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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

SIMULATIONS OF ALFVÉN AND KINK WAVE DRIVING OF THE SOLAR CHROMOSPHERE: EFFICIENT HEATING AND SPICULE LAUNCHING

Two of the central problems in our understanding of the solar chromosphere are how the upper chromosphere is heated and what drives spicules. Estimates of the required chromospheric heating, based on radiative and conductive losses, suggest a rate of ∼0.1 erg cm{sup −3} s{sup −1} in the lower chromosphere and drops to ∼10{sup −3} erg cm{sup −3} s{sup −1} in the upper chromosphere. The chromosphere is also permeated by spicules, higher density plasma from the lower atmosphere propelled upwards at speeds of ∼10–20 km s{sup −1}, for so-called Type I spicules, which reach heights of ∼3000–5000 km above the photosphere. A clearer understanding of chromospheric dynamics, its heating, and the formation of spicules is thus of central importance to solar atmospheric science. For over 30 years it has been proposed that photospheric driving of MHD waves may be responsible for both heating and spicule formation. This paper presents results from a high-resolution MHD treatment of photospheric driven Alfvén and kink waves propagating upwards into an expanding flux tube embedded in a model chromospheric atmosphere. We show that the ponderomotive coupling from Alfvén and kink waves into slow modes generates shocks, which both heat the upper chromosphere and drive spicules. These simulations show that wave driving of the solar chromosphere can give a local heating rate that matches observations and drive spicules consistent with Type I observations all within a single coherent model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Further Investigation on Chromospheric and Prominence Activity of the RS Canum Venaticorum Star SZ Piscium

To continue our study on chromospheric activity and detection for possible prominence events of the very active RS Canum Venaticorum star SZ Piscium (SZ Psc), long-term high-resolution spectroscopic observations were obtained during several observing runs from 2014 to 2018. Based on the spectral subtraction technique, the chromospheric emission of the Ca ii IRT (λ8662, λ8542, and λ8498), H{sub α}, Na i D{sub 1}, D{sub 2} doublet, H{sub β}, and Ca ii H & K lines is mainly associated with the K1 IV primary star of the SZ Psc system, in good agreement with the previous studies, and the F8 V secondary star also shows some chromospheric emission, implying its active chromosphere. Moreover, an optical flare characterized by the He i D{sub 3} line emission together with stronger emission in the other indicators was detected. Furthermore, two chromospheric active longitudes around the two quadratures of the system were identified for most of the time, and the chromospheric activity shows significant changes during a few orbital cycles. The chromospheric activity level seems to show a long-term variation during our observations. There were some excess absorption features in the subtracted H{sub α} line and the other activity indicators, which would be caused by prominence-like materials associated with the K1 IV primary star of the system. Prominence materials could absorb the chromospheric emission and continuum from the K1 IV primary star and even the F8 V secondary one.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

ON THE MISALIGNMENT BETWEEN CHROMOSPHERIC FEATURES AND THE MAGNETIC FIELD ON THE SUN

Observations of the upper chromosphere show an enormous amount of intricate fine structure. Much of this comes in the form of linear features, which are most often assumed to be well aligned with the direction of the magnetic field in the low plasma β regime that is thought to dominate the upper chromosphere. We use advanced radiative magnetohydrodynamic simulations, including the effects of ion-neutral interactions (using the generalized Ohm’s law) in the partially ionized chromosphere, to show that the magnetic field is often not well aligned with chromospheric features. This occurs where the ambipolar diffusion is large, i.e., ions and neutral populations decouple as the ion-neutral collision frequency drops, allowing the field to slip through the neutral population; where currents perpendicular to the field are strong; and where thermodynamic timescales are longer than or similar to those of ambipolar diffusion. We find this often happens in dynamic spicule or fibril-like features at the top of the chromosphere. This has important consequences for field extrapolation methods, which increasingly use such upper chromospheric features to help constrain the chromospheric magnetic field: our results invalidate the underlying assumption that these features are aligned with the field. In addition, our results cast doubt on results from 1D hydrodynamic models, which assume that plasma remains on the same field lines. Finally, our simulations show that ambipolar diffusion significantly alters the amount of free energy available in the coronal part of our simulated volume, which is likely to have consequences for studies of flare initiation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SIMULATIONS OF THE MG ii K AND CA ii 8542 LINES FROM AN ALFVÉN WAVE-HEATED FLARE CHROMOSPHERE

We use radiation hydrodynamic simulations to examine two models of solar flare chromospheric heating: Alfvén wave dissipation and electron beam collisional losses. Both mechanisms are capable of strong chromospheric heating, and we show that the distinctive atmospheric evolution in the mid-to-upper chromosphere results in Mg ii k-line emission that should be observably different between wave-heated and beam-heated simulations. We also present Ca ii 8542 Å profiles that are formed slightly deeper in the chromosphere. The Mg ii k-line profiles from our wave-heated simulation are quite different from those from a beam-heated model and are more consistent with Interface Region Imaging Spectrograph observations. The predicted differences between the Ca ii 8542 Å in the two models are small. We conclude that careful observational and theoretical study of lines formed in the mid-to-upper chromosphere holds genuine promise for distinguishing between competing models for chromospheric heating in flares.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A Three-dimensional Magnetohydrodynamic Simulation of the Formation of Solar Chromospheric Jets with Twisted Magnetic Field Lines

This paper presents a three-dimensional simulation of chromospheric jets with twisted magnetic field lines. Detailed treatments of the photospheric radiative transfer and the equations of state allow us to model realistic thermal convection near the solar surface, which excites various MHD waves and produces chromospheric jets in the simulation. A tall chromospheric jet with a maximum height of 10–11 Mm and lifetime of 8–10 minutes is formed above a strong magnetic field concentration. The magnetic field lines are strongly entangled in the chromosphere, which helps the chromospheric jet to be driven by the Lorentz force. The jet exhibits oscillatory motion as a natural consequence of its generation mechanism. We also find that the produced chromospheric jet forms a cluster with a diameter of several Mm with finer strands. These results imply a close relationship between the simulated jet and solar spicules.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

( Hinode Hinode) and IRIS observations of the magnetohydrodynamic waves propagating from the photosphere to the chromosphere in a sunspot

Magnetohydrodynamic (MHD) waves have been considered as energy sources for heating the solar chromosphere and the corona. Although MHD waves have been observed in the solar atmosphere, there are a lack of quantitative estimates on the energy transfer and dissipation in the atmosphere. We performed simultaneous Hinode and Interface Region Imaging Spectrograph observations of a sunspot umbra to derive the upward energy fluxes at two different atmospheric layers (photosphere and lower transition region) and estimate the energy dissipation. The observations revealed some properties of the observed periodic oscillations in physical quantities, such as their phase relations, temporal behaviors, and power spectra, making a conclusion that standing slow-mode waves are dominant at the photosphere with their high-frequency leakage, which is observed as upward waves at the chromosphere and the lower transition region. Our estimates of upward energy fluxes are 2.0×10{sup 7} erg cm{sup −2} s{sup −1} at the photospheric level and 8.3×10{sup 4} erg cm{sup −2} s{sup −1} at the lower transition region level. The difference between the energy fluxes is larger than the energy required to maintain the chromosphere in the sunspot umbrae, suggesting that the observed waves can make a crucial contribution to the heating of the chromosphere in the sunspot umbrae. In contrast, the upward energy flux derived at the lower transition region level is smaller than the energy flux required for heating the corona, implying that we may need another heating mechanism. We should, however, note a possibility that the energy dissipated at the chromosphere might be overestimated because of the opacity effect.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

First detection of chromospheric magnetic field changes during an X1-flare

Stepwise changes of the photospheric magnetic field, which often becomes more horizontal, have been observed during many flares. Previous interpretations include coronal loops that contract, and it has been speculated that such jerks could be responsible for sunquakes. Here we report the detection of stepwise chromospheric line-of-sight magnetic field (B{sub LOS}) changes obtained through spectropolarimetry of Ca ii 8542 Å with DST/IBIS during the X1-flare SOL20140329T17:48. These changes are stronger (<640 Mx cm{sup −2}) and appear in larger areas than their photospheric counterparts (<320 Mx cm{sup −2}). The absolute value of B{sub LOS} more often decreases than increases. Photospheric changes are predominantly located near a polarity inversion line, and chromospheric changes near the footpoints of loops. The locations of changes are near, but not exactly co-spatial to hard X-ray emission and neither to enhanced continuum emission nor to a small sunquake. Enhanced chromospheric and coronal emission is observed in nearly all locations that exhibit changes of B{sub LOS}, but the emission also occurs in many locations without any B{sub LOS} changes. Photospheric and chromospheric changes of B{sub LOS} show differences in timing, sign, and size and seem independent of each other. A simple model of contracting loops yields changes of the opposite sign to those observed. An explanation for this discrepancy could be increasing loop sizes or loops that untwist in a certain direction during the flare. It is yet unclear which processes are responsible for the observed changes and their timing, size, and location, especially considering the incoherence between the photosphere and the chromosphere.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Two-dimensional Radiative Magnetohydrodynamic Simulations of Partial Ionization in the Chromosphere. II. Dynamics and Energetics of the Low Solar Atmosphere

We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion–neutral interaction effects using the generalized Ohm’s law, i.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere, and transition region partially ionized. Our simulations reveal that the interactions between ionized particles and neutral particles have important consequences for the magnetothermodynamics of these modeled layers: (1) ambipolar diffusion increases the temperature in the chromosphere; (2) sporadically the horizontal magnetic field in the photosphere is diffused into the chromosphere, due to the large ambipolar diffusion; (3) ambipolar diffusion concentrates electrical currents, leading to more violent jets and reconnection processes, resulting in (3a) the formation of longer and faster spicules, (3b) heating of plasma during the spicule evolution, and (3c) decoupling of the plasma and magnetic field in spicules. Our results indicate that ambipolar diffusion is a critical ingredient for understanding the magnetothermodynamic properties in the chromosphere and transition region. The numerical simulations have been made publicly available, similar to previous Bifrost simulations. This will allow the community to study realistic numerical simulations with a wider range of magnetic field configurations and physics modules than previously possible.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

ALFVÉNIC WAVE HEATING OF THE UPPER CHROMOSPHERE IN FLARES

We have developed a numerical model of flare heating due to the dissipation of Alfvénic waves propagating from the corona to the chromosphere. With this model, we present an investigation of the key parameters of these waves on the energy transport, heating, and subsequent dynamics. For sufficiently high frequencies and perpendicular wave numbers, the waves dissipate significantly in the upper chromosphere, strongly heating it to flare temperatures. This heating can then drive strong chromospheric evaporation, bringing hot and dense plasma to the corona. We therefore find three important conclusions: (1) Alfvénic waves, propagating from the corona to the chromosphere, are capable of heating the upper chromosphere and the corona, (2) the atmospheric response to heating due to the dissipation of Alfvénic waves can be strikingly similar to heating by an electron beam, and (3) this heating can produce explosive evaporation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

CHROMOSPHERIC EMISSION OF PLANET CANDIDATE HOST STARS: A WAY TO IDENTIFY FALSE POSITIVES

It has been hypothesized that the presence of closely orbiting giant planets is associated with enhanced chromospheric emission of their host stars. The main cause for such a relation would likely be enhanced dynamo action induced by the planet. We present measurements of chromospheric emission in 234 planet candidate systems from the Kepler mission. This ensemble includes 37 systems with giant-planet candidates, which show a clear emission enhancement. The enhancement, however, disappears when systems that are also identified as eclipsing binary candidates are removed from the ensemble. This suggests that a large fraction of the giant-planet candidate systems with chromospheric emission stronger than the Sun are not giant-planet systems, but false positives. Such false-positive systems could be tidally interacting binaries with strong chromospheric emission. This hypothesis is supported by an analysis of 188 eclipsing binary candidates that show increasing chromospheric emission as function of decreasing orbital period.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

CHROMOSPHERIC HEATING BY ACOUSTIC WAVES COMPARED TO RADIATIVE COOLING

Acoustic and magnetoacoustic waves are among the possible candidate mechanisms that heat the upper layers of the solar atmosphere. A weak chromospheric plage near the large solar pore NOAA 11005 was observed on 2008 October 15, in the Fe i 617.3 nm and Ca ii 853.2 nm lines of the Interferometric Bidimemsional Spectrometer attached to the Dunn Solar Telescope. In analyzing the Ca ii observations (with spatial and temporal resolutions of 0.″4 and 52 s) the energy deposited by acoustic waves is compared to that released by radiative losses. The deposited acoustic flux is estimated from the power spectra of Doppler oscillations measured in the Ca ii line core. The radiative losses are calculated using a grid of seven one-dimensional hydrostatic semi-empirical model atmospheres. The comparison shows that the spatial correlation of the maps of radiative losses and acoustic flux is 72%. In a quiet chromosphere, the contribution of acoustic energy flux to radiative losses is small, only about 15%. In active areas with a photospheric magnetic-field strength between 300 and 1300 G and an inclination of 20°–60°, the contribution increases from 23% (chromospheric network) to 54% (a plage). However, these values have to be considered as lower limits and it might be possible that the acoustic energy flux is the main contributor to the heating of bright chromospheric network and plages.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

CHROMOSPHERIC AND CORONAL WAVE GENERATION IN A MAGNETIC FLUX SHEATH

Using radiation magnetohydrodynamic simulations of the solar atmospheric layers from the upper convection zone to the lower corona, we investigate the self-consistent excitation of slow magneto-acoustic body waves (slow modes) in a magnetic flux concentration. We find that the convective downdrafts in the close surroundings of a two-dimensional flux slab “pump” the plasma inside it in the downward direction. This action produces a downflow inside the flux slab, which encompasses ever higher layers, causing an upwardly propagating rarefaction wave. The slow mode, excited by the adiabatic compression of the downflow near the optical surface, travels along the magnetic field in the upward direction at the tube speed. It develops into a shock wave at chromospheric heights, where it dissipates, lifts the transition region, and produces an offspring in the form of a compressive wave that propagates further into the corona. In the wake of downflows and propagating shock waves, the atmosphere inside the flux slab in the chromosphere and higher tends to oscillate with a period of ν ≈ 4 mHz. We conclude that this process of “magnetic pumping” is a most plausible mechanism for the direct generation of longitudinal chromospheric and coronal compressive waves within magnetic flux concentrations, and it may provide an important heat source in the chromosphere. It may also be responsible for certain types of dynamic fibrils.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

RELATIONSHIP BETWEEN CHROMOSPHERIC EVAPORATION AND MAGNETIC FIELD TOPOLOGY IN AN M-CLASS SOLAR FLARE

Chromospheric evaporation is observed as Doppler blueshift during solar flares. It plays a key role in the dynamics and energetics of solar flares; however, its mechanism is still unknown. In this paper, we present a detailed analysis of spatially resolved multi-wavelength observations of chromospheric evaporation during an M 1.0-class solar flare (SOL2014-06-12T21:12) using data from NASA’s Interface Region Imaging Spectrograph and HMI/ SDO (the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory), and high-resolution observations from VIS/NST (the Visible Imaging Spectrometer at the New Solar Telescope). The results show that the averaged over the flare region Fe xxi blueshift of the hot (10{sup 7} K) evaporating plasma is delayed relative to the C ii redshift of the relatively cold (10{sup 4} K) chromospheric plasma by about one minute. The spatial distribution of the delays is not uniform across the region and can be as long as two minutes in several zones. Using vector magnetograms from HMI, we reconstruct the magnetic field topology and the quasi-separatrix layer, and find that the blueshift delay regions as well as the H α flare ribbons are connected to the region of the magnetic polarity inversion line (PIL) and an expanding flux rope via a system of low-lying loop arcades with a height of ≲4.5 Mm. As a result, the chromospheric evaporation may be driven by the energy release in the vicinity of PIL, and has the observed properties due to a local magnetic field topology.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

KELVIN–HELMHOLTZ INSTABILITY IN SOLAR CHROMOSPHERIC JETS: THEORY AND OBSERVATION

Using data obtained by the high-resolution CRisp Imaging SpectroPolarimeter instrument on the Swedish 1 m Solar Telescope, we investigate the dynamics and stability of quiet-Sun chromospheric jets observed at the disk center. Small-scale features, such as rapid redshifted and blueshifted excursions, appearing as high-speed jets in the wings of the H α line, are characterized by short lifetimes and rapid fading without any descending behavior. To study the theoretical aspects of their stability without considering their formation mechanism, we model chromospheric jets as twisted magnetic flux tubes moving along their axis, and use the ideal linear incompressible magnetohydrodynamic approximation to derive the governing dispersion equation. Analytical solutions of the dispersion equation indicate that this type of jet is unstable to Kelvin–Helmholtz instability (KHI), with a very short (few seconds) instability growth time at high upflow speeds. The generated vortices and unresolved turbulent flows associated with the KHI could be observed as a broadening of chromospheric spectral lines. Analysis of the H α line profiles shows that the detected structures have enhanced line widths with respect to the background. We also investigate the stability of a larger-scale H α jet that was ejected along the line of sight. Vortex-like features, rapidly developing around the jet’s boundary, are considered as evidence of the KHI. The analysis of the energy equation in the partially ionized plasma shows that ion–neutral collisions may lead to fast heating of the KH vortices over timescales comparable to the lifetime of chromospheric jets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Chromospheric and coronal activity in the 500 MYR old open cluster M37: evidence for coronal stripping?

We present the results of a spectroscopic survey to characterize chromospheric activity, as measured by Hα emission, in low-mass members of the 500 Myr old open cluster M37. Combining our new measurements of Hα luminosities (L{sub Hα}) with previously cataloged stellar properties, we identify saturated and unsaturated regimes in the dependence of the L{sub Hα}-to-bolometric luminosity ratio, L{sub Hα}/L{sub bol}, on the Rossby number R{sub o}. All rotators with R{sub o} smaller than 0.03 ± 0.01 converge to an activity level of L{sub Hα}/L{sub bol}=(1.27±0.02)×10{sup −4}. This saturation threshold (R{sub o,sat}=0.03±0.01) is statistically smaller than that found in most studies of the rotation–activity relation. In the unsaturated regime, slower rotators have lower levels of chromospheric activity, with L{sub Hα}/L{sub bol}(R{sub o}) following a power-law of index β=−0.51±0.02, slightly shallower than that found for a combined ≈650 Myr old sample of Hyades and Praesepe stars. By comparing this unsaturated behavior to that previously found for coronal activity in M37 (as measured via the X-ray luminosity, L{sub X}), we confirm that chromospheric activity decays at a much slower rate than coronal activity with increasing R{sub o}. While a comparison of L{sub Hα} and L{sub X} for M37 members with measurements of both reveals a nearly 1:1 relation, removing the mass-dependencies by comparing instead L{sub Hα}/L{sub bol} and L{sub X}/L{sub bol} does not provide clear evidence for such a relation. Finally, we find that R{sub o,sat} is smaller for our chromospheric than for our coronal indicator of activity (R{sub o,sat}=0.03±0.01 versus 0.09 ± 0.01). We interpret this as possible evidence for coronal stripping.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Multi-fluid Modeling of Magnetosonic Wave Propagation in the Solar Chromosphere: Effects of Impact Ionization and Radiative Recombination

In order to study chromospheric magnetosonic wave propagation including, for the first time, the effects of ion–neutral interactions in the partially ionized solar chromosphere, we have developed a new multi-fluid computational model accounting for ionization and recombination reactions in gravitationally stratified magnetized collisional media. The two-fluid model used in our 2D numerical simulations treats neutrals as a separate fluid and considers charged species (electrons and ions) within the resistive MHD approach with Coulomb collisions and anisotropic heat flux determined by Braginskiis transport coefficients. The electromagnetic fields are evolved according to the full Maxwell equations and the solenoidality of the magnetic field is enforced with a hyperbolic divergence-cleaning scheme. The initial density and temperature profiles are similar to VAL III chromospheric model in which dynamical, thermal, and chemical equilibrium are considered to ensure comparison to existing MHD models and avoid artificial numerical heating. In this initial setup we include simple homogeneous flux tube magnetic field configuration and an external photospheric velocity driver to simulate the propagation of MHD waves in the partially ionized reactive chromosphere. In particular, we investigate the loss of chemical equilibrium and the plasma heating related to the steepening of fast magnetosonic wave fronts in the gravitationally stratified medium.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A Model of the Solar Chromosphere: Structure and Internal Circulation

A model of the solar chromosphere that consists of two fundamentally different regions, a lower region and an upper region, is proposed. The lower region is covered mostly by weak locally closed magnetic field and small network areas of extremely strong, locally open field. The field in the upper region is relatively uniform and locally open, connecting to the corona. The chromosphere is heated by strong collisional damping of Alfvén waves, which are driven by turbulent motions below the photosphere. The heating rate depends on the field strength, wave power from the photosphere, and altitude in the chromosphere. The waves in the internetwork area are mostly damped in the lower region, supporting radiation in the lower chromosphere. The waves in the network area, carrying more Poynting flux, are only weakly damped in the lower region. They propagate into the upper region. As the thermal pressure decreases with height, the network field expands to form the magnetic canopy where the damping of the waves from the network area supports radiation in the whole upper region. Because of the vertical stratification and horizontally nonuniform distribution of the magnetic field and heating, one circulation cell is formed in each of the upper and lower regions. The two circulation cells distort the magnetic field and reinforce the funnel-canopy-shaped magnetic geometry. The model is based on classical processes and is semi-quantitative. The estimates are constrained according to observational knowledge. No anomalous process is invoked or needed. Overall, the heating mechanism is able to damp 50% of the total wave energy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

RESOLVING THE FAN-SPINE RECONNECTION GEOMETRY OF A SMALL-SCALE CHROMOSPHERIC JET EVENT WITH THE NEW SOLAR TELESCOPE

Jets are ubiquitously present in both quiet and active regions on the Sun. They are widely believed to be driven by magnetic reconnection. A fan-spine structure has been frequently reported in some coronal jets and flares, and has been regarded as a signature of ongoing magnetic reconnection in a topology consisting of a magnetic null connected by a fan-like separatrix surface and a spine. However, for small-scale chromospheric jets, clear evidence of such structures is rather rare, although it has been implied in earlier works that showed an inverted-Y-shaped feature. Here we report high-resolution (0.″16) observations of a small-scale chromospheric jet obtained by the New Solar Telescope (NST) using 10830 Å filtergrams. Bi-directional flows were observed across the separatrix regions in the 10830 Å images, suggesting that the jet was produced due to magnetic reconnection. At the base of the jet, a fan-spine structure was clearly resolved by the NST, including the spine and the fan-like surface, as well as the loops before and after the reconnection. A major part of this fan-spine structure, with the exception of its bright footpoints and part of the base arc, was invisible in the extreme ultraviolet and soft X-ray images (observed by the Atmosphere Imaging Assembly and the X-Ray Telescope, respectively), indicating that the reconnection occurred in the upper chromosphere. Our observations suggest that the evolution of this chromospheric jet is consistent with a two-step reconnection scenario proposed by Török et al.

79 ASTRONOMY AND ASTROPHYSICS↗