S Y Huang

K Jiang

Z G Yuan

M Zhou

F Sahraoui

H S Fu

X H Deng

Yu V Khotyaintsev

X D Yu

L H He

D Deng

C J Pollock

R B Torbert

J L Burch

Observations of Flux Ropes With Strong Energy Dissipation in the Magnetotail

An ion-scale flux rope (FR), embedded in a high-speed electron flow (possibly an electron vortex), is investigated in the magnetotail using observations from the Magnetospheric Multiscale (MMS) spacecraft. Intense electric field and current and abundant waves are observed in the exterior and interior regions of the FR. Comparable parallel and perpendicular currents in the interior region imply that the FR has a non-force-free configuration. Electron demagnetization occurs in some subregions of the FR. It is surprising that strong dissipation (J × E' up to 2,000 pW/m 3 ) occurs in the center of the FR without signatures of secondary reconnection or coalescence of two FRs, implying that FR may provide another important channel for energy dissipation in space plasmas. These features indicate that the observed FR is still highly dynamical, and hosts multiscale coupling processes, even though the FR has a very large scale and is far away from the reconnection site.

Plain Language Summary Flux ropes, 3-D helical magnetic structures, in which magnetic field lines twist with each other, play an important role in the macroscopic and microscopic physical process during magnetic reconnection. Most of previous studies focused on the flux ropes in the reconnection region. However, some physical process inside macroscopic flux ropes far away from the reconnection site in the magnetotail is still unclear due to the lack of high time resolution data. In this letter, thanks to the unprecedented high time resolution data of the Magnetospheric Multiscale (MMS) mission, we report an ion-scale flux rope and study its dynamics. Our observations demonstrate that the observed flux rope is still highly dynamical, and hosting multiscale coupling processes and strong energy dissipation, even though the flux rope has very large scale and is far away from the reconnection site. Key Points: • An ion-scale flux rope, embedded in possible electron vortex, is investigated in the magnetotail in details • Electron demagnetization occurs in some subregions of the flux rope, and abundant waves are detected in the exterior and interior regions • Strong dissipation occurs in the flux rope, implying that flux rope provides another important channel for energy dissipation in space plasma

Introduction

Magnetic reconnection is one of the most important physical processes in space, astrophysical, and laboratory plasmas, which can effectively convert magnetic energy into plasma kinetic and thermal energy in a bursty way, changing the topology of the magnetic field. Flux ropes (FRs) are 3-D helical magnetic structures in which magnetic field lines twist with each other and a strong core field generally exists; FRs can be formed by single X-line or multiple X-line magnetic reconnection (e.g., [START_REF] Deng | Geotail encounter with reconnection diffusion region in the Earth's magnetotail: Evidence of multiple X lines collisionless reconnection[END_REF][START_REF] Fu | How to find magnetic nulls and reconstruct field topology with MMS data[END_REF][START_REF] Fu | Identifying magnetic reconnection events using the FOTE method[END_REF][START_REF] Fu | Intermittent energy dissipation by turbulent reconnection[END_REF]Huang, Pang, et al., 2014;[START_REF] Huang | Electron acceleration in the reconnection diffusion region: Cluster observations[END_REF]Huang, Zhou, et al., 2014;Huang, Zhou, et al., 2015;[START_REF] Lee | A theory of magnetic flux transfer at the Earth 's magnetopause[END_REF][START_REF] Nakamura | Structure of the magnetopause reconnection layer and of flux transfer events: Ion kinetic effects[END_REF][START_REF] Slavin | Geotail observations of magnetic flux ropes in the plasma sheet[END_REF][START_REF] Zhou | Electric field structure inside the secondary island in the reconnection diffusion region[END_REF][START_REF] Zhou | Coalescence of macroscopic flux ropes at the subsolar magnetopause: Magnetospheric Multiscale observations[END_REF]. FRs have been frequently observed in the Earth's magnetosphere (e.g., [START_REF] Chen | Observation of energetic electrons within magnetic islands[END_REF]Huang, Retino, et al., 2016;[START_REF] Huang | MMS observations of ion-scale magnetic island in the magnetosheath turbulent plasma[END_REF][START_REF] Huang | Electron acceleration in the reconnection diffusion region: Cluster observations[END_REF][START_REF] Retinò | Cluster observations of energetic electrons and electromagnetic fields within a reconnecting thin current sheet in the Earth's magnetotail[END_REF][START_REF] Slavin | Geotail observations of magnetic flux ropes in the plasma sheet[END_REF][START_REF] Wang | Observations of energetic electrons up to 200 keV associated with a secondary island near the center of an ion diffusion region: A cluster case study[END_REF][START_REF] Zhao | Coalescence of magnetic flux ropes observed in the tailward high-speed flows[END_REF][START_REF] Zong | Cluster observations of earthward flowing plasmoid in the tail[END_REF]. FRs can have multiscale structures or multiple layers (e.g., Huang, Retino¸et al., 2016;[START_REF] Hwang | The substructure of a flux transfer event observed by the MMS spacecraft[END_REF], and may show different features in the electron velocity distributions (e.g., [START_REF] Zhong | Three-dimensional magnetic flux rope structure formed by multiple sequential X-line reconnection at the magnetopause[END_REF] and different wave properties in different subregions (e.g., Huang, Retino, et al., 2016;[START_REF] Khotyaintsev | Observations of slow electron holes at a magnetic reconnection site[END_REF][START_REF] Wang | Coalescence of magnetic flux ropes in the ion diffusion region of magnetic reconnection[END_REF].

It is believed that FRs play an important role in the macroscopic and microscopic physical processes occurring during magnetic reconnection, such as modulation of reconnection rates and electron accelerations (e.g., [START_REF] Chen | Observation of energetic electrons within magnetic islands[END_REF][START_REF] Daughton | Fully kinetic simulations of undriven magnetic reconnection with open boundary conditions[END_REF][START_REF] Daughton | Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas[END_REF][START_REF] Drake | Electron acceleration from contracting magnetic islands during reconnection[END_REF][START_REF] Fu | Dipolarization fronts as a consequence of transient reconnection: In situ evidence[END_REF]Fu, Khotyaintsev, et al., 2013;[START_REF] Fujimoto | Bursty emission of whistler waves in association with plasmoid collision[END_REF]. Simulations have shown that the electrons can be accelerated by the contracting of FRs via the Fermi acceleration mechanism [START_REF] Drake | Electron acceleration from contracting magnetic islands during reconnection[END_REF][START_REF] Fu | The process of electron acceleration during collisionless magnetic reconnection[END_REF], by the reconnection electric field in the secondary FRs (Oka, Fujimoto, et al., 2010), and by the coalescence of FRs (Oka, Phan, et al., 2010;[START_REF] Pritchett | Energetic electron acceleration during multi-island coalescence[END_REF][START_REF] Zhou | Plasma physics of magnetic island coalescence during magnetic reconnection[END_REF] in the reconnection region. The enhancement of energetic electrons has been observed inside the FRs [START_REF] Chen | Observation of energetic electrons within magnetic islands[END_REF][START_REF] Huang | Electron acceleration in the reconnection diffusion region: Cluster observations[END_REF][START_REF] Retinò | Cluster observations of energetic electrons and electromagnetic fields within a reconnecting thin current sheet in the Earth's magnetotail[END_REF][START_REF] Wang | Observations of energetic electrons up to 200 keV associated with a secondary island near the center of an ion diffusion region: A cluster case study[END_REF]. The observational evidence of the coalescence of FRs has been shown using high-resolution data from the Cluster and MMS missions [START_REF] Wang | Electrostatic and electromagnetic fluctuations detected inside magnetic flux ropes during magnetic reconnection[END_REF]Zhao, Wang, & Du, 2016;[START_REF] Zhou | Coalescence of macroscopic flux ropes at the subsolar magnetopause: Magnetospheric Multiscale observations[END_REF]. In one particular event, an ongoing reconnection site (i.e., electron diffusion region) with strong energy dissipation was directly detected in the interaction region of two macroscopic FRs at the magnetopause [START_REF] Zhou | Coalescence of macroscopic flux ropes at the subsolar magnetopause: Magnetospheric Multiscale observations[END_REF]. However, some physical processes occurring inside macroscopic FRs far away from the reconnection site in the magnetotail are still unclear due to the lack of high time resolution data. In this paper, we use the unprecedented high-resolution data from NASA's MMS mission to investigate FRs in the near-Earth magnetotail, and try to understand the physical process occurring inside the FRs.

MMS Observations

The magnetic field data recorded by the Fluxgate Magnetometer [START_REF] Russell | The Magnetospheric Multiscale magnetometers[END_REF] and Search-Coil Magnetometer (Le Contel et al., 2016), the electric field data collected by the Electric Double Probe [START_REF] Ergun | The axial double probe and fields signal processing for the mms mission[END_REF][START_REF] Lindqvist | The spin-plane double probe electric field instrument for MMS[END_REF], and the 3-D particle distribution functions and the plasma moments measured by the Fast Plasma Instrument [START_REF] Pollock | Fast plasma investigation for Magnetospheric Multiscale[END_REF] onboard the MMS spacecraft are used in this study.

Figure 1 displays an overview when the MMS encountered a series of FRs and crossed the current sheet repeatedly. The four MMS spacecraft formed a tetrahedron with the maximum separation ~26 km. The data recorded by four MMS spacecraft are nearly identical at such small separation, so we only present MMS1's data here. During the interval of interest, MMS spacecraft were located at [-17.7, 3.7, 2.4] R E in GSM coordinates (R E is the Earth's radius). From the typical ion spectrogram (Figure 1a), plasma density (N i ~0.4 cm 3 ; Figure 1d), high ion temperature (~several keV; Figure 1e), and large plasma β (up to 10 3 ; Figure 1f), one can infer that the MMS were in the magnetotail plasma sheet [START_REF] Cao | Joint observations by Cluster satellites of bursty bulk flows in the magnetotail[END_REF]. MMS initially stayed in the southern hemisphere and then crossed the current sheet 6 times and finally went back to the southern hemisphere (Figure 1b). V ix is generally positive and has maximum values of more than 800 km/s around 00:56:20 UT during this interval, implying that the MMS spacecraft were embedded in earthward plasma flow. With the bipolar variations in B z component (from negative to positive), peaks in B x or B y component, and amplitude of magnetic field B t in the earthward flow, one can identify at least five earthward moving FRs (as indicated by the red dashed circles in Figure 1b). There are enhancements of ion temperature and density in the FRs. The third FR indicated by two black dashed lines will be discussed below in detail.

Figure 2 shows the details of the third FR in LMN coordinates (L = [0.98, -0.13, -0.15], M = [0.15, 0.97, 0.19], N = [0.13, -0.21, 0.97] in GSM coordinates). The LMN coordinates are determined by minimum variance analysis (MVA; [START_REF] Sonnerup | Minimum and maximum variance analysis[END_REF]from 00:56:25.9050 UT to 00:56:28.3152 UT). The angle between N direction of LMN and normal direction ([-0.05, 0.30, -0.95]) determined by timing analysis is 7°; thus, the results in LMN coordinates are reliable. The MMS spacecraft stayed off-equator in the southern hemisphere of the plasma sheet since the B L component is negative (up to -28 nT), comparable to B t . When B N changes from negative to positive (Figure 2d) in the earthward flow (V iL > 0 in Figure 2e), both B t and B L have a peak (Figures 2a and2b). These signatures are all unambiguous features of an earthward moving FR. The scale of the FR is estimated to be 2,210 ± 230 km from timing analysis, that is, ~6.1 ± 0.6 λ i (λ i ~360 km is ion inertial length based on the average asymptotic plasma parameters |B|~22 nT, N i = N e ~0.4 cm 3 ), implying that this FR is an ion-scale structure. Different features of the plasma observations can be used to distinguish the exterior and interior regions of this FR (see bars at the top of Figure 2a). Accompanying the earthward flow, V iM increases inside the FR (~400 km/s in Figure 2f), indicating that a high-speed duskward component of ion flow is present in the interior region (BC) of the FR. It is worth noting that strong electron flow is detected in the exterior region of FR: V eL is up to -14,000 km/s, V eM is ~-4,000 km/s, and V eN is ~-3,000 km/s (Figures 2h-2j) from 00:54:13.5 UT to 00:54:16 UT in the inbound exterior region (AB) prior to entering the FR; while V eL is up to -7,500 km/s, V eM is ~-5,000 km/s, and V eN is ~3,000 km/s from 00:54:20.5 UT to 00:54:24 UT in the outbound exterior region (CD) of the FR. Thus, V eL stays negative but V eN changes from negative to positive in the exterior region, which indicates that the FR may be surrounded by an electron vortex (as illustrated in Figure 2m). However, the electron flow is smaller in the interior region than in the exterior region except for one peak in V eN (up to 2,000 km/s) in the center of the FR that is marked by the cyan bar in Figure 2. Both electron temperature and density increase in the FR, and an obvious electron temperature anisotropy is detected in the center of the FR (T e|| > T e⊥ in Figure 2k).

Figure 3 presents the electric field, current density, and J × E' associated with the FR. The electric field is very intense in the exterior and interior regions of the FR, especially reaching values of up to 150 mV/m in the center of FR (Figures 3b-3d), while the electric field is small and close to zero far away from the FR (before 00:54:13 UT and after 00:54:24 UT). V i × B and V e × B are also calculated to compare with electric field E in Figures 3b-3d. It is interesting that V i × B does not agree with the three components of electric field during the entire interval, which occurs because the FPI underestimates the ions in the plasma sheet since its energy range is limited to <30 keV [START_REF] Pollock | Fast plasma investigation for Magnetospheric Multiscale[END_REF] while ions with energy >30 keV are dominant in the entire plasma sheet at this time (Figure 1a). Fortunately, the FPI can accurately measure the entire electrons population. One can see that there are some differences between electric field and V e × B in short time periods in the FR. To clearly identify such differences, E' = E + V e × B is calculated and shown in Figure 3e. The nonzero E' in the FR implies that there are some filaments with decoupling between the electrons and magnetic field lines. The strongest nonzero peak of E' occurs in the center of the FR (marked by the cyan bar), up to 100 mV/m, indicating that the electrons can be demagnetized even in an ion-scale FR. The parallel electric field E || has large fluctuations with ~50 mV/m amplitude in the exterior region, but smaller fluctuations with ~25 mV/m amplitude in the interior region. Intense currents calculated by the curlometer method are observed both in the exterior and interior regions of FR (Figure 3g). Parallel current is dominant in the exterior region, while it becomes comparable to the perpendicular one in the interior region (Figure 3h), implying that the FR has a non-force-free configuration. Different polarities of parallel current outside and inside the FR can cause magnetic dip in the interfaces between exterior and interior regions (see B t in Figure 3a). There are several peaks of (f) parallel electric field and error; (g) three components of current J calculated by curlometer method; (h) parallel and perpendicular currents; and (i) the dissipation term where J curl × E' calculated from curlometer method, and J pla × E' calculated from plasma data. current density in the FR, implying the existence of current filaments (e.g., [START_REF] Fu | Intermittent energy dissipation by turbulent reconnection[END_REF]. The energy dissipation parameter (J × E') derived from both the curlometer method and plasma method are shown in Figure 3i. The results from the two methods are similar. One can see that strongest energy dissipation (J × E' up to 2,000 pW/m 3 ; energy transfer from magnetic field to the particles) occurs in the center of the FR where intense nonzero E' and intense current exist, which is even stronger than the dissipation in the magnetotail reconnection site [START_REF] Huang | Observations of the electron jet generated by secondary reconnection in the terrestrial magnetotail[END_REF]. Such measurements support the proposition that energy dissipation occurs at O-lines, but not X-lines in the reconnection region by [START_REF] Fu | Intermittent energy dissipation by turbulent reconnection[END_REF].

Figure 4 displays ion and electron differential energy fluxes and electron pitch angle distributions. Significant increase of ion fluxes (from several keV to >30 keV; Figure 4b), and enhancements of electron fluxes (from several keV to tens of keV in Figure 4d, and up to 100 keV in Figure 4c) are observed in the FR. Due to the low quality of the FPI data for electrons with energy below 100 eV, Figures 4e-4x only show the pitch angle distributions of the electrons with the energy from 149 eV to 20 keV. It can be clearly seen that a parallel electron beam is present at the energy levels from ~1 to ~5 keV in the exterior region and a field-aligned electron beam also exists at the energy levels from ~2 to 20 keV in the interior region. In addition, there are enhancements of phase space densities at ~90°at energy above 5 keV in the interior region, implying that these electrons may be trapped in the FR. Such distributions of electrons in the observed FR may lead to plasma instabilities and cause the generations of waves. Figure 5 illustrates intense wave activity from f ci (proton gyrofrequency) to f ce (electron gyrofrequency). There are at least three different types of waves associated with the FR. The first type is intermittent whistler mode waves with enhancements of electromagnetic power spectral densities between 0.1 f ce and f ce (Figures 5b and5d), right-hand polarization (red in Figure 5e), and quasi-parallel propagation (blue in Figure 5f), both in the exterior and interior regions of the FR (as marked by black dashed circles in Figure 5). The whistlers propagate parallel to the magnetic field in the exterior region, while they propagate antiparallel to the magnetic field in the interior region (Figure 5h). The second type is lower hybrid waves both in the exterior region and interior region, which appears as enhancements of electromagnetic power spectral densities around the lower hybrid frequency (f lh ). The third type is an electrostatic solitary wave [START_REF] Omura | Electron beam instabilities as generation mechanism of electrostatic solitary waves in the magnetotail[END_REF]. Figures 5i-5m show a series of bipolar signatures in the parallel electric field with a duration of tens of milliseconds and amplitudes of 15~50 mV/m in the exterior and interior regions of the FR (as marked below Figure 5h by black arrows), which are consistent with typical features of electrostatic solitary waves.

Discussion

There are many dynamical instabilities, different types of waves, and multiscale processes occurring in reconnection regions (e.g., [START_REF] Cao | MMS observations of whistler waves in electron diffusion region[END_REF][START_REF] Huang | Wave properties in the magnetic reconnection diffusion region with high β: Application of the k-filtering method to cluster multispacecraft data[END_REF][START_REF] Huang | Electron acceleration in the reconnection diffusion region: Cluster observations[END_REF][START_REF] Vaivads | Plasma waves near reconnection sites[END_REF][START_REF] Zhou | Plasma physics of magnetic island coalescence during magnetic reconnection[END_REF]. Electrostatic and electromagnetic lower hybrid frequency range waves are detected and are associated with FRs in the magnetotail ion diffusion region [START_REF] Wang | Electrostatic and electromagnetic fluctuations detected inside magnetic flux ropes during magnetic reconnection[END_REF]. One ion-scale FR, away far from the reconnection site, was identified in the turbulent magnetosheath for the first time (Huang, Retino, et al., 2016). Electrostatic solitary waves and strong lower hybrid drift waves are detected inside the FR, while whistler waves, weak electromagnetic lower hybrid drift waves, and strong broadband electrostatic noise are detected at the edges of FR (Huang, Retino, et al., 2016). In the present study, several types of waves are detected associated with the FR in the magnetotail. Intermittent whistler emissions (electron-scale), electrostatic solitary waves (electron-scale), and lower hybrid waves are observed both in the exterior and interior regions of the ion-scale FR; however, this FR is not observed in or near the reconnection site. Thus, the observations of the waves associated with the FRs indicate that highly dynamical and multiscale coupled processes can also occur in the FRs even far away from the reconnection site.

The intermittent whistler waves are observed in the exterior and interior regions of the FR in our event. The whistlers in the exterior region propagate parallel to the magnetic field, while the whistlers in the interior region propagate antiparallel to the magnetic field. This may indicate that the observed whistlers have different sources. Recently, kinetic simulations [START_REF] Fujimoto | Wave activities in separatrix regions of magnetic reconnection[END_REF][START_REF] Fujimoto | Whistler waves associated with magnetic reconnection[END_REF][START_REF] Huang | Two types of whistler waves in the hall reconnection region[END_REF][START_REF] Huang | Occurrence rate of whistler waves in the magnetotail reconnection region[END_REF] have confirmed that there are two different types of whistler waves in the reconnection region: one is triggered in the equatorial plane of the pileup region and propagates downstream and the other is generated at the separatrix region and propagates toward the X-line. Thus, one may deduce that the whistlers in the exterior region are produced at the separatrix region and propagate toward the X-line that is located at the right side of the observed FR; the whistlers in the interior region are generated at the equatorial plane of the pileup region of the X-line. Both whistlers pass through the spacecraft after they are generated.

Strong energy dissipation typically occurs in the electron diffusion region during magnetic reconnection (e.g., [START_REF] Burch | Electron-scale measurements of magnetic reconnection in space[END_REF][START_REF] Zhou | Coalescence of macroscopic flux ropes at the subsolar magnetopause: Magnetospheric Multiscale observations[END_REF] and at dipolarization fronts (Huang, Zhou, et al., 2012;Huang, Fu, et al., 2015;[START_REF] Liu | Electron-scale measurements of dipolarization front[END_REF]. [START_REF] Fu | Intermittent energy dissipation by turbulent reconnection[END_REF] have found strongest energy dissipation at O-lines (can be treated as FRs) in one magnetic reconnection diffusion region due to the strongest currents and kinetic turbulence there. However, as reported here, MMS detected strongest energy dissipation in the center of a largescale FR that is far away from the reconnection site. In addition, there is no direct evidence for the existence of coalescence of two FRs or secondary reconnection in the FR. Only one clue is the density dip in the core region with the strongest currents that can be the consequence of the coalescence of two FRs [START_REF] Retinò | Cluster observations of energetic electrons and electromagnetic fields within a reconnecting thin current sheet in the Earth's magnetotail[END_REF], indicating that strong dissipation may be caused by the coalescence of FRs. Our observations imply that the FR provides an important channel for the energy dissipation in space plasmas.

Summary

We report an ion-scale FR in the magnetotail observed by MMS spacecraft. This FR, surrounded by highspeed electron flow (possibly an electron vortex), is embedded in an earthward plasma flow. Both electron density and temperature increase in the FR, and intense currents are found in the interior and exterior regions of the FR. Parallel and perpendicular currents are comparable in the interior region, implying that the FR has a non-force-free configuration. There are strong electric fields in the FR and large parallel electric fields in the exterior region. The electric field in the electron frame (E + V e × B) is nonzero (up to ~100 mV/m) in the subregions of the FR, especially in the center, indicating that the electrons are decoupled from magnetic field lines. Wave activity, including whistler waves, lower hybrid waves, and electrostatic solitary waves, is observed in the FR, implying that multiscale coupling processes occur in the large-scale FR. Strongest dissipation is detected in the center of FR, indicating that the FR is still highly dynamical even though it has a very large scale and is far away from the reconnection site.

Figure 1 .

 1 Figure 1. Overview of MMS1 observations in GSM coordinates: (a) ion differential energy flux, (b) magnetic field, ion (c) velocity, (d) density, (e) temperature, and (f) plasma β. The red dashed circles mark the observed FRs and the black dashed lines mark the interval of the FR investigated in this work.

Figure 2 .

 2 Figure 2. Detailed observations of the third FR in Figure 1. (a-j) All four MMS spacecraft observations. (a-d) Magnetic field; L, M, N components of (e-g) ion velocity and (h-j) electron velocity; (k) electron temperature and (l) density recorded by MMS1; and (m) cartoon diagram of the FR with the MMS trajectory and electron flow. The cyan and red shadow indicate the exterior and interior regions of the FR. The vertical black dashed lines mark the FR and the cyan shade marks the interval of significant dissipation. The color bars at the top of the figure indicate the exterior region (blue) and interior region (red) of the FR, unless specified indicated.

Figure 3 .

 3 Figure 3. Detailed observations of the third FR. (a) Magnetic field; (b-d) L, M, and N components of electric field, -V e × B and -V i × B, respectively; (e) E' = E + V e × B;(f) parallel electric field and error; (g) three components of current J calculated by curlometer method; (h) parallel and perpendicular currents; and (i) the dissipation term where J curl × E' calculated from curlometer method, and J pla × E' calculated from plasma data.

Figure 5 .

 5 Figure 5. The wave analysis of MMS1. (a) Magnetic field, the magnetic spectra (b) (SCM; 8,192 Hz), (c) (FGM; 128 Hz), (d) the electric spectra (EDP; 8,192 Hz), (e) ellipticities (red: right-hand polarization; blue: left-hand polarization), (f) propagation angles, θ k , (g) planarity of polarization, (h) Poynting flux, and (i-m) parallel electric field during the five intervals marked by arrows below (h). The black dashed circles mark the whistler waves. The magenta, white, and black horizontal lines in (b)-(h) represent electron plasma frequency (f pe ), electron gyrofrequency (f ce , 0.5 f ce , 0.1 f ce ; from top to bottom), and lower hybrid frequency (f lh ), respectively.

Acknowledgments

We thank the entire MMS team and instrument leads for the data access and support. This work was supported by the National Natural Science Foundation of China (41674161, 41874191). S.Y.H. acknowledges the project supported by the Specialized Research Fund for Shandong Provincial Key Laboratory and the support by Young Elite Scientists Sponsorship Program by CAST (2017QNRC001). MMS data are publicly available from the MMS Science Data Center at http:// lasp.colorado.edu/mms/sdc/.


Oana Balalau
email: obalalau@mpi-inf.mpg.de

Carlos Castillo

Mauro Sozio
email: sozio@telecom-paristech.fr

EviDense: a Graph-based Method for Finding Unique High-impact Events with Succinct Keyword-based Descriptions

Despite the significant efforts made by the research community in recent years, automatically acquiring valuable information about high impact-events from social media remains challenging. We present EVIDENSE, a graph-based approach for finding high-impact events (such as disaster events) in social media. Our evaluation shows that our method outperforms state-of-the-art approaches for the same problem, in terms of having higher precision, lower number of duplicates, while providing a keyword-based description that is succinct and informative.

Introduction

Social media have been playing increasingly a major role during crises and disasters. For example, the American Red Cross (ARC) pointed out the effectiveness of social media and mobile apps in handling emergency situations such as those generated by a disaster event. 1 .

Unfortunately, despite the significant efforts made by the research community in recent years, automatically acquiring valuable information about high impact-events from social media remains challenging. This is due to fact that social content is often noisy, inconsistent and ambiguous. As a result, making sense of a large collection of tweets, for example, is non-trivial even in the case when the collection of tweets is static and it does not evolve over time.

One of the challenges we address in our work is how to provide a succinct keyword-based description of highimpact events containing the most relevant information about the events, such as what happened, where, and when. According to a survey by the US Congressional Service, the administrative cost for monitoring multiple social media sources, which typically produce large amounts of noisy data, is significant [START_REF] Lindsay | Social media and disasters: Current uses, future options, and policy considerations[END_REF]. Therefore, in order to alleviate the burden of analyzing social content, a succinct and informative description of the events is needed.

Our approach consists of the following steps: i) filtering of the tweets by retaining only those containing at least one term in a given lexicon. ii) finding locations whose number of occurrences in tweets deviates significantly on a given time window from their average frequency; iii) a graph mining approach for selecting the relevant keywords in the description, based on a novel definition of a clique and a quasiclique in the weighted case. Our definition of a weighted clique, which is a generalization of a clique in an unweighted graph, ensures an event is described in a succinct manner by relevant keywords. We call our approach EVIDENSE, as our graph mining approach is based on finding "dense" regions in the graph representing the co-occurrence of keywords in the tweets.

We evaluate this algorithm against state-of-the-art approaches for the same or similar problems on a collection of tweets covering the period between November 2015 and February 2016, by means of a crowdsourcing platform. Our experimental evaluation shows that our approach outperforms the baselines both in terms of precision (at k) and number of duplicates, while the keyword-based description provided by our algorithm is succinct and informative.

Given these results, we consider EVIDENSE could represent a valuable tool for analyzing both social content and news articles from mainstream media, as well as for studying how they compare. It could also be used to boost the performance of other approaches. For example, collections of tweets labeled as related to disasters by our approach could be used to create training sets for automatic classifiers.

Related Work. In our survey of the related work and in our experimental evaluation, we focus on those approaches that allow a large-scale analysis over a long period of time. In particular, we focus on unsupervised approaches that enforce or allow to enforce some kind of constraint on the output size. We summarize the relevant related work as follows. [START_REF] Weng | Event Detection in Twitter[END_REF] developed an event detection algorithm (EDCOW) based on clustering of the waveletbased signal of words. The approach developed in [START_REF] Guille | Mention-anomaly-based Event Detection and Tracking in Twitter[END_REF] aims at finding words with similar temporal patterns in a given time window. EDCOW has been shown to perform better than several other event detection techniques in a recent study [START_REF] Weiler | Evaluation Measures for Event Detection Techniques on Twitter Data Streams[END_REF]. [START_REF] Angel | Dense subgraph maintenance under streaming edge weight updates for real-time story identification[END_REF]) developed an algorithm for maintaining overlapping dense subgraphs with limited size in a dynamic graph. Another graph mining technique for real-time event discovery is presented in [START_REF] Agarwal | Real Time Discovery of Dense Clusters in Highly Dynamic Graphs: Identifying Real World Events in Highly Dynamic Environments[END_REF]. Finding dense subgraphs of an input graph has received increasing attention in recent years, in the graph mining community: [START_REF] Balalau | Finding subgraphs with maximum total density and limited overlap[END_REF], (Danisch, Balalau, and Sozio ), [START_REF] Danisch | Large scale densityfriendly graph decomposition via convex programming[END_REF], [START_REF] Epasto | Efficient densest subgraph computation in evolving graphs[END_REF].

Algorithm

Our algorithm consists of the following main steps: 1) collection of tweets containing keywords related to disaster events by means of the Twitter API; 2) recognition and tagging of mentions of locations in the tweets; 3) finding bursts of mentions of locations; 4) mentions of locations are finally complemented with related keywords so as to provide more informative results. Each of these steps is described in the following paragraphs. Collection of Tweets and Preprocessing. Tweets are filtered using disaster keywords [START_REF] Olteanu | CrisisLex: A Lexicon for Collecting and Filtering Microblogged Communications in Crises[END_REF]) and for the recognition and tagging of locations, we use an entity recognition tagger that was trained on Twitter data [START_REF] Ritter | Named entity recognition in tweets: An experimental study[END_REF]. We remove stopwords, URLs and special characters such as emoticons. Finding Bursts of Locations. When an event such as a disaster event occurs, we observe a burst of activity on Twitter with terms pertinent to the event increasing suddenly their frequency in tweets. In our approach (where tweets contain keywords related to disaster events), a burst in the number of mentions of a location gives us a first signal that a disaster event is unfolding at that location. Previous works [START_REF] Pan | Event detection with spatial latent dirichlet allocation[END_REF] have used geolocation of posts and not mentions of locations. We argue that using mentions of locations makes our algorithm more versatile, allowing it to analyze datasets coming from different sources. Burstiness of words in streams of data is a well-studied topic [START_REF] Zhu | Efficient Elastic Burst Detection in Data Streams[END_REF][START_REF] Lappas | On Burstiness-Aware Search for Document Sequences[END_REF]) and in our approach, we use a simple technique, similar to other event detection methods [START_REF] Guille | Mention-anomaly-based Event Detection and Tracking in Twitter[END_REF].

For each location, we compute a set of intervals in which the deviation between the frequency of the location and its expected frequency is always above a threshold. Our intuition is that all tweets (dealing with the same location) posted during each of those intervals refer to the same event.

We refer to such intervals as interesting intervals and we are interested in finding maximal interesting intervals. The expected frequency of a location is computed assuming that location frequencies can be approximated by the binomial distribution. Then, all the (location, maximal interesting interval) pairs are ranked according to how much the frequency of a location deviates from its expected frequency and we retain the top k pairs. Finding Quasi-Cliques. In order to complement the set of locations with additional information about the corresponding event, we employ a graph mining approach. In particular, for each location and each interesting interval for that location, we wish to find a set of terms which induce a dense region in the co-occurrence graph during that time interval. Given an interesting interval I and a collection of tweets, we define a weighted undirected graph G I = (V I , E I ), where V I consists of the set of terms in the collection of tweets, while there is an edge between two nodes if the corresponding terms co-occur in at least one tweet posted within I. A weight function c : E → R + represents the number of cooccurrences of terms in tweets posted within I.

Several definitions of weighted cliques have been provided in the literature, such as a subgraph of maximum total weight where any two nodes are connected ( Östergård 1999), as well as a subgraph with maximum total weight and number of nodes no larger than a threshold provided in input [START_REF] Alidaee | Solving the maximum edge weight clique problem via unconstrained quadratic programming[END_REF]. Observe that both definitions would favor the graph on the left in Figure 1, which exhibit weak connections between the set of nodes {1, 2} and {3,4}. As a result, those two different parts of the graph might actually refer to two different events. It is more likely that the nodes of the graph on the right in Figure 1 refer to the same event, as the edges of the graph have the same weight.

This motivates the following novel definitions of cliques and quasi-cliques. We say that a graph H is a weighted clique if all pairs of nodes in H are connected by an edge with the same weight. Given a parameter γ > 0, we then define a weighted quasi-clique as follows.

Definition 1 (Weighted Quasi-Clique) Given an undirected weighted graph H = (V (H), E(H), w), 0 < γ ≤ 1, we say that H is a weighted γ-quasi-clique if the following holds:

e∈E(H) w(e) ≥ γ • w max (H) |V (H)| 2 ,
where w max (H) = max e∈E(H) (w(e)).

We define the function q G : V → (0, 1] (q for short) to be the function which associates to every set S ⊆ V a rational number γ such that the subgraph induced by S in G is a γquasi-clique and γ is the largest value for which this holds.

Finding quasi-cliques is an NP-hard problem, therefore we resort to the following heuristic for finding quasi-cliques containing a node v and at most s nodes. The algorithm starts with v and adds the edge with maximum weight containing v. At any given step, let S be set of current nodes. If |S| = s, the algorithm stops. Otherwise, it adds a node x in the neighborhood of S maximizing q(S ∪ {x}) provided that by adding x the resulting subgraph is still a γ-quasi-clique.

Experimental Evaluation

Corpora. We collect tweets posted over a period of 4 months between November 2015 and February 2016. We use the Twitter Streaming API while filtering the tweets so that they contain at least one term related to disasters [START_REF] Olteanu | CrisisLex: A Lexicon for Collecting and Filtering Microblogged Communications in Crises[END_REF]) and they are written in English. We obtain approx 3M tweets in total, which we divide into four datasets (one per month). Related work. We compare against MABED (Guille and Favre 2014) and EDCOW [START_REF] Weng | Event Detection in Twitter[END_REF]. All approaches are evaluated on the same collection of tweets. There has been significant disagreement among the crowd workers when interpreting the results of [START_REF] Angel | Dense subgraph maintenance under streaming edge weight updates for real-time story identification[END_REF]. Therefore, we omit such an approach from our study, deferring a more careful evaluation to future work. Parameter settings. In our approach, we find the top 20 events and we set the size of the quasi-clique to be at most 10 and the γ parameter at least 0.5. We run MABED using the implementation provided by the authors and the setting specified in the original paper [START_REF] Guille | Mention-anomaly-based Event Detection and Tracking in Twitter[END_REF], that is p = 10, θ = 0.7 and σ = 0.5. For the EDCOW algorithm we use the implementation of [START_REF] Weiler | Evaluation Measures for Event Detection Techniques on Twitter Data Streams[END_REF] and we set the parameters as follows: the size of first level of intervals is s = 100s, while we take ∆ = 32, setting a size of 3200s for the second-level intervals and, as in [START_REF] Weiler | Evaluation Measures for Event Detection Techniques on Twitter Data Streams[END_REF], we set γ = 1. As EDCOW does not enforce any constraint on the size of the output, we order the results according to (as defined in the original paper), which measures the relevance of the results and retain only the top k results. Metrics. We evaluate the precision at k, denoted with P (or precision for short), which is defined as the number of true events in the top k results, divided by k. In addition to the precision, we compute the fraction of duplicate events among all the events retrieved, i.e. the DeRate [START_REF] Li | Twevent: Segment-based Event Detection from Tweets[END_REF]. From these two metrics, we can infer a third one, which measures the fraction of unique events (i.e. duplicates do not contribute) in the top k results. We denote such a metric with U @k. We observe that if an algorithm performs best in terms of U @k, it performs best also in terms of recall. Therefore, we do not report recall in our experimental evaluation. Crowdsourcing Settings. In order to ensure a fair comparison, we use a crowdsourcing service, GetHybrid2 . For each result produced by any of the approaches, we ask 5 workers to determine whether it was a disaster event, that is an event considered to be a disaster by the US Government or the International Disaster Database. 3 We added to the description of a result two relevant tweets in order to facilitate the labeling task. In order to evaluate a result, a worker would select one of the following answers to the question of what type of event do the keywords and tweets describe: (A) A natural disaster (earthquake, landslide, volcano, extreme temperature, hurricane, large and dense fog, large storm, flood, tsunami, drought, wildfire, epidemic, large accident involving animals, asteroid impact), (B) A technological disaster (chemical spill, building collapse, explosion, fire, gas leak, large poisoning, nuclear, radiation, cyberattack), (C) A human-induced disaster (war, terror attack), (D) A large transport accident (air, road, rail, water), (E) Not a natural, technological, or human-induced disaster, or large transport accident.

Answers A-D correspond to a disaster. We label a result as a disaster if 3 out of 5 workers confirmed. In order to compute the DeRate, we considered duplicate events to be subevents or consequences of an event. Two events are considered to be duplicates if 3 out of 5 workers confirmed. Estimating DeRate and U@k. The task of estimating the average number of duplicate events is non-trivial, given the large number of results. Asking the workers in GetHybrid to estimate the number of duplicate events in a list containing approximately 20 or more results is time-consuming and most probably would result in a non-accurate evaluation. Therefore, we draw a random sample from the set of all possible event pairs. Each worker is then asked to determine whether a given pair of events in the sample contains duplicate events or not. The resulting fraction of duplicate event pairs in the sample is used to infer a 95% confidence interval on the fraction of duplicate event pairs on the whole dataset, using the Wilson score method [START_REF] Newcombe | Two-sided confidence intervals for the single proportion: comparison of seven methods[END_REF]. From the fraction of duplicate pairs we can estimate the number of unique events, U @k.

Comparison. In Table 1 we present the average P @20 for all the approaches over the time period Nov. 2015-Feb. 2016. We observe that EVIDENSE outperforms the other two approaches.

Method

Average P @20 EDCOW 0.325 MABED 0.537 EVIDENSE 0.737

Table 1: Average precision over Nov. 2015-Feb. 2016.

We evaluate the number of duplicate events in the results. First, we measure the fraction of duplicate event pairs in our sample. This is shown in Table 2. Observe, that EVIDENSE produces less duplicate event pairs. In particular, our results are better with a 95% confidence. From the results shown in Table 2, we obtain a 95% confidence interval on the fraction of duplicate events, i.e. the DERate. We obtain a 95% confidence interval of [0.000, 0.846] for EDCOW, [0.372, 0.906] for MABED, and [0.000, 0.474] for EVIDENSE. From the latter result, it is difficult to determine which algorithm performs best in terms of DERate. Moreover, observe that approaches with higher precision might be penalized by the DERate, in that, they tend to have a larger number of duplicates. For example, an approach which retrieves exactly one event has a DERate of zero. Therefore, we also consider the U @k metric, that is, the fraction of unique events in the top k results. The results are shown in Table 3. We can see that even with a pessimistic estimate, EVIDENSE outperforms the other approaches in terms of U @k, while the fraction of unique events in the top-20 results can be up to 73.7%.

Method

U @20 EDCOW 0.050 to 0.325 MABED 0.050 to 0.337 EVIDENSE 0.387 to 0.737 Table 3: Average ratio of unique events Nov. 2015 -Feb. 2016.

The output of our algorithm is shown in Table 4. We can see that the description of each of the events is succinct and informative. In particular, one can easily retrieve the location of the event (in bold), its time-frame and what happened.

Conclusions

We presented EVIDENSE, a graph-based approach for finding high-impact events in social media. We address the challenge of providing a succinct and informative description of the events retrieved with our approach while focusing on disaster events.

EVIDENSE could represent a valuable tool for analyzing social content and could also be used to boost the performance of other approaches. For example, collections of tweets labeled as related to disasters by our approach could be used to create training sets for automatic classifiers.

Figure 1 :

 1 Figure 1: The left subgraph has a larger weight than the right one, but the nodes in the right subgraph are better connected.

  -year-old, Tamir Rice, charged, death, grand, indict, jury, police Table4: Top 5 events discovered in December 2015 by EVI-DENSE. The event is centered on the location given in bold.

Table 2 :

 2 Fraction of duplicate event pairs.

	Method	Fraction in sample 95% Confidence Interval
	EDCOW	0.120	0.049 to 0.250
	MABED	0.220	0.145 to 0.316
	EVIDENSE	0.020	0.003 to 0.077

https://www.gethybrid.io

https://www.ready.gov/be-informed, http:// www.emdat.be/classification

https://github.com/nyxpho/evidense

Acknowledgments

Part of this work was done while O. Balalau was a student at Télécom ParisTech University. C. Castillo is partially funded by La Caixa project LCF/PR/PR16/11110009. M. Sozio is partially funded by the French National Agency (ANR) under project FIELDS (ANR-15-CE23-0006).

Data and code sharing. The ids of the tweets we use in our evaluation are publicly available, together with our code. 4