A comparative study of geomagnetic storms for solar cycles 23 and 24

The aim of this paper is to investigate the association of the geomagnetic storms with the magnitude of interplanetary magnetic field IMF (B), solar wind speed (V), product of IMF and wind speed (\(V \cdot B)\), Ap index and solar wind plasma density (\(n_{\mathrm{p}})\) for solar cycles 23 and 24. A Chree analysis by the superposed epoch method has been done for the study. The results of the present analysis showed that \(V \cdot B\) is more geoeffective when compared to V or B alone. Further the high and equal anti-correlation coefficient is found between Dst and Ap index (? 0.7) for both the solar cycles. We have also discussed the relationship between solar wind plasma density (\(n_{\mathrm{p}})\) and Dst and found that both these parameters are weakly correlated with each other. We have found that the occurrence of geomagnetic storms happens on the same day when IMF, V, Ap and \(V \cdot B\) reach their maximum value while 1 day time lag is noticed in case of solar wind plasma density with few exceptions. The study of geomagnetic storms with various solar-interplanetary parameters is useful for the study of space weather phenomenon.     

Investigation of the Geoeffectiveness of Disk-Centre Full-Halo Coronal Mass Ejections

We studied the occurrence and characteristics of geomagnetic storms associated with disk-centre full-halo coronal mass ejections (DC-FH-CMEs). Such coronal mass ejections (CMEs) can be considered as the most plausible cause of geomagnetic storms. We selected front-side full-halo coronal mass ejections detected by the Large Angle and Spectrometric Coronagraph onboard the Solar and Heliospheric Observatory (SOHO/LASCO) from the beginning of 1996 till the end of 2015 with source locations between solar longitudes E10 and W10 and latitudes N20 and S20. The number of selected CMEs was 66 of which 33 (50%) were deduced to be the cause of 30 geomagnetic storms with \(\mathrm{Dst} \leq- 50~\mbox{nT}\). Of the 30 geomagnetic storms, 26 were associated with single disk-centre full-halo CMEs, while four storms were associated, in addition to at least one disk-centre full-halo CME, also with other halo or wide CMEs from the same active region. Thirteen of the 66 CMEs (20%) were associated with 13 storms with \(-100~\mbox{nT} < \mbox{Dst} \leq- 50~\mbox{nT}\), and 20 (30%) were associated with 17 storms with \(\mbox{Dst}\leq- 100~\mbox{nT}\). We investigated the distributions and average values of parameters describing the DC-FH-CMEs and their interplanetary counterparts encountering Earth. These parameters included the CME sky-plane speed and direction parameter, associated solar soft X-ray flux, interplanetary magnetic field strength, \(B_{t}\), southward component of the interplanetary magnetic field, \(B_{s}\), solar wind speed, \(V_{sw}\), and the \(y\)-component of the solar wind electric field, \(E_{y}\). We found only a weak correlation between the Dst of the geomagnetic storms associated with DC-FH-CMEs and the CME sky-plane speed and the CME direction parameter, while the correlation was strong between the Dst and all the solar wind parameters (\(B_{t}\), \(B_{s}\), \(V_{sw}\), \(E_{y}\)) measured at 1 AU. We investigated the dependences of the properties of DC-FH-CMEs and the associated geomagnetic storms on different phases of solar cycles and the differences between Solar Cycles 23 and 24. In the rise phase of Solar Cycle 23 (SC23), five out of eight DC-FH-CMEs were geoeffective (\(\mbox{Dst} \leq- 50~\mbox{nT}\)). In the corresponding phase of SC24, only four DC-FH-CMEs were observed, three of which were nongeoeffective (\(\mbox{Dst} > - 50~\mbox{nT}\)). The largest number of DC-FH-CMEs occurred at the maximum phases of the cycles (21 and 17, respectively). Most of the storms with \(\mbox{Dst}\leq- 100~\mbox{nT}\) occurred at or close to the maximum phases of the cycles. When comparing the storms during epochs of corresponding lengths in Solar Cycles 23 and 24, we found that during the first 85 months of Cycle 23 the geoeffectiveness rate of the disk-centre full-halo CMEs was 58% with an average minimum value of the Dst index of \(- 146~\mbox{nT}\). During the corresponding epoch of Cycle 24, only 35% of the disk-centre full-halo CMEs were geoeffective with an average value of Dst of \(- 97~\mbox{nT}\).     

Study of Geomagnetic Storms and Solar and Interplanetary Parameters for Solar Cycles 22 and 24

The aim of this paper is to investigate the association of geomagnetic storms with the component of the interplanetary magnetic field (IMF) perpendicular to the ecliptic (\(Bz\)), the solar wind speed (\(V\)), the product of solar wind speed and \(Bz\) (VBz), the Kp index, and the sunspot number (SSN) for two consecutive even solar cycles, Solar Cycles 22 (1986?–?1995) and 24 (2009?–?2017). A comparative study has been done using the superposed epoch method (Chree analysis). The results of the present analysis show that \(Bz\) is a geoeffective parameter. The correlation coefficient between Dst and \(Bz\) is found to be 0.8 for both Solar Cycles 22 and 24, which indicates that these two parameters are highly correlated. Statistical relationships between Dst and Kp are established and it is shown that for the two consecutive even solar cycles, Solar Cycles 22 and 24, the patterns are strikingly similar. The correlation coefficient between Dst and Kp is found to be the same for the two solar cycles (?0.8), which clearly indicates that these parameters are well anti-correlated. For the same studied period we found that the SSN does not show any relationship with Dst and Kp, while there exists an inverse relation between Dst and the solar wind speed, with some time lag. We have also found that VBz is a more relevant parameter for the production of geomagnetic storms, as compared to \(V\) and \(Bz\) separately. In addition, we have found that in Solar Cycles 22 and 24 this combined parameter is more relevant during the descending phase as compared to the ascending phase.     

Effects of Geometries and Substructures of ICMEs on Geomagnetic Storms

To better understand geomagnetic storm generations by ICMEs, we consider the effect of substructures (magnetic cloud, MC, and sheath) and geometries (impact location of flux-rope at the Earth) of the ICMEs. We apply the toroidal magnetic flux-rope model to 59 CDAW CME–ICME pairs to identify their substructures and geometries, and select 20 MC-associated and five sheath-associated storm events. We investigate the relationship between the storm strength indicated by minimum Dst index \((\mathrm{Dst}_{\mathrm{min}})\) and solar wind conditions related to a southward magnetic field. We find that all slopes of linear regression lines for sheath-storm events are steeper (\({\geq}\,1.4\)) than those of the MC-storm events in the relationship between \(\mathrm{Dst}_{\mathrm{min}}\) and solar wind conditions, implying that the efficiency of sheath for the process of geomagnetic storm generations is higher than that of MC. These results suggest that different general solar wind conditions (sheaths have a higher density, dynamic and thermal pressures with a higher fluctuation of the parameters and higher magnetic fields than MCs) have different impact on storm generation. Regarding the geometric encounter of ICMEs, 100% (2/2) of major storms (\(\mathrm{Dst}_{\mathrm{min}} \leq -100~\mbox{nT}\)) occur in the regions at negative \(P_{Y}\) (relative position of the Earth trajectory from the ICME axis in the \(Y\) component of the GSE coordinate) when the eastern flanks of ICMEs encounter the Earth. We find similar statistical trends in solar wind conditions, suggesting that the dependence of geomagnetic storms on 3D ICME–Earth impact geometries is caused by asymmetric distributions of the geoeffective solar wind conditions. For western flank events, 80% (4/5) of the major storms occur in positive \(P_{Y}\) regions, while intense geoeffective solar wind conditions are not located in the positive \(P_{Y}\). These results suggest that the strength of geomagnetic storms depends on ICME–Earth impact geometries as they determine the solar wind conditions at Earth.     

A study of the geomagnetic indices asymmetry based on the interplanetary magnetic field polarities

Data of geomagnetic indices (aa, Kp, Ap, and Dst) recorded near 1 AU over the period 1967–2016, have been studied based on the asymmetry between the interplanetary magnetic field (IMF) directions above and below of the heliospheric current sheet (HCS). Our results led to the following conclusions: (i) Throughout the considered period, 31 random years (62%) showed apparent asymmetries between Toward (\(\mathbf{T}\)) and Away (\(\mathbf{A}\)) polarity days and 19 years (38%) exhibited nearly a symmetrical behavior. The days of \(\mathbf{A}\) polarity predominated over the \(\mathbf{T}\) polarity days by 4.3% during the positive magnetic polarity epoch (1991–1999). While the days of \(\mathbf{T}\) polarity exceeded the days of \(\mathbf{A}\) polarity by 5.8% during the negative magnetic polarity epoch (2001–2012). (ii) Considerable yearly North–South (N–S) asymmetries of geomagnetic indices observed throughout the considered period. (iii) The largest toward dominant peaks for \(aa\) and \(Ap\) indices occurred in 1995 near to minimum of solar activity. Moreover, the most substantial away dominant peaks for \(aa\) and \(Ap\) indices occurred in 2003 (during the descending phase of the solar cycle 23) and in 1991 (near the maximum of solar activity cycle) respectively. (iv) The N–S asymmetry of \(Kp\) index indicated a most significant away dominant peak occurred in 2003. (v) Four of the away dominant peaks of Dst index occurred at the maxima of solar activity in the years 1980, 1990, 2000, and 2013. The largest toward dominant peak occurred in 1991 (at the reversal of IMF polarity). (vi) The geomagnetic indices (aa, Ap, and \(Kp\)) all have northern dominance during positive magnetic polarity epoch (1971–1979), while the asymmetries shifts to the southern solar hemisphere during negative magnetic polarity epoch (2001–2012).     

Geomagnetic Effects of Corotating Interaction Regions

We present an analysis of the geoeffectiveness of corotating interaction regions (CIRs), employing the data recorded from 25 January to 5 May 2005 and throughout 2008. These two intervals in the declining phase of Solar Cycle 23 are characterised by a particularly low number of interplanetary coronal mass ejections (ICMEs). We study in detail how four geomagnetic-activity parameters (the Dst, Ap, and AE indices, as well as the Dst time derivative, \(\mathrm{dDst}/\mathrm{d}t\)) are related to three CIR-related solar wind parameters (flow speed, \(V\), magnetic field, \(B\), and the convective electric field based on the southward Geocentric solar magnetospheric (GSM) magnetic field component, \(\mathit{VB}_{s}\)) on a three-hour time resolution. In addition, we quantify statistical relationships between the mentioned geomagnetic indices. It is found that Dst is correlated best to \(V\), with a correlation coefficient of \(\mathrm{cc}\approx0.6\), whereas there is no correlation between \(\mathrm{dDst}/\mathrm{d}t\) and \(V\). The Ap and AE indices attain peaks about half a day before the maximum of \(V\), with correlation coefficients ranging from \(\mathrm{cc}\approx0.6\) to \(\mathrm{cc}\approx0.7\), depending on the sample used. The best correlations of Ap and AE are found with \(\mathit{VB}_{s}\) with a delay of 3 h, being characterised by \(\mathrm{cc}\gtrsim 0.6\). The Dst derivative \(\mathrm{dDst}/\mathrm{d}t\) is also correlated with \(\mathit{VB}_{s}\), but the correlation is significantly weaker \(\mathrm{cc}\approx 0.4\)?–?0.5, with a delay of 0?–?3 h, depending on the employed sample. Such low values of correlation coefficients indicate that there are other significant effects that influence the relationship between the considered parameters. The correlation of all studied geomagnetic parameters with \(B\) are characterised by considerably lower correlation coefficients, ranging from \(\mathrm{cc}=0.3\) in the case of \(\mathrm{dDst}/\mathrm{d}t\) up to \(\mathrm{cc}=0.56\) in the case of Ap. It is also shown that peak values of geomagnetic indices depend on the duration of the CIR-related structures. The Dst is closely correlated with Ap and AE (\(\mathrm{cc}=0.7\)), Dst being delayed for about 3 h. On the other hand, \(\mathrm{dDst}/\mathrm{d}t\) peaks simultaneously with Ap and AE, with correlation coefficients of 0.48 and 0.56, respectively. The highest correlation (\(\mathrm{cc}=0.81\)) is found for the relationship between Ap and AE.     

A Major Geoeffective CME from NOAA 12371: Initiation,CME–CME Interactions,and Interplanetary Consequences

In this article, we present a multi-wavelength and multi-instrument investigation of a halo coronal mass ejection (CME) from active region NOAA 12371 on 21 June 2015 that led to a major geomagnetic storm of minimum \(\mathrm{Dst} = -204\) nT. The observations from the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory in the hot EUV channel of 94 Å confirm the CME to be associated with a coronal sigmoid that displayed an intense emission (\(T \sim6\) MK) from its core before the onset of the eruption. Multi-wavelength observations of the source active region suggest tether-cutting reconnection to be the primary triggering mechanism of the flux rope eruption. Interestingly, the flux rope eruption exhibited a two-phase evolution during which the “standard” large-scale flare reconnection process originated two composite M-class flares. The eruption of the flux rope is followed by the coronagraphic observation of a fast, halo CME with linear projected speed of 1366 km?s^?1. The dynamic radio spectrum in the decameter-hectometer frequency range reveals multiple continuum-like enhancements in type II radio emission which imply the interaction of the CME with other preceding slow speed CMEs in the corona within \(\approx10\)?–?\(90~\mbox{R} _{\odot}\). The scenario of CME–CME interaction in the corona and interplanetary medium is further confirmed by the height–time plots of the CMEs occurring during 19?–?21 June. In situ measurements of solar wind magnetic field and plasma parameters at 1 AU exhibit two distinct magnetic clouds, separated by a magnetic hole. Synthesis of near-Sun observations, interplanetary radio emissions, and in situ measurements at 1 AU reveal complex processes of CME–CME interactions right from the source active region to the corona and interplanetary medium that have played a crucial role towards the large enhancement of the geoeffectiveness of the halo CME on 21 June 2015.     

Relating Solar Energetic Particle Event Fluences to Peak Intensities

Recently we (Kahler and Ling, Solar Phys.292, 59, 2017: KL) have shown that time–intensity profiles [\(I(t)\)] of 14 large solar energetic particle (SEP) events can be fitted with a simple two-parameter fit, the modified Weibull function, which is characterized by shape and scaling parameters [\(\alpha\) and \(\beta\)]. We now look for a simple correlation between an event peak energy intensity [\(I_{\mathrm{p}}\)] and the time integral of \(I(t)\) over the event duration: the fluence [\(F\)]. We first ask how the ratio of \(F/I_{\mathrm{p}}\) varies for the fits of the 14 KL events and then examine that ratio for three separate published statistical studies of SEP events in which both \(F\) and \(I_{\mathrm{p}}\) were measured for comparisons of those parameters with various solar-flare and coronal mass ejection (CME) parameters. The three studies included SEP energies from a 4?–?13 MeV band to \(E > 100~\mbox{MeV}\). Within each group of SEP events, we find a very robust correlation (\(\mathrm{CC} > 0.90\)) in log–log plots of \(F\)versus\(I_{\mathrm{p}}\) over four decades of \(I_{\mathrm{p}}\). The ratio increases from western to eastern longitudes. From the value of \(I_{\mathrm{p}}\) for a given event, \(F\) can be estimated to within a standard deviation of a factor of \({\leq}\,2\). Log–log plots of two studies are consistent with slopes of unity, but the third study shows plot slopes of \({<}\,1\) and decreasing with increasing energy for their four energy ranges from \(E > 10~\mbox{MeV}\) to \({>}\,100~\mbox{MeV}\). This difference is not explained.     

Correlation Between the Magnetic Field and Plasma Parameters at 1 AU

The physical parameters of the solar wind observed in-situ near 1 AU have been studied for several decades, and relationships between them, such as the positive correlation between the solar wind plasma temperature, \(T\), and velocity, \(V\), and the negative correlation between density, \(N\), and velocity, \(V\), are well known. However, the magnetic field intensity, \(B\), does not appear to be well correlated with any individual plasma parameter. In this article, we discuss previously under-reported correlations between \(B\) and the combined plasma parameters \(\sqrt{N V^{2}} \) as well as between \(B\) and \(\sqrt{NT}\). These two correlations are strong during periods of corotating interaction regions and high-speed streams, and moderate during intervals of slow solar wind. The results indicate that the magnetic pressure in the solar wind is well correlated both with the plasma dynamic pressure and the thermal pressure.     

GONG p-Mode Parameters Through Two Solar Cycles

We investigate the parameters of global solar p-mode oscillations, namely damping width \(\Gamma\), amplitude \(A\), mean squared velocity \(\langle v^{2}\rangle\), energy \(E\), and energy supply rate \(\mathrm{d}E/\mathrm{d}t\), derived from two solar cycles’ worth (1996?–?2018) of Global Oscillation Network Group (GONG) time series for harmonic degrees \(l=0\,\mbox{--}\,150\). We correct for the effect of fill factor, apparent solar radius, and spurious jumps in the mode amplitudes. We find that the amplitude of the activity-related changes of \(\Gamma\) and \(A\) depends on both frequency and harmonic degree of the modes, with the largest variations of \(\Gamma\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le3300~\upmu\mbox{Hz}\) and \(31\le l \le60\) with a minimum-to-maximum variation of \(26.6\pm0.3\%\) and of \(A\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le 3300~\upmu\mbox{Hz}\) and \(61\le l \le100\) with a minimum-to-maximum variation of \(27.4\pm0.4\%\). The level of correlation between the solar radio flux \(F_{10.7}\) and mode parameters also depends on mode frequency and harmonic degree. As a function of mode frequency, the mode amplitudes are found to follow an asymmetric Voigt profile with \(\nu_{\text{max}}=3073.59\pm0.18~\upmu\mbox{Hz}\). From the mode parameters, we calculate physical mode quantities and average them over specific mode frequency ranges. In this way, we find that the mean squared velocities \(\langle v^{2}\rangle\) and energies \(E\) of p modes are anticorrelated with the level of activity, varying by \(14.7\pm0.3\%\) and \(18.4\pm0.3\%\), respectively, and that the mode energy supply rates show no significant correlation with activity. With this study we expand previously published results on the temporal variation of solar p-mode parameters. Our results will be helpful to future studies of the excitation and damping of p modes, i.e., the interplay between convection, magnetic field, and resonant acoustic oscillations.     

Intermittency of the Solar Magnetic Field and Solar Magnetic Activity Cycle

Small-scale solar magnetic fields demonstrate features of fractal intermittent behavior, which requires quantification. For this purpose we investigate how the observational estimate of the solar magnetic flux density \(B\) depends on resolution \(D\) in order to obtain the scaling \(\ln B_{D} = - k \ln D +a\) in a reasonably wide range. The quantity \(k\) demonstrates cyclic variations typical of a solar activity cycle. In addition, \(k\) depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity \(a\) demonstrates some cyclic variation, but it is much weaker than in the case of \(k\). The scaling obtained generalizes previous scalings found for the particular cycle phases. The scaling is typical of fractal structures. In our opinion, the results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection.     

Average Magnetic Field Magnitude Profiles of <Emphasis Type="Italic">Wind</Emphasis> Magnetic Clouds as a Function of Closest Approach to the Clouds’ Axes and Comparison to Model

We examine the average magnetic field magnitude (\(| \boldsymbol{B} | \equiv B\)) within magnetic clouds (MCs) observed by the Wind spacecraft from 1995 to July 2015 to understand the difference between this \(B\) and the ideal \(B\)-profiles expected from using the static, constant-\(\alpha\), force-free, cylindrically symmetric model for MCs of Lepping, Jones, and Burlaga (J. Geophys. Res. 95, 11957, 1990, denoted here as the LJB model). We classify all MCs according to an assigned quality, \(Q_{0}\) (\(= 1, 2, 3\), for excellent, good, and poor). There are a total of 209 MCs and 124 when only \(Q_{0} = 1\), 2 cases are considered. The average normalized field with respect to the closest approach (\(\mathit{CA}\)) is stressed, where we separate cases into four \(\mathit{CA}\) sets centered at 12.5 %, 37.5 %, 62.5 %, and 87.5 % of the average radius; the averaging is done on a percentage-duration basis to treat all cases the same. Normalized \(B\) means that before averaging, the \(B\) for each MC at each point is divided by the LJB model-estimated \(B\) for the MC axis, \(B_{0}\). The actual averages for the 209 and 124 MC sets are compared to the LJB model, after an adjustment for MC expansion (e.g. Lepping et al. in Ann. Geophys. 26, 1919, 2008). This provides four separate difference-relationships, each fitted with a quadratic (Quad) curve of very small \(\sigma\). Interpreting these Quad formulae should provide a comprehensive view of the variation in normalized \(B\) throughout the average MC, where we expect external front and rear compression to be part of its explanation. These formulae are also being considered for modifying the LJB model. This modification will be used in a scheme for forecasting the timing and magnitude of magnetic storms caused by MCs. Extensive testing of the Quad formulae shows that the formulae are quite useful in correcting individual MC \(B\)-profiles, especially for the first \({\approx\,}1/3\) of these MCs. However, the use of this type of \(B\) correction constitutes a (slight) violation of the force-free assumption used in the original LJB MC model.     

Spatial Distribution of Element Abundances and Ionization States in Solar Energetic-Particle Events

We have studied the spatial and temporal distribution of abundances of chemical elements in large “gradual” solar energetic-particle (SEP) events, and especially the source plasma temperatures, derived from those abundances, using measurements from the Wind and Solar TErrestrial RElations Observatory (STEREO) spacecraft, widely separated in solar longitude. A power-law relationship between abundance enhancements and mass-to-charge ratios [\(A/Q\)] of the ions can be used to determine \(Q\)-values and source plasma temperatures at remote spacecraft with instruments that were not designed for charge-state measurements. We search for possible source variations along the accelerating shock wave, finding one clear case where the accelerating shock wave appears to dispatch ions from \(3.2\pm 0.8~\mbox{MK}\) plasma toward one spacecraft and those from \(1.6\pm 0.2~\mbox{MK}\) plasma toward another, 116^° away. The difference persists for three days and then fades away. Three other SEP events show less-extreme variation in source temperatures at different spacecraft, in one case observed over 222^° in longitude. This initial study shows how the power-law relation between abundance enhancements and ion \(A/Q\)-values provides a new technique to determine \(Q\) and plasma temperatures in the seed population of SEP ions over a broad region of space using remote spacecraft with instruments that were not originally designed for measurements of ionization states.     

LASCO White-Light Observations of Eruptive Current Sheets Trailing CMEs

Many models of eruptive flares or coronal mass ejections (CMEs) involve formation of a current sheet connecting the ejecting CME flux rope with a magnetic loop arcade. However, there is very limited observational information on the properties and evolution of these structures, hindering progress in understanding eruptive activity from the Sun. In white-light images, narrow coaxial rays trailing the outward-moving CME have been interpreted as current sheets. Here, we undertake the most comprehensive statistical study of CME-rays to date. We use SOHO/LASCO data, which have a higher cadence, larger field of view, and better sensitivity than any previous coronagraph. We compare our results to a previous study of Solar Maximum Mission (SMM) CMEs, in 1984?–?1989, having candidate magnetic disconnection features at the CME base, about half of which were followed by coaxial bright rays. We examine all LASCO CMEs during two periods of minimum and maximum activity in Solar Cycle 23, resulting in many more events, \(\sim130\) CME-rays, than during SMM. Important results include: The occurrence rate of the rays is \(\sim11~\%\) of all CMEs during solar minimum, but decreases to \(\sim7~\%\) at solar maximum; this is most likely related to the more complex coronal background. The rays appear on average 3?–?4 hours after the CME core, and are typically visible for three-fourths of a day. The mean observed current sheet length over the ray lifetime is \(\sim12~R_{\odot}\), with the longest current sheet of \(18.5~R_{\odot}\). The mean CS growth rates are \(188~\mbox{km}\,\mathrm{s}^{-1}\) at minimum and \(324~\mbox{km}\,\mathrm{s}^{-1}\) at maximum. Outward-moving blobs within several rays, which are indicative of reconnection outflows, have average velocities of \(\sim350~\mbox{km}\,\mathrm{s}^{-1}\) with small positive accelerations. A pre-existing streamer is blown out in most of the CME-ray events, but half of these are observed to reform within \(\sim1\) day. The long lifetime and long lengths of the CME-rays challenge our current understanding of the evolution of the magnetic field in the aftermath of CMEs.     

Dynamics of Large-Scale Solar-Wind Streams Obtained by the Double Superposed Epoch Analysis: 3. Deflection of the Velocity Vector

This work is a continuation of our previous articles (Yermolaev et al. in J. Geophys. Res.120, 7094, 2015 and Yermolaev et al. in Solar Phys.292, 193, 2017), which describe the average temporal profiles of interplanetary plasma and field parameters in large-scale solar-wind (SW) streams: corotating interaction regions (CIRs), interplanetary coronal mass ejections (ICMEs, including both magnetic clouds (MCs) and ejecta), and sheaths as well as interplanetary shocks (ISs). Changes in the longitude angle, \(\varphi\), in CIRs from ?2 to \(2^{\circ}\) agree with earlier results (e.g. Gosling and Pizzo, 1999). We have also analyzed the average temporal profiles of the bulk velocity angles in sheaths and ICMEs. We have found that the angle \(\varphi\) in ICMEs changes from 2 to \(-2^{\circ}\), while in sheaths it changes from ?2 to \(2^{\circ}\) (similar to the change in CIRs), i.e. the angle in CIRs and sheaths deflects in the opposite sense to ICMEs. When averaging the latitude angle \(\vartheta\) on all the intervals of the chosen SW types, the angle \(\vartheta\) is almost constant at \({\sim}\,1^{\circ}\). We made for the first time a selection of SW events with increasing and decreasing \(\vartheta\) and found that the average \(\vartheta\) temporal profiles in the selected events have the same “integral-like” shape as for \(\varphi\). The difference in \(\varphi\) and \(\vartheta\) average profiles is explained by the fact that most events have increasing profiles for the angle in the ecliptic plane as a result of solar rotation, while for the angle in the meridional plane, the numbers of events with increasing and decreasing profiles are equal.     

Satellite de-orbiting via controlled solar radiation pressure

We analyze the families of central configurations of the spatial 5-body problem with four masses equal to 1 when the fifth mass m varies from 0 to \(+\infty \). In particular we continue numerically, taking m as a parameter, the central configurations (which all are symmetric) of the restricted spatial (\(4+1\))-body problem with four equal masses and \(m=0\) to the spatial 5-body problem with equal masses (i.e. \(m=1\)), and viceversa we continue the symmetric central configurations of the spatial 5-body problem with five equal masses to the restricted (\(4+1\))-body problem with four equal masses. Additionally we continue numerically the symmetric central configurations of the spatial 5-body problem with four equal masses starting with \(m=1\) and ending in \(m=+\infty \), improving the results of Alvarez-Ramírez et al. (Discrete Contin Dyn Syst Ser S 1: 505–518, 2008). We find four bifurcation values of m where the number of central configuration changes. We note that the central configurations of all continued families varying m from 0 to \(+\infty \) are symmetric.     

Propagation of Coronal Mass Ejections Observed During the Rising Phase of Solar Cycle 24

In this study, we investigate the interplanetary consequences and travel time details of 58 coronal mass ejections (CMEs) in the Sun–Earth distance. The CMEs considered are halo and partial halo events of width \({>}\,120\)°. These CMEs occurred during 2009?–?2013, in the ascending phase of the Solar Cycle 24. Moreover, they are Earth-directed events that originated close to the centre of the solar disk (within about \(\pm30\)° from the Sun’s centre) and propagated approximately along the Sun–Earth line. For each CME, the onset time and the initial speed have been estimated from the white-light images observed by the LASCO coronagraphs onboard the SOHO space mission. These CMEs cover an initial speed range of \({\sim}\,260\,\mbox{--}\,2700~\mbox{km}\,\mbox{s}^{-1}\). For these CMEs, the associated interplanetary shocks (IP shocks) and interplanetary CMEs (ICMEs) at the near-Earth environment have been identified from in-situ solar wind measurements available at the OMNI data base. Most of these events have been associated with moderate to intense IP shocks. However, these events have caused only weak to moderate geomagnetic storms in the Earth’s magnetosphere. The relationship of the travel time with the initial speed of the CME has been compared with the observations made in the previous Cycle 23, during 1996?–?2004. In the present study, for a given initial speed of the CME, the travel time and the speed at 1 AU suggest that the CME was most likely not much affected by the drag caused by the slow-speed dominated heliosphere. Additionally, the weak geomagnetic storms and moderate IP shocks associated with the current set of Earth-directed CMEs indicate magnetically weak CME events of Cycle 24. The magnetic energy that is available to propagate CME and cause geomagnetic storm could be significantly low.     

First integrals for the Kepler problem with linear drag

In this work we consider the Kepler problem with linear drag, and prove the existence of a continuous vector-valued first integral, obtained taking the limit as \(t\rightarrow +\infty \) of the Runge–Lenz vector. The norm of this first integral can be interpreted as an asymptotic eccentricity \(e_{\infty }\) with \(0\le e_{\infty } \le 1\). The orbits satisfying \(e_{\infty } <1\) approach the singularity by an elliptic spiral and the corresponding solutions \(x(t)=r(t)e^{i\theta (t)}\) have a norm r(t) that goes to zero like a negative exponential and an argument \(\theta (t)\) that goes to infinity like a positive exponential. In particular, the difference between consecutive times of passage through the pericenter, say \(T_{n+1} -T_n\), goes to zero as \(\frac{1}{n}\).     

Deflection and Rotation of CMEs from Active Region 11158

Between 13 and 16 February 2011, a series of coronal mass ejections (CMEs) erupted from multiple polarity inversion lines within active region 11158. For seven of these CMEs we employ the graduated cylindrical shell (GCS) flux rope model to determine the CME trajectory using both Solar Terrestrial Relations Observatory (STEREO) extreme ultraviolet (EUV) and coronagraph images. We then use the model called Forecasting a CME’s Altered Trajectory (ForeCAT) for nonradial CME dynamics driven by magnetic forces to simulate the deflection and rotation of the seven CMEs. We find good agreement between ForeCAT results and reconstructed CME positions and orientations. The CME deflections range in magnitude between \(10^{\circ }\) and \(30^{\circ}\). All CMEs are deflected to the north, but we find variations in the direction of the longitudinal deflection. The rotations range between \(5^{\circ}\) and \(50^{\circ}\) with both clockwise and counterclockwise rotations. Three of the CMEs begin with initial positions within \(2^{\circ}\) from one another. These three CMEs are all deflected primarily northward, with some minor eastward deflection, and rotate counterclockwise. Their final positions and orientations, however, differ by \(20^{\circ}\) and \(30^{\circ}\), respectively. This variation in deflection and rotation results from differences in the CME expansion and radial propagation close to the Sun, as well as from the CME mass. Ultimately, only one of these seven CMEs yielded discernible in situ signatures near Earth, although the active region faced toward Earth throughout the eruptions. We suggest that the differences in the deflection and rotation of the CMEs can explain whether each CME impacted or missed Earth.     

Fourier Power Spectra of Solar Noise Storms

We analyzed three noise storms recorded on 200?–?400 MHz Trieste Callisto radio spectra on 2 July 2012, 8 July 2012, and 16 July 2012 by the Fourier method. We divided intervals of the noise storms into five-minute intervals, and in these intervals we computed the mean Fourier spectra as a function of the wave numbers in the frequency and height-scale spaces. We found that these Fourier spectra, where the spectrum from the quiet-activity interval was subtracted, are power-law spectra. The mean power-law index of these spectra in the range \(\ln(k_{z}) = [1.8, 2.9]\) (where \(k_{z}\) is the wave number in the height-scale space) is \(-1.7\pm0.14\), \(-1.6\pm0.14\), and \(-1.5 \pm0.12\) for the 2 July 2012, the 8 July 2012, and the 16 July 2012 noise storms, respectively. It appears that as the number of Type-I bursts in the studied interval increases, the power-law index becomes closer to \(-5/3\); this is known as the Kolmogorov spectral index. The power-law index of the noise storms is very similar to that of the narrowband dm-spikes found in our previous studies. Furthermore, we found a break in the power spectra at \(\ln(k_{z}) \approx2.9\), and the mean power-law index values above this break are \(-2.9\pm0.46\), \(-3.1\pm0.65\), and \(-3.4\pm0.98\), respectively.