponds to the 120°a ngular span in latitude for powerful CMEs originating at the solar limbs (Gopalswamy et al. 2015), supporting the CMEdriven shock picture for high-energy proton acceleration. Figure 2 shows that it is the third of GLEs with the lowest F 430 values that are primarily responsible for the broad W20-100 peak in the overall distribution of source longitudes. Apparently, these weaker GLEs (Figure 1(b)) benefit from the proximity of their source to the ∼W55 footpoint of the magnetic field-line connected to Earth.
In the CME-driven shock picture of high-energy proton acceleration, we would expect GLE spectra to result from some combination of quasi-perpendicular and quasi-parallel shock acceleration. Figure 3 gives hints as to how this apportionment occurs with source longitude. Quasi-perpendicular shock acceleration, in which the shock is propagating perpendicularly to the ambient magnetic field, is a special case of DSA (Jokipii 1982(Jokipii , 1987Tylka et al. 2005;Zank et al. 2006) that produces a harder spectrum than quasi-parallel acceleration. The hard spectra of the eight (>W100) events in Figure 3 are interpreted as a signature of dominant quasi-perpendicular acceleration by a shock driven across the face of the Sun by the lateral expansion of a CME to reach the magnetic field-line to Earth rooted >40°in longitude from the flare site. The corresponding radial motion of the CME responsible for quasiparallel shock acceleration is directed away from the Earth-Sun line and the Archimedean-spiral magnetic field line to Earth. As a result, the bow shock driven outward by the CME is unlikely to strike the Earth (see, e.g., Figure 2 in Cane et al. 1988) or to remotely produce a strong proton response there by accelerating protons on Earth-directed field lines (Table 2(b)). Highenergy protons produced near the Sun at the nose of the bow shock (e.g., Gopalswamy et al. 2013) for a far west GLE will sweep past 1 au ahead of the Earth in its orbit.
The softening of the GLE proton spectrum at Earth as one moves from the west limb toward ∼W60 can be explained in terms of an increasing (decreasing) contribution from quasiparallel (quasi-perpendicular) shock acceleration of highenergy protons. The quasi-perpendicular contribution to GLEs should have its minimum at ∼W60. This follows from the location of the eruptive flare under, rather than flanking, open field lines to Earth and is consistent with the relative lack of hard-spectra GLEs from W40 to 80 (Figure 3). GLEs originating east of W40, like those west of this longitude zone, can have a quasi-perpendicular component, and there are six GLEs in this zone with hard spectra (SI 30/200 1.5). The bulk (15/21) of GLEs east of W40, however, have SI 30/200 >1.5, suggesting dominant quasi-parallel shock acceleration of protons. In contrast to eruptive flares arising from >W100, a bow shock from a central meridian (E20-W20) GLE-parent flare has a high probability of being detected in situ at Earth (Table 2(a)). During its journey to Earth, it can (1) accelerate protons on the field lines to Earth on its western flank because of the eastward curvature of the interplanetary magnetic field (while those accelerated near the Sun at the shock nose will pass behind the Earth), and/or (2) accelerate protons as it converges with earlier slower CMEs (e.g., Pomerantz & Duggal 1974;Kallenrode & Cliver 2001). At Earth, it can produce an ESP event due either to local acceleration (Reames 2013) or a magnetically trapped population (Lario & Decker 2002). Because the CME-driven shock will decelerate and weaken over time, proton acceleration at the bow shock will produce a progressively softer spectrum at Earth during the time that the shock is connected to the magnetic spiral to Earth-a time that will naturally be greater for central meridian eruptions than for those from beyond the west limb. The resulting soft proton spectra for these various processes make bow shocks from central meridian CMEs the principal candidate for the cause of the broad peak in SI 30/200 from ∼E20 to W20 in the scatter plot in Figure 3. E.W.C. and F.M. acknowledge participation in the workshop on the Hostile Sun at Nagoya University in 2018 October organized by F. Miyake and I. Usoskin. E.W.C. has benefited from membership in the ongoing ISSI Team on high-energy SPEs led by A. Papaioannou. He thanks L. Fletcher for kindly sponsoring his stay at the University of Glasgow.