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At least 19 records

WHAT CAUSES THE INTER-SOLAR-CYCLE VARIATION OF TOTAL SOLAR IRRADIANCE?

The Physikalisch Meteorologisches Observatorium Davos total solar irradiance (TSI), Active Cavity Radiometer Irradiance Monitoring TSI, and Royal Meteorological Institute of Belgium TSI are three typical TSI composites. Magnetic Plage Strength Index (MPSI) and Mount Wilson Sunspot Index (MWSI) should indicate the weak and strong magnetic field activity on the solar full disk, respectively. Cross-correlation (CC) analysis of MWSI with three TSI composites shows that TSI should be weakly correlated with MWSI, and not be in phase with MWSI at timescales of solar cycles. The wavelet coherence (WTC) and partial wavelet coherence (PWC) of TSI with MWSI indicate that the inter-solar-cycle variation of TSI is also not related to solar strong magnetic field activity, which is represented by MWSI. However, CC analysis of MPSI with three TSI composites indicates that TSI should be moderately correlated and accurately in phase with MPSI at timescales of solar cycles, and that the statistical significance test indicates that the correlation coefficient of three TSI composites with MPSI is statistically significantly higher than that of three TSI composites with MWSI. Furthermore, the cross wavelet transform (XWT) and WTC of TSI with MPSI show that the TSI is highly related and actually in phase with MPSI at a timescale of a solar cycle as well. Consequently, the CC analysis, XWT, and WTC indicate that the solar weak magnetic activity on the full disk, which is represented by MPSI, dominates the inter-solar-cycle variation of TSI.

79 ASTRONOMY AND ASTROPHYSICS↗

THREE-DIMENSIONAL FEATURES OF THE OUTER HELIOSPHERE DUE TO COUPLING BETWEEN THE INTERSTELLAR AND INTERPLANETARY MAGNETIC FIELDS. IV. SOLAR CYCLE MODEL BASED ON ULYSSES OBSERVATIONS

The solar cycle has a profound influence on the solar wind (SW) interaction with the local interstellar medium (LISM) on more than one timescales. Also, there are substantial differences in individual solar cycle lengths and SW behavior within them. The presence of a slow SW belt, with a variable latitudinal extent changing within each solar cycle from rather small angles to 90 Degree-Sign , separated from the fast wind that originates at coronal holes substantially affects plasma in the inner heliosheath (IHS)-the SW region between the termination shock (TS) and the heliopause (HP). The solar cycle may be the reason why the complicated flow structure is observed in the IHS by Voyager 1. In this paper, we show that a substantial decrease in the SW ram pressure observed by Ulysses between the TS crossings by Voyager 1 and 2 contributes significantly to the difference in the heliocentric distances at which these crossings occurred. The Ulysses spacecraft is the source of valuable information about the three-dimensional and time-dependent properties of the SW. Its unique fast latitudinal scans of the SW regions make it possible to create a solar cycle model based on the spacecraft in situ measurements. On the basis of our analysis of the Ulysses data over the entire life of the mission, we generated time-dependent boundary conditions at 10 AU from the Sun and applied our MHD-neutral model to perform a numerical simulation of the SW-LISM interaction. We analyzed the global variations in the interaction pattern, the excursions of the TS and the HP, and the details of the plasma and magnetic field distributions in the IHS. Numerical results are compared with Voyager data as functions of time in the spacecraft frame. We discuss solar cycle effects which may be reasons for the recent decrease in the TS particles (ions accelerated to anomalous cosmic-ray energies) flux observed by Voyager 1.

79 ASTRONOMY AND ASTROPHYSICS↗

SIMULATIONS OF A DYNAMIC SOLAR CYCLE AND ITS EFFECTS ON THE INTERSTELLAR BOUNDARY EXPLORER RIBBON AND GLOBALLY DISTRIBUTED ENERGETIC NEUTRAL ATOM FLUX

Since 2009, observations by the Interstellar Boundary Explorer (IBEX) have vastly improved our understanding of the interaction between the solar wind (SW) and local interstellar medium through direct measurements of energetic neutral atoms (ENAs), which inform us about the heliospheric conditions that produced them. An enhanced feature of flux in the sky, the so-called IBEX ribbon, was not predicted by any global models before the first IBEX observations. A dominating theory of the origin of the ribbon, although still under debate, is a secondary charge-exchange process involving secondary ENAs originating from outside the heliopause. According to this mechanism, the evolution of the solar cycle should be visible in the ribbon flux. Therefore, in this paper we simulate a fully time-dependent ribbon flux, as well as globally distributed flux from the inner heliosheath (IHS), using time-dependent SW parameters from Sokół et al. as boundary conditions for our time-dependent heliosphere simulation. After post-processing the results to compute H ENA fluxes, our results show that the secondary ENA ribbon indeed should be time dependent, evolving with a period of approximately 11 yr, with differences depending on the energy and direction. Our results for the IHS flux show little periodic change with the 11 yr solar cycle, but rather with short-term fluctuations in the background plasma. While the secondary ENA mechanism appears to emulate several key characteristics of the observed IBEX ribbon, it appears that our simulation does not yet include all of the relevant physics that produces the observed ribbon.

79 ASTRONOMY AND ASTROPHYSICS↗

Association of Supergranule Mean Scales with Solar Cycle Strengths and Total Solar Irradiance

We analyze the long-term behavior of the supergranule scale parameter, in active regions (ARs) and quiet regions (QRs), using the Kodaikanal digitized data archive. This database provides century-long daily full disk observations of the Sun in Ca ii K wavelengths. In this paper, we study the distributions of the supergranular scales, over the whole data duration, which show identical shape in these two regimes. We found that the AR mean scale values are always higher than that of the QR for every solar cycle. The mean scale values are highly correlated with the sunspot number cycle amplitude and also with total solar irradiance (TSI) variations. Such a correlation establishes the cycle-wise mean scale as a potential calibrator for the historical data reconstructions. We also see an upward trend in the mean scales, as has already been reported in TSI. This may provide new input for climate forcing models. These results also give us insight into the different evolutionary scenarios of the supergranules in the presence of strong (AR) and weak (QR) magnetic fields.

79 ASTRONOMY AND ASTROPHYSICS↗

On the possible relations between solar activities and global seismicity in the solar cycle 20 to 23

Solar activities consist of high energetic particle streams, electromagnetic radiation, magnetic and orbital gravitational forces. The well-know solar activity main indicator is the existence of sunspot which has mean variation in 11 years, named by solar cycle, allow for the above fluctuations. Solar activities are also related to the space weather affecting all planetary atmospheric variability, moreover to the Earth’s climate variability. Large extreme space and geophysical events (high magnitude earthquakes, explosive volcanic eruptions, magnetic storms, etc.) are hazards for humankind, infrastructure, economies, technology and the activities of civilization. With a growing world population, and with modern reliance on delicate technological systems, human society is becoming increasingly vulnerable to natural hazardous events. The big question arises to the relation between solar forcing energy to the Earth’s global seismic activities. Estimates are needed for the long term occurrence-rate probabilities of these extreme natural hazardous events. We studied connectivity from yearly seismic activities that refer to and sunspot number within the solar cycle 20 to 23 of year 1960 to 2013 (53 years). We found clear evidences that in general high magnitude earthquake events and their depth were related to the low solar activity.

58 GEOSCIENCES↗

The evolution of 1 AU equatorial solar wind and its association with the morphology of the heliospheric current sheet from solar cycles 23 to 24

The solar wind can be categorized into three types based on its 'freeze-in' temperature (T {sub freeze-in}) in the coronal source: low T {sub freeze-in} wind mostly from coronal holes, high T {sub freeze-in} wind mostly from regions outside of coronal holes, including streamers (helmet streamer and pseudostreamer), active regions, etc., and transient interplanetary coronal mass ejections (ICMEs) usually possessing the hottest T {sub freeze-in}. The global distribution of these three types of wind has been investigated by examining the most effective T {sub freeze-in} indicator, the O{sup 7+}/O{sup 6+} ratio, as measured by the Solar Wind Ion Composition Spectrometer on board the Advanced Composition Explorer (ACE) during 1998-2008 by Zhao et al. In this study, we extend the previous investigation to 2011 June, covering the unusual solar minimum between solar cycles 23 and 24 (2007-2010) and the beginning of solar cycle 24. We find that during the entire solar cycle, from the ascending phase of cycle 23 in 1998 to the ascending phase of cycle 24 in 2011, the average fractions of the low O{sup 7+}/O{sup 6+} ratio (LOR) wind, the high O{sup 7+}/O{sup 6+} ratio (HOR) wind, and ICMEs at 1 AU are 50.3%, 39.4%, and 10.3%, respectively; the contributions of the three types of wind evolve with time in very different ways. In addition, we compare the evolution of the HOR wind with two heliospheric current sheet (HCS) parameters, which indicate the latitudinal standard deviation (SD) and the slope (SL) of the HCS on the synoptic Carrington maps at 2.5 solar radii surface. We find that the fraction of HOR wind correlates with SD and SL very well (slightly better with SL than with SD), especially after 2005. This result verifies the link between the production of HOR wind and the morphology of the HCS, implying that at least one of the major sources of the HOR wind must be associated with the HCS.

79 ASTRONOMY AND ASTROPHYSICS↗

Cycle length dependence of stellar magnetic activity and solar cycle 23

Solar cycle (SC) 23 was extraordinarily long with remarkably low magnetic activity. We have investigated whether this is a common behavior of solar-type stars. From the Ca ii H and K line intensities of 111 stars observed at Mount Wilson Observatory from 1966 to 1991, we have retrieved data of all 23 G-type stars and recalculated their cycle lengths using the damped least-squares method for the chromospheric activity index S as a function of time. A regression analysis was performed to find relations between the derived cycle length, P{sub avg}, and the index for excess chromospheric emission, R{sub HK}{sup ′}. As a noteworthy result, we found a segregation between young and old solar-type stars in the cycle length-activity correlation. We incorporated the relation for the solar-type stars into the previously known rule for stellar chromospheric activity and brightness to estimate the variation of solar brightness from SC 22 to SC 23 as (0.12 ± 0.06)%, much higher than the actual variation of total solar irradiance (TSI) ≤0.02%. We have then examined solar spectral irradiance (SSI) to find a good phase correlation with a sunspot number in the wavelength range of 170–260 nm, which is close to the spectral range effective in heating the Earth’s atmosphere. Therefore, it appears that SSI rather than TSI is a good indicator of the chromospheric activity, and its cycle length dependent variation would be more relevant to the possible role of the Sun in the cyclic variation of the Earth’s atmosphere.

79 ASTRONOMY AND ASTROPHYSICS↗

SOLAR CYCLE VARIATIONS OF THE RADIO BRIGHTNESS OF THE SOLAR POLAR REGIONS AS OBSERVED BY THE NOBEYAMA RADIOHELIOGRAPH

We have analyzed daily microwave images of the Sun at 17 GHz obtained with the Nobeyama Radioheliograph (NoRH) in order to study the solar cycle variations of the enhanced brightness in the polar regions. Unlike in previous works, the averaged brightness of the polar regions is obtained from individual images rather than from synoptic maps. We confirm that the brightness is anti-correlated with the solar cycle and that it has generally declined since solar cycle 22. Including images up to 2013 October, we find that the 17 GHz brightness temperature of the south polar region has decreased noticeably since 2012. This coincides with a significant decrease in the average magnetic field strength around the south pole, signaling the arrival of solar maximum conditions in the southern hemisphere more than a year after the northern hemisphere. We do not attribute the enhanced brightness of the polar regions at 17 GHz to the bright compact sources that occasionally appear in synthesized NoRH images. This is because they have no correspondence with small-scale bright regions in images from the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory with a broad temperature coverage. Higher-quality radio images are needed to understand the relationship between microwave brightness and magnetic field strength in the polar regions.

79 ASTRONOMY AND ASTROPHYSICS↗

Role of asymmetric meridional circulation in producing north-south asymmetry in a solar cycle dynamo model

Solar cycles in the north and south hemispheres differ in cycle length, amplitude, profile, polar fields, and coronal structure. To show what role differences in meridional flow could play in producing these differences, we present the results of three sets of numerical simulations from a flux transport dynamo in which one property of meridional circulation has been changed in the south only. The changes are in amplitude and the presence of a second cell in latitude or in depth. An ascending phase speedup causes weakening of polar and toroidal fields; a speed decrease in a late descending phase does not change amplitudes. A long-duration speed increase leads to lower toroidal field peaks but unchanged polar field peaks. A second high-latitude circulation cell in an ascending phase weakens the next polar and toroidal field peaks, and the ascending phase is lengthened. A second cell in a late descending phase speeds up the cycle. A long-duration second cell leads to a poleward branch of the butterfly diagram and weaker polar fields. A second cell in depth reverses the tilt of the butterfly wing, decreasing polar fields when added during an ascending phase and increasing them during a late descending phase. A long-duration presence of a second cell in radius evolves the butterfly diagram far away from the observed one, with different dynamo periods in low and high latitudes. Thus, a second cell in depth is unlikely to persist more than a few years if the solar dynamo is advection-dominated. Our results show the importance of time variation and north-south asymmetry in meridional circulation in producing differing cycles in the north and south.

79 ASTRONOMY AND ASTROPHYSICS↗

ON POLAR MAGNETIC FIELD REVERSAL AND SURFACE FLUX TRANSPORT DURING SOLAR CYCLE 24

As each solar cycle progresses, remnant magnetic flux from active regions (ARs) migrates poleward to cancel the old-cycle polar field. We describe this polarity reversal process during Cycle 24 using four years (2010.33-2014.33) of line-of-sight magnetic field measurements from the Helioseismic and Magnetic Imager. The total flux associated with ARs reached maximum in the north in 2011, more than two years earlier than the south; the maximum is significantly weaker than Cycle 23. The process of polar field reversal is relatively slow, north-south asymmetric, and episodic. We estimate that the global axial dipole changed sign in 2013 October; the northern and southern polar fields (mean above 60° latitude) reversed in 2012 November and 2014 March, respectively, about 16 months apart. Notably, the poleward surges of flux in each hemisphere alternated in polarity, giving rise to multiple reversals in the north. We show that the surges of the trailing sunspot polarity tend to correspond to normal mean AR tilt, higher total AR flux, or slower mid-latitude near-surface meridional flow, while exceptions occur during low magnetic activity. In particular, the AR flux and the mid-latitude poleward flow speed exhibit a clear anti-correlation. We discuss how these features can be explained in a surface flux transport process that includes a field-dependent converging flow toward the ARs, a characteristic that may contribute to solar cycle variability.

79 ASTRONOMY AND ASTROPHYSICS↗

Understanding Solar Cycle Variability

The level of solar magnetic activity, as exemplified by the number of sunspots and by energetic events in the corona, varies on a wide range of timescales. Most prominent is the 11-year solar cycle, which is significantly modulated on longer timescales. Drawing from dynamo theory, together with the empirical results of past solar activity and similar phenomena for solar-like stars, we show that the variability of the solar cycle can be essentially understood in terms of a weakly nonlinear limit cycle affected by random noise. In contrast to ad hoc “toy models” for the solar cycle, this leads to a generic normal-form model, whose parameters are all constrained by observations. The model reproduces the characteristics of the variable solar activity on timescales between decades and millennia, including the occurrence and statistics of extended periods of very low activity (grand minima). Comparison with results obtained with a Babcock–Leighton-type dynamo model confirm the validity of the normal-mode approach.

79 ASTRONOMY AND ASTROPHYSICS↗

HEMISPHERIC ASYMMETRIES IN THE POLAR SOLAR WIND OBSERVED BY ULYSSES NEAR THE MINIMA OF SOLAR CYCLES 22 AND 23

We examined solar wind plasma and interplanetary magnetic field (IMF) observations from Ulysses' first and third orbits to study hemispheric differences in the properties of the solar wind and IMF originating from the Sun's large polar coronal holes (PCHs) during the declining and minimum phase of solar cycles 22 and 23. We identified hemispheric asymmetries in several parameters, most notably {approx}15%-30% south-to-north differences in averages for the solar wind density, mass flux, dynamic pressure, and energy flux and the radial and total IMF magnitudes. These differences were driven by relatively larger, more variable solar wind density and radial IMF between {approx}36 Degree-Sign S-60 Degree-Sign S during the declining phase of solar cycles 22 and 23. These observations indicate either a hemispheric asymmetry in the PCH output during the declining and minimum phase of solar cycles 22 and 23 with the southern hemisphere being more active than its northern counterpart, or a solar cycle effect where the PCH output in both hemispheres is enhanced during periods of higher solar activity. We also report a strong linear correlation between these solar wind and IMF parameters, including the periods of enhanced PCH output, that highlight the connection between the solar wind mass and energy output and the Sun's magnetic field. That these enhancements were not matched by similar sized variations in solar wind speed points to the mass and energy responsible for these increases being added to the solar wind while its flow was subsonic.

79 ASTRONOMY AND ASTROPHYSICS↗

Rotation of solar magnetic fields for the current solar cycle 24

The rotation of solar magnetic fields for the current solar cycle 24 is investigated through a cross-correlation analysis of the Carrington synoptic maps of solar photospheric magnetic fields during Carrington rotation numbers 2076-2146 (2008 October to 2014 January). The sidereal rotation rates of positive and negative magnetic fields at some latitudes are shown, and it can be found that the positive (negative) fields generally rotate faster than the negative (positive) fields in the southern (northern) hemisphere at low latitudes. The mean rotation profiles of total, positive, and negative magnetic fields between ±60° latitudes in the time interval are also obtained. It should be noted that both of the mean rotation profiles of the positive and negative magnetic fields, as well as the mean rotation profile of the total magnetic field, exhibit a quasi-rigid rotation at latitudes above about 55°. The mean rotation rates of the positive (negative) polarity reach their maximum values at about 9°(6)° latitude in the southern (northern) hemisphere. The mean rotation profile of the total magnetic field displays an obvious north-south asymmetry, where the rotation seems to be more differential in the northern hemisphere. The latitude variation in the rotation rate differences between positive and negative magnetic fields is further studied, and it is found that magnetic fields with the same polarity as the leading sunspots at a given hemisphere rotate faster than those with the opposite polarity, except for the zones around 52° latitude of the southern hemisphere and around 35° latitude of the northern hemisphere. The implication of these results is discussed. It is clear that the obtained results can provide some observational constraints on the theoretical research of the mechanisms of differential rotation and solar cycle.

79 ASTRONOMY AND ASTROPHYSICS↗

SIMULATION STUDY OF HEMISPHERIC PHASE-ASYMMETRY IN THE SOLAR CYCLE

Observations of the Sun suggest that solar activities systematically create north–south hemispheric asymmetries. For instance, the hemisphere in which sunspot activity is more active tends to switch after the early half of each solar cycle. Svalgaard and Kamide recently pointed out that the time gaps of polar field reversal between the northern and southern hemispheres are simply consequences of the asymmetry of sunspot activity. However, the mechanism underlying the asymmetric feature in solar cycle activity is not yet well understood. In this paper, in order to explain the cause of the asymmetry from the theoretical point of view, we investigate the relationship between the dipole- and quadrupole-type components of the magnetic field in the solar cycle using the mean-field theory based on the flux transport dynamo model. As a result, we found that there are two different attractors of the solar cycle, in which either the north or the south polar field is first reversed, and that the flux transport dynamo model explains well the phase-asymmetry of sunspot activity and the polar field reversal without any ad hoc source of asymmetry.

79 ASTRONOMY AND ASTROPHYSICS↗

SOLAR-CYCLE VARIATION OF SOUND SPEED NEAR THE SOLAR SURFACE

We present evidence that the sound-speed variation with solar activity has a two-layer configuration, similar to the one observed below an active region, which consists of a negative layer near the solar surface and a positive one in the layer immediately below the first one. Frequency differences between the activity minimum and maximum of solar cycle 23, obtained applying global helioseismology to the Michelson Doppler Imager on board the Solar and Heliospheric Observatory, is used to determine the sound-speed variation from below the base of the convection zone to a few Mm below the solar surface. We find that the sound speed at solar maximum is smaller than at solar minimum at the limit of our determination (5.5 Mm). The min-to-max difference decreases in absolute values until {approx}7 Mm. At larger depths, the sound speed at solar maximum is larger than at solar minimum and the difference increases with depth until {approx}10 Mm. At this depth, the relative difference ({delta}c{sup 2}/c{sup 2}) is less than half of the value observed at the lowest depth determination. At deeper layers, it slowly decreases with depth until there is no difference between maximum and minimum activity.

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical properties of solar flares and coronal mass ejections through the solar cycle

Waiting Time Distributions (WTDs) of solar flares are investigated all through the solar cycle. The same approach applied to Coronal Mass Ejections (CMEs) in a previous work is considered here for flare occurrence. Our analysis reveals that flares and CMEs share some common statistical properties, which result dependent on the level of solar activity. Both flares and CMEs seem to independently occur during minimum solar activity phases, whilst their WTDs significantly deviate from a Poisson function at solar maximum, thus suggesting that these events are correlated. The characteristics of WTDs are constrained by the physical processes generating those eruptions associated with flares and CMEs. A scenario may be drawn in which different mechanisms are actively at work during different phases of the solar cycle. Stochastic processes, most likely related to random magnetic reconnections of the field lines, seem to play a key role during solar minimum periods. On the other hand, persistent processes, like sympathetic eruptions associated to the variability of the photospheric magnetism, are suggested to dominate during periods of high solar activity. Moreover, despite the similar statistical properties shown by flares and CMEs, as it was mentioned above, their WTDs appear different in some aspects. During solar minimum periods, the flare occurrence randomness seems to be more evident than for CMEs. Those persistent mechanisms generating interdependent events during maximum periods of solar activity can be suggested to play a more important role for CMEs than for flares, thus mitigating the competitive action of the random processes, which seem instead strong enough to weaken the correlations among flare event occurrence during solar minimum periods. However, it cannot be excluded that the physical processes at the basis of the origin of the temporal correlation between solar events are different for flares and CMEs, or that, more likely, more sophisticated effects are at work at the same time leading to an even more complex picture. This work represents a first step for further investigations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A STUDY OF THE HEMISPHERIC ASYMMETRY OF SUNSPOT AREA DURING SOLAR CYCLES 23 AND 24

Solar activity indices vary over the Sun's disk, and various activity parameters are not considered to be symmetric between the northern and southern hemispheres of the Sun. The north-south asymmetry of different solar indices provides an important clue to understanding subphotospheric dynamics and solar dynamo action, especially with regard to nonlinear dynamo models. In the present work, we study the statistical significance of the north-south asymmetry of sunspot areas for the complete solar cycle 23 (1996-2008) and rising branch of cycle 24 (first 45 months). The preferred hemisphere in each year of cycles 23 and 24 has been identified by calculating the probability of hemispheric distribution of sunspot areas. The statistically significant intermediate-term periodicities of the north-south asymmetry of sunspot area data have also been investigated using Lomb-Scargle and wavelet techniques. A number of short- and mid-term periods including the best-known Rieger one (150-160 days) are detected in cycle 23 and near Rieger-type periods during cycle 24, and most of them are found to be time variable. We present our results and discuss their possible explanations with the help of theoretical models and observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

THE 'TWIN-CME' SCENARIO AND LARGE SOLAR ENERGETIC PARTICLE EVENTS IN SOLAR CYCLE 23

Energetic particles in large solar energetic particle (SEP) events are a major concern for space weather. Recently, Li et al. proposed a 'twin-CME' scenario for ground-level events. Here we extend that study to large SEP events in solar cycle 23. Depending on whether preceding coronal mass ejections (CMEs) within 9 hr exist and whether ions >10 MeV nucleon{sup -1} exceed 10 pfu, we categorize fast CMEs with speed >900 km s{sup -1} and width >60 Degree-Sign from the western hemisphere source regions into four groups: groups I and II are 'twin' and single CMEs that lead to large SEPs; groups III and IV are 'twin' and single CMEs that do not lead to large SEPs. The major findings of this paper are: first, large SEP events tend to be 'twin-CME' events. Of 59 western large SEP events in solar cycle 23, 43 are 'twin-CME' (group I) events and 16 are single-CME (group II) events. Second, not all 'twin CMEs' produced large SEPs: 28 twin CMEs did not produce large SEPs (group III events). Some of them produced excesses of particles up to a few MeV nucleon{sup -1}. Third, there were 39 single fast CMEs that did not produce SEPs (group IV events). Some of these also showed an excess of particles up to a few MeV nucleon{sup -1}. For all four groups of events, we perform statistical analyses on properties such as the angular width, the speed, the existence of accompanying metric type II radio bursts, and the associated flare class for the main CMEs and the preceding CMEs.

79 ASTRONOMY AND ASTROPHYSICS↗