HOW COMMON ARE HOT MAGNETIC FLUX ROPES IN THE LOW SOLAR CORONA? A STATISTICAL STUDY OF EUV OBSERVATIONS

Coronal mass ejections (CMEs) are large-scale expulsions of coronal plasma and the magnetic field entrained therein into the heliosphere. Several models of CME initiation have been developed (e.g., Chen 2011, and references therein). All models agree that CMEs may result from a catastrophic loss of mechanical equilibrium of plasma confined by the coronal magnetic field. However, there is no consensus about the pre-eruptive magnetic configuration; the CME models can be divided into two groups depending on the state of the coronal magnetic field prior to the eruption. The models of the first group assume that a magnetic flux rope (i.e., a coherent magnetic structure of magnetic field lines that collectively wind about a central, axial field line) exists prior to the eruption (e.g., Forbes & Isenberg 1991; Forbes & Priest 1995; Gibson & Low 1998; Titov & Démoulin 1999; Roussev et al. 2003; Amari et al. 2004, 2005; Fan & Gibson 2004, 2007; Archontis & Török 2008; Fan 2010; Archontis & Hood 2012). The models of the second group rely on the existence of sheared magnetic arcades (i.e., an arrangement of loops with planes deviating significantly from the local normal to the polarity inversion line) that become unstable and erupt once some critical state is reached in the corona (e.g., Linker & Mikić 1995; Amari et al. 1999, 2000; Antiochos et al. 1999; Manchester 2003; MacNeice et al. 2004; Roussev et al. 2004; Jacobs et al. 2006; van der Holst et al. 2007; Archontis & Hood 2008; Lynch et al. 2008; Karpen et al. 2012).

While the question on which pre-eruptive magnetic configuration leads to CMEs is open, all models and simulations agree that the erupting structure is a flux rope. There is no physical mechanism that can produce a large-scale eruption from the corona without ejecting a flux rope, except under very specific magnetic configurations (Jacobs et al. 2009). In the first group of models the flux rope is an essential ingredient of the pre-eruptive configuration while in the second group of models the flux rope is formed once the CME is underway, i.e., on-the-fly.

Indirect evidence for the existence of pre-eruptive flux ropes in active regions (ARs) located close to disk center comes from nonlinear force-free field (NLFFF) extrapolations that use data from photospheric vector magnetograms as boundary condition (e.g., Yan et al. 2001; Bleybel et al. 2002; Canou et al. 2009; Guo et al. 2010, 2012; Nindos et al. 2012; Sun et al. 2012; Jiang & Feng 2013; Cheng et al. 2014b). The temporal resolution of NLFFF extrapolations is determined by the cadence of the available vector magnetograms which, is currently 12 minutes, at best. Therefore, the extrapolation products are unable to capture the rapidly changing magnetic fields that erupt. Furthermore, there is a non-vanishing Lorentz force that makes the magnetic field non-force-free, once the eruption gets underway.

Another piece of indirect evidence for pre-existing flux ropes are soft X-ray (SXR) and EUV observations of S- or reverse S-shaped (sigmoidal) regions. Sigmoidal ARs have a high likelihood of producing an eruption (e.g., Canfield et al. 1999). If a sigmoidal source of SXR or EUV emission, which follows the magnetic field lines, crosses the polarity inversion line in the inverse direction of what a potential arcade would do then it is considered as disk signature of a flux rope viewed from above. This, however, is conclusive only if the sigmoidal source survives an eruption (e.g., Gibson & Fan 2006; Green & Kliem 2009; Green et al. 2011), because only then S-shaped field lines in a sheared arcade (Antiochos et al. 1994) can be excluded.

Yohkoh (Ogawara et al. 1991) Soft X-ray Telescope (SXT; Tsuneta et al. 1991) data (Ohyama & Shibata 1998, 2008; Nitta & Akiyama 1999; Kim et al. 2004, 2005a, 2005b) and Hinode (Kosugi et al. 2007) X-Ray Telescope (XRT; Golub et al. 2007) data (Savage et al. 2010; Landi et al. 2013; Lee et al. 2015) have revealed the existence of hot ejecta during CMEs. The ejecta formed coherent hot structures but in most of these publications were not identified as magnetic flux ropes.

The availability of high sensitivity data recorded with unprecedented spatial and temporal resolution in hot, flare-like EUV wavelengths by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) onboard the Solar Dynamics Observatory (SDO; Pesnell et al. 2012) confirmed the existence of coherent structures identified as hot flux ropes (Cheng et al. 2011, 2012, 2013, 2014a, 2014b, 2014c; Reeves & Golub 2011; Zhang et al. 2012; Li & Zhang 2013; Patsourakos et al. 2013; Joshi et al. 2014; Song et al. 2014). The heating of the flux rope may be a consequence of magnetic reconnection. The standard solar eruption model predicts that the reconnected magnetic flux under the CME is channeled into both the flare loops and the erupting flux rope.

Several case studies of hot flux ropes associated with impulsive CMEs have been published. The main focus of these publications was the question of whether the flux rope forms before or during the eruption. Most studies were in favor of pre-existing flux ropes (Zhang et al. 2012; Cheng et al. 2013, 2014a, 2014b, 2014c; Li & Zhang 2013; Patsourakos et al. 2013) although cases of hot flux ropes formed on-the-fly during the eruption (Cheng et al. 2011; Song et al. 2014) have been reported as well as cases of hot flux ropes involved in confined eruptions (Cheng et al. 2014b; Patsourakos et al. 2013; Joshi et al. 2014). All these events originated in ARs close to the solar limb.

These works were exclusively single-event studies, leaving an unclear picture on the role/importance of hot flux ropes in CMEs. To remedy this situation, we undertake the present study to search for hot flux rope events using an extensive dataset of large flares that occurred away from disk center. To keep this paper focused, we do not address the question on whether the flux ropes formed before or during the eruptions. Instead, we address the more fundamental question of how common hot flux ropes are in the low corona. Our aim is to place past and future case studies in a broader context. Our paper is organized as follows. The observations and data analysis are presented in Section 2. Our classification scheme is introduced in Section 3. In Section 4 we discuss the events with hot flux ropes and in Section 5 the events without hot flux rope morphology. In Section 6 we compare the AIA data with data obtained from the Hinode XRT. We conclude in Section 7.

We have compiled a catalog of M-class and X-class flares that occurred from early 2010 November until the end of 2014 March at longitudes equal to or larger than 50° from the central meridian. We selected events away from the disk center because the identification of flux ropes becomes easier due to projection effects. We set an M-class threshold because the higher energy release is more likely to produce hot flux ropes. We do not preclude the existence of flux ropes in other flare types. Our catalog consists of 141 events. We analyzed each event using EUV images of the low corona from the SDO/AIA. The field of view, pixel size, and cadence of the AIA images are 1.3 R_⊙, 06, and 12 s, respectively. To reduce data volume, we used AIA images with a cadence of one minute. Inspection of full cadence movies of selected events showed that the one minute cadence was sufficient to resolve the various dynamics.

We used AIA images in narrowband channels centered at 131, 171, and 304 Å. In the remainder of the paper we will refer to any given channel by simply supplying the wavelength of peak response: for example, 131 Å channel will be referred to as 131. The 131 emission arises from two dominant ions formed at different temperatures: Fe viii at 4 × 10⁵ K and Fe xxi at 10⁷ K (Lemen et al. 2012). The signal in 131 is dominated by multi-million Kelvin plasma only during flares. The dominant ions in the 171 and 304 channels are Fe ix and He ii, respectively. Their peak formation temperatures are 6 × 10⁵ and 5 × 10⁴ K, respectively (Lemen et al. 2012).

In addition to the AIA data we used white-light coronagraph data from the Large Angle Spectroscopic Coronagraph (LASCO; Brueckner et al. 1995) C2 coronagraph on board the Solar and Heliospheric Observatory (Domingo et al. 1995) mission. The LASCO C2 field of view covers the range of 2.2–6 R_⊙ with a pixel size of 12'', and nominal cadence of 12 minutes during the period of our observations. For the overall temporal evolution of the flares, we used GOES X-ray total flux measurements.

Our first analysis step was to search for signatures of hot flux ropes in 131 movies. The observed morphology of flux ropes depends on its inherent twist and viewing angle but their identification is often challenging because: (1) the hot flux rope emission at 131 Å may be weak, (2) more often than not, flux ropes are weakly twisted, and (3) other structures (e.g., loops), and saturation from the flare may contaminate the line of sight (LOS). Based on our experience, we settled on the following set of criteria for flux rope identification in the 131 images.

• 1.  
  Flux ropes seen edge-on. They correspond to round blobs or ring-like structures. They appear to overlay structures with a variety of morphologies: ${\rm{\Lambda }}$-shaped loop-like structures, cusp-like structures or thin elongated emissions presumably associated with current sheets. Examples of flux ropes seen edge-on appear in Figure 1.
• 2.  
  Flux ropes seen face-on. The clearest cases show tangled threads of emission that appear to wind around an axis. Structures that show a twisted/writhed shape could also be interpreted as flux ropes seen face-on. Examples of flux ropes seen face-on appear in Figure 2.
• 3.  
  Flux ropes viewed from intermediate angles. They show intermediate morphologies between the morphologies of flux ropes seen edge-on and face-on. Examples are presented in Figure 3.
• 4.  
  The candidate flux rope should appear in at least two successive 131 Å images.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Because we are searching for hot flux ropes, the candidate structures in the 131 Å data must be hot. An obvious approach would be the calculation of the differential emission measure of the structures and the subsequent computation of emission measure maps in different temperature intervals. We decided against such an approach at this time due to the large size of our database and the added complexity of the DEM calculation procedures. Instead, we adopt a simple, but straightforward approach, to check for the simultaneous appearance of the candidate flux ropes in 171 and 304 movies. If the candidates do not appear in these colder channels, then the 131 emission must arise from Fe xxi and hence from 10 MK plasma. We note that this was the case for all candidate hot flux ropes that we identified in 131 data.

We tried especially hard to avoid over-interpretation of the data. Several features have the potential to be misinterpreted as flux ropes. These include cusps, ascending post-CME loops (especially those seen edge-on) and small-scale emission depletions that are not surrounded by clear twisted/writhed structures or ring-like structures, but result from the projection of loops of different shapes and orientations on the plane of the sky.

Finally we used movies of LASCO C2 data to determine whether the events in our database were associated with CMEs. The association was checked for all events of our database, irrespective of being hot flux ropes or not. The CMEs were also classified as flux rope CMEs (FR-CMEs) or not using the criteria defined by Vourlidas et al. (2013).

Our database consists of 141 events shown in Table 1. The first six columns give (from left to right) the event number, the date of the event, the flare start and peak times, the flare location in heliographic coordinates, the NOAA number of the host AR, and the GOES classification of the flare. The seventh column contains the information on the associated CME, if there was one. The eighth column provides our classification of the events into five subcategories.

Overall, 45 flares were associated with hot flux ropes and 96 flares were not. This simple division, however, does not provide much insight into the problem. We refined our classification to reflect the wealth of observed morphologies and eruption paths present in the data. According to this refined scheme, the events were classified into the following groups (Table 1, column 8).

• 1.  
  Confined flare events with hot flux ropes (CFR in Table 1). No evidence of eruption but detection of a hot flux rope in the AIA images.
• 2.  
  Eruptions with hot flux ropes (EFR in Table 1). Evidence for the eruptive nature of the events was provided by post-flare/post-CME loops, cusps, or overall opening of the AR's configuration.
• 3.  
  Prominence eruption events without hot flux ropes (PE in Table 1).
• 4.  
  Eruptions without hot flux ropes or prominences (PFL in Table 1).
• 5.  
  Confined flare events without hot flux ropes (CFL in Table 1). There was no evidence of an eruption or a hot flux rope.

4.1. Morphology of Hot Flux Ropes

4.2. Confined Events with Hot Flux Ropes

4.3. Eruptive Events with Hot Flux Ropes

There are 19 prominence eruption events without signatures of hot flux ropes in our database (PEs in Table 1). A typical example (event 33 of Table 1) is presented in Figure 8. In all PE events the erupting prominence material was detected in all three AIA passbands. At 304 Å we detect cool chromospheric plasma while at 171 and 131 passbands we detect warmer plasmas that may come either from the prominence-corona transition region (the warm plasma between the building blocks of the prominence and the adjacent hot corona, e.g., Luna et al. 2012) or from the mild heating to temperatures in excess of 2 × 10⁵ K that erupting prominences sometimes experience (e.g., Landi et al. 2010).

Zoom In Zoom Out Reset image size

LASCO observations were available for 18 of the 19 PE events (there was a LASCO data gap for event 57). An inspection of the LASCO movies showed that 17 out of the 18 PE events were associated with CMEs. This is consistent with the well-known association of prominence/filament eruptions to CMEs (i.e., Gopalswamy et al. 2003 reported that 72% of the filament eruptions they studied were associated to CMEs). We note that 5 of the 17 CMEs were FR-CMEs.

We want to make clear that the lack of hot flux rope signatures for these 19 PE events does not preclude in any way the existence of a flux rope. Five of the events were associated with a FR-CME after all. We merely argue there was no trace of hot flux ropes, according to our criteria in Section 2.

The database contains 24 eruptive events without the presence of a hot flux rope or a prominence (PFLs in Table 1). Figure 9 presents an example of a PFL event (event 72) associated with an M1.0-class flare on 2012 August 17 in AR11548. The top row shows the evolution of the flare in 131 Å; in panel (a) we present a pre-flare image while the image of panel (b) corresponds to one minute before the flare peak. In panel (b) a cusp-shaped morphology appears as well as bright loops underneath the cusp. These features are in agreement with the standard model of eruptive events. In panel (c), taken about 7 minutes after the flare peak, the cusp is still present although the reverse Y morphology of panel (b) is not so prominent, Just above the tip of the cusp, a faint hollow elliptical feature has been marked by an arrow. That feature could be misinterpreted as hot flux rope. However, we could not follow it with certainty in subsequent images and its appearance may not be associated with a unique physical entity; instead, its appearance may come from the alignment of the emission from the tip of the cusp with faint background emission along the LOS. Panel (d) corresponds to the decay phase of the flare; the cusp morphology is still present, however its height has decreased. The cusp does not show in the 171 Å data (see middle row of Figure 9). It is possible that its emission was either obscured by the bright background emission or that it did not have the right temperature to show in 171 data. However, the cusp appears at 304 Å (bottom row of Figure 9) several minutes after the flare maximum (panel (i)) and it is probably Si xi 303.4 Å line emission from 1.8 MK plasma (e.g., Figure 4 in Stenborg et al. 2008).

Zoom In Zoom Out Reset image size

Inspection of LASCO movies shows that 20 out of the 24 PFL events were associated with CMEs, thus confirming the eruptive nature of those events.

We classified as PFLs all eruptive events that did not show clear prominence eruptions and for which we were not confident about the presence of hot flux ropes (see the discussion in Section 2 about the care we took to avoid over-interpetation of the data). But 10 out of the 20 CMEs associated with PFL events were FR-CMEs. Therefore, some fraction (at least) of the PFL events must had flux rope configuration, but it did not conform to our identification criteria.

The database contains 53 events of confined flares with no signatures of hot flux ropes (CFLs in Table 1). The confined nature of the flares was derived from the study of the AIA data (i.e., lack of dimmings or EUV waves) and LASCO C2 observations. LASCO data were available for 50 of the events (due to a data gap, there were no LASCO observations for events 58, 59, and 60). None of them showed evidence for CMEs in agreement with the AIA data.

In Figure 10 we show a characteristic example of a CFL event (event 50) that occurred on 2012 February 6 in AR11410. We show only the 131 passband, because the evolution of the event was similar in the 171 and 304 passbands. The event was a gradual M1.0-class flare. Panel (a) shows the AR configuration at the time of the flare start, where different sets of sheared loops appear. In panel (b), at the rise phase of the flare, some of the loops appear brighter and their configuration has been simplified (at least partly). However, a new set of tangled loops has appeared southwest of the initial configuration. The image of panel (c) was taken one minute after the flare maximum while the image of panel (d) corresponds to the decay phase of the flare. Figure 10 indicates that the flare was confined because no trace of rising arcades, cusps or major opening up of the of AR's configuration were detected.

Zoom In Zoom Out Reset image size

The existence or absence of hot flux ropes in 131 Å data was checked against data obtained with the XRT on the Hinode mission. Forty events of our catalog were also observed by the XRT. These flares were observed in various combinations of thin, medium-thickness, and thick XRT filters with cadence ranging from about 30 s to about 2 minutes. The field of view was either 384'' × 384'' (pixel size of about 1''), 512'' × 512'' (pixel size of about 2''), or 1536'' × 1024'' (pixel size of about 4''). The thin filters have peak temperature responses from about 8 MK to about 10 MK while the medium-thickness and thick filters have peak temperature responses at about 13 MK. However, all XRT filters are able to detect a wide range of temperatures (the thin filters above 2 MK) because of their broad responses (see Narukage et al. 2011, for details on the XRT filter response functions). Therefore, checking the broadband thin-filter XRT data may be roughly equivalent to checking data from narrowband AIA channels centered at 211, 335, and 94 Å whose dominant ions are formed at 2.0, 2.5, and 6.3 MK, respectively (Lemen et al. 2012).

In Table 2 we present the statistics of the events observed by both AIA and XRT. 14 of the 40 flares (35%) contained hot flux ropes in the AIA data (4 CFRs and 10 EFRs). Therefore, the sample of events observed by both instruments represents a fairly typical subset of the whole catalog (32% of the flares of the whole AIA database contained hot flux rope morphologies; see Table 3 and Section 7). We searched for signatures of flux ropes in the XRT data using the same morphological criteria that we used for the detection of flux ropes in 131 Å AIA data.

We found that 43% (17/40) of the XRT flares showed flux rope morphologies. All of the XRT flux ropes were observed with the thin filters, while two events were also observed with the medium-thickness Al filter and one event was also observed with the thick Be and thick Al filters. 11 out of the 14 events with 131 Å hot flux ropes (∼79%) showed flux rope morphologies in XRT data as well. A characteristic example (event 1 of Table 1) is presented in Figure 11 (panels (a) and (b)); the appearance of the flux rope is similar in both images. The three EFRs that were not detected by the XRT were rather weak events whose flux rope topology was hard to discern probably due to saturation from the flare.

Zoom In Zoom Out Reset image size

Table 2 indicates that XRT detected flux rope morphologies in six events that showed no evidence for hot flux ropes in the AIA data (one PE, three PFLs, and 2 CFLs). In all six events the flux ropes were detected in thin-filter images only. A typical example appears in panels c and d of Figure 11 that show 131 Å and XRT observations, respectively, of event 53. The AIA image shows a PFL event (eruption without hot flux rope or prominence) whereas the XRT image shows a flux-rope-candidate feature that is indicated by an arrow. Its morphology bears some resemblance to the hot flux rope of event 89 (Figure 3(f)). The flux rope of event 53 might be too cool to show in 131 Å and too hot to show in 171 and 304 Å, but it may have the right temperature to appear in the broadband Be thin XRT image; its temperature may be higher than 2 MK and below 10 MK. Similar arguments apply to the other five events that showed flux ropes in XRT but not in AIA.

This is the first large-scale survey of EUV flare observations to assess whether hot (10 MK) flux ropes are common, irrespective of their formation time relative to the CME eruption. We considered only M- and X-class flare events as hot flux ropes are more likely to exist in association to large flares. The flux ropes were identified in 131 Å data using certain morphological criteria (Section 2). They were identified as hot flux ropes if they were visible only in 131 Å data and not in the 171 and 304 Å data. A summary of our results is presented in Table 3 and in the pie diagram of Figure 12. The main conclusions of our work are as follows.

Zoom In Zoom Out Reset image size

(1) 32% of the flares in our database contain clear hot flux rope morphologies (45/141). In 34 cases the flux rope erupts (EFR events) and in 11 cases it does not (CFR events). There were 70 flares associated with CMEs so a hot flux rope configuration was involved in 49% of the eruptive events.

(2) The number of confined events with hot flux ropes is about three times smaller than the number of eruptive hot flux rope events whereas half of the flares of our catalog were confined. It is likely that confined hot flux ropes reach lower altitudes than eruptive ones thus hindering their identification.

(3) Only a small number of hot flux ropes is seen face-on (i.e., with their axis perpendicular to the LOS). Most of them are viewed either edge-on (i.e., with their axis parallel to the LOS) or at intermediate angles. The smaller number of flux ropes seen face-on may result from two factors: (1) the natural tendency of AR neutral lines to lie parallel to the LOS and (2) the weaker signal due to the small LOS integration path for face-on structures compared to edge-on ones.

(4) The database contains 19 prominence eruptions without signatures of hot flux rope and 7 cases of eruptive hot flux ropes accompanied with prominence material. In the latter, the hot ejected plasma appears either intermingled with the cooler ejected plasma or spatially separated from it.

(5) Thirty-three of the 34 events with eruptive hot flux ropes were associated with CMEs and 27 of them (about 80%) were clear FR-CMEs. The remaining 6 might also be FR-CMEs but the flux rope topology was hard to discern for several reasons: they may propagate at large angles from the plane of the sky or through areas disturbed by previous events or they may be too compact to discern their flux rope morphology (Vourlidas et al. 2013). We conclude that a hot flux rope morphology in the EUV is a very good predictor for a FR-CME.

Based on Yohkoh SXT and LASCO data, Kim et al. (2005b) found higher percentages of SXR ejecta associated with CMEs. However, their dataset contained a smaller percentage of confined events than ours.

(6) Table 3 shows that 60% of the observed CMEs in our sample have flux rope structures while Vourlidas et al. (2013) found that at least 40% of the LASCO CMEs between 1997 and 2010 had flux rope structures. Our higher percentage could be due to a combination of reasons. First, most of our events occurred close to the limb which makes the identification of a flux rope morphology easier. Second, our database contains large events that presumably are associated with stronger than average reconnection thus facilitating the formation of hot flux ropes. Finally, lower percentage of FR-CMEs is not surprising given the fact that the Vourlidas et al. (2013) statistics include both quiet Sun and AR eruptions that may or may not be associated with flares.

(7) Forty of the events were also observed by XRT on Hinode. 35% of these flares contained hot flux ropes in AIA while 43% of them showed flux ropes in XRT data. Therefore the XRT data show that flux ropes are a rather common ingredient in events associated with M- and X-class flares. Flux ropes were detected in half of the 40 flares irrespective of the instrument used for their detection.

We found that 49% of our events have hot flux ropes but practically all CME models expect the erupting structure to be a flux rope. This raises the question of the magnetic configuration in the remaining 51% of the database (36 cases). Is there a magnetic flux rope configuration or not? We believe that there is a straightforward explanation. The flux rope exists but it is simply too cool to be detected in 131 Å and possibly too hot to show in 171, 304 Å, or even, 193 Å. There is quite a substantial amount of evidence to support our assertion: (i) the higher percentage of FR-CMEs (60%) suggests that 20% of the flux ropes, in our study, were not visible in 131 Å. (ii) the strong association between hot flux ropes and FR-CMEs (80%) reflects the expected association between the length of the erupting neutral line, the amount of free magnetic energy available for the eruption and subsequently the percentage of magnetic energy available to heat the plasma. Since the maximum temperature attained during impulsive heating events is proportional to the volumetric heating (e.g., Cargill 1994; Patsourakos & Klimchuk 2006) it is anticipated that longer (shorter) flux ropes will reach lower (higher) temperatures, for a given magnetic field thus magnetic free energy. We, therefore expect a spectrum of erupting flux ropes with temperatures correlated to the available magnetic energy. As further support, we submit (i) the detection of flux ropes with the XRT in 6 events that did not show such signatures in 131 Å data (see Section 6) and (ii) the detection of a flux rope in 284 Å (∼1.8 MK) but not in 195 Å reported by Vourlidas et al. (2012) for an AR eruption during the early rise of Cycle 24. Finally, the appearance of hot flux ropes could be compromised by projection effects, loops seen along the LOS and saturated emission. This could be especially problematic for face-on cases.

Based on the above discussion, we conclude that our estimate of 32% for the rate of occurrence of hot flux ropes in the flares above M class, and of 49% occurrence rate of hot flux ropes in the eruptive events, constitute lower limits.

An obvious extension of this work is a survey of our database to assess the timing of the formation of the eruptive hot flux ropes with respect to the initiation of the associated CMEs.

We thank the referee for his/her constructive comments. This research has been partly co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF)—Research Funding Program: "Thales. Investing in knowledge society through the European Social Fund." S.P. acknowledges support from an FP7 Marie Curie Grant (FP7-PEOPLE-2010-RG/268288). A.V. was also supported by internal JHU/APL funds.