In this study, we investigated the relationships between the physical parameters of filament eruptions (three-dimensional velocity, filament length, and direction of eruption) and their CME associations using 28 events observed by SDDI at Hida Observatory. We found that the filament eruptions are well separated into two groups of events, one with and the other without CMEs, according to the product of the normalised maximum ascending velocity (\(V_{\text{r}\_\max} / V_{0}\)) and the normalised filament length (\(L / L_{0}\)) to the power of 0.96, and that among the filament eruptions with \(\left( \frac{V_{\text{r}\_\max}}{V_{0}}\right) \times \left( \frac{L}{L_{0}}\right) ^{0.96} > 0.80\), 93% are associated with CMEs, and 100% of filament eruptions with the product \(< 0.80\) are not associated with CMEs. The apparent velocity and the length of filaments measured in H\(\alpha\) observation could also provide a good measure for predicting the occurrence of CMEs, though the accuracy of the prediction using the apparent velocity is worse than that using the radial velocity. Our results suggest that the three-dimensional velocity, or more specifically the radial velocity derived from it, and the length of the erupting filament are the notable parameters for improving the predictability of CME association. And thus, we suggests the importance of observations of the three-dimensional velocity of filament eruptions for the prediction of CMEs. It should be noted, however, that improvement of statistics, i.e., studies with a larger number of examples, are strongly required to confirm these results.
Here, we propose a possible physical interpretation for the solid line in the top left panel of Fig. 1. This line, which is represented by Eq. (1), successfully separates events into those with and without CMEs. We assume that (1) the cross section of filaments, A, follows the relationship of
$$\left( \frac{A}{A_{0}}\right) = \left( \frac{L}{L_{0}}\right) ,$$
(6)
where \(A_{0}\) is the typical cross section of filaments (100 \(\text {Mm}^{2}\)), and that (2) the average hydrogen density is common among filaments, i.e., 10\(^{11}\) \(\text {cm}^{-3}\), which is a typical value for quiescent prominences (Heinzel et al. 2008). Then, if we regard Eq. (1) as
$$\left( \frac{V_{\text{r}\_\max}}{V_{0}}\right) \times \left( \frac{L}{L_{0}}\right) \sim 0.80,$$
(7)
or \(V_{\text{r}\_\max} \times L \sim 8.0 \times 10^{6}\ \text {km}^{2}\ \text {s}^{-1}\), then its square represents the kinetic energy of an erupting filament, i.e., \(\frac{1}{2}\times\) proton mass \(\times\) density \(\times\) volume \(\times\) \({V_{\text{r}\_\max}}^{2}\) = 5.4 \(\times\) 10\(^{28}\) erg. This relationship could be regarded as the kinetic-energy threshold above which filament eruptions are associated with CMEs. Note that if the length of a filament is 100 Mm, the deduced mass gets 1.7 \(\times\) 10\(^{15}\) g. (Gilbert et al. 2006) reported the masses of 18 prominences, which ranged from (\(1.08 \pm 0.52\))\(\times 10^{14}\) to (2.09 ± 0.80)\(\times 10^{15}\) g. Our assumed “typical” mass is consistent with the reported values.
As mentioned in “Introduction” section, the CME association rates of filament eruptions reported to date range from \(\sim\) 10 to \(\sim\) 90%. Here, we provide a possible interpretation of this wide range based on our results. We showed that the product of the normalised radial velocity of eruptions and the normalised filament length makes a key contribution to the CME association. The high association rates of 80–90% in the past studies might be attributable to the criteria they used to select the events, under which the prominences have a predominantly large radial velocity and a large size. Gilbert et al. (2000) reported that 94% of eruptive prominences (for the definition, see “Introduction” section) were associated with CMEs. Gopalswamy et al. (2003) also reported that 83% of radial prominence eruptions were associated with CMEs. Their selected prominence eruptions should have had a predominant radial velocity. In addition, Gopalswamy et al. (2003) and Hori and Culhane (2002) detected prominences with the NoRH that has its spatial resolution of 10 arcsec (Nakajima et al. 1994), which is worse than the spatial sampling of the SDDI (1.23 arcsec pixel\(^{-1}\)). Therefore, the selected prominences in these studies seem to have a larger size (e.g., larger than 70 Mm, because 75% of the filaments smaller than 70 Mm were not associated with CMEs according to our result).
The association rate could also depend on whether studies include disk events (filament disappearances) in the records. In contrast to the high association rates (80 to 90%) reported in the studies taking into account only limb events (prominence disappearances) (Gilbert et al. 2000; Gopalswamy et al. 2003; Hori and Culhane 2002), some studies (Pojoga and Huang 2003; Jing et al. 2004; Seki et al. 2019a) in which both disk and limb events were considered manifested the association rate of approximately 40–50%. Pojoga and Huang (2003) reported that 39% of filament and prominence eruptions observed in H\(\alpha\) were associated with CMEs. Jing et al. (2004) reported that 56% of filament eruptions were associated with CMEs by automatically detecting filament disappearances in H\(\alpha\). In our study, considering only credible events, we found that 50% of filament eruptions in H\(\alpha\) were associated with CMEs.
Additionally, the observational wavelengths at which filaments or prominences are detected could also affect the association rate. In H\(\alpha\), as mentioned in the previous paragraph, approximately 40 to 50% of disappearance events were associated with CMEs. By contrast, McCauley et al. (2015) used full-disk solar images in the 171, 193, and 304 Å AIA passbands and reported an association rate of 72%.
The low association rate (17%, Al-Omari et al. 2010) might be attributable to the fact that the authors include ejecta such as surges in addition to filament eruptions in their sample. Among their 7332 events, they introduced 15 “filament types”, including coronal rain, sprays, and surges. In our study, we did not refer to these ejecta as filaments, and we excluded them from our list. Thus, the definition of filaments in that study was different from ours. Moreover, most of their events (\(\sim\) 80%) were smaller than \(\sim\) 70 Mm [see Figure 8 in Al-Omari et al. (2010)]. According to our result (see Fig. 1 or 3), 75% of the eruptions of filaments with lengths smaller than 70 Mm were not associated with CMEs. Assuming that this relation holds for coronal rain, surges, and sprays, \(\sim\) 60% (80% \(\times\) 75%) of all their selected events may not be associated with CMEs in our criteria. Therefore, the low association rate in their study can also be attributed to the event selection criteria; i.e., a significant portion of their events is thought to be located below the threshold line proposed in this paper.
The results of this study can be used to develop a methodology to predict the occurrence of CMEs by measuring the three-dimensional velocities of filament eruptions. Moreover, our previous works suggest that the occurrence of filament eruptions can be predicted prior to their initiation by \(1.3 \pm 0.47\) hour for intermediate filaments, on the basis of the mean and standard deviation of the LOS velocity distribution in filaments (Seki et al. 2017, 2019b). Hence, by using SDDI data and measuring the LOS velocity of filaments, we could predict the occurrence of filament eruptions \(\sim\) 1 h in advance and also, during eruptions, estimate the possibility of CME association before coronagraph observations.