Photometric and Statistical Analysis of Solar Energetic Particle ( SEP ) for the Peak of Solar Cycle 24

The major solar energetic particle events for the peak of solar cycle (24) for years (2012-2015) are analyzed by using the Energetic and Relativistic Nucleus and Electrons (ERNE) detectors and Large Angle and Spectrometric Coronagraph Experiment (LASCO) on board SOHO. It is found that the number of events which satisfies the required condition was 82 events. LASCO give information about Central Position Angle (CPA), Angular Width (AW), the speed of associated Coronal Mass Ejections (CMEs) and their basic features which cataloged in a data base SOHO/LASCO. The logarithmic intensity-time profile of SEP for the peak of solar cycle (24) was provided by ERNE, and from this profile the injection time, width, speed and onset time were estimated. All results that arise from these photometric analysis were statistically analyzed by using the statistical program SPSS (version 19). It have been concluded that 90% of these events were halo (360 ̊) CPA, 1% of North West, 4% South West and 2% North East and South East, as well as it was found that 39% gradual events and 29% impulsive events while 32% were not clear events, and also the acceleration of the energetic particle is not only in the interplanetary but also in the location of the event. We found from the statistical analysis for these events that the acceleration is inversely proportional to speed and the relationship between them is not relevant and also the speed increase in two regions, from year 2012 and 2014. This confirms that the peak of solar cycle (24) really is double peak. All these investigations were employed as data base for the space agencies to protect the solar wind.


Introduction
The investigation of solar activity is a very important part of space physics because of the significant impact on Earth technological systems.The effective part of solar activity is solar storm which in turn consists of three parts namely The Coronal Mass Ejections (CMEs), Flares and The Solar Energetic Particles (SEPs).The output of X-ray and UV-variation are various with solar cycle and all of these are related to the transients released from large amount of energy from Sun [1].SEPs are one population of near-Earth particles; they have intermediate energies from some 10 keV/nuclei to the GeV range and occur in events that last from some hour's to a few days and increase above background by many orders of magnitude.Occasionally eruptions are directed toward the Earth change the conditions of near-Earth space in several ways, including a cut in the electricity power in high latitudes on the Earth and damaged of some satellites [2].There are two types of SEP, "gradual SEP" and "impulsive SEP"; in this investigation the two types of events have been analyzed specially the high speed events for the peak of solar cycle (24) for years (2012)(2013)(2014)(2015).All observations for this study were taken from Large Angle and Spectroscopic Coronagraph (LASCO), which provide the first ever CMEs database to cover a full solar cycle with a single instrument, thus opening investigations to the solar cycle dependence on CME properties [3].By using the photometric scale observations of LASCO, so there will be able to find the speed of Coronal Mass Ejections (CMEs), angular width (AW) and the Central Position Angle (CPA), as for finding the intensity-time profile, the energy and the shape of the events which can be obtained from ERNE detectors system.LASCO and ERNE are scientific instruments boarded on SOHO [4].The main objective of this study is to detect and analyze when and where SEPs take place by finding the location of CMEs and find the time of the events as well as find a statistical description to SEP for the peak of solar cycle (24) for years selected by taking high speed events CMEs with velocities > 1000 (km/s) and angular width > 200 (deg).

Observations and Data Handling
Research activity has been related to the observation of big solar eruptions.In big solar events, before the magnetic storm hits the Earth, SEPs bombard Earth earlier, and may be both (storm and particles) come from the eruption which is called CME.Observed eruptions are associated with different composition and energy spectra.So the investigation of their source is very important to learn SEPs [5].SOHO which placed into the hole orbit close to lagrangian point L1 carries twelve scientific instruments, LASCO & ERNE are some of these devices that data were obtained by them for this study.ERNE provide an opportunity to analyze protons and helium nuclei intensity-time profile with high resolution and LASCO give information about acceleration, CPA, and AW, the speed of CME and their basic attributes which cataloged in a data base known as the SOHO/LASCO catalog Figure 1.The logarithmic intensity-time Profile of SEP associated to CME for the peak of solar cycle (24) for years (2012)(2013)(2014)(2015) were provided by ERNE detectors [6].From this profile the injection time, speed, width, acceleration, CPA and onset time were estimated.The Injection time (T inj ) representing the time of particles that Injected from the Sun and it gives the acceleration time for the particles [5]: Equation ( 1) gives the observer to set a real time at the detector.
The flight time can be realized by using beta equation, (this cannot be done without finding the ratio velocity of particles to the velocity of light which is called relativistic velocity coefficient (β) [7].
where v = the speed of particles= s/t f , c = the speed of light.
(t 0 ) onset time is observed by the detectors, (8.3 min) have been added to represent the time of light to reach the Earth from the Sun, and the flight time (T f ) given by equation (3): where (s) is the fixed path length for the particles which equal the distance between the Sun and the detector (=1.2 AU) [8], and β equal ( ) ( ) P is the energy of proton = 938 Mev, E is the proton kinetic energy [9].The injection time will be compared with the appearing time from LASCO [7] to ensure the accuracy of the events time and energy.

ERNE/LASCO Analysis
In this study all selected observations for the peak of solar cycle (24) (2012-2015) have been analyzed.As indicated in paragraph 2, to find the features of solar eruptions by tracking SEP associated with CME for the peak of solar cycle (24) (2012-2015), on this basis the most important events will be analyzed.So for this study 82 event were selected and provided that its speed (v > 1000 km/s) and of (AW > 200˚).The analysis of the data related to logarithmic intensity-time profile of proton for resolution time of 1 hour from ERNE for 16 significant event filtered from the 82 event were represented in (Figures 2-7) and this is filtered based on events which have the highest number of CME for each year of the peak of solar cycle (24).By using equations (1, 2, 3, 4) for the adopted events, onset time have been created with the fixed path length method, the flight time of the non-scattered protons along the Archimedean field line of nominal length (1.2 AU) has been calculated so the injection time will be extracted.While the characteristics of the CMEs in C2 for 82 events have been taken from LASCO and analyzed which is shown in Table 1.

Statistical Analysis
The statistical approaches are an important process to detect the correlations among the features phase of the solar cycles.All observations had been analyzed by means of the statistical software (SPSS) program to find out the correlations between speed and acceleration, the distribution of the CPA in degree of the CMEs for the peak        of solar cycle (24) (2012-2015), speed and years, acceleration and year as well as the distribution for the number of SEP events as a function of its types for 82 SEP event for the peak of solar cycle (24) (2012)(2013)(2014)(2015).SPSS version 19 Windows based program that can be used to perform data entry and analysis and to create tables and graph and it is capable of handling large amounts of data as well as can perform all of the analyses covered in the text and much more.In order to get clear statistical analysis, 82 peak events of solar cycle (24) (2012-2015) of speed > 1000 (km/s) and angular width > 200˚ have been verified.Figure 6 shows three events on (1, 2, 10) September 2014, SOHO/ERNE detected a SEPs events onset at (22:30, 02:30 and 18:30) UT proton injection time at (22:11, 02:11 and 18:11) UT for proton energies (63.9 -80.3)Mev, CPA of (Halo, 121 ˚ and Halo) and linear velocity of (1404, 1141 and 1267) kms −1 .

Discussion
From Table 1 summarizing the handled observations from LASCO and updating of previous investigations, also exhibit the first appearance, CPA, AW, speed, acceleration and the number of associated CME s which is selected for this study ( the peak of solar cycle 24).Table 2 represents onset time and energy for the clear events by the intensity-time profiles obtained from ERNE for the same observations, the injection time, time of flight (T f ) and β calculation.While the first appearance time taken from LASCO in order to compare it with onset time for the promotion of the calculations.From Table 2 we find that the onset time and appearance time are convergent.
Figure 8 shows that 90% of the events was halo (360˚) central position angle (CPA), North West 1%, South West 4%, North East and South East 2%, and the average speed 1374 (km/s) for the selected observation of this study.Figure 9 shows a scatter plot (using SPSS software vir.19) between the measured acceleration, A (m/s 2 ) and speed, v (km/s) that calculated in Table 1 for the handled observation (82 event) of the CMEs for which the acceleration estimate was possible.Despite the large scatter, acceleration has a probable correlation, where from Table 3 we find the parameter of the regression equation, B ° = 1347.029and B 1 = −0.913,since the principle equation of regression is Y= B ° ± B 1 X that is mean (A= 1347.029− 0.913v) or A= −0.913 (v-1475.388).And as shown in Figure 9 and Table 3 that the correlation coefficient is a negative value and its absolute value less than 0.5 (0.122), this shows inverse relationship between speed and acceleration in this region of solar cycle ( 24    compatible and statistically this refers to accurate chose of the observations for the peak of solar cycle (24), and also from Figure 10 we note the existence of two peaks for the speed, the first peak in the year 2012 and the other in the year 2014, this corresponds that solar cycle (24) have double peaks [11], as well as the behavior of the curves in Figure 10 and Figure 11 verified the approaches of Figure 9, that acceleration inversely proportional to the speed as mentioned before.From Figure 12 we note that 39% of total events are gradual and 29% are impulsive, the remaining is 32% are not clear events.

Summary
In this study the data analysis of the present work leads us to conclude the following: 1) The number of events for the peak of solar cycle (24) (2012-2015) which verifies the required conditions was 82 event, and this was from SOHO/LASCO CME Catalog [7] and ERNE.
2) The filtered events from 82 events as described in paragraph 2, were 16 events for the peak of solar cycle (24) which were verified by ERNE from the logarithmic intensity-time profile of these events.
3) It turns out that from these 82 events, 90% of the events were halo (360˚) central position angle (CPA), North West 1%, South West 4%, North East and South East 2%, as well as for associated SEP found that 39%  of gradual events and 29% of impulsive events while 32% were not clear events.4) All results obtained in (Table 1 and Table 2) and (Figures 2-7) were hired for the purpose of statistical characteristics of SEP solar events for the peak of solar cycle (24), and we note that the onset time and appearance time almost identical and this shows the accuracy of analysis.
5) The results of injection time show that the bulk of the particle acceleration occurs during the impulsive phase of the events near the Sun.

Figure 1 .
Figure 1.The top page of the SOHO/LASCO CME catalog.One row corresponds to all the months in the year.Months not underlined (no link) have no data [10].

Figure 2 .
Figure 2. Intensity-time profile of event (7-28) March 2012, the top panel appears the CME1, CME2, CME3 and CME4 (the first C2 appearance), the lower panel appears the intensity time profile from SOHO/ERNE with 1 hour time resolution, all channels.

Figure 3 .
Figure 3. Intensity-time profile of events (13-22) May 2013, the top panel appears the CME1, CME2, CME3, CME4 and CME5 (the first C2 appearance), the lower panel appears the intensity time profile from SOHO/ERNE with 1 hour time resolution, all channels.

Intensity ( 1 /(cm 2 *CME1Figure 4 .
Figure 4. Intensity-time profile of event 12 December 2013, the top panel appears the CME (the first C2 appearance), the lower panel appears the intensity time profile from SOHO/ERNE with 1 hour time resolution, all channels.

Figure 5 .
Figure 5. Intensity-time profile of event 28 December 2013, the top panel appears the CME (the first C2 appearance), the lower panel appears the intensity time profile from SOHO/ERNE with 1hour time resolution, all channels.

Intensity ( 1 /(cm 2 *Figure 6 .
Figure 6.Intensity-time profile of events (1-10) September 2014, the top panel appears the CME1, CME2 and CME3, (the first C2 appearance), the lower panel appears the intensity time profile from SOHO/ERNE with 1 hour time resolution, all channels.

Figure 7 . 5 p
Figure 7. Intensity-time profile of events (21-22) June 2015, the top panel appears the CME1 and CME2 (the first C2 appearance), the lower panel appears the intensity time profile from SOHO/ERNE with 1hour time resolution, all channels.

Figure 2
Figure2shows SOHO/ERNE detection for four important clear events especially the particular event on 7

Figure 8 .
Figure 8.The distribution of the Central Position Angle (CPA) (deg.) of the CMEs for the peak of solar cycle (24) (2012-2015).

Figure 9 .
Figure 9. Scatter plot between the acceleration (m/s 2 ) and speed (km/s) of 82 events for the peak of solar cycle (24) (2012-2015), "R" is the correlation coefficient of the distribution.

Figure 12 .
Figure 12.Histogram distribution for the number of events as a function of its type for 82 events for the peak of solar cycle (24) (2012-2015).

Table 1 .
The characteristics of CME of the significant events for the peak of solar cycle (24) (2012-2015).
* First C2App: The first appearance time from C2.

Table 2 .
Represents onset time and energy from ERNE, injection time, flight time (T f ) and β for the clear events.And the first appearance time of the associated CMEs (peak of solar cycle 24).

Table 3 .
Model Summary of the relation between acceleration and speed from (2012-2015).