1 Introduction

Coronal mass ejections (CMEs) are expulsions of huge masses of plasma and magnetic field into the heliosphere. When intercepting the Earth, they can trigger geomagnetic storms, i.e. major disturbances of the terrestrial magnetic field (Gold, 1962; Gonzalez and Tsurutani, 1987; Gosling, 1993; Zhang et al., 2007; Gopalswamy, 2010). CMEs are often associated with soft X-ray (SXR) bursts (Tandberg-Hanssen and Emslie, 1988), which are routinely observed by the Geosynchronous Operational Environmental Satellites (GOES) spacecraft. SXR bursts reveal the heating of plasma in a flaring active region. The mechanical energy release to CMEs and the thermal energy release are closely related in many models on the origin of large-scale instabilities in the corona (Forbes et al. (2006), and references therein). Observational studies confirm such a close relationship: they revealed that the acceleration phase of a CME is temporally associated with intense energy release during the rise of the associated SXR burst (Zhang et al., 2001, 2004; Maričić et al., 2007). Relationships between the speed or kinetic energy of CMEs on the one hand and the importance of the SXR burst, most often the peak flux, on the other hand have also been revealed by many statistical studies (Moon et al., 2003; Burkepile et al., 2004; Vršnak, Sudar, and Ruždjak, 2005; Maričić et al., 2007; Yashiro and Gopalswamy, 2009; Bein et al., 2012). Occasional negative reports (Aggarwal et al., 2008) and the broad scatter in the statistical relationship show, however, that the quantitative relationship between CMEs and SXR bursts is complex.

The interest in clarifying the situation is twofold: on the one hand, such statistical relationships show to which extent different manifestations of magnetic energy release in solar eruptions are related. On the other hand, empirical relationships between different parameters of solar activity can assist space weather forecasting. This is especially interesting for Earth-directed CMEs whose velocity is not directly measurable by coronagraphs on the Sun–Earth line. Understanding how different quantities describing the output of eruptive solar activity are related is also essential if correlation analyses are to be used to derive physical relationships with a third quantity, for instance the intensity of solar energetic particle events (see, e.g., Trottet et al. 2015).

A major source of errors in statistical studies involving CME speed comes from the uncertainly of the measurement in coronagraphic images by projection effects. Moon et al. (2003), Burkepile et al. (2004), and Yashiro and Gopalswamy (2009) investigated these correlations with event samples restricted to CMEs that originated near the solar limb, where projection effects are not expected to affect the CME speed. These authors suggested that the correlations are indeed improved. However, they did not consider the statistical uncertainties of the correlation coefficients. Yashiro and Gopalswamy (2009) also concluded that the CME speed is more strongly correlated with SXR fluence than with SXR peak flux, but again without addressing the uncertainties in their comparison.

In the present work we re-assess the correlation between CME speed and both SXR peak flux and SXR fluence, restricting ourselves to CMEs near the solar limb. The event selection based on CMEs between 1996 and 2008 from the LASCO CME catalog and the associated GOES SXR bursts is described in Section 2. In Section 3 the results of the statistical analysis are presented, and empirical relationships between CME speed and SXR parameters are derived. The empirical relationships are used in Section 4 in an attempt to predict the arrival times of interplanetary CMEs (ICMEs) at Earth. The results are compared with predictions using CME measurements from SOHO/LASCO and with the observations of ICME arrival near 1 AU.

2 Methodology and Data Selection

The data set we analyzed consists of parameters of CMEs originating near the solar limb and of the associated SXR bursts. CME parameters (position angles, widths, heights, and speeds) are provided in the catalog of CMEsFootnote 1 observed by the Large Angle and Spectrometric Coronagraph experiment (LASCO; Brueckner et al. 1995) of the Solar and Heliospheric Observatory (SOHO), during the period from 1996 until 2008. Time histories of SXR flux measured by the GOES satellites in the 0.1 – 0.8 nm range were retrieved through the database at NASA/GSFC using the IDL routine goes.pro in the SolarSoft package.

2.1 Selection of Limb CMEs

Limb CMEs were selected in two steps. We first excluded events whose central position angle (PA, measured counterclockwise from solar north) was within ± 60∘ of the projected solar north and south, because such CMEs can only be associated with activity at relatively small central meridian distances. To obtain only CMEs with a well-defined direction of propagation, we delimited also the CME width to between 60∘ and 120∘, especially avoiding halo CMEs. We also excluded CMEs whose speed was ≤ 100 km s−1 to facilitate the flare association.

For the subsequent correlation studies, we checked the quality of the linear fits to the time-height trajectory and the representativity of the derived CME speed in the LASCO/CME catalog. We found some CMEs whose time-height diagram showed acceleration or deceleration phases in the LASCO field of view (FOV). We included events in which only few points at low altitudes were affected by this acceleration/deceleration, and the linear fit gave a satisfactory estimate of the final speed. In 11 events the acceleration/deceleration was pronounced in the LASCO/C2 FOV. In this case, we used the speed at a distance of 20 solar radii inferred from the constant acceleration fit as approximation of the final CME speed.

2.2 Identification of the Associated Flares

For the final determination of the CME origins, we identified CMEs associated with flares close to the limb. As a compromise between proximity to the limb and a significant number of events, we focused on flares located, according to Solar Geophysical Data,Footnote 2 at central meridian distance between 70∘ and 85∘. The events too close to the limb were excluded to avoid a partial occultation of the SXR emission. The CME-associated flares were searched in a first step within a fixed time interval with respect to the CME origin. The CME speed (see Section 2.1) and the time and heliocentric distance when the CME was first detected were used to extrapolate its trajectory to the limb of the Sun. An automated procedure was used to identify SXR bursts that peaked between an hour before and an hour after the instant when the backward-extrapolated trajectory intersected the solar limb. This way, we identified 77 CMEs associated with flares near the limbs; 44 occurred in the eastern and 33 in the western solar hemisphere.

The time profile of each SXR burst of this sample was studied in detail to identify cases when the CME-flare association found by the automated search was ambiguous. We discarded weak bursts because they would not allow us to obtain reliable values of the fluence.

Three different types of time profiles were identified (see Figure 1): (a) a well-defined peak, (b) a burst with more than one peak, which may mean a superposition of different bursts, and (c) a very complex profile where no burst could be unambiguously associated with the CME. The events in the latter category were discarded. For the cases with several peaks, we verified the coordinates of the flare related to each peak in the time profile directly through the analysis of image sequences from SOHO/EIT 19.5 nm (Delaboudinière et al., 1995) or Yohkoh/SXT (Tsuneta et al., 1991). The events where images revealed flares in active regions within ± 70∘ from the central meridian or at the opposite limb of the CME were eliminated, as well as events where several peaks were associated with the same active region without possibility of distinguishing whether one or several were actually associated with the CME. We also discarded cases when the CME reported in the catalog was not clearly recognizable in the LASCO daily movies. We eventually obtained a list of 49 events for which the correlation between CME speed and SXR peak flux and fluence could be studied. They are listed in Table 1. The fluence calculation is discussed in Section 3.

Figure 1
figure 1

Time profiles of three different SXR bursts: (a) a well-defined burst with a single peak, (b) a superposition of two different soft X-ray bursts, and (c) a burst with a very complex time profile. Vertical black lines delimit the 2-h window centered on the time when the extrapolated CME trajectory intersected the solar limb. The vertical red line marks the peak of the SXR burst associated with the CME.

Full size image
Table 1 Table of events: date (column 1), time (2), heliocentric distance (3) of the first detection of the CME in the SoHO/LASCO field of view, speed in the plane of the sky (4), time when the linear backward extrapolation of the time-height trajectory intersected the solar limb (5), times of onset (6), peak (7), peak flux (8), start-to-peak fluence (9) of the SXR bursts, quality flag of the fluence determination (10).
Full size table

The CME speeds in the sample range from 154 to 1822 km s−1, with a median of 639 km s−1, the SXR peak fluxes from 6×10−7 to 1.6×10−3 W m−2, i.e. from GOES X-ray flare classes B6 to X16.

3 Correlation Between CME Speed and SXR Peak Flux and Fluence

Based on the new short list of 49 events (25 at the eastern and 24 at the western limb), we related the speeds of the CMEs with parameters of the associated SXR bursts as observed by GOES in the 0.1 – 0.8 nm channel. Figure 2 displays the scatter plot of the CME speed vs the SXR peak flux on a double-logarithmic scale. We found a positive correlation of r=0.48±0.12 between the logarithms of the CME speed and of the SXR peak flux. Here and in the following, the errors were calculated using a bootstrap method (Wall and Jenkins, 2012, Chapter 6.6): the correlation coefficient was calculated repeatedly for a randomly selected sample of 49 out of the 49 observed data pairs, and the mean and standard deviation are quoted as the correlation coefficient and its statistical uncertainty.

Figure 2
figure 2

The logarithmic plot of the speed of CMEs near the solar limb during the period 1996 – 2008 versus the SXR peak F of the associated flares. The straight line is the result of a least-absolute deviation fit. The inset shows the correlation coefficient, the parameters of the straight line, and the number of events.

Full size image

In addition to the peak flux, we also considered the fluence. Two types of fluence were calculated in the 0.1 – 0.8 nm band for these events, namely start-to-peak fluence and total fluence. The background was determined as the average flux in a suitable time interval before the SXR burst. The start-to-peak fluence was calculated by integrating the background-subtracted flux from the start of the SXR burst until its maximum, including possible small earlier peaks that we considered as precursors. The existence of such precursor peaks and problems with background determination introduce uncertainties in the fluence calculation. The quality flag in column 10 of Table 1 is an assessment based on visible inspection. Qu=1 means that the fluence is reliable, Qu=2 labels less certain cases.

The total fluence is more difficult to calculate because the end of the SXR burst is generally poorly defined, and new events may be superposed on the decay phase of the burst of interest. Kahler, Sheeley, and Liggett (1989) defined the end of the burst as the time when the X-ray flux returns to the GOES C2 level, while Yashiro and Gopalswamy (2009) used the time when the soft X-ray flux decays to half of the peak value. We fitted the decay from the main peak by an exponential and calculated the fluence analytically until infinity. This avoids contamination by new SXR bursts during the decay phase as well as an arbitrary definition of the end time.

We obtained the same correlation between the CME speed and the SXR start-to-peak fluence and total fluence, r=0.58±0.09. The probability of obtaining this or a higher correlation coefficient from an unrelated sample is 1.3×10−5. The result is similar to those of Moon et al. (2002) and Yashiro and Gopalswamy (2009), who found correlations of 0.47 and 0.56, respectively.

The relationship between the logarithms of the CME speed V CME and of the peak flux F and fluence (start-to-peak fluence ϕ sp and total fluence ϕ p) of the associated SXR burst were inferred using linear fits minimizing least-squares deviation and least-absolute deviation. Differences between the resulting velocities amounted to some tens of km s−1 in extreme cases. Although these differences are small compared to the overall statistical uncertainty, in the following we use the result from the least-absolute deviation fit, which is less sensitive to outliers. This leads to the following empirical relationships:

$$\begin{aligned} \log V_{\mathrm{CME}} =&(0.20\pm0.08)\log F+(3.83\pm0.38) , \end{aligned}$$
(1)
$$\begin{aligned} \log V_{\mathrm{CME}} =&(0.24\pm0.05)\log\phi_{\mathrm{sp}}+(3.36\pm 0.12) , \end{aligned}$$
(2)
$$\begin{aligned} \log V_{\mathrm{CME}} =&(0.22\pm0.05)\log\phi_{\mathrm{p}}+(3.21\pm0.10). \end{aligned}$$
(3)

These results are the same regardless of whether we use all events or only those with quality flag 1.

Our analysis is simplified in several respects. We used a standard minimization technique that is in principle only justified when all the measurement uncertainties are in the dependent variable, here the CME speed, whereas the independent variable is assumed to be exactly known. This is of course not the case, and we would have to apply a more general technique, such as total least-squares minimization. We checked this and found no significant difference with the results of the standard fits above.

A second problem is a bias in our statistics that is the result of rejecting CMEs that were accompanied by weak or undetected SXR bursts. The fitted straight line would be expected to have a steeper slope if these events, which are located in the lower left corner of Figures 2 and 3, had been considered. We found indeed that the straight line steepened when we gradually extended the minimum fluence considered from 10−2 J m−2 to the lowest value detected, and it would likely steepen more than indicated by Equation (2) if weak SXR bursts were not hidden in the background. These relationships may hence overestimate the speeds of CMEs associated with weak SXR bursts and underestimate those of CMEs with intense SXR emission.

Figure 3
figure 3

The logarithmic plot of the speed of CMEs near the solar limb during the period 1996 – 2008 versus the SXR start-to-peak fluence Φsp of the associated flares. See caption of Figure 2.

Full size image

4 Application of the CME–SXR Relationship to ICME Propagation

In this section we test the relationship between CME speed and SXR fluence by applying it to the prediction of ICME arrival times at Earth.

The arrival of an ICME at Earth is one of the rare cases in space weather where the Sun leaves a substantial warning time. Yet predicting the arrival time is difficult: on the one hand, the speeds of Earth-directed CMEs cannot be directly measured by a coronagraph on the Earth-Sun line. On the other hand, the CME is not a rigid object, but changes during propagation in the interplanetary medium, where CMEs expand, change shape because of compression and reconnection, and are accelerated or decelerated. The relevant processes are reviewed, e.g., in Forbes et al. (2006) and Démoulin (2010). Detailed analyses using heliospheric imaging from STEREO were reported by Colaninno, Vourlidas, and Wu (2013) and Möstl et al. (2014); see also the review of Rouillard (2011).

Many attempts were undertaken in the literature to derive simple methods to forecast ICME arrival times at Earth using CME observations at the Sun. These models must take account of the acceleration or deceleration of CMEs in the interplanetary medium (Gopalswamy et al., 2001; Schwenn et al., 2005; Vršnak et al., 2010).

Gopalswamy et al. (2001) proposed a simple analytical treatment of the interplanetary propagation. It was based on an empirical relationship between the acceleration, which was assumed to be constant out to a limiting heliocentric distance, and the radial front speed of the CME in the corona. We applied the empirical relationship from their Equation (4), which can be formulated as

$$a\ \bigl[\mbox{m}\,\mbox{s}^{-2}\bigr] = -0.0054 \bigl(V_{\mathrm{CME}} - 406\ \bigl[\mbox{km}\,\mbox{s}^{-1}\bigr] \bigr). $$

We assumed that the acceleration ceases either when the ICME attains a speed of 406 km s−1 or at the latest when it is at heliocentric distance 0.76 AU. This differs slightly from Gopalswamy et al. (2001), who considered that the acceleration or deceleration always continued out to 0.76 AU. For CME speeds below 800 km s−1 the travel times derived from the two methods differ by a few hours. We call this the empirical interplanetary propagation model in the following. We estimated the CME speed in the corona in two different ways: firstly, using the speed measurements from LASCO and secondly, using Equation (2) to infer the CME speed from the SXR fluence.

4.1 Results

We compared the predicted arrival time with observations at Wind and ACE for a list of selected ICMEs with well-observed arrival times at the spacecraft. We used 26 ICMEs listed by Gopalswamy et al. (2001), in the online catalog of Richardson and Cane,Footnote 3 and by Möstl et al. (2014).

The predicted arrival times were compared with the observed arrival of both the shock and the driver. The driver is considered to be the ICME. While the shock arrival at the spacecraft was usually well determined by a sudden increase of the temperature, density, and magnetic field intensity, the arrival of the ICME was often ambiguous and may depend on the parameter used to identify it. We employed one or a combination of the following: the start of a magnetic field enhancement, of a depression of proton temperature or the proton plasma beta, of a gradually decreasing high solar wind speed, or of magnetic field rotation.

The 26 CME/ICME pairs displayed in Table 2 are those for which we could i) confirm the onset time identified in the published lists to within one or two hours, ii) clearly associate a SXR burst with the CME. ICMEs where such bursts could not be identified were discarded (e.g., ICMEs on 10 January and 10 February 1997).

Table 2 Comparison of the travel time of CMEs based on Wind and ACE measurements and based on inferred speeds using the empirical interplanetary propagation model. An asterisk (*) in column 1 indicates that the ICME arrival is uncertain. Suffix (f) in column 2 indicates that probably only the flank of the ICME passed over the spacecraft.
Full size table

The first column of Table 2 shows the event number followed by the time of ICME arrivals identified from Wind and ACE measurements. In all cases but event 5, we used the ICME arrivals from Wind. In four cases (6, 20, 21, and 24) only the flank of the ICME passed over the spacecraft, making the determination of the arrival time uncertain. These events are identified with the label “f” in Table 2 after the date. The next three columns summarize the CME data from the LASCO catalog and the predicted arrival time of the ICME at the Earth using the LASCO speed as input to the empirical interplanetary propagation model, and taking as reference the heliocentric distance and the time of the first detection of the CME by LASCO as given in the catalog. The last columns give the start time and start-to-peak fluence of the related SXR bursts, the CME speed inferred from the fluence, and the arrival time of the ICMEs as calculated by the propagation model. The reference is the start time of the burst. Values within parentheses give the uncertainty interval of the expected ICME arrival due to the uncertainty of the coefficients of Equation (2).

A graphical comparison between the predicted and observed arrival times is given in Figure 4. The reference zero of the vertical axis is the time when the ICME, i.e. the driver, reached the Wind spacecraft. The vertical bars indicate the time interval between the arrival of the shock and the driver, that is, the size of the sheath region. The arrival time predicted using the LASCO CME speed is represented by an open square, the prediction using the propagation speed inferred from Equation (2) by a cross.

Figure 4
figure 4

Representation of the predictions of arrival at Earth with reference to the observed ICME arrival (0 on the ordinate). The vertical lines indicate the time interval between the shock arrival and the ICME arrival at the Wind spacecraft.

Full size image

On average, we observe that the arrival times predicted using the SXR parameters are closer to the observed arrival times than those predicted using LASCO measurements. Figure 5 gives another comparison between the two predictions of the ICME arrival time and the observations in panels (b) and (d). The comparison with the observed shock arrival time is given in panels (a) and (c). Predictions using the LASCO observations are shown in the top row, those based on the SXR fluence in the bottom row. The events are grouped into 12 h intervals with respect to the arrival of the ICME shock (a, c) and the driver (b, d). The first bar hence gives the number of events where the absolute value of the delay between the predicted and observed arrival is greater or equal to 0 and less than 12 h, etc. The figure confirms the impression from Figure 4 that ICME travel times estimated from the SXR fluence tend to cluster more closely around the arrival times of both the shock and the driver than the travel times inferred from the LASCO measurements. In 15/26 events the SXR-inferred CME speed leads to an ICME arrival prediction within ± 12 h of the observed time. Only 9/26 cases where coronagraphic observations are used achieve this. The median error of the prediction is 11.5 h when SXR fluence is used and 14.5 h when LASCO measurements are used. Caution is of course necessary because of the small event sample.

Figure 5
figure 5

Comparison of predicted ICME arrival at 1 AU with the observed onset of the shock and ICME at the Wind spacecraft. The predictions are compared with the observed arrival of the shock in histograms (a) and (c), and of the ICME in histograms (b) and (d). Histograms in the top row show the predictions using LASCO measurements, those in the bottom row predictions using the propagation speed inferred from SXR fluence.

Full size image

4.2 Assessment of Failed Predictions

In 8 of 26 events the observed arrival time of the ICME is outside the range of uncertainty of the SXR fluence prediction (events 2, 4, 8, 18, 19, 22, 23, and 26). This set includes the six events in the three highest bins of Figure 5(d) and two other events where the ICME arrival prediction was incorrect by more than 20 h. Five of these events are also poorly predicted when the CME speed from LASCO is used, while in the three others (8, 19, and 26), the speeds from LASCO observations lead to a better estimate of the ICME arrival than the estimation based on the SXR fluence.

In some of the events we obtained an over- or underestimation of the speed that affected the predictions of ICME arrival. In events 2, 4, and 8, we found low speeds of 355, 309, and 314 km s−1, respectively, with a corresponding delay of the ICME arrival of 29, 20, and 29 h, respectively. The LASCO measurements were similarly slow for events 2 and 4, but not for event 8, where the observed speed was 832 km s−1, providing a prediction in advance by only 1 h of the observed ICME arrival.

In the remaining events we can use published observation from the Solar Terrestial Relations Observatory (STEREO) for a more detailed assessment of the failed predictions. For event 18 on 3 April 2010, the SXR prediction is late by 48 h, while LASCO is late by 36 h. The studied CME is moderately fast, with a higher speed observed by LASCO (668 km s−1) than inferred from the SXR fluence (456 km s−1). This event was observed by STEREO B at the limb with a speed of 833 km s−1 (Wood et al., 2011). When this speed is used in the ICME propagation model, an interplanetary travel time of about 51 h and an ICME arrival at 1 AU near 12 UT on 5 April is predicted, which excellently agrees with the observations. This means that the failed ICME prediction based on the speeds from LASCO and from the SXR fluence is most likely due to the erroneous estimates of the Earth-directed CME speed.

The SXR prediction of the ICME arrival for event 19 on 15 February 2011 is early by 25 h, while the prediction from LASCO measurements is late by 10 h. The CME speed inferred from the SXR fluence is higher (1152 km s−1) than from LASCO observations (669 km s−1). An intermediate CME speed of 945 km s−1 was measured by STEREO A, where the event occurred near the limb (Schrijver et al., 2011). The travel time to 1 AU is about 65 h, predicting the arrival of the ICME on 17 February near 19 UT, that is, about 6 h too early. On the other hand, the three-dimensional (3D) modeling by Temmer et al. (2014) and Mishra and Srivastava (2014) gave initial CME speeds of about 1000 – 1100 km s−1, in good agreement with the speed inferred from SXR fluence. Mishra and Srivastava (2014) reported a pronounced deceleration from 1100 km s−1 at 6 R⊙ to 580 km s−1 at 11 R⊙. This suggests that in this case the CME speed inferred from the SXR fluence was an adequate estimate, but the interplanetary transport was complex, probably due to the interaction with previous CMEs (Temmer et al., 2014; Mishra and Srivastava, 2014).

For event 22 on 19 January 2012, the SXR fluence-based prediction is early by 39 h, LASCO by 28 h. The CME is fast, with a lower speed estimate from LASCO observations (1120 km s−1) than from the SXR fluence (1319 km s−1). A CME speed of 1335 km s−1 was inferred from 3D modeling (Möstl et al., 2014), confirming our estimation from the SXR fluence. The failure of our arrival predictions is hence not likely to be due to erroneous estimate of the CME speed in the corona. The detailed analysis of the CME and its interplanetary propagation (Liu et al., 2013) reveals a rapid deceleration of the CME down to 700 – 800 km s−1 within 35 R⊙ from the Sun and a subsequent propagation at roughly constant speed. The simple propagation model applied in the present study predicts such speeds only at the imposed terminal distance of 0.76 AU and therefore underestimates the interplanetary travel time.

The CME in event 23 on 7 March 2012 is very fast, with a higher speed observed by LASCO (2684 km s−1) than inferred from the SXR fluence (1683 km s−1). A similarly high speed as in the LASCO measurement (2585 km s−1) was found in the 3D modeling (Möstl et al., 2014). But this CME has a complex propagation into the interplanetary medium (Rollett et al., 2014). The speed inferred from SXR fluence underestimates the CME speed. On the other hand, a deceleration of this ICME in the interplanetary space was observed by Liu et al. (2013), Davies et al. (2013), and Rollett et al. (2014). The analyses of Liu et al. (2013) and Rollett et al. (2014) suggest that the deceleration was enhanced by the interaction of the fast CME with previous ones. The interplanetary propagation cannot be described by a simple empirical propagation model in this case.

Finally, for event 26 (12 July 2012), the prediction of arrival time of the ICME based on the SXR fluence is early by 28 h and that based on LASCO observations is early by 8 h. The CME speed inferred from SXR fluence is high (1545 km s−1), while the LASCO measurement is 885 km s−1. From the analysis of STEREO observations with a drag model of interplanetary transport, Hess and Zhang (2014) derived an initial speed of 1316 km s−1. This speed would predict a travel time of about 43 h and an ICME arrival near 12 UT on 14 July, which is well in advance of the observed arrival. The issue is hence rather one of the interplanetary propagation of the CME than of the speed determination from the SXR fluence, which is closer to the result of the STEREO observations than the speed from LASCO.

5 Summary and Discussion

5.1 Summary of Observational Results

The re-assessment we conducted of the correlation between the speed of a CME near the limb and the parameters of the associated SXR burst, provided such a burst can be identified, is summarized as follows:

  1. i)

    We confirm the frequently found correlation between CME speed and SXR peak flux.

  2. ii)

    The correlation of the CME speed is slightly higher with SXR fluence (r=0.58±0.09) than with SXR flux (r=0.48±0.12).

  3. iii)

    The SXR-inferred CME speed performed better than the speed measured by LASCO as an input to the arrival time prediction of ICMEs at Earth using a simple empirical interplanetary propagation model based on Gopalswamy et al. (2001).

5.2 Comparison with Earlier Work

Detailed comparisons of the kinematical evolution of CMEs in the low corona revealed a close relationship with energy release to the thermal plasma observed in SXR (Zhang et al., 2001, 2004). The statistical studies of Maričić et al. (2007) and Bein et al. (2012) demonstrated that the CME acceleration is usually pronounced between the start and peak of the SXR burst, with a maximum near the time of the steepest rise of the time profile. After the SXR peak, the CME propagates at roughly constant speed in the corona. This relationship suggests a correlation between the terminal speed of the CME and parameters of the SXR burst, although exceptions from the general trend do exist (Maričić et al., 2007) and are expected to blur the correlation.

The correlation coefficient between the logarithms of CME speed and of SXR peak flux we derived, r=0.48±0.12, is similar to values reported by others: r=0.47 (Moon et al., 2002), r=0.35 (Vršnak, Sudar, and Ruždjak, 2005), r=0.50 (Yashiro and Gopalswamy, 2009), and r=0.32±0.13 (Bein et al., 2012). A distinctly higher correlation, r=0.93, was found by Moon et al. (2003) in a carefully selected small sample of eight flare-CME events, where for four of them that were located on the solar disk, the CME speed was corrected for projection effects.

Moon et al. (2002), Yashiro and Gopalswamy (2009), and the present study were restricted to limb CMEs, where projection effects on the CME speed measurements are expected to be minimized. While the correlation coefficients in these limb-event studies are higher, the increase is not significant when compared with the statistical uncertainties derived in the present study and Bein et al. (2012). We note, however, that the coefficient of the logarithm of SXR peak flux F in the linear relationship logV CME=alogF+b is higher in our study of limb events (a=0.20±0.08) than in the unrestricted sample of Bein et al. (2012) (a=0.08±0.03).

The correlation is only slightly increased when the SXR fluence is used (r=0.58±0.09) instead of the SXR peak flux. Yashiro and Gopalswamy (2009) found r=0.56 for a larger sample, but without error estimate. The use of fluence does not significantly improve the correlation between SXRs and CME speed. Burkepile et al. (2004) considered the correlation of the kinetic energy of the CME, instead of the speed, with SXR peak flux of limb events. They reported a high correlation (r=0.74 for 24 events), well above the r=0.48 of Yashiro and Gopalswamy (2009). The absence of an error estimate precludes a comparison of the two values, but the scatter plot in Figure 6 of Burkepile et al. (2004) suggests that the high correlation coefficient is favored by the two extreme events of their sample and that a lower value might be obtained from a larger sample.

We conclude that the focus on the limb events did provide an improved determination of the relationship between the logarithms of CME speed and of SXR fluence and peak flux. But a considerable scatter remains, probably due to physical differences between individual events. In their analysis of a 2D model of a flux rope eruption, Reeves and Moats (2010) found a power-law relationship between the peak acceleration and the peak SXR flux for a given reconnection rate, measured by the Alfvén Mach number of the plasma inflow into the current sheet. The authors showed that for a given CME peak acceleration the peak GOES flux is expected to increase with decreasing reconnection rate and concluded that different reconnection rates may contribute to explaining the broad scatter in the observed relationships between CME kinematics and SXR emission.

5.3 SXR Observations and the Prediction of ICME Arrival at Earth

We tested the performance of the SXR fluence as a proxy of the CME speed by applying it to the prediction of the ICME arrival near Earth, using an empirical interplanetary acceleration model based on Gopalswamy et al. (2001). For a set of 26 well-defined CME–ICME pairs with associated SXR bursts, we found that the SXR-inferred speed tended to perform better than the plane-of-the sky expansion speed measured by a coronagraph on the Earth-Sun line. This suggests that SXR observations can serve as an input to ICME prediction schemes, provided the existence of a CME is ascertained by coronagraphic observations. Problems arise with particularly slow and particularly fast CMEs, where our empirical relationship seems to be a poor predictor. This is probably at least partly due to an inadequate treatment of the bias of the CME–SXR relationship, which in turn is a result of the incomplete detection of slow CMEs and faint SXR bursts. Comparisons of selected events with CME speed from STEREO measurements and 3D modeling confirm the performance of the SXR fluence as a proxy of CME speed.

Recent work using STEREO emphasizes the importance of the interplanetary dynamics of the CME (Kilpua et al., 2012; Colaninno, Vourlidas, and Wu, 2013; Möstl et al., 2014) in arrival time predictions, which cannot be captured by a simple empirical model. But when sophisticated tools such as heliospheric imaging of the Sun–Earth system from a viewpoint away from the Sun–Earth line are not available, the SXR emission can provide valuable constraints for the ICME arrival prediction.