1 Introduction

One of the important aspects of space weather studies is the study of different phenomena observed on the solar surface which can affect life on Earth. Many scientific studies in space science are trying to find the relationship between different solar activities, to better understand their origin and mechanism, which can help in their prediction and possible influence on the earth.

Many of these studies were investigating the relationship between two important and powerful solar activities, the CME and the solar flares (e.g. Mahrous et al. 2009; Fomin et al. 2005; Aarnio et al. 2011).

Coronal mass ejections (CMEs) are the ejection of solar material (magnetized plasma) into space and are regarded as the main cause of geomagnetic disturbances (Gosling 1993). Scientific studies are interested in studying CMEs’ arrival time and their possible influence on the Earth (e.g. Rollett et al. 2016; Mawad et al. 2016; Korsós and Ruderman 2016; Xie et al. 2009; Gopalswamy and Xie 2008). Many scientific studies tried to investigate the origin of CMEs to understand the relationship between CMEs and solar flare (Mahrous et al. 2009; Fomin et al. 2005; Aarnio et al. 2011), Sunspots (Korsós and Ruderman 2016), filament and prominence (Mawad et al. 2015; Alissandrakis et al. 2013; Jing et al. 2003) and coronal holes (Wood et al. 2012; Gopalswamy et al. 2009).

Coronal mass ejections with large-scale eruptions of plasma and magnetic field often accompanied by localized energy release in the form of flares, because of dissipative magnetic-field reconfiguration. Previous studies of the CME-flare relationships depend on the flare’s location, as the source location of the CMEs and it can indicate the earth-direction possibility (Mahrous et al. 2009; Youssef et al. 2013; Mawad et al. 2015, 2016).

Solar flare is an explosive phenomenon that emits electromagnetic radiation extending over a very broad range of wavelengths from long radio waves to the short γ -rays. Measurements of solar flares in Hard X-rays (HXRs) (up to 300 keV) indicate the presence of energetic electrons (energies up to a few MeV), which produce bremsstrahlung in the dense regions of the corona and chromosphere. Observations in the microwave wavelengths indicate synchrotron emission by relativistic electrons in ̴100 G strong magnetic fields. In some observations of X-class flares made by GOES (Geostationary Operational Environmental Satellite) electron bremsstrahlung emission is observed exceeding tens of MeV (Trottet et al. 1998). Nuclear γ -ray lines (1–10 MeV) and continuum radiation above 100 MeV produced by accelerated protons, α particles, and heavy ions have been detected by instruments on the board of the Compton Gamma Ray Observatory (CGRO), the Solar Maximum Mission (SMM), and RHESSI (Lin et al. 2002), these lines are produced by the de-excitation of accelerated ions. The continuum radiation results from interactions of (> 300 MeV) protons and (> 800 MeV) α-particles with ambient ions producing both charged and neutral pions (Murphy et al. 1987). The decay of neutral pions produces a couple 67.5 MeV γ-rays, while the decay of charged pions produces energetic positrons, electrons, and neutrinos (Ramaty and Mandzhavidze 1993). Other detectors of Gamma-ray solar flares are the Large Area Telescope (LAT; Atwood et al. 2009) and Gamma-ray Burst Monitor (GBM; Meegan et al. 2009) instruments on the Fermi Gamma-Ray Space Telescope. The LAT is detecting high-energy γ-ray emission associated with GOES M-class and X-class X-ray flares accompanied by coronal mass ejections and SEP events. In some cases, LAT has detected gamma rays with energies up to several hundreds of MeV during the impulsive phase and gamma rays up to GeV energies sustained for several hours after the impulsive phase (Omodei et al. 2012).

CME and flare relationship is one of the most important topics to improve the Space weather flares and CMEs forecasting as pointed out by Mahrous et al. (2009), Youssef et al. (2013), Harrison (1995, 2006), Aurass (1997), Hundhausen (1999) and Gopalswamy (2000). A high degree of synchronization between the acceleration of a CME and the impulsive phase of a flare has been reported (Zhang et al. 2001; Zhang and Dere 2006).

In the investigation of the CME-flare relationship, it is important to set spatial and temporal criteria (Vršnak et al. 2005; Mahrous et al. 2009; Youssef et al. 2013). These studies showed a good temporal relationship between the physical processes of eruptive flares and CMEs.

Kharayat et al. (2017) have studied the association of solar energetic particle (SEP) events, halo coronal mass ejections and solar flares during the solar cycles 23 and 24 (1997–2014), they found that halo CMEs are more influential in producing SEP events. The shock front of a CME sometimes accelerates SEPs, to energies > 300 MeV required for the γ-ray production (Reames 2013), but its contribution to the acceleration of the particles that produce γ -rays remains unclear.

Mahrous et al. (2009) investigated the simultaneous associations of solar flares and CMEs during solar cycle 23rd, they found that the time interval between the triggering time of the X-ray flare and the lifting-off time of CME associated events occur within a range of 0.4 h ≤ Δt ≤ 1 h. Youssef et al. (2013) found that the CME happened after the starting time of the solar flares during a time interval of 1–2 h as reported also by Compagnino et al. (2017).

Lysenko et al. (2018) concluded that the solar flares often happen after a preflare/preheating phase, which is almost or entirely thermal. While, there are the so-called early impulsive flares that do not show a (significant) preflare heating, but instead often show the Neupert effect (a relationship where the impulsive phase is followed by a gradual, cumulative-like, thermal response).

Ackermann et al. (2014) studied 18 solar flares detected in high-energy γ -rays (above 100 MeV) with the Fermi Large Area Telescope (LAT), they suggest that particle acceleration up to very high energies in solar flares is more common than previously thought, occurring even in modest flares, and for longer durations. Interestingly, all these flares are associated with fast coronal mass ejections (CMEs).

Hundhausen (1999) studied the correlation between the flare’s strength and kinetic energy of associated CMEs and Moon et al. (2002) studied the relationship between the speed of CMEs and the integrated X-ray flux. Both studies found only about 50% correlation. Similar results were reported by Temmer et al. (2008, 2010), who found, in three well- observed events, a very high degree of synchronization of the CME acceleration and the flare hard X-ray burst. Kay et al. (2003) have studied 69 ejective and non-ejective solar flare events and found that, while there is some relationship between the rise and decay times of flares, there are no systematic differences between the ejective and non-ejective flares. Solar flares have been classified into impulsive [short-duration (< 1 h), compact (1026–1027 cm3), and low-lying (104 km)] and gradual [long duration (a few hours), large volumes (1028–1029 cm3), and great heights (105 km)] [see, e.g. Pallavicini et al. (1977), Moore et al. (1999)]. The probability of CME–flare association increases with the increase in flare’s duration (Sheeley et al. 1983): 26% for duration < 1 h and 100% for duration > 6 h. It is important to mention that some major flares associated with large-scale CMEs are not long in duration events (Nitta and Hudson 2001; Chertok et al. 2004).

The flare–CME association relationship is based on three ideas:

  1. 1.

    Flares produce CMEs (see, e.g. Dryer (1996)),

  2. 2.

    Flares are byproducts of CMEs (Hundhausen 1999), and

  3. 3.

    Flares and CMEs are part of the same magnetic eruption process (Harrison 1995; Zhang et al. 2001).

Studies on CMEs—flares temporal correspondence have concluded that CME onset typically precedes the associated X-ray flare onset by several minutes and this observational fact is a serious difficulty for flares to produce CMEs (Hundhausen 1999). The flaring process—reconnection that forms post-flare loops—can be considered as the force that propels overlying loops as CMEs (Anzer and Pneuman 1982). Against such a model argued Kahler et al. (1989) because they could not find evidence for a flare impulsive phase affecting the height-time history of CMEs.

Zhang et al. (2001) investigated four CMEs and compared their time evolution with GOES X-ray flares. They found that the CMEs started accelerating impulsively until the peak of the soft X-ray flare, inconsistency with an earlier result that flare-associated CMEs are in general faster than other CMEs (MacQueen and Fisher 1983). A weak correlation (r = 0.53) between soft X-ray flare intensities and associated CME energies was found by other studies (Hundhausen 1999; Moon et al. 2002). Moon et al. (2002) found that median speed of CMEs associated with solar flares is higher than those associated with eruptive filaments and that the median speed of CMEs associated with strong flares is higher than that of weak flare-associated CMEs.

Vršnak et al. (2005) studied statistically 545 flare-associated CMEs and 104 non-flare associated, they concluded that both data sets have similar characteristics. Michalek (2009) analyzed statistically 578 flare-associated CMEs and found that two different types of flare-associated CMEs (CMEs that follow and precede flare onset) have different characteristics. Therefore, it is of a great importance to examine whether a mechanism of CME occurrence (e.g., magnetic reconnection which may influence CME speed and acceleration) is different in the two types of events.

Mawad and Abdel-Sattar (2020) studied the characteristics of 14786 coronal mass ejection (CME) events and 5092 γ-ray Burst solar flare events recorded during 2008–2017, they found 845 (about 16%) CME events associated with γ-ray burst solar flare events and best time interval is 0–2 h before flare’s start time.

The purpose of this study is to investigate the relationship between CMEs and the Gamma burst post-flare detected in GBM (Gamma ray probably associated with X-Ray) and RHESSI (Hard X-ray probably associated with γ-ray), to get a clear understanding of the characteristics and dependence of these two phenomena. A complete discussion of this study is introduced in Sects. 3 and 4, and a brief conclusion of the results in Sect. 5.

2 Data Sources

The dataset used in this analysis was acquired from the observations of solar flares recorded by RHESSI, and from Gamma-ray Burst Monitor (GBM) obtained by Fermi above 10 keV (all flares ≥ GOES C-Class). Both instruments are detecting the solar flare in X-Ray and Gamma-Ray. The CME records obtained from Large Angle and Spectrometric Coronagraph on board of the Solar and Heliospheric Observatory SOHO/LASCO (CDA) catalog have been used.

From the selected dataset in the period Nov-2008 to 2017, obtained 14786 CME events and 5092 GBM solar flare events.

3 CME-Flare Matching Criteria

For selecting the CME—post-flare associated events, we applied both a spatial and temporal criterion, by requiring that both flare and CME occur within a specific time window and angular separation.

3.1 Temporal Condition

We initially set the time window to select CMEs which occur after the lifetime of the solar flare. We found the popular interval time is 1 h as shown in Fig. 1.

Fig. 1
figure 1

Histogram of the time interval

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The solar flares are instantly recorded by the GBM and RHESSI, while the CMEs are plasma ejected from the Sun and it will be detected after a time period depending on the velocity of the plasma. In fact, CME time recorded in the Coordinated Data Analysis Workshops (CDAW) catalog is not the time of CME emergence. The CME emerged before it appeared in LASCO C2 FOV. The determination of actual CME emerged time is one of considerable difficulty.

Hence, our temporal criteria for association CMEs with GBM solar flares means that the selected solar flare occurred and ended before ejection of associated CMEs.

3.2 Spatial Condition

The position of the CMEs is obtained in projective-circular coordinates (in position angle) in 2-dimensions on the solar disk plane. On the other hand, the solar flare’s locations obtained by RHESSI are recorded in projective-Cartesian coordinates in x and y (in arc seconds). The solar flare’s position can be converted to heliographic coordinates by using the IDL module called: coord_cart_helio.

In order to apply the spatial condition, it is needed to convert the calculated spherical coordinate of the solar flares (longitude λ and latitude β) to 2-dimensional plane coordinate (position angle). This can be done using the following equation:

$$\varPsi_{\text{Flare}} = \arctan \left[ {{\text{Sin}}\lambda /{\text{Tan}}\beta } \right]$$
(1)

The angular separation ΔF of these position-matched CMEs and flares is given by:

$$\Delta {\text{F}} = \left[ {\varPsi_{\text{CME}} {-}\varPsi_{\text{Flare}} } \right]$$
(2)

where ΨCME is the position angle of the CME (the angle measured on the solar disk between the solar North Pole and the line directed to the ejection of the CME), ΨFlare is the flare’s position angle (Mahrous et al. 2009; Youssef et al. 2013; Mawad et al. 2015).

4 Result and Discussion

Studied 14786 CME events and 5092 GBM solar flare events recorded during the solar period 2008–2017, found 503 CME events associated with Gamma burst solar flare events only (GBM post-flare–CME) listed in Table 2, using the spatial and temporal criteria mentioned earlier. A complete list of these flares is shown in Table 2.

From these 503 associated events, all CME events (100%) are associated with solar flares that are detected in both GBM and RHESSI.

4.1 The Rate of Associated Events

After applying the above criteria, we obtained the total number of GBM post-flare—CME pairs in the sample. The final sample contains 503 GBM post-flare—CME events (about 10%) associated with total 14786 CMEs and 5092 GBM solar flare events observed during the period 2008–2017.

Youssef et al. (2013) and Suryanarayana (2018) in their work found that CMEs can happen after the end time of X-ray solar flare events, which is in agreement with the results here. By the same conditions criteria used, Youssef et al. (2013) found 388 post-flare—CME associated events.

Mahrous et al. (2009) found 224 associated simultaneously CME–flare events during the solar period 1996–2005.

Previous studies for rates of CMEs associated with flares found different association rates or ratios, 40% (Munro et al. 1979), 34% (St. Cyr and Webb 1991) and 11% (Aarnio et al. 2011). The small ratio obtained here can be described, as we focused our study on the CME-flare pairs only and applied more restrictions to the selection of events.

4.2 GBM Post-Flare—CME Interval Time and Duration

Found that the time interval for the GBM post-flare—CME association is 29.9 ± 0.76 min.

Found that the flare’s duration has a mean value 12.8 ± 0.6 (minutes) during the selected period of study, as shown in Table 1.

Table 1 Summary of the statistical analysis
Full size table

Mahrous et al. (2009) found the lift-off time within the range of 0.4—1.0 h of CME–flare simultaneously associated events. Youssef et al. (2013) found that the CME happened after the starting time of the solar flares during a time interval of 1–2 h, as reported also by Compagnino et al. (2017) (Table 2).

Table 2 The list of all GBM post-flare—CME associated events
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4.3 CME’s Width

The angular width is defined as the position angle extent on the sky plane. For CMEs originating close to the limb, the measured width is more likely to be the true width. For CMEs away from the limb, the measured width is more likely to be an overestimate. To check whether the GBM post-flare–CME is wider than the non-associated CME, found that many CMEs show an increase in width as they move out, so measurements are made when the width approaches a certain value. The mean value of the CME width distribution of GBM post-flare—CME associated event is 69.77° ± 2.55°, which is wider than non-associated CME (53.5° ± 0.52°), as shown in Fig. 2 and Table 1.

Fig. 2
figure 2

CME Angular width of GBM post-flare—CME associated events

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Youssef et al. (2013) found that CME width equals 103, 107, 146 and 215 degrees for post-flare classes B, C, M, and X respectively. Here we notice that the X-ray post-flare is wider than the GBM post-flare—CME associated event.

Yashiro et al. (2004) found that the annual averages of non-halo CME width range are between 47° and 61°.

The associated CMEs with post-flare—CME events are wider than non-associated CME events. These results indicate that, as the flare’s flux increases, the width of the associated CME increases. It is similar to the results obtained by Youssef et al. (2013) and with some differences with results obtained by Aarnio et al. (2011). These differences may be owed either to the distinction of the period of each study, where their period was from 1996 to 2006 only or may be due to the difference of the selected CME-Flare associated events (Youssef et al. 2013).

The CDAW catalog contains inconsistencies in the reporting of LASCO CMEs due to changes in personnel that used their own criteria (observer bias). These observer biases resulted in many more narrow CMEs added to the catalog after 2004 which significantly skewed CME width rates (Robbrecht et al. 2009; Yashiro et al. 2008). The previous studies of CME-Flare associated simultaneously and post-flare—CME associated events did not consider the effect of observer bias on the CME width property. Consequently, I used the width which is obtained from the CDAW catalog for comparison purposes only.

4.4 CME’s Position Angle

From Fig. 3, we see clearly that the most of CMEs associated with Gamma and X-ray solar flares are ejected from the solar equator, most of the events originated in the west side of the solar disk.

Fig. 3
figure 3

Position angle of GBM post-flare—CME associated events

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GBM post-flare-CME associated events have a mean value of CME position angle 227.63° ± 3.58°, while the non-associated event has a position angle of 177.23° ± 0.86°.

4.5 The CME Acceleration

Found that the mean value of the CME acceleration of the GBM post-flare—CME associated events is (1.6 ± 1.49) m/s2 smaller than non-associated events ~ (4.82 ± 0.37) m/s2 during the selected period 2008–2017 as shown in Fig. 4. The Gamma burst solar flares accelerate CMEs but with less extent than do non-associated or associated with X-ray solar flare only events.

Fig. 4
figure 4

CME acceleration of GBM post-flare—CME associated events

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Youssef et al. (2013) found that the post-flare–CME associated events have negative mean acceleration (− 2.72 m/s2). Flare-CME associated simultaneously have both accelerated and decelerated CME events (Mawad et al. 2016). Youssef et al. (2013) concluded the post-flare–CME associated events are in average more decelerated than CME-Flare associated simultaneously events and other CMEs.

4.6 The CME Speeds

Found that the CME initial speeds of the selected 503 GBM post-flare—CME associated events are mainly near the solar wind speed and have the value ~ (387.25 ± 12.18) km/s as shown in Fig. 5, while non-associated CME has a mean value ~ (322 ± 2) km/s. This means that the Gamma-ray with X-ray is playing a role in slightly increasing the speed of the CMEs.

Fig. 5
figure 5

The CME speed of GBM post-flare—CME associated events

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Youssef et al. (2013) found that the average CME linear speed of the selected 388 post-flare–CME associated events have 880 km/s. While the CMEs non-associated with flares speed was (400 ± 2) km/s. Gosling et al. (1976), Moon et al. (2003) and Aarnio et al. (2011) found that the CME-flare associated events have a higher linear speed than those not associated with flares.

The obtained results agree with previous studies, it indicates that the GBM post-flare—CME associated events have a mean speed equal to solar wind average speed approximately (which is less than those CMEs associated with X-ray solar flares only) and faster than non-associated events. The dominant CME initial speed of the GBM post-flare—CME associated events is ~ 300 (Km/s).

4.7 The CME Mass

The mass in a CME is estimated by determining the CME volume and the number of electrons in the CME with the assumption that the CME is fully ionized hydrogen plasma with 10% helium. Mass estimates have also been made using radio wave observations (Gopalswamy and Kundu 1992; Ramesh et al. 2003).

Found that the CME mean mass of the GBM post-flare—CME associated events is 1.5 × 10+15 ± 1.4 × 10+14 g (as shown in Fig. 6 and Table 1), while the mean mass for non-associated CME events is 1.3 × 10+15 ± 3.5 × 10+13 g.

Fig. 6
figure 6

CME Mass of the GBM post-flare—CME associated events

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Youssef et al. (2013) indicated the mean mass of post-flare—CME associated events to be 1.83 × 10+15 g, while the mean mass for non-associated CME events to be 1.18 × 10+15 g. This result indicates that the CMEs occurred after the solar flare is on average more massive than other CMEs.

4.8 The CME Mass–Width Relationship

In Fig. 7, the mass of the GBM post-flare—CME associated events is plotted as a function of the CME width. The linear fitting that describes this relationship is of the form:

Fig. 7
figure 7

The relationship between CME’s width and mass of GBM post-flare—CME associated events

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$$M = - 8.6246 \times 10^{ + 14} + 2.9392 \times 10^{ + 13} \times W$$
(3)

Where M is the mass of CME in grams and W is the angular width of CME in degrees. The correlation coefficient of the linear fitting is R = 0.60. This result implies that the wide CMEs are more massive than narrow CMEs; this is in a good agreement with the result obtained by Youssef et al. (2013) and Aarnio et al. (2011), but the correlation coefficient obtained in this work is higher than their results.

5 Conclusion

After studying 14786 CME events and 5092 GBM solar flare events recorded during 2008–2017, found 503 (about 10%) CME events associated with γ-ray and X-ray solar flare events only (GBM post-flare–CME), using the spatial and temporal criteria mentioned earlier. From these 503 associated events, all CME events (100%) associated with solar flares that are detected in both GBM and RHESSI.

Found that the time interval for the GBM post-flare—CME association is 29.9 ± 0.76 min.

Found that the flare’s duration has a mean value 12.8 ± 0.6 (min) during the selected period of study.

The mean value of the CME width distribution of GBM post-flare—CME associated event is 69.77° ± 2.55°, which is wider than non-associated CME (53.5° ± 0.52°).

These results indicate that, as the flare’s flux increases, the width of the associated CME increases.

The most of CMEs associated with GBM- post-flare are ejected near the solar equator, most of the events are originated in the west side of the solar disk.

GBM post-flare-CME associated events have a mean value of CME position angle 227.63° ± 3.58°, while the non-associated event has a position angle of 177.23° ± 0.86°.

The mean value of the CME acceleration of the GBM post-flare—CME associated events is (1.6 ± 1.49) m/s2, which is lower than non-associated events ~ (4.82 ± 0.37) m/s2 during the selected period 2008–2017. The GBM solar flares accelerate CMEs but to a less extent than do non-associated or associated with X-ray solar flare only events.

The CME initial speeds of the selected 503 GBM post-flare—CME associated events are meanly near the solar wind speed and have the value ~ (387.25 ± 12.18) km/s, while non-associated CME has a mean value ~ (322 ± 2) km/s. This means that the Gamma burst solar flare is playing a role in slightly increasing the speed of CME.

The GBM post-flare—CME associated events have a mean speed equal to solar wind average speed approximately (which is less than those CMEs associated with X-ray solar flares only) and faster than non-associated events. The dominant CME initial speed of the GBM post-flare—CME associated events is ~ 300 (Km/s).

The CME mean mass of the GBM post-flare—CME associated events is 1.5 × 10+15 ± 1.4 × 10+14 g, while the mean mass for non-associated CME events is 1.3 × 10+15 ± 3.5 × 10+13 g. This result indicates that the CMEs occurred after the solar flare is on average more massive than other CMEs.

Found the relationship between the mass of the GBM post-flare—CME associated events and the CME width to be on the form:

$$\left( {{\text{CME Mass }}\,{\text{(g)}}} \right) = - 8.6246 \times 10^{ + 14} + 2.9392 \times 10^{ + 13} \times \left( {{\text{CME}}\,{\text{width}}} \right)$$

The correlation coefficient of the linear fitting is R = 0.60.