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Home All issues Volume 558 (October 2013) A&A, 558 (2013) A85 Full HTML
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A&A
Volume 558, October 2013
Article Number A85
Number of page(s) 10
Section The Sun
DOI https://doi.org/10.1051/0004-6361/201220417
Published online 08 October 2013

© ESO, 2013

1. Introduction

Dynamical processes in the solar atmosphere continuously affect the Earth in a variety of ways. The solar-terrestrial relationship to which we refer in this paper considers phenomena associated with varying outflow of the solar wind that affects the Earth’s magnetosphere.

The most important process in the interaction of the solar wind and magnetosphere is magnetic reconnection by which the solar wind magnetic field becomes connected across the dayside magnetopause to the Earth’s magnetic field. This enables the energy transfer from the solar wind into the magnetosphere (e.g., Dungey 1961). In particular, energy transfer from the solar wind into the magnetosphere is most favorable when the interplanetary magnetic field (IMF) has a strong southward component Bs (where Bs = Bz for Bz < 0 and Bs = 0 for Bz > 0) (e.g., Gonzalez et al. 1994; Kivelson & Russel 1995). The major solar agents that account for the presence of Bs, and thus for the geomagnetic disturbances, are interplanetary coronal mass ejections (ICMEs) and solar wind high speed streams (HSSs) that originate from equatorial coronal holes. For a discussion of the interplanetary causes of geomagnetic storms see, e.g., Tsurutani & Gonzalez (1997), Zhang et al. (2007b) and Echer et al. (2008).

The magnetic field component Bs associated with ICMEs is contained in their internal structure and/or in the turbulent sheath region between the ICME-driven shock and the ejection (e.g., Lavraud et al. 2006). However, the interaction of the HSS and the slow wind forms a corotating interaction region (CIR), containing regions of compressed plasma (e.g., Gosling 1996, and references therein) indicated by enhanced plasma density and magnetic field intensity. In HSS/CIRs the Bs is associated with these compressions and/or Alfvénic waves in the HSS itself (e.g., Burlaga & Lepping 1977; Schwenn 1983; Tsurutani & Gonzalez 1987; Tsurutani et al. 2004; Prolss 2004). The occurrence rate of ICMEs peaks during the solar cycle maximum (e.g., Borovsky & Denton 2006; Richardson & Cane 2010, and references therein), and then their geomagnetic effects dominate. On the other hand, during the descending phase of solar cycle the geomagnetic activity is dominantly driven by HSS/CIRs, since the CME occurrence rate is low (e.g., Richardson et al. 2001; Richardson & Cane 2012).

The geoeffectiveness of ICMEs and HSS/CIRs has been studied by many researchers (e.g., Schwenn et al. 2005; Huttunen et al. 2005; Borovsky & Denton 2006; Georgieva et al. 2006; Lavraud et al. 2006; Alves et al. 2006; Richardson et al. 2006; Yermolaev & Yermolaev 2006; Vršnak et al. 2007; Zhang et al. 2007b; Gopalswamy 2008; Echer et al. 2008; Verbanac et al. 2011a; Richardson & Cane 2010, 2012; Verbanac et al. 2011b, and references therein). In most of these studies, the level of the geomagnetic activity is commonly quantified with the storm-time disturbance index Dst, which is a relatively good measure of the ring current strength (Gonzalez & Tsurutani 1987; Wang et al. 2003; Kane 2005; Alves et al. 2006; Bakare & Chukwuma 2010). However, we note that consideration of only Dst does not provide the information of the geomagnetic activity at mid and high latitudes. Moreover, the observed Dst has contributions not only from the ring current, but also from magnetopause currents, tail currents, induced currents in the solid Earth, and other sources not yet fully quantified (e.g., Gonzalez et al. 1994; Verbanac et al. 2007).

Verbanac et al. (2011a and b), hereafter Paper I and Paper II, studied the geoeffectiveness of HSS/CIRs during the declining phase of the solar cycle 23, by employing various geomagnetic indices. In this paper we expand the analysis focusing on a detailed comparison of the geomagnetic responses to ICMEs and HSS/CIRs. For this purpose, we separately investigate the ICME- and HSS/CIR-driven geomagnetic activity at low, mid, and high latitudes by analyzing geomagnetic indices Dst, Ap, and AE. The aim is to find out if there are relative differences in the response of different current systems within the Earth’s magnetosphere to the impact of ICMEs and HSS/CIRs. Finally, we also relate the coronagraphic observations of the ICME take-off to their in situ properties and the geomagnetic-activity characteristics, looking for a way to forecast the geomagnetic activity at various latitudes using the coronagraphic observations of the ICME take-off.

Following Möstl et al. (2012), we define an ICME as the full interval of the solar wind signature that appears as a change of the background solar wind attributable to the presence of the eruption. In other words, we consider the effect of the overall disturbance, which includes the shock, the sheath region, and the magnetic ejection, making no distinction between the geoeffectiveness of individual structural elements.

This paper is organized as follows. In Sect. 2 we describe the data set and the method of analysis. In Sect. 3 the overall characteristics of the employed samples are presented. Section 4 contains the cross-correlation analysis between ICME parameters and geomagnetic indices (Dst, Ap, and AE), and the analysis of the relationship between the considered geomagnetic indices. The same cross-correlation analysis is preformed for HSS/CIRs in Sect. 5. In Sect. 6 we present the comparison between ICMEs and HSS/CIRs cross-correlation results. In Sect. 7, we relate the ICMEs in situ properties (V and B) and geomagnetic indices (Dst, Ap, and AE) to the coronagraphic CME speed. Finally, all the results are discussed, and conclusions are drawn in Sect. 8.

2. Data sets and method

Our study is based on the following data sets:

  • one-hour averages of the solar wind velocity V and the magnetic field strength B;

  • one-hour averages of geomagnetic indices Dst and AE;

  • three-hour averages of geomagnetic index Ap;

  • the mean speed of the CME measured by the Large Angle Spectroscopic Coronagraph (LASCO; Brueckner et al. 1995), VCME.

The solar wind data were obtained from the Solar Wind Electron Proton and Alpha Monitor (SWEPAM; McComas et al. 1998) and the Magnetometer (MAG; Smith et al. 1998) onboard the Advanced Composition Explorer (ACE; Stone et al. 1998). We used the merged hour-averaged level-2 ACE data1.

Five of the considered ICMEs have gaps in the ACE velocity data. These data gaps were filled by WIND data when possible. In these cases, the 92-s resolution WIND data2 were employed to calculate the hour averages.

Planetary geomagnetic activity index Ap, the storm-time disturbance index Dst, and the auroral electrojet index AE can be downloaded from http://wdc.kugi.kyoto-u.ac.jp/cgi-bin/kp-cgi, http://swdcwww.kugi.kyoto-u.ac.jp/dstdir/, and http://wdc.kugi.kyoto-u.ac.jp/dstae/index.html, respectively. For more detailed information about the indices, we refer to Prolss (2004) and Verbanac et al. (2011a, 2010). Among the available geomagnetic indices, these three indices have been chosen for the evaluation of the geomagnetic activity since their variations can be physically interpreted and related to the specific current system, for example, the ring current and polar electrojet.

The mean speeds of CMEs in the LASCO field of view are obtained from http://cdaw.gsfc.nasa.gov/CME-list/.

Table 1

Overall characteristics of the employed data set (six-hour resolution), compared with characteristics of samples used in some other studies.

Although it is known that the southward magnetic field component Bs is the major parameter controlling geomagnetic activity, as the first step in this paper we used the magnetic field strength B for the following reason. We are exploring the possibility that our study will have value for space weather forecasting. Via statistical relationships, we linked the directly observed solar features (e.g., VCME) with magnetosheric responses (presented in Sect. 7). The ICME magnetic field strength B and bulk plasma speed V measured in-situ are linked to VCME. On the other hand, we do not know Bs on the Sun and it does not depend on the velocity at the Sun. Prediction of southward Bz requires a much more sophisticated approach.

For ICMEs we performed the analysis on two time resolutions, one-hour (three-hour) and six-hour resolutions. The six-hour means are calculated from hourly data of all quantities (for Ap three-hour values). The influence of the time-resolution on the results is presented in Sect. 4.

We focused on six-hour means for the following reasons.

First, when studying the geoeffectiveness (based on the consideration of different geomagnetic indices Dst, Ap, and AE) of HSS/CIRs in Paper I, we performed a preliminary analysis testing various options, and found that the six-hour resolution (obtained by averaging one-hour values), is the optimal one for all three indices, since when shorter intervals are applied the results of the correlation analysis do not change much, only the noise level increases. Moreover, we observed prolonged periods of AE activity (discussed in Paper I and Paper II) associated with enhanced convection which provides an additional energy injection in both ring current and polar current. With six-hour resolution such activity is better taken into account. To make a comparison with the magnetospheric response to the impact of ICMEs, we employed the same resolution for the ICME speeds and magnetic fields. Furthermore, since our study aims to be used for the purposes of the space weather forecasting, we are interested in how the observed overall interplanetary parameters are related to the overall magnetospheric perturbation. Thus, the longer duration aspect of the solar wind disturbance becomes more important than individual shorter-duration peaks in the data. The duration of the considered events (defined here as the time interval of the enhanced magnetic field) are larger than six hours, so the individual spikes seen at a higher resolution might not represent well the cause of the overall geomagnetic perturbation. We emphasize that by the six-hour averaging we smoothed the one-hour values, but we kept the original information so that the results based on six- and one-hour averages could be compared (Sect. 4).

In the analysis we focus on ICME- and HSS/CIR-related geomagnetic activity during solar cycle 23.

The ICME sample analyzed in this paper includes 43 events classified as ICME in Table B.1 in Appendix B of Dumbović et al. (2011) which was based on the list of CME-ICME pairs prepared by Schwenn et al. (2005), and 21 CME-ICME pairs from Zhang et al. (2007a). The majority of the selected ICME-driven storms were driven by a single ICME. Yet, the sample includes several events of a more complex structure resulting from ICME-ICME interactions, which enabled us to encompass also the strongest storms of cycle 23. We note that this sample represents the general sample of events, which includes different levels of geomagnetic activity, from very low to very high. That allows us to study both the lower and upper limits on the strength of the geomagnetic disturbance.

As in Paper II, here we study the HSS/CIR events that occurred during the ICME-less periods in the declining phase of solar cycle 23: in 2005 (day of year, DOY = 25−125) and in 2006 (DOY = 60−261). The original data set contains 32 HSS/CIR structures (see Paper I and Paper II). We identified four ICMEs just before HSS/CIRs. In these cases it was not possible to distinguish the ICME and HSS/CIR peaks, especially in the magnetic field data. These events were excluded from the analysis. We supplemented this sample by ten HSS/CIRs from Zhang et al. (2007a), out of which only two occurred in 2005, i.e., in the period overlapping with the initial data set. Other events cover different phases of cycle 23 (1998, 2002, 2003, and 2004), when the general state of the heliosphere is much more affected by the CME activity. We note that these events are the strongest CIR-related events.

3. Overall characteristics of the employed samples

The 1 AU parameters characterizing the employed samples of HSS/CIRs and ICMEs are considerably different. In Table 1 we present overall characteristics of the samples, where the first three columns describe the 1 AU properties of HSS/CIRs and ICMEs, whereas the next three columns represent the related geomagnetic activity. For estimated peak values of all considered parameters, we calculated maximum, mean and median values (deWe noted as MAX, MEAN and MEDIAN respectively in Table 1).

The highest V and B peaks found among all the events, are significantly higher for ICMEs than for HSS/CIRs. The differences are also present in average and median values of B, whereas the differences are less pronounced for V. The differences are also pronounced in the maximum, average and median BV peak values.

The geomagnetic activity related to the analyzed ICMEs, as quantified by all three geomagnetic indices, is significantly stronger than that related to HSS/CIRs. For ICMEs, the highest Dst amplitude (−341 nT) is related with V = 663 km s-1, accompanied by strong magnetic field (B = 42 nT) The strongest Ap peak (345 nT) is associated with the maximum V peak (1176 km s-1), accompanied by strong B (42 nT). The highest AE peak (1575 nT) is found for V = 966 km s-1 and the strongest B (48 nT).

Following the terminology of Sugiura & Chapman (1960); Gonzalez et al. (1994), intense storms are those with Dst below −100 nT, moderate storms are those with Dst in the range between −50 nT and −100 nT, and weak storms fall between −30 nT and −50 nT. Most of the observed Dst peaks fall into the range −200 < Dst < 0 nT, and following the above criteria we can say that within our sample of events storms of different intensities occurred, from weak to intense.

For HSS/CIRs, the strongest Dst peak (−116 nT) associated and the strongest Ap peak (157 nT) are associated with maximum peak V = 742 km s-1 and B = 14 nT peak. The highest AE peak (874 nT) is associated with V = 509 km s-1 and the B = 17 nT.

Most HSS/CIR-driven storms were weak (Dst peaks between −80 nT and −20 nT). These storm levels indicate that intense events have lower probability of occurrence than weaker storms, as already noticed in previous studies (Tsurutani et al. 2006; Alves et al. 2006, see also Paper I and II). Richardson et al. (2006) also show the lower occurrence of weaker events for a 159 CIR sample (see their Fig. 9). We note that, CIRs alone occasionally may produce intense storms (Richardson et al. 2006; Zhang et al. 2003).

We note that maximum peak values of different geomagnetic indices do not occur in the same event. This may indicate that different current systems within the Earth’s magnetosphere (as measured by ground magnetometers at different latitudes and quantified by geomagnetic indices) show different responses on the geoeffective solar wind flow. This is observed for both ICMEs and HSS/CIRs.

4. Cross-correlations for ICMEs

In the following we investigate the relationships between the ICME parameters B, V, and BV, and geomagnetic indices Ap, Dst, and AE, by applying the cross-correlation analysis. For all relationships, we performed linear and power-law least-squares fitting. The latter option is found to be important for the relationships between BV and all three geomagnetic indices, as described below. We employ the simple power-law fit of the form y = axb, which can be solved analytically and does not depend on the used numerical procedure.

The scatter-plot relating the peak values of the ICME magnetic field and velocity is presented in Fig. 1. There is a modest correlation between B and V (R = 0.64). The range of values in the data scatter reveals that large values of B, for example B ~ 30 nT, occur at V ~ 600 km s-1. However, we note that there are also fast ICMEs without strongly enhanced magnetic fields (e.g., at V ~ 1050 km s-1, according to the scatter plot, B ~ 15 nT may be expected). Nevertheless, the fitted linear relation clearly shows a trend that ICMEs with stronger magnetic fields propagate at higher velocities (the fits gives the most probable values i.e., B = 20 nT at V = 600 km s-1 and B = 36 nT at V = 1050 km s-1).

This has implications for geoeffectiveness since the product BV, related to the electric field, is enhanced by both factors, V and B. Our V − B correlation is generally in agreement with the linear correlations found by other studies (e.g., Gonzalez et al. 1998; Gopalswamy et al. 2008; Dal Lago et al. 2001; Richardson & Cane 2010). Differences could be attributed to different sample sizes, different ways in which peak-values were determined, and the fact that we did not consider separately different ICMEs substructures (e.g., shock, sheath, MC). For instance, (Richardson & Cane 2010) obtained modest V − B correlation for magnetic clouds, while there was little correlation for other events. For a discussion of the relationship between ICME magnetic field intensities and speeds see also Owens et al. (2005) and Richardson & Cane (2010).

thumbnail Fig. 1

Relationship between the ICME peak velocity and peak magnetic field. The parameters and the correlation coefficient R of the linear least-squares fit are shown in the inset.

In Table 2 we present the linear least squares correlation coefficients between ICME parameters and geomagnetic indices. The highest correlations are for the relationships B − Dst, B − Ap, and BV − Ap. The AE is most tightly correlated with V and BV (R = 0.69 and R = 0.65, respectively), whereas Dst is most tightly correlated with B and BV (R = −0.85 and −0.79, respectively). The Dst is generally better correlated with the ICME parameters than AE. The only exception is V − AE correlation, which is higher than the V − Dst correlation. The relatively tight correlations between all geomagnetic indices and peak ICME speed may be related to a good V–B relationship (R = 0.64), shown in Fig. 1. Both linear relationships V − Dst and B − Dst have also been investigated for example, by Alves et al. (2006) and Gopalswamy et al. (2008). The V − Dst relationship is also discussed in e.g., Kane (2005), Richardson & Cane (2010).

Table 2

Linear least squares correlation coefficient for the relationship between geomagnetic indices and ICME parameters.

thumbnail Fig. 2

Correlations V − Ap, V − Dst, V − AE for ICMEs. The linear least-squares fit parameters and the correlation coefficient R are presented in the insets; dashed lines represent the residual standard deviation.

The V − Ap, V − Dst and V − AE scatter plots are shown in Fig. 2. In Fig. 3 the scatter plots B − Ap, B − Dst, and B − AE are displayed. According to the linear regression analysis (Fig. 3) weak, moderate, and intense storms (−50 < Dst < −30 nT, −100 < Dst < −50 nT, and Dst < −100, respectively) are on average caused by ICMEs characterized by, say, B < 15 nT, 15 < B < 20 nT, and B > 20 nT, respectively. However, the data scatter reveals that these storm levels (weak, moderate, and intense) could also occur for different magnetic field strengths. We note that such values of B are considerably higher than the typical field magnitudes of 5 nT in the quiet solar wind (see, e.g., King 1986).

thumbnail Fig. 3

Correlations B − Ap, B − Dst, B − AE for ICMEs. The linear least-squares fit parameters and the correlation coefficient R are presented in the insets. Dashed lines represent the residual standard deviation.

In Fig. 4 the scatter-plot of Ap, Dst, and AE, versus BV is shown, together with the linear and power-law least-squares fits. These dependencies are investigated for two time resolutions, i.e., applying one-hour (three-hour for Ap) and six-hour averaging (both shown in Fig. 4). Most of the geomagnetic-index peaks are related to BV values below ~35 mV m-1. At six-hour resolution, the highest AE peak (1575 nT) is found for the strongest BV peak (BV = 45 mV m-1). On the other hand, the highest values of Ap and of Dst peaks (345 nT and −341 nT, respectively) are associated with a somewhat lower value, BV = 35 mV m-1 and BV = 27 mV m-1, respectively. The data distributions show that, generally, a higher BV causes a stronger geomagnetic activity at all latitudes.

thumbnail Fig. 4

Linear y = ax + b (solid line) and power-law y = axb (dashed line) fits for the relationships BV − Ap (top), BV − Dst (middle), and BV − AE (bottom) for ICMEs. Blue circles and red crosses represents one-hour resolution data (three-hour resolution for Ap) and six-hour resolution data, respectively. Fit parameters and correlation coefficients are displayed in Table 3.

Table 3

Linear and power-law least-squares fits (y = ax + b, y = axb, respectively), and corresponding correlation coefficients R, describing the relationships between ICME BV and geomagnetic indices for one/three hour-resolution and six-hour resolution.

The results of linear fitting (y = ax + b) and power-law fitting (y = axb) for different time resolutions are displayed in Table 3. For both resolutions, the correlation coefficients for the BV − Dst relationship show that linear fit and power-law fit describe the data equally well. We note, the exponent of the power-law fit at both resolution is close to one, highlighting that Dst is linearly dependent on BV (not depending on the data resolution). The fitted dependencies are shown in the middle panel of Fig. 4. Below ~5 mV m-1 all Dst peaks are below −50 nT. The fits indicate that, on average, BV has to be around ~10 mV m-1 and ~35 mV m-1 in order to cause an intense geomagnetic storm (Dst < −100 nT) and extreme storm (Dst < −300 nT), respectively. However, the data distribution shows that storms of these intensities could occur at BV even below these values. We note that for very large BV (BV > 40 mV m-1) there are storms with Dst below −250 nT. However, at such high BV values, we do not have sufficient data points to reach a general conclusion. For additional information about the conditions leading to intense geomagnetic-storm Dst levels, we refer to studies by, e.g., Gonzalez & Tsurutani (1987), Echer et al. (2008), Ji et al. (2010), and Richardson & Cane (2010).

For the BV − Ap relationship, the correlation coefficients show that the power-law dependence is slightly better than the linear dependence at both resolutions (the uppermost panel of Fig. 4). The six-hour resolution data (as well as fitted lines) are moved to somewhat lower values compared to the three-hour resolution data. Below ~5 mV m-1Ap peaks have low values (<50  nT). We note the tendency of a kind of a saturation of Ap peak values at BV > 20 mV m-1 which is not well reproduced by the power-law fit.

In the case of the BV − AE relationship the linear and power-law fits are very similar at the six-hour resolution, while at the one-hour resolution the power-law provides a better fit. The power-law exponent is close to 1/2, regardless of the resolution. At the six-hour resolution the data (and fits) in the scatter plot are moved toward lower values compared to the data at one-hour resolution, as seen in the bottom panel of Fig. 4. It is interesting to note a different type of data distribution compared to BV − Ap data. In the case of AE, there is a clear upper limit to the data. This upper-limit boundary, located some 500 nT above the power-law fit, rises up to ~25 mV m-1, and then indicates a kind of saturation. On the other hand, at very high BV, there is also a lower limit to the data, namely there is no AE below ~600 nT. It is also worth noting that even at very low BV peak values (≲5 mV m-1), some significant AE values are observed, up to 700 nT. We note that the scatter in the BV plots is partly due to the strong field that can be oriented northward (weak activity) or southward (strong activity).

The above results clearly indicate different magnetospheric responses on the same input from the solar wind driver (BV) at various latitudes. Our sample reveals that the equatorial current system’s response is linear, while the polar current system’s response is likely to be non-linear.

The presented analysis of the influence of the time-resolution influences on the results shows that for Ap and Dst, there is practically no difference between the one-hour (three-hour for Ap) and six-hour option. For AE, the one-hour data distribution shows more clearly the non-linear dependence on BV.

The different responses of the polar and equatorial magnetosphere reflect the different nature of geomagnetic storms at these latitudes. Namely, the geomagnetic storms at polar region may be viewed as the results of a series of geomagnetic disturbances, that consist of a series of pulses (seen in the AE index), each lasting a few hours.

5. Cross-correlations for HSS/CIRs

A complete time-series analysis of the HSS/CIR-driven geomagnetic activity was performed in Papers I and II. Here, we focus on the peak values of HSS/CIR solar-wind parameters and geomagnetic indices, to compare the ICME- and HSS/CIR-driven geomagnetic activity at various latitudes (Sect. 6).

5.1. Cross-correlation between HSS/CIR parameters and geomagnetic indices

In the following we investigate the relationship between the HSS/CIR parameters B, V, and BV, and geomagnetic indices Ap, Dst, and AE, by applying the cross-correlation analysis. As in the case of ICMEs, for all relationships we apply linear and power-law least-squares fitting.

Table 4

Correlation coefficients for the relationship between the HSS/CIR parameters and geomagnetic indices.

thumbnail Fig. 5

Linear least-squares fit V − Dst for HSS/CIRs. The events from Paper I and Paper II are depicted by the blue pluses (the corresponding linear fit Dst = −0.14V + 49 is shown by blue line), and the events from Zhang et al. (2007a) by red crosses.

In Table 4 we present the correlation coefficients of the linear and power-law fit. The table shows that there is no correlation between geomagnetic indices and V. On the other hand, the correlations between geomagnetic indices and B and BV are relatively well defined. The best ones are B − Dst and BV − Dst correlations. The B − Ap and B − AE correlations are somewhat weaker, while BV − Ap correlation is somewhat better than the BV − AE correlation. For all dependencies, a power law is found to better describe the data than the linear fit.

thumbnail Fig. 6

Linear and power-law least-squares fits B − Ap, B − Dst, and B − AE for HSS/CIRs. Fit parameters and the correlation coefficients are presented in the insets.

thumbnail Fig. 7

Linear and power-law least-squares fit BV − Ap, BV − Dst and BV − AE for HSS/CIRs. Fit parameters and the correlation coefficients are presented in the insets.

Regarding the relationship between V and geomagnetic indices, it is interesting to note that when we examine separately events from our previous papers (Paper I and Paper II), namely CIR/HSSs occurring in 2005 and 2006, which were not affected by ICMEs, we obtain moderate-to-weak correlations for V − Ap (R = 0.42) and V − Dst (R = −0.37), and somewhat better correlation for V − AE (R = 0.58). As an illustration, we show in Fig. 5 the scatter plot V − Dst. The linear fit for the data from Paper I and Paper II (displayed as blue plusses) is shown by a blue line. Inspecting the plot, three group of events can be noticed: 1) the events in the lower-left part having 450 < V < 550 km s-1 and −120 < Dst < −80 nT (events only from Zhang et al. 2007a); 2) the events in the range 550 < V < 750 km s-1 and −120 < Dst < −60 nT (events from Zhang et al. 2007a and from our Paper I and Paper II) and 3) the events in the uppermost part having 530 < V < 750 km s-1 and −50 < Dst < 0 nT (events only from Paper I and Paper II).

The events from Zhang et al. (2007a) were selected as having intense storms. Hence, they will lie at lower Dst than the other set of events. We note that these strongest CIR-related events are distributed through different years and phases of the solar cycle, when the general state of the heliosphere is significantly more complex than it is in the phases when the occurrence rate of CMEs is low. One may speculate that because of the permanent CMEs activity, these CIRs (from Zhang et al. 2007a) produced different effects than those that occurred in the period of low CME activity (from Paper I and Paper II).

The scatter plots B − Ap, B − AE, and B − Dst displayed in Fig. 6 show that B has to reach 8 nT in order to trigger at least some geomagnetic activity. It can also be noticed that there is an upper limit in Dst and lower limit in Ap data distributions that roughly have a form of a power-law. The largest Dst dip (−116 nT) and the highest Ap peak (157 nT) occur at ~14 nT. These values are about two (four) times higher than the Dst (Ap) values given by the corresponding linear-regression fits. At this value of B, the upper (lower) limits suggest Dst ~ −20 nT (Ap ~ 20 nT). We note that the power-law fit is more pronounced for B − Ap dependence. The B − AE data distribution reveals the presence of both the lower and upper limit that have the form of a power-law curve; as soon as B gets enhanced, it results in a recognizable AE disturbance.

The BV − Ap, BV − AE, and BV − Dst data are drawn in Fig. 7 and show that BV has to reach ~4 mV m-1 in order to trigger at least some geomagnetic activity. Generally, stronger geomagnetic activity is related to higher BV values. The highest values of Ap (157 nT) and Dst (−116 nT) are associated with the strongest BV (10 mV m-1) while the strongest AE (874 nT) is associated with BV = 7 mV m-1. Interestingly, we obtain BV − Dst dependence that has a form close to the quadratic (the power-law exponent is 2.2). Furthermore, the power-law fit indicates that, on average, HSS/CIRs drive intense low-latitude geomagnetic storms (Dst < −100) for BV above 9 mV m-1. However, according to the data scatter, such storms can already occur at BV    ~   5 mV m-1.

Finally, we note that Ap and AE correlations with BV are better than with B, although the correlations with V is practically zero. Namely, the velocity here plays the important role only indirectly. Higher velocities lead to a stronger compression, so the B enhancement is stronger, and thus, BV gets stronger too. For Dst, we found that Dst − BV correlations are weaker than the Dst − B correlation, suggesting that V does not play an important role in producing Dst.

6. Comparison of ICME and HSS/CIR cross-correlation results

6.1. Cross-correlation between geomagnetic indices

Table 5

Linear least-squares correlation coefficients for the relationship between geomagnetic indices.

In Table 5, the correlation coefficients for the linear relationships between geomagnetic indices for ICMEs and HSS/CIRs are compared. The presented values show that in the case of ICMEs the best correlation is Dst − Ap, and the lowest is Dst − AE. For HSS/CIRs, again the strongest correlation is Dst − Ap. We note that the Dst − Ap correlation is better for ICMEs than for HSS/CIRs, while both Dst − AE and AE − Ap correlations are higher for HSS/CIRs. This is consistent with the locations of the geomagnetic observatories used for deriving a certain geomagnetic index. The obtained correlations indicate that for stronger storms (ICMEs), the auroral oval shifts to lower latitudes and the substorm strength, as quantified by the AE index, starts showing a reduced level of activity.

6.2. Relationship between solar wind parameters and geomagnetic indices

By comparing Tables 2 and 4 one finds that the corresponding correlations are weaker for HSS/CIRs than for ICMEs. In particular, the correlations between all three geomagnetic indices and V are significant for ICMEs, while no correlations is found for HSS/CIRs.

In the following, we compare in detail the ICMEs and HSS/CIRs linear dependencies BV − Ap, BV − AE, and BV − Dst. To compare the significance of these relationships (as quantified by the correlation coefficients), it is necessary to use the same dynamical BV range, for both ICMEs and HSS/CIRs. Thus, we consider here the ICMEs for which BV < 12 mV m-1, which is the highest value of BV in the studied HSS/CIR sample. The outcome of the cross-correlation analysis is presented in Table 6. As expected, the ICME correlations in the restricted range of BV values are weaker than the ICME correlations for the whole BV range. Now, only for Ap is the ICME correlation coefficient considerably higher than for HSS/CIRs (R = 0.79 and R = 0.56, respectively); the correlations for the Dst and Ap indices are almost the same. Table 6 reveals that the slopes of the regression lines for ICMEs and HSS/CIRs are the same within the error limits for all three indices. The parameter b of the linear least-squares fits for HSS/CIRs are lower, meaning that at the same BV ICMEs are more geoeffective at all latitudes. In the considered range, the mean BV value is 7.4 ± 2.5 mV m-1 for ICMEs and 6.5 ± 1.7 mV m-1 for HSS/CIRs. In case of ICMEs, the mean values of Ap, Dst, and AE are 63 ± 47 nT, -73 ± 45 nT, and 652 ± 234 nT, respectively. For HSS/CIRs these values are somewhat lower, equaling 49 ± 33 nT, −52 ± 33 nT, and 572 ± 165 nT.

Table 6

Linear least-squares fits (y = ax + b) and correlation coefficients R describing the relationships between BV (BV < 12 mV m-1) and geomagnetic indices.

thumbnail Fig. 8

Dependence of ICME peak velocity V (top) and ICME peak magnetic field B (bottom) on the coronagraphic CME mean speed VCME. The linear least-squares fits are shown by the solid lines (parameters and the correlation coefficients R are shown in the insets).

7. Relationship to the coronagraphic CME speed

For space-weather forecasting purposes, in the following we apply the cross-correlation analysis to the relationships between:

  • peak values of the ICME parameters B and V, and the coronagraphic CME velocity VCME;

  • peak values of geomagnetic indices Ap, Dst, and AE and the velocity VCME.

In Fig. 8 we show how the ICME parameters V and B are related to the mean speed of CMEs measured in the LASCO field of view, VCME. The ICME speed V is relatively well correlated with VCME (R = 0.61), whereas the correlation VCME − B is rather weak (R = 0.27). Values of VCME are in the range ~250−3000 km s-1. The corresponding speeds at the Earth (1 AU) are in the range ~380 to ~1200 km s-1. The narrower range of speeds at Earth is a direct result of the interaction between CMEs and the solar wind (e.g., Lindsay et al. 1999; Gopalswamy 2010; Vršnak et al. 2010).

thumbnail Fig. 9

Correlations VCME − Ap, VCME − Dst, and VCME − AE.

The V(VCME) linear fit gives the value V = 410 km s-1 for the y-axis intercept (VCME = 0). Furthermore, we find that V becomes equal to VCME for VCME = 512 km s-1. Thus, for VCME below this value, ICMEs are accelerated, i.e., V > VCME, whereas if VCME is higher than this value, ICMEs show V < VCME, implying they are decelerated.

Although the correlation VCME − B is quite weak, the linear fit (Fig. 8, bottom panel) indicates that higher-speed CMEs tend to have a stronger magnetic field B near the Earth. However, we note that the fastest two CMEs in our sample were associated with only modestly enhanced B at the Earth. We note also that slow CMEs do not result in a strong ICME field (data void in the upper-left part of the graph). The relationship between ICME parameters B, V, and CME speed have also been discussed by, e.g., Lindsay et al. (1999); Gopalswamy (2008, 2010) and Richardson & Cane (2011).

In Fig. 9 we present the relationships between VCME and Ap, Dst, and AE. The correlation coefficients are considerably lower (by about a factor of 2) than for the correlations obtained employing the ICME speed V. The best correlation is found for the dependence VCME − Ap (R = 0.35). The correlation coefficients for the relationships VCME − AE and VCME − Dst are similar (R = 0.30 and R = −0.28, respectively),

Finally, it should be noted that there are fast CMEs that have almost no geomagnetic effect at low and mid latitudes as seen from the VCME − Ap and VCME − Dst graphs. On the other hand, in the case of AE, the lower limit shows that at large VCME there will be always some geomagnetic activity triggered.

8. Discussion and conclusions

The geomagnetic activity associated with 63 ICMEs and 38 HSS/CIRs in the period 1998−2006 has been studied. We considered the effect of the overall ICME disturbances, which includes the shock, the sheath region, and the magnetic ejection, making no distinction between the geoeffectiveness of individual structural elements. Most of the selected HSS/CIRs occurred in periods when the activity of coronal mass ejections was low (two periods in 2005 and 2006 were considered, as in Paper II).

We have analyzed various linear and power-law least-squares relationships, separately for ICMEs and HSS/CIRs, to examine similarities/differences in the magnetospheric response at low, mid, and high latitudes to ICMEs and HSS/CIRs. We summarize our results as follows (the quoted values of V, B, Dst, Ap, and AE represent six-hours averages).

For ICMEs the fitted linear relation V − B clearly shows a trend that ICMEs with stronger magnetic field propagate at higher velocities. This has implications for geoeffectiveness since the product BV, related to the electric field, is enhanced by both factors, V and B.

For ICMEs the power-law least-squares fits are found to be important only for the relationships between geomagnetic indices and BV. The performed analysis for two time resolutions obtained by one-hour (three-hour for Ap) and six-hour averaging show: Dst is linearly dependent on BV, and does not depend on the data resolution. Below ~5 mV m-1, all Dst peaks are below −50 nT. The fits indicate that an intense geomagnetic storm (Dst < −100 nT) and a very intense storm (Dst < −300 nT) occur, on average, at BV ~ 10 mV m-1 and ~35 mV m-1, respectively. However, the data distribution shows that such storm intensities could occur at BV even below these values. For the BV − Ap relationship, the power-law dependence is slightly better than the linear dependence at both resolutions. Below BV ~ 5 mV m-1, Ap peaks have low values (<50  nT). The cross-correlation coefficient of the power-law BV − Ap fit is the largest one. In the case of the BV − AE relationship, the linear and power-law fits are very similar at the six-hour resolution, while at the one-hour resolution the power-law provides a better fit. This indicates that the response of the polar magnetosphere is more sensitive to fast fluctuations in the solar wind (here quantified by the product BV) than is the equatorial current system. Thus, for studying the nature of the temporal variability of the magnetic activity at high latitudes that is caused by ICMEs, the one-hour resolution is probably more appropriate. The power-law exponent is close to 1/2, regardless of the resolution. The BV − AE data distribution indicates a pronounced upper limit to the data. This upper-limit boundary, located about 500 nT above the power-law fit, rises up to BV ~ 25 mV m-1, and then indicates a kind of saturation. On the other hand, at very high BV values, there is also a lower limit to the data, i.e., there is no AE below ~600 nT. It is worth noting that even at very low BV peak values (≲5 mV m-1), some significant AE values are observed, up to 700 nT.

For HSS/CIRs there is no correlation between geomagnetic indices and V. However, when we examine separately events from our previous papers (Paper I and Paper II), namely CIR/HSSs occurring in 2005 and 2006, which were not affected by ICMEs, we obtain moderate-to-weak correlations between V and geomagnetic indices.

For all HSS/CIRs dependencies, power law is found to describe the data better than the linear least-squares fit. The best correlations are B − Dst and BV − Dst.

The HSS/CIRs BV − Ap, BV − AE, and BV − Dst data distribution show that BV has to reach ~4 mV m-1 in order to drive at least some geomagnetic activity.

The power-law BV − Dst fit indicates that, on average, HSS/CIRs drive intense low-latitude geomagnetic storms (Dst < −100) for BV above 9 mV m-1. However, according to the data scatter, these storms can occur already at BV~5 mV m-1.

We observed that the HSS/CIRs velocity is important for Ap and AE, though only indirectly, while it does not play an important role in producing Dst.

The Dst − Ap correlation is better for ICMEs than for HSS/CIRs, while both Dst − AE and AE − Ap correlations are higher for HSS/CIRs.

Within the same dynamical BV range (BV < 12 mV m-1), only the ICMEs Ap(BV) correlation is considerably stronger than the HSS/CIRs Ap(BV) correlation (R = 0.79 and R = 0.56, respectively). Nevertheless, the regression parameters indicate that at the same value of BV ICMEs are more geoeffective at all latitudes.

For ICMEs the correlation coefficients for AE(BV) and Dst(BV) drop significantly when BV < 12 mV m-1 was analyzed. This may indicate that both the polar electrojet and ring current are quite sensitive to the BV amplitude.

The ICME speed V is relatively well correlated with CME speed VCME (R = 0.61), whereas the correlation VCME − B is rather weak (R = 0.27). Anyway, the linear fit VCME − B indicates that higher-speed CMEs tend to have a stronger magnetic field B near the Earth. We note also that slow CMEs do not result in a strong ICME field.

We observed that there are fast CMEs that have almost no geomagnetic effect at low and mid latitudes. On the other hand, at large VCME there will be always some geomagnetic activity triggered at high latitudes. This is an important finding regarding the space weather forecasting.

For both ICMEs and HSS/CIRs, the maximum peak values of different geomagnetic indices do not occur in the same event. This suggests that different current systems within the Earth’s magnetosphere (as measured by ground magnetometers at different latitudes and quantified by geomagnetic indices) show different responses to the geoeffective solar wind flow.

The results clearly indicate different magnetospheric responses to the same input from the solar wind driver (BV) at various latitudes. Furthermore, we observed relative differences in the response of different current systems within the Earth’s magnetosphere to the impact of ICMEs and HSS/CIRs.

The ICME-driven activity shows that the development of the equatorial and polar current systems are not always in constant proportion (as we noted by Gonzalez et al. 1994). Namely, the Dst(BV) correlations are stronger than AE(BV) correlations, and the AE(Dst) dependence is the weakest one of the three geomagnetic indices analyzed. For ICMEs the highest impact at mid latitudes probably reflects the contribution from both current systems in these regions, and consequently a growth of ionospheric currents. Moreover, during the intense particles injection into the magnetosphere, the substorm currents may be formed at lower latitudes, and so will not be as strong as expected at high-latitude observatories. Instead, the Ap index will be additionally increased.

For HSS/CIRs, the AE and Dst are tightly related, suggesting that development of the ring current and auroral electrojet are closely related for this type of solar wind disturbances. This aspect should be investigated further.

In conclusion, our study shows that the magnetosphere reaction on both solar drivers (ICMEs and HSS/CIRs) is different at various latitudes. Thus, the full picture of the ICMEs and HSS/CIRs driven geomagnetic activities can be obtained only by studying the development of different current systems within the Earth’s magnetosphere and ionosphere.

Acknowledgments

The presented work has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n 263252 [COMESEP].

References

  1. Alves, M. V., Echer, E., & Gonzalez, W. D. 2006, J. Geophys. Res. (Space Phys.), 111, A07S05 [NASA ADS] [CrossRef] [Google Scholar]
  2. Bakare, N. O., & Chukwuma, V. U. 2010, Indian J. Radio Space Phys., 39, 150 [Google Scholar]
  3. Borovsky, J. E., & Denton, M. 2006, J. Geophys. Res., 111 [Google Scholar]
  4. Brueckner, G. E., Howard, R. A., Koomen, M. J., et al. 1995, Sol. Phys., 162, 357 [NASA ADS] [CrossRef] [Google Scholar]
  5. Burlaga, L. F., & Lepping, R. 1977, Planet. Space Sci., 25, 1151 [NASA ADS] [CrossRef] [Google Scholar]
  6. Dal Lago, A., Gonzalez, W. D., de Gonzalez, A. L. C., & Vieira, L. E. A. 2001, J. Atmos. Sol. Terr. Phys., 63, 451 [NASA ADS] [CrossRef] [Google Scholar]
  7. Dumbović, M., Vršnak, B., Čalogović, J., & Karlica, M. 2011, A&A, 531, A91 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  8. Dungey, J. 1961, Phys. Rev. Lett., 6, 47 [NASA ADS] [CrossRef] [Google Scholar]
  9. Echer, E., Gonzalez, W. D., Tsurutani, B., & Gonzalez, A. 2008, J. Geophys. Res., 113, A05221 [NASA ADS] [CrossRef] [Google Scholar]
  10. Georgieva, K., Kirov, B., & Gavruseva, E. 2006, Phys. Chem. Earth, 31, 81 [CrossRef] [Google Scholar]
  11. Gonzalez, W. D., & Tsurutani, B. T. 1987, Planet. Space Sci., 35, 1101 [Google Scholar]
  12. Gonzalez, W. D., Joselyn, J., Kamide, Y., et al. 1994, J. Geophys. Res., 99, 5771 [Google Scholar]
  13. Gonzalez, W. D., Chía de Gonzalez, A. L., Dal Lago, A., et al. 1998, Geophys. Res. Lett., 25, 963 [NASA ADS] [CrossRef] [Google Scholar]
  14. Gopalswamy, N. 2008, J. Atmos. Sol. Terr. Phys., 70, 2078 [NASA ADS] [CrossRef] [Google Scholar]
  15. Gopalswamy, N. 2010, in IAU Symp., 264, 326 [Google Scholar]
  16. Gopalswamy, N., Akiyama, S., Yashiro, S., Michalek, G., & Lepping, R. P. 2008, J. Atmos. Sol. Terr. Phys., 70, 245 [Google Scholar]
  17. Gosling, J. T. 1996, ARA&A, 34, 35 [Google Scholar]
  18. Huttunen, K. E. J., Schwenn, R., Bothmer, V., & Koskinen, H. E. J. 2005, Ann. Geophys., 23, 625 [NASA ADS] [CrossRef] [Google Scholar]
  19. Ji, E., Moon, Y., Kim, H., & Lee, H. 2010, J. Geophys. Res., 115, A10232 [NASA ADS] [CrossRef] [Google Scholar]
  20. Kane, R. P. 2005, J. Geophys. Res. (Space Phys.), 110, A9, A02213 [Google Scholar]
  21. King, H. J. 1986, in Solar Wind-Magnetosphere Coupling, eds. Y. Kamide, & J. Slavin (Tokyo: Terra Scientific), 163 [Google Scholar]
  22. Kivelson, M. G., & Russel, C. T. 1995, Introduction to Space Physics (Cambridge University press) [Google Scholar]
  23. Lavraud, B., Thomsen, M. F., Borovsky, J. E., Denton, M. H., & Pulkkinen, T. I. 2006, J. Geophys. Res. (Space Phys.), 111, A09208 [NASA ADS] [CrossRef] [Google Scholar]
  24. Lindsay, G. M., Luhmann, J. G., Russell, C. T., & Gosling, J. T. 1999, J. Geophys. Res., 104, 12515 [Google Scholar]
  25. McComas, D., Bame, S. J., Barker, P., et al. 1998, Space Sci. Rev., 86, 563 [NASA ADS] [CrossRef] [Google Scholar]
  26. Möstl, C., Farrugia, C. J., Kilpua, E. K. J., et al. 2012, ApJ, 758, 10 [NASA ADS] [CrossRef] [Google Scholar]
  27. Owens, M., Cargill, P., Pagel, C., Siscoe, G., & Crooker, N. 2005, J. Geophys. Res., 110, A0110 [Google Scholar]
  28. Prolss, G. 2004, Physics of the Earth’s Space Environment (Berlin, Heidelberg: Springer-Verlag) [Google Scholar]
  29. Richardson, I. G., & Cane, H. 2010, Sol. Phys, 264, 189 [NASA ADS] [CrossRef] [Google Scholar]
  30. Richardson, I. G., & Cane, H. 2011, Space Weather, 9, S07005 [NASA ADS] [CrossRef] [Google Scholar]
  31. Richardson, I. G., & Cane, H. 2012, J. Space Weather Space Climate, 2, A01 [NASA ADS] [Google Scholar]
  32. Richardson, I. G., Cliver, E., & Cane, H. 2001, Geophys. Res. Lett., 28, 2569 [Google Scholar]
  33. Richardson, I. G., Webb, D. F., Zhang, J., et al. 2006, J. Geophys. Res., 111, A07S09 [Google Scholar]
  34. Schwenn, R. 1983, Space Sci. Rev., 34, 85 [NASA ADS] [CrossRef] [Google Scholar]
  35. Schwenn, R., dal Lago, A., Huttunen, E., & Gonzalez, W. D. 2005, Ann. Geophys., 23, 1033 [NASA ADS] [CrossRef] [Google Scholar]
  36. Smith, C. W., L’Heureux, J., Ness, N. F., et al. 1998, Space Sci. Rev., 86, 613 [NASA ADS] [CrossRef] [Google Scholar]
  37. Stone, E., Frandsen, A., Mewaldt, R., et al. 1998, Space Sci. Rev., 86, 1 [Google Scholar]
  38. Sugiura, M., & Chapman, S. 1960, Abandal. Akad. Wiss., Gottingen Math. Phys., K1, 4 [Google Scholar]
  39. Tsurutani, B. T., & Gonzalez, W. D. 1987, Planet. Space Sci., 35, 405 [NASA ADS] [CrossRef] [Google Scholar]
  40. Tsurutani, B., & Gonzalez, W. 1997, in The interplanetary causes of magnetic storms: A review, eds. B. Tsurutani, W. Gonzalez, Y. Kamide, & J. Arballo, Geophys. Monogr. Ser., 98, 1 [Google Scholar]
  41. Tsurutani, B. T., Gonzalez, W. D., Guarnieri, F., et al. 2004, J. Atmos. Sol. Terr. Phys., 66, 167 [Google Scholar]
  42. Tsurutani, B. T., McPherron, R. L., Gonzalez, W. D., et al. 2006, J. Geophys. Res., 111, 1 [Google Scholar]
  43. Verbanac, G., Lühr, H., Rother, M., Korte, M., & Mandea, M. 2007, Earth, Planet. Space, 59, 251 [NASA ADS] [Google Scholar]
  44. Verbanac, G., Vršnak, B., Temmer, M., Mandea, M., & Korte, M. 2010, J. Atmos. Sol. Terr. Phys., 607 [Google Scholar]
  45. Verbanac, G., Vršnak, B., Temmer, M., & Veronig, A. 2011a, A&A, 526, A20 [Google Scholar]
  46. Verbanac, G., Vršnak, B., Živković, S., et al. 2011b, A&A, 533, A49 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  47. Vršnak, B., Temmer, M., & Veronig, A. 2007, Sol. Phys., 240, 331 [Google Scholar]
  48. Vršnak, B., Žic, T., Falkenberg, T. V., et al. 2010, A&A, 512, A43 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  49. Wang, Y., Shen, C. L., Wang, S., & Ye, P. Z. 2003, Geophys. Res. Lett., 30, 2039 [NASA ADS] [CrossRef] [Google Scholar]
  50. Yermolaev, Y., & Yermolaev, M. 2006, Adv. Space Res, 37, 6, 1175 [CrossRef] [Google Scholar]
  51. Zhang, J., Dere, K. P., Howard, R. A., & Bothmer, V. 2003, ApJ, 582, 520 [Google Scholar]
  52. Zhang, J., Richardson, I. G., Webb, D. F., et al. 2007a, J. Geophys. Res. (Space Phys.), 112, 12103 [NASA ADS] [CrossRef] [Google Scholar]
  53. Zhang, J., Richardson, I. G., Webb, D. F., et al. 2007b, J. Geophys. Res. (Space Phys.), 112, 10102 [Google Scholar]

All Tables

Table 1

Overall characteristics of the employed data set (six-hour resolution), compared with characteristics of samples used in some other studies.

In the text
Table 2

Linear least squares correlation coefficient for the relationship between geomagnetic indices and ICME parameters.

In the text
Table 3

Linear and power-law least-squares fits (y = ax + b, y = axb, respectively), and corresponding correlation coefficients R, describing the relationships between ICME BV and geomagnetic indices for one/three hour-resolution and six-hour resolution.

In the text
Table 4

Correlation coefficients for the relationship between the HSS/CIR parameters and geomagnetic indices.

In the text
Table 5

Linear least-squares correlation coefficients for the relationship between geomagnetic indices.

In the text
Table 6

Linear least-squares fits (y = ax + b) and correlation coefficients R describing the relationships between BV (BV < 12 mV m-1) and geomagnetic indices.

In the text

All Figures

thumbnail Fig. 1

Relationship between the ICME peak velocity and peak magnetic field. The parameters and the correlation coefficient R of the linear least-squares fit are shown in the inset.
In the text
thumbnail Fig. 2

Correlations V − Ap, V − Dst, V − AE for ICMEs. The linear least-squares fit parameters and the correlation coefficient R are presented in the insets; dashed lines represent the residual standard deviation.
In the text
thumbnail Fig. 3

Correlations B − Ap, B − Dst, B − AE for ICMEs. The linear least-squares fit parameters and the correlation coefficient R are presented in the insets. Dashed lines represent the residual standard deviation.

In the text
thumbnail Fig. 4

Linear y = ax + b (solid line) and power-law y = axb (dashed line) fits for the relationships BV − Ap (top), BV − Dst (middle), and BV − AE (bottom) for ICMEs. Blue circles and red crosses represents one-hour resolution data (three-hour resolution for Ap) and six-hour resolution data, respectively. Fit parameters and correlation coefficients are displayed in Table 3.

In the text
thumbnail Fig. 5

Linear least-squares fit V − Dst for HSS/CIRs. The events from Paper I and Paper II are depicted by the blue pluses (the corresponding linear fit Dst = −0.14V + 49 is shown by blue line), and the events from Zhang et al. (2007a) by red crosses.

In the text
thumbnail Fig. 6

Linear and power-law least-squares fits B − Ap, B − Dst, and B − AE for HSS/CIRs. Fit parameters and the correlation coefficients are presented in the insets.
In the text
thumbnail Fig. 7

Linear and power-law least-squares fit BV − Ap, BV − Dst and BV − AE for HSS/CIRs. Fit parameters and the correlation coefficients are presented in the insets.
In the text
thumbnail Fig. 8

Dependence of ICME peak velocity V (top) and ICME peak magnetic field B (bottom) on the coronagraphic CME mean speed VCME. The linear least-squares fits are shown by the solid lines (parameters and the correlation coefficients R are shown in the insets).
In the text
thumbnail Fig. 9

Correlations VCME − Ap, VCME − Dst, and VCME − AE.
In the text

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