2. Understanding SEP properties through Neutron Monitor data modeling Neutron Monitor Network: a tool for revealing the relativistic SEP properties Ground Level Enhancement (GLE) data recorded by the worldwide Neutron Monitor (NM) Network are a useful resource for space weather modeling during solar extreme events. Several techniques for modeling the dynamical behavior of GLEs throughout their evolving are presently available (e.g. Shea and Smart, 1982; Humble et al., 1991; Belov et al., 2005a; 2005b; Bombardieri et al., 2007; Plainaki et al., 2007; Vashenyuk et al., 2011; Mishev et al., 2014; Plainaki et al., 2010; 2014). Basic idea: the responses of an adequate number of ground level NMs world wide are modeled to determine a best fit spectrum and spatial distribution of the energetic particles arriving from the Sun during a GLE event. The functions that are being used are chosen as to represent the physical processes involved in the particle rigidity distribution and propagation as well as the response of the atmosphere to energetic solar particle fluxes. GLE60 15 April 2001 GLE71 17 May 2012 Recent SEP event-observations associated with GLEs registered by NM stations Left: two-ribbon flare in SDO/AIA 1600 Å overlaid with the RHESSI HXR sources (from Li et al., 2013) on 17 May 2012 Right: CME observation by SOHO/LASCO on 17 May 2012 http://www.spaceweather.com/images2012/17may12/cme _anim.gif?PHPSESSID=gmt7p9bqv1taqfhivucgnrg640 CME observation by SOHO/LASCO on 15 April 2001 http://soho.nascom.nasa.gov/ hotshots/2001_04_15/ Technically, the accurate modeling of a GLE event depends on: the number of the NMs used in the analysis and their spatial distribution around the world; For example, in order to avoid a biasing of the modeling-results, data originating from NMs that are almost equally distributed between the two hemispheres should be used (see discussion in Bütikofer and Flückiger, 2013). Christina Plainaki[1][2], Helen Mavromichalaki[2], Monica Laurenza[1], Maria Andriopoulou[3], Anatoly Belov[4], Eugenia Eroshenko[4], Victor Yanke[4] [1]INAF-IAPS, Via del Fosso del Cavaliere, 00133, Rome, Italy; [2]Nuclear and Particle Physics Section, Physics Dpt., National and Kapodistrian University of Athens, Greece [3]Space Research Institute, Austrian Academy of Sciences, Graz, Austria; [4]Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation by Pushkov (IZMIRAN), Moscow, Russia

3. The NMBANGLE PPOLA model The NMBANGLE PPOLA model is based on Dorman's coupling coefficient method and couples SEP at some altitude in the Earth's atmosphere with their secondary products detected at ground level NMs during GLEs. NMBANGLE PPOLA stands for Neutron Monitor Anisotropic GLE Pure Power Law model Among the numerous space weather models available to the community, the NMBANGLE PPOLA (Plainaki et al., Solar Physics, 2010) aims at the calculation of the SEP properties during GLEs through the exclusive use of ground-based NM data from the worldwide Network. In this paper, we present a short overview of the application of the NMBANGLE PPOLA model to two different GLEs, discussing the derived characteristics of the relativistic SEP fluxes. This model calculates dynamically the SEP spectrum and the SEP flux spatial distribution, at some altitude of the Earth’s atmosphere assuming a power law spectrum for the SEP. From Plainaki et al., PhD thesis,2007 NM worldwide Network W(R, h, t 0 ) : is the rigidity dependent coupling function between secondary and primary cosmic rays γ(t): is the exponent of the power law primary SEP spectrum Ω(R,t): is the solid angle defined by the vertical asymptotic directions of a NM at rigidity R and the location of the SEP source at the same altitude, as defined in Plainaki et al. (2007) R u : is the theoretical upper limit for the rigidity of the primary SEP particles b(t): is the amplitude of the primary SEP differential flux (in protons m -2 s -1 sr -1 GV -1 ) I 0 (R,t 0 ): is the Galactic Cosmic Ray (GCR) differential flux (in protons m -2 s -1 sr -1 GV -1 ) where A(R,Ω,t): is a dimensionless normalized function that describes the spatially anisotropic arrival of the SEP at 1 AU, given by: The possible time variations, ΔN/N 0, of the total neutron counting rate, N 0, observed at cut-off rigidity, R c, at level h in the atmosphere at some moment t, are determined by the following expression (Dorman 2004; Belov et al. 2005a; b; Plainaki et al. 2010; 2015): A brief description Definition of Ω in the NMBANGLE PPOLA model From Plainaki et al., JGR, 2007

4. Five-minute GLE data from 28 NM stations (for GLE60) and 29 NM stations (for GLE71), widely distributed around the Earth, were incorporated to fit the NMBANGLE PPOLA model equations, applying the Levenberg– Marquardt non-linear optimization algorithm. The data were obtained from the NMDB (www.nmdb.eu). Plainaki et al., JPhCS, 2015 The SEP events as registered at the ground During the GLE 71 (GLE 60), no NM with geomagnetic cutoff rigidity above ~3 GV (~5 GV) has observed count rate increases. On 2001 April 15, a strong flare (X14.4/2B) was observed at the west limb of the solar surface at the position S20W85, associated with a fast CME (>1200 km/s) (see Muraki et al. 2008 and Gopalswamy et al. 2003 for details). Following the detection of gamma and X-rays, the High Energy Proton and Alpha Detector on board GOES 10 satellite recorded sudden increases in relativistic protons. High energy protons and possibly neutrons, associated with the above mentioned solar events, were detected by the ground-level NMs of the worldwide network, starting at about 13:50 UT, in 5- min NM data. The event was seen by polar and mid-latitude NMs, as well as by some low- altitude NMs. The maximum NM % count increase was 225.4%, at South Pole NM. Early on 2012 May 17, the Energetic Particle Sensor (EPS) onboard GOES spacecraft recorded an increase in the proton and electron channels, extended also to high energies. The > 100 MeV proton event began at 02:00 UT, reached a maximum of ~20 pfu at 02:30 UT and ended at 17:25 UT. The SEP event is associated with the M5/1f flare (peak time on May 17 at 01:47 UT) occurring in the Active Region (AR) 11476, located at N11W76. Based on the flare longitude the SEP event was relatively “well-connected” to the source region, also considering the observed solar wind speed of ~400 Km/s preceding the event. Secondary particles, associated with this SEP event were detected by the ground-level NMs of the worldwide network (e.g. Mishev et al. 2014), with a maximum increase of ~17% at South Pole NM. Among the numerous mid-latitude NMs, GLE71 was registered at Kiel, at Kerguelen and at Yakutsk. The low-latitude NMs did not register GLE 71.

5. From Plainaki et al., JPhCS, 2015 SEP spectra comparison The spectrum at 1 GV for GLE 71 is in good agreement with the SEP flux in the direction of anisotropy obtained by Balabin et al., 2013. The anisotropic direction of arrival of solar particles might play a role in the high intensities estimated by our model. Plainaki et al. (2014) estimated that there has been an anisotropy in the arrival direction in the time interval 2012 May 17 02:15-02:20 UT hence the spatially averaged spectrum is not representative.. The small magnitude of this event in any case can be an additional reason for which the increases in the NMs were not significant and the latitude effect was absent. The latter has been pointed out also by other researchers as well (see Li et al., 2013). We note that Model Results for GLE 60 and GLE 71 Why ? Therefore the high rigidity particles (if present) could be sensed through their secondaries only by those NMs that had direction of viewing (corresponding to these high rigidities, i.e. in the range 3-10 GV) located close to the maximum flux of the apparent particle source. Reason 1: Reason 2: The SEP intensity in the direction of anisotropy obtained by Mishev et al. 2014 at 1 GV is about one order of magnitude higher. For GLE71, the spatially averaged proton spectrum continues to exceed the GCR background (dotted line in Figure 3) even at rigidities > 3 GV (red line). At 3 GV our modeled intensities are almost one order of magnitude higher than those shown in Balabin et al. (2013) and Mishev et al. (2014).

6. From Plainaki et al., JPhCS, 2015 SEP spectra comparison Model Results for GLE 60 and GLE 71 Possible Explanation The NMBANGLE PPOLA model application gives a harder spatially averaged spectrum for GLE 71 than for GLE 60: in the rigidity range from 2 to ~ 4 GV the mean differential flux of the primary SEPs during GLE 71 is higher than its values during GLE 60, by up to one order of magnitude. The above comparison of the two SEP spectra refers to the main phase of each event, i.e. after the registration of the maximum NM intensity variation, and not to the main SEP acceleration phase that had taken place during the first 5-min intervals after the flare in each case. The high rigidity SEPs during GLE 60 were registered mainly during this initial phase (see for example Plainaki et al., 2014). Therefore a relatively soft SEP spectrum in the main phase of GLE 60 is reasonable. This result seems to contradict the fact that during GLE 60, SEPs with higher maximum energy than those during GLE 71 have been observed. Moreover, although the GLE 60 shows intensity variations in the ground observations significantly higher than during GLE 71, the spatial distribution of the primary flux is more anisotropic, consistently with NM observations. As a consequence, the peak secondary flux (at the ground) can be measured mainly at specific locations that are magnetically favorable with respect to the SEP source (Plainaki et al., 2015). Therefore, the spatially averaged modeled-SEP spectrum is less representative of the actual GLE 60 event evolution, since the averaged SEP fluxes smoothen too much the actual flux variations in rigidity. Conclusions A hard rigidity spectrum of accelerated protons was found during the initial phase of GLE 60 and a rather soft spectrum in later phases, i.e. after 14:00 UT (γ ~ -5.5). During the main phase of GLE 71, the rigidity spectrum index γ was estimated to be ~ -2.1; in later phases, i.e. after 02:20 UT, a softer spectrum of accelerated protons (γ ~ -3.8) has been derived. The corresponding values for the energy spectrum are -1.55 and -2.4, respectively. The results for GLE 71 are consistent with the typical range found by Ellison and Ramaty (1985) for shock wave acceleration in case of relativistic SEP events (see also Mewaldt et al., 2012), although a direct flare contribution cannot be excluded (see also Plainaki et al., 2014). The model-results can provide realistic estimation of the SEP fluxes in the energy range where NM increases are registered. For both GLEs, the model seems to overestimate the spatially averaged SEP spectrum in the high rigidity range, where no NM increases are registered. Comparison of the results obtained for the two events is more trustful mainly in the rigidity range 1-3 GV. The spectrum computed in the event main phase results to be harder for GLE 71. This could be due to the different SEP flux spatial distribution with respect to the NM direction of viewing and the different GCR background level (that is reduced during GLE60) The integral SEP fluxes calculated by the NMBANGLE PPOLA model are in good agreement with GOES observations if extrapolated to the lower energy range. Acknowledgements The authors acknowledge all colleagues at the NM stations who kindly provided us with the data used in this study and the Referees of both our related papers for their useful comments. Thanks are also due to the High-resolution Neutron Monitor NMDB database, founded under the European Union’s FP7 Program (contract No. 213007) for providing cosmic ray data. Special acknowledgements to Dr. Marisa Storini for important discussions and contribution to the related published works and to Dr. Kanellakopoulos for his contribution to the data analysis.