Collisional De-excitation Research Articles

VLT near- to mid-IR imaging and spectroscopy of the M 17 UC1 – IRS5 region

We investigate the surroundings of the hypercompact HII region M17 UC1 to probe the physical properties of the associated young stellar objects and the environment of massive star formation. Five of the seven point sources in this region show $L$-band excess emission. Geometric match is found between the H_2 emission and near-IR polarized light in the vicinity of IRS5A, and between the diffuse mid-IR emission and near-IR polarization north of UC1. The H_2 emission is typical for dense PDRs, which are FUV pumped initially and repopulated by collisional de-excitation. The spectral types of IRS5A and B273A are B3-B7 V/III and G4-G5 III, respectively. The observed infrared luminosity L_IR in the range 1-20 micron is derived for three objects; we obtain 2.0x10^3 L_\sun for IRS5A, 13 L_\sun for IRS5C, and 10 L_\sun for B273A. IRS5 might be a young quadruple system. Its primary star IRS5A is confirmed to be a high-mass protostellar object (~ 9 M_\sun, ~1x10^5 yrs); it might have terminated accretion due to the feedback from the stellar activities (radiation pressure, outflow) and the expanding HII region of M17. UC1 might also have terminated accretion because of the expanding hypercompact HII region ionized by itself. The disk clearing process of the low-mass YSOs in this region might be accelerated by the expanding HII region. The outflows driven by UC1 are running in south-north with its northeastern side suppressed by the expanding ionization front of M17; the blue-shifted outflow lobe of IRS5A is seen in two types of tracers along the same line of sight in the form of H_2 emission filament and mid-emission. The H_2 line ratios probe the properties of M17 SW PDR, which is confirmed to have a clumpy structure with two temperature distributions: warm, dense molecular clumps with n_H>10^5 cm^-3 and T~575 K and cooler atomic gas with n_H~3.7x10^3-1.5x10^4 cm-3 and T~50-200 K.

Collisional quenching of highly rotationally excited HF

Collisional excitation rate coefficients play an important role in the dynamics of energy transfer in the interstellar medium. In particular, accurate rotational excitation rates are needed to interpret microwave and infrared observations of the interstellar gas for nonlocal thermodynamic equilibrium line formation. Theoretical cross sections and rate coefficients for collisional deexcitation of rotationally excited HF in the vibrational ground state are reported. The quantum-mechanical close-coupling approach implemented in the nonreactive scattering code MOLSCAT was applied in the cross section and rate coefficient calculations on an accurate 2D HF-He potential energy surface. Estimates of rate coefficients for H and H$_2$ colliders were obtained from the HF-He collisional data with a reduced-potential scaling approach. The calculation of state-to-state rotational quenching cross sections for HF due to He with initial rotational levels up to $j=20$ were performed for kinetic energies from 10$^{-5}$ to 15000 cm$^{-1}$. State-to-state rate coefficients for temperatures between 0.1 and 3000 K are also presented. The comparison of the present results with previous work for lowly-excited rotational levels reveals significant differences. In estimating HF-H$_2$ rate coefficients, the reduced-potential method is found to be more reliable than the standard reduced-mass approach. The current state-to-state rate coefficient calculations are the most comprehensive to date for HF-He collisions. We attribute the differences between previously reported and our results to differences in the adopted interaction potential energy surfaces. The new He rate coefficients can be used in a variety of applications. The estimated H$_2$ and H collision rates can also augment the smaller datasets previously developed for H$_2$ and electrons.

Effect of trapping of resonance radiation in a free-burning Ar arc

A modified method for the solution of the Holstein-Biberman transport equation is proposed for cylindrical geometry, arbitrary absorption coefficient accounting for plasma inhomogeneity and a Lorentz spectral lineshape. The method is applied to the plasma generated by a free-burning arc in argon at atmospheric pressure in order to study the effect of trapping of resonance radiation on the population of the resonance state Ar(1s4). The results obtained are compared with those of a self-consistent nonequilibrium model of the arc including excited atomic levels. They show an enhanced (compared to the results of the nonequilibrium model) population of the resonance state outside of the arc core as an effect of the trapping of resonance radiation and almost negligible collisional de-excitation. In the arc core, the effect is negligible so that the calculated population of the Ar(1s4) state confirms the results obtained with the nonequilibrium model.

Influence of excitation and deexcitation processes on the dynamics of laser-excited argon clusters

The excitation of atomic clusters by intense infrared laser pulses leads to the creation of highly charged ions and to the emission of energetic photons. These phenomena, which follow from ionization processes occurring in the cluster, depend significantly on the population of ground states and excited states in the laser-produced nanoplasma. This makes it necessary to account for collisional excitation and deexcitation processes. We investigate the interaction of femtosecond laser pulses with argon clusters by means of a nanoplasma model. Considering laser excitation with single and double pulses, we analyze the role of excitation and deexcitation processes in detail and calculate the yield of highly charged ions and of energetic photons in different wavelength regimes.

The dynamics of collapsing cores and star formation

Low-mass stars are generally understood to form by the gravitational collapse of the dense molecular clouds known as starless cores. Continuum observations have not been able to distinguish among the several different hypotheses that describe the collapse because the predicted density distributions are the almost the same, as they are for all spherical self-gravitating clouds. However, the predicted contraction velocities are different enough that the models can be discriminated by comparing the velocities at large and small radii. This can be done by observing at least two different molecular line transitions that are excited at different densities. For example, the spectral lines of the H2O (110 - 101) and C18O (1-0) have critical densities for collisional de-excitation that differ by 5 orders of magnitude. We compare observations of these lines from the contracting starless core L1544 against the spectra predicted for several different hypothetical models of contraction including the Larson-Penston flow, the inside-out collapse of the singular isothermal sphere, the quasi-equilibrium contraction of an unstable Bonnor-Ebert sphere, and the non-equilibrium collapse of an over-dense Bonnor-Ebert sphere. Only the model of the unstable quasi-equilibrium Bonnor-Ebert sphere is able to produce the observed shapes of both spectral lines. This model allows us to interpret other observations of molecular lines in L1544 to find that the inward velocities seen in observations of CS(2-1) and N2H+ are located within the starless core itself, in particular in the region where the density profile follows an inverse square law. If these conclusions were to hold in the analysis of other starless cores, this would imply that the formation of hydrostatic clouds within the turbulent interstellar medium is not only possible but not exceptional and may be an evolutionary phase in low-mass star formation.

Collisional energy transfer in highly excited molecules.

The excitation/de-excitation step in the Lindemann mechanism is investigated in detail using model development and classical trajectory studies based on a realistic potential energy surface. The model, based on a soft-sphere/line-of-centers approach and using elements of Landau-Teller theory and phase space theory, correctly predicts most aspects of the joint probability distribution P(ΔE,ΔJ) for the collisional excitation and de-excitation process in the argon-allyl system. The classical trajectories both confirm the validity of the model and provide insight into the energy transfer. The potential employed was based on a previously available ab initio intramolecular potential for the allyl fit to 97418 allyl electronic energies and an intermolecular potential fit to 286 Ar-allyl energies. Intramolecular energies were calculated at the CCSD(T)/AVTZ level of theory, while intermolecular energies were calculated at the MP2/AVTZ level of theory. Trajectories were calculated for each of four starting allyl isomers and for an initial rotational level of Ji = 0 as well as for Ji taken from a microcanonical distribution. Despite a dissimilarity in Ar-allyl potentials for fixed Ar-allyl geometries, energy transfer properties starting from four different isomers were found to be remarkably alike. A contributing factor appears to be that the orientation-averaged potentials are almost identical. The model we have developed suggests that most hydrocarbons should have similar energy transfer properties, scaled by differences in the potential offset of the atom-hydrogen interaction. Available data corroborate this suggestion.

Radiative cooling II: effects of density and metallicity

This work follows Lykins et al. discussion of classic plasma cooling function at low density and solar metallicity. Here we focus on how the cooling function changes over a wide range of density (n_H<10^12 cm^(-3)) and metallicity (Z<30Z _sun ). We find that high densities enhance the ionization of elements such as hydrogen and helium until they reach local thermodynamic equilibrium. By charge transfer, the metallicity changes the ionization of hydrogen when it is partially ionized. We describe the total cooling function as a sum of four parts: those due to H&He, the heavy elements, electron-electron bremsstrahlung and grains. For the first 3 parts, we provide a low-density limit cooling function, a density dependence function, and a metallicity dependence function. These functions are given with numerical tables and analytical fit functions. For grain cooling, we only discuss in ISM case. We then obtain a total cooling function that depends on density, metallicity and temperature. As expected, collisional de-excitation suppresses the heavy elements cooling. Finally, we provide a function giving the electron fraction, which can be used to convert the cooling function into a cooling rate.

Optical trail widths of faint meteors observed with the Canadian Automated Meteor Observatory

The optical trail widths of 30 faint meteors (average magnitude ∼+3, m ∼ 10 −4 kg) were resolved and measured using the Canadian Automated Meteor Observatory (CAMO). CAMO is an automated, high-resolution intensified digital video system capable of detecting meteors as faint as magnitude +5. The observatory’s two stations, separated by a baseline of 50 km, and each comprised of a narrow- and wide-field camera, observed the meteors for this survey. Data from the wide-field cameras were used to derive a trajectory solution for each meteor with the software package METAL, while data from the narrow-field cameras were used to measure trail widths with the image analysis software IMAGEJ. Raw widths were measured as a function of distance along the meteor trail for each frame of the video. To ensure that instrumental bloom did not artificially increase trail widths, the width of a star imaged with the narrowfield camera, with equivalent brightness to the meteor trail at the point of measurement, was subtracted from each observed raw width. Corrected trail widths up to 100 m at heights above 110 km were observed, varying with height as the inverse of atmospheric density. 14 of the 30 events were observed with both narrow-field cameras and each showed good agreement of trail width values after bloom correction. This suggested that the widths were true physical sizes, and not instrumental artefacts. Preliminary investigation suggests collisional de-excitation of energetic atoms is a plausible process for the formation of these wide trails.

HUBBLE SPACE TELESCOPEIMAGING OF THE BINARY NUCLEUS OF THE PLANETARY NEBULA EGB 6

EGB 6 is an ancient, low-surface-brightness planetary nebula. The central star, also cataloged as PG 0950+139, is a very hot DAOZ white dwarf (WD) with an apparent M dwarf companion, unresolved from the ground but detected initially through excesses in the JHK bands. Its kinematics indicates membership in the Galactic disk population. Inside of EGB 6 is an extremely dense emission knot -- completely unexpected since significant mass loss from the WD should have ceased ~10^5 y ago. The electron density of the compact nebula is very high (2.2x10^6 cm^-3), as indicated by collisional de-excitation of forbidden emission lines. Hubble Space Telescope imaging and grism spectroscopy are reported here. These resolve the WD and apparent dM companion -- at a separation of 0."166, or a projected 96(+204,-45) AU at the estimated distance of 576(+1224, -271) pc (using the V magnitude). Much to our surprise, we found that the compact emission nebula is superposed on the dM companion, far from the photoionizing radiation of the WD. Moreover, a a striking mid-infrared excess has recently been reported in Spitzer/IRAC and MIPS bands, best fit with two dust shells. The derived ratio L_IR/L_WD = 2.7 x 10^-4 is the largest yet found for any WD or planetary nucleus. The compact nebula has maintained its high density for over three decades. We discuss two possible explanations for the origin and confinement of the compact nebula, neither of which is completely satisfactory. This leaves the genesis and confinement of the compact nebula an astrophysical puzzle, yet similar examples appear in the literature.

Nitrogen fluorescence in air for observing extensive air showers

Extensive air showers initiate the fluorescence emissions from nitrogen molecules in air. The UV-light is emitted isotropically and can be used for observing the longitudinal development of extensive air showers in the atmosphere over tenth of kilometers. This measurement technique is well-established since it is exploited for many decades by several cosmic ray experiments. However, a fundamental aspect of the air shower analyses is the description of the fluorescence emission in dependence on varying atmospheric conditions. Different fluorescence yields affect directly the energy scaling of air shower reconstruction. In order to explore the various details of the nitrogen fluorescence emission in air, a few experimental groups have been performing dedicated measurements over the last decade. Most of the measurements are now finished. These experimental groups have been discussing their techniques and results in a series of Air Fluorescence Workshops commenced in 2002. At the 8$^{\rm{th}}$ Air Fluorescence Workshop 2011, it was suggested to develop a common way of describing the nitrogen fluorescence for application to air shower observations. Here, first analyses for a common treatment of the major dependences of the emission procedure are presented. Aspects like the contributions at different wavelengths, the dependence on pressure as it is decreasing with increasing altitude in the atmosphere, the temperature dependence, in particular that of the collisional cross sections between molecules involved, and the collisional de-excitation by water vapor are discussed.

Metastable density in nitrogen barrier discharges: I. LIF diagnostics and absolute calibration by Rayleigh scattering

The density of the metastable state of the nitrogen molecule is measured by laser-induced fluorescence (LIF) spectroscopy in an asymmetric barrier discharge at 500 mbar in the filamentary mode. The absolute density calibration is performed by comparison of the time-resolved signals from LIF and Rayleigh scattering. Due to the different physics of both processes, the LIF signal is the temporal convolution of the Rayleigh signal with an exponential decay defined by the effective lifetime of the laser excited state. The result is a delay of the LIF signal with respect to the Rayleigh signal and a slower decay of the LIF signal. This is proven experimentally by a pressure variation from 100 to 1000 mbar. Furthermore, the calibration method allows an implicit measurement of the effective lifetimes and the fluorescence yield, which is important at atmospheric pressure due to the dominance of collisional de-excitation (quenching). The calculated densities in the range of 1013 cm−3 are in good agreement with results from the literature.

HD 172555: detection of 63μm [OI] emission in a debris disc

Context. HD 172555 is a young A7 star belonging to the Beta Pictoris Moving Group that harbours a debris disc. The Spitzer IRS spectrum of the source showed mid-IR features such as silicates and glassy silica species, indicating the presence of a warm dust component with small grains, which places HD 172555 among the small group of debris discs with such properties. The IRS spectrum also shows a possible emission of SiO gas. Aims. We aim to study the dust distribution in the circumstellar disc of HD 172555 and to asses the presence of gas in the debris disc. Methods. As part of the GASPS Open Time Key Programme, we obtained Herschel-PACS photometric and spectroscopic observations of the source. We analysed PACS observations of HD 172555 and modelled the Spectral Energy Distribution (SED) with a modified blackbody and the gas emission with a two-level population model with no collisional de-excitation. Results. We report for the first time the detection of OI atomic gas emission at 63.18 microns in the HD 172555 circumstellar disc. We detect excesses due to circumstellar dust toward HD 172555 in the three photometric bands of PACS (70, 100, and 160 microns). We derive a large dust particle mass of 4.8e-4 Earth masses and an atomic oxygen mass of 2.5e-2*R^2 Earth masses, where R in AU is the separation between the star and the inner disc. Thus, most of the detected mass of the disc is in the gaseous phase.

Ionized gas diagnostics from protoplanetary discs in the Orion nebula and the abundance discrepancy problem

We present results from integral field spectroscopy with PMAS. The observed field contains: five protoplanetary discs (also known as proplyds), the high-velocity jet HH 514 and a bowshock. Spatial distribution maps are obtained for different emission line fluxes, the c(H{\beta}) coefficient, electron densities and temperatures, ionic abundances of different ions from collisionally excited lines (CELs), C2+ and O2+ abundances from recombination lines (RLs) and the abundance discrepancy factor of O2+, ADF(O2+). We find that collisional de-excitation has a major influence on the line fluxes in the proplyds. If this is not properly accounted for then physical conditions deduced from commonly used line ratios will be in error, leading to unreliable chemical abundances for these objects. We obtain the intrinsic emission of the proplyds 177-341, 170-337 and 170-334 by a direct subtraction of the background emission, though the last two present some background contamination due to their small sizes. A detailed analysis of 177-341 spectra reveals the presence of high-density gas (3.8\times10^5 cm^-3) in contrast to the typical values observed in the background gas of the nebula (3800 cm^-3). We also explore how the background subtraction could be affected by the possible opacity of the proplyd. We construct a physical model for the proplyd 177-341 finding a good agreement between the predicted and observed line ratios. Finally, we find that the use of reliable physical conditions returns an ADF(O2+) about zero for the intrinsic spectra of 177-341, while the background emission presents the typical ADF(O2+) observed in the Orion Nebula. We conclude that the presence of high-density ionized gas is severely affecting the abundances determined from CELs and, therefore, those from RLs should be considered as a better approximation to the true abundances.

The Detection of Energetic Materials by Laser Photoacoustic Overtone Spectroscopy

Laser-based sensors offer high sensitivity and species selectivity with real-time capabilities for monitoring the vapors of some energetic materials. However, the extremely low vapor pressure of many solid energetic materials under ambient conditions impedes these sensors. In this paper, we report on a novel technique based on laser photoacoustic overtone spectroscopy to detect and differentiate solid 1,3,5-trinitrotoluene (TNT), 1.3.5-trinitro-1,3,5-triazacyclohexane (RDX), and 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) in real time at ambient conditions. A tunable, near-infrared laser excites the target compound in the spectral region between 5800 to 6100 cm−1, and a microphone monitors the sound that they generate by non-radiative, collisional de-excitation processes. The photoacoustic signals result from first-overtone and combination absorptions of the energetic material's C–H vibrations, and the collisional processes enhance the signal at atmospheric pressure. The spectra reveal features that are unique to each measured material and these features can serve as a fingerprint for that material. We report the effects of laser energy and wavelength on signal intensity and estimate a detection limit for these compounds.

COSMIC-RAY AND X-RAY HEATING OF INTERSTELLAR CLOUDS AND PROTOPLANETARY DISKS

Cosmic-ray and X-ray heating are derived from the electron energy loss calculations of Dalgarno, Yan and Liu for hydrogen-helium gas mixtures. These authors treated the heating from elastic scattering and collisional de-excitation of rotationally excited hydrogen molecules. Here we consider the heating that can arise from all ionization and excitation processes, with particular emphasis on the reactions of cosmic-ray and X-ray generated ions with the heavy neutral species, which we refer to as chemical heating. In molecular regions, chemical heating dominates and can account for 50 per cent of the energy expended in the creation of an ion pair. The heating per ion pair ranges in the limit of negligible electron fraction from about 4.3 eV for diffuse atomic gas, to about 13 eV for the moderately dense regions of molecular clouds and to about 18 eV for the very dense regions of protoplanetary disks. An important general conclusion of this study is that cosmic-ray and X-ray heating depends on the physical properties of the medium, i.e., on the molecular and electron fractions, the total density of hydrogen nuclei, and to a lesser extent on the temperature. It is also noted that chemical heating, the dominant process for cosmic-ray and X-ray heating, plays a role in UV irradiated molecular gas.

Selective production of the doubly excited2p2(1D) state in He-like Ar16+ions by resonant coherent excitation

Selective production of the doubly excited state in 464 MeV/u He-like Ar${}^{16+}$ ions was accomplished using three-dimensional resonant coherent excitation in a thin foil of silicon crystal. Through a coherent interaction with the periodic crystal field, the Ar${}^{16+}$ ions were resonantly excited sequentially from the ground state to the $1s2p$ (${}^{1}\phantom{\rule{-0.16em}{0ex}}P$) state and then $2{p}^{2}$ (${}^{1}\phantom{\rule{-0.16em}{0ex}}D$) state in a way analogous to two-color x-ray laser excitation. The periodic crystal fields of 10${}^{11}$ V/m in the projectile's frame are equivalent to the fields generated by x-ray lasers with photon energies of 3139.55 and 3286.95 eV and an energy flux of 10${}^{16}$ W/cm${}^{2}$. We confirmed the doubly excited state formation through observation of the subsequent collisional ionization, Auger ionization, and radiative deexcitation.

Diagnostic line ratios in the IC 1805 optical gas complex

Large HII regions, with angular dimensions exceeding 10 pc, usually enclose numerous massive O-stars. Stellar winds from such stars are expected to play a sizeable role in the dynamical, morphological and chemical evolution of the targeted nebula. Kinematically, stellar winds remain hardly observable i.e., the typical expansion velocities of wind-blown bubbles being often confused with other dynamical processes also regularly found HII regions. However, supersonic shock waves, developed by stellar winds, should favor shock excitation and leave a well-defined spectral signature in the ionized nebular content. In this work, the presence of stellar winds, observed through shock excitation, is investigated in the brightest portions of the Galactic IC 1805 nebula, a giant HII region encompassing at least 10 O-stars from main-sequence O9 to giant and supergiant O4. The use of the imaging Fourier transform spectrometer SpIOMM enabled the simultaneous acquisition of the spectral information associated to the Halpha6563A, [NII]6548, 6584A, and [SII]6716, 6731A ionic lines. Diagnostic diagrams, first introduced by Sabbadin and collaborators, were used to circumscribe portions of the nebula likely subject to shock excitation from other areas dominated by photoionization. The gas compression, expected from supersonic shocks, is investigated by comparing the pre- and post-shocked material's densities computed from the [SII]/[SII] line ratio. The typical [NII]/[NII] line ratio slightly exceeds the theoretical value of 3 expected in low-density regimes. To explain such behavior, a scenario based on collisional de-excitations affecting the [NII]6548A line is proposed.

Electron-impact coherence parameters for electron-impact excitation of laser-excited 174Yb (…6s6p 3P1)

We have measured and calculated the P3 collision Stokes parameter for electron-impact collisional de-excitation to the ytterbium (…6s6p 3P1) level from the higher-lying 1P1, 3D1, 2, 3 and 3S1 levels for 20 eV residual energy. These processes are the time-reverse of the experimentally measured processes, where an impact energy of 20 eV was used to collisionally excite the 3P1 target, prepared by resonant laser pumping. Measurements were performed using a crossed-beam apparatus, where excited-state atomic targets were produced using resonant laser radiation incident on the electron–atom interaction region. Calculations were performed in the relativistic convergent close-coupling, convergent close-coupling and relativistic distorted-wave approximations. The theoretical calculations show that the h electron-impact coherence parameter (EICP) is equal to 1/2, independent of the scattering angle. We use this result to present the L⊥ EICP for the (…6s7s 3S1)→(…6s6p 3P1) collision process.

H2infrared line emission from the ionized region of planetary nebulae

The analysis and interpretation of the H2 line emission from planetary nebulae have been done in the literature assuming that the molecule survives only in regions where the hydrogen is neutral, as in photodissociation, neutral clumps or shocked regions. However, there is strong observational and theoretical evidence that at least part of the H2 emission is produced inside the ionized region of such objects. The aim of the present work is to calculate and analyze the infrared line emission of H2 produced inside the ionized region of planetary nebulae using a one-dimensional photoionization code. The photoionization code Aangaba was improved in order to calculate the statistical population of the H2 energy levels and the intensity of the H2 infrared emission lines in physical conditions typical of planetary nebulae. A grid of models was obtained and the results are analyzed and compared with the observational data. We show that the contribution of the ionized region to the H2 line emission can be important, particularly in the case of nebulae with high temperature central stars. This result explains why H2 emission is more frequently observed in bipolar planetary nebulae (Gatley's rule), since this kind of object typically has hotter stars. Collisional excitation plays an important role on the population of the rovibrational levels of the electronic ground state of H2. Radiative mechanisms are also important, particularly for the upper vibrational levels. Formation pumping can have minor effects on the line intensities produced by de-excitation from very high rotational levels, especially in dense and dusty environments. We included the effect of the H2 on the thermal equilibrium of the gas, concluding that H2 only contributes to the thermal equilibrium in the case of a very high temperature of the central star or a high dust-to-gas ratio, mainly through collisional de-excitation.

Time‐averaged spatial profile of Xe excitation efficiency in PDPs

Abstract— The Xe excitation efficiency for various Xe content was analyzed by monitoring the panel luminance and IR emission intensity. It was found that dependences of the Xe excitation efficiency and luminous efficacy on the sustain voltage show almost the same tendency. A decrease for increasing sustaining voltage was found in a low‐Xe‐content panel and an increase was found in a high‐Xe‐content panel. A reduction in the effective electron temperature and a reduction in plasma saturation contribute to the efficacy improvement. The time‐averaged spatial profile of the Xe excitation efficiency in PDPs was investigated by measuring the distribution of IR and blue‐phosphor emissions. The results show that the Xe excitation efficiency is similar in the cathode and anode regions even though the spatial and time development of the discharge in these regions is very different. An extended theory that takes into account not only the radiative transition process but also the collisional de‐excitation process from Xe** to Xe* is proposed for investigating the pressure dependence of the Xe excitation efficiency. By using the proposed theory, it was found that Xe excitation efficiency increases, attains a maximum value at 30% Xe, then decreases as the Xe content is increased, when the rate coefficient of the collisional de‐excitation process is less than 1.0 × 10−10 cm3/sec.