The solar atmosphere is dominated by loops of magnetic flux which connect the multi-million-degree corona to the much cooler chromosphere. The temperature and density structure of quasi-static loops is determined by the continuous flow of energy from the hot corona to the lower solar atmosphere. Loop scaling laws provide relationships between global properties of the loop (such as peak temperature, pressure, and length); they follow from the physical variable dependencies of various terms in the energy equation, and hence the form of the loop scaling law provides insight into the key physics that controls the loop structure. Traditionally, scaling laws have been derived under the assumption of collision-dominated thermal conduction. Here we examine the impact of different regimes of thermal conduction -- collision-dominated, turbulence-dominated, and free-streaming -- on the form of the scaling laws relating the loop temperature and heating rate to its pressure and half-length. We show that the scaling laws for turbulence-dominated conduction are fundamentally different than those for collision-dominated and free-streaming conduction, inasmuch as the form of the scaling laws now depend primarily on conditions at the low-temperature, rather than high-temperature, part of the loop. We also establish regimes in temperature and density space in which each of the applicable scaling laws prevail.
We investigate the impact of turbulent suppression of parallel heat conduction on the cooling of post-flare coronal loops. Depending on the value of the mean free path $λ_T$ associated with the turbulent scattering process, we identify four main cooling scenarios. The overall temperature evolution, from an initial temperature in excess of $10^7$~K, is modeled in each case, highlighting the evolution of the dominant cooling mechanism throughout the cooling process. Comparison with observed cooling times allows the value of $λ_T$ to be constrained, and interestingly this range corresponds to sit…
It is known from numerical simulations that thermal conduction along magnetic field lines plays an important role in the evolution of the kink instability in coronal loops. This study presents the observational signatures of the kink instability in long coronal loops when parallel thermal conduction is included. The 3D nonlinear magnetohydrodynamic equations are solved numerically to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The loop has length 80 Mm, width 8 Mm and an initial maximum twist of Phi = 11.5 pi, where Phi is a function of the radius. Th…
We investigate the effect of a variable, i.e. time-dependent, background on the standing acoustic (i.e. longitudinal) modes generated in a hot coronal loop. A theoretical model of 1D geometry describing the coronal loop is applied. The background temperature is allowed to change as a function of time and undergoes an exponential decay with characteristic cooling times typical for coronal loops. The magnetic field is assumed to be uniform. Thermal conduction is the dominant mechanism of cooling the hot background plasma in the presence of an unspecified thermodynamic source that maintains the i…
Coronal supra-arcade downflows (SADs) are observed as dark trails descending towards hot turbulent fan shaped regions. Due to the large temperature values, and gradients in these fan regions the thermal conduction should be very efficient. While several models have been proposed to explain the triggering and the evolution of SADs, none of these scenarios address a systematic consideration of thermal conduction. Thus, we accomplish this task numerically simulating the evolution of SADs within this framework. That is, SADs are conceived as voided (subdense) cavities formed by non-linear waves tr…
Slow magnetoacoustic waves were first detected in hot ($>$6 MK) flare loops by the SOHO/SUMER spectrometer as Doppler shift oscillations in Fe XIX and Fe XXI lines. Recently, such longitudinal waves have been found by SDO/AIA in the 94 and 131 Å channels. Wang et al. (2015) reported the first AIA event revealing signatures in agreement with a fundamental standing slow-mode wave, and found quantitative evidence for thermal conduction suppression from the temperature and density perturbations in the hot loop plasma of $\gtrsim$ 9 MK. The present study extends the work of Wang et al. (2015) by us…
To understand the nonlinear dynamics of the Parker scenario for coronal heating, long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry are carried out. A loop is modeled as a box extended along the direction of the strong magnetic field $B_0$ in which the system is embedded. At the top and bottom plates, which represent the photosphere, velocity fields mimicking photospheric motions are imposed. We show that the nonlinear dynamics is described by different regimes of MHD anisotropic turbulence, with spectra characterized by intertial range power laws who…
The effect of temperature inhomogeneity on the periods, their ratios (fundamental vs. first overtone), and the damping times of the standing slow modes in gravitationally stratified solar coronal loops are studied. The effects of optically thin radiation, compressive viscosity, and thermal conduction are considered. The linearized one-dimensional magnetohydrodynamic (MHD) equations (under low-$β$ condition) were reduced to a fourth--order ordinary differential equation for the perturbed velocity. The numerical results indicate that the periods of non-isothermal loops (i.e. temperature increase…
Slow magnetoacoustic waves represent an important tool for probing the solar coronal plasma. We quantitatively assess the applicability of the weak thermal conduction theory to coronal seismology by slow waves. We numerically model the linear standing slow wave in a 1D coronal loop, with field-aligned thermal conduction $κ_\parallel$ as a free parameter and no restrictions on its efficiency. The time variations of the perturbed plasma parameters, obtained numerically with full conductivity, are treated as potential observables and analysed with the standard data processing techniques. The slow…
Observations of slow magneto-acoustic waves have been demonstrated to possess a number of applications in coronal seismology. Determination of the polytropic index ($γ$) is one such important application. Analysing the amplitudes of oscillations in temperature and density corresponding to a slow magneto-acoustic wave, the polytropic index in the solar corona has been calculated and based on the obtained value it has been inferred that thermal conduction is highly suppressed in a very hot loop in contrast to an earlier report of high thermal conduction in a relatively colder loop. In this study…
We simulate a coronal mass ejection (CME) using a three-dimensional magnetohydrodynamic (MHD) code that includes coronal heating, thermal conduction, and radiative cooling in the energy equation. The magnetic flux distribution at 1 R$_s$ is produced by a localized subsurface dipole superimposed on a global dipole field, mimicking the presence of an active region within the global corona. Transverse electric fields are applied near the polarity inversion line to introduce a transverse magnetic field, followed by the imposition of a converging flow to form and destabilize a flux rope, producing …
Analysis of a longitudinal wave event observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) is presented. A time sequence of 131 A images reveals that a C-class flare occurred at one footpoint of a large loop and triggered an intensity disturbance (enhancement) propagating along it. The spatial features and temporal evolution suggest that a fundamental standing slow-mode wave could be set up quickly after meeting of two initial disturbances from the opposite footpoints. The oscillations have a period of ~12 min and a decay time of ~9 min. The measured …
The scaling laws which relate the peak temperature $T_M$ and volumetric heating rate $E_H$ to the pressure $P$ and length $L$ for static coronal loops were established over 40 years ago; they have proved to be of immense value in a wide range of studies. Here we extend these scaling laws to {\it dynamic} loops, where enthalpy flux becomes important to the energy balance, and study impulsive heating/filling characterized by upward enthalpy flows. We show that for collision-dominated thermal conduction, the functional dependencies of the scaling laws are the same as for the static case, when the…
Recent studies of a flaring loop oscillation event on 2013 December 28 observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) have revealed the suppression of thermal conduction and significant enhancement of compressive viscosity in hot ($\sim$10 MK) plasma. In this study we aim at developing a new coronal seismology method for determining the transport coefficients based on a parametric study of wave properties using a 1D nonlinear MHD loop model in combination with the linear theory. The simulations suggest a two-step scheme: we first determine the effect…
We study the formation of coronal jets through numerical simulation of the emergence of a twisted magnetic flux rope into a pre-existing open magnetic field. Reconnection inside the emerging flux rope in addition to that between the emerging and pre-existing fields give rise to the violent eruption studied. The simulated event closely resembles the coronal jets ubiquitously observed by Hinode/XRT and demonstrates that heated plasma is driven into the extended atmosphere above. Thermal conduction implemented in the model allows us to qualitatively compare simulated and observed emission from su…
Context. The structure and heating of coronal loops are investigated since decades. Established scaling laws relate fundamental quantities like the loop apex temperature, pressure, length, and the coronal heating. Aims. We test such scaling laws against a large-scale 3D MHD model of the Solar corona, which became feasible with nowadays high-performance computing. Methods. We drive an active region simulation a with photospheric observations and found strong similarities to the observed coronal loops in X-rays and EUV wavelength. A 3D reconstruction of stereoscopic observations showed that our …
The Enthalpy Based Thermal Evolution of Loops (EBTEL) approximate model for static and dynamic coronal loops is developed to include the effect of a loop cross-sectional area which increases from the base of the transition region (TR) to the corona. The TR is defined as the part of a loop between the top of the chromosphere and the location where thermal conduction changes from an energy loss to an energy gain. There are significant differences from constant area loops due to the manner in which the reduced volume of the TR responds to conductive and enthalpy fluxes from the corona. For static…
We study a series of relations between physical parameters in coronal loops of the quiet Sun reconstructed by combining tomographic techniques and modeling of the coronal magnetic field. We use differential emission measure tomography (DEMT) to determine the three-dimensional distribution of the electron density and temperature in the corona, and we model the magnetic field with a potential-field source-surface (PFSS) extrapolation of a synoptic magnetogram. By tracing the DEMT products along the extrapolated magnetic field lines, we obtain loop-averaged electron density and temperature. Also,…
Using the "enthalpy-based thermal evolution of loops" (EBTEL) model, we investigate the hydrodynamics of the plasma in a flaring coronal loop in which heat conduction is limited by turbulent scattering of the electrons that transport the thermal heat flux. The EBTEL equations are solved analytically in each of the two (conduction-dominated and radiation-dominated) cooling phases. Comparison of the results with typical observed cooling times in solar flares shows that the turbulent mean free-path $λ_T$ lies in a range corresponding to a regime in which classical (collision-dominated) conduction…
Srivastava et al. (2010) have observed a highly twisted coronal loop, which was anchored in AR10960 during the period 04:43 UT-04:52 UT on 4 June 2007. The loop length and radius are approximately 80 Mm and 4 Mm, with a twist of 11.5 $π$. These observations are used as initial conditions in a three dimensional nonlinear magnetohydrodynamic simulation with parallel thermal conduction included. The initial unstable equilibrium evolves into the kink instability, from which synthetic observables are generated for various high-temperature filters of SDO/AIA. These observables include temporal and s…
We investigate the effect of coronal temperature on the formation process of solar chromospheric jets using two-dimensional magnetohydrodynamic simulations of the region from the upper convection zone to the lower corona. We develop a new radiative magnetohydrodynamic code for the dynamic modeling of the solar atmosphere, employing a LTE equation of state, optically thick radiative loss in the photosphere, optically thin radiative loss in the chromosphere and the corona, and thermal conduction along the magnetic field lines. Many chromospheric jets are produced in the simulations by shock wave…
The Interface Region Imaging Spectrograph (IRIS) has observed bright spots at the transition region footpoints associated with heating in the overlying loops, as observed by coronal imagers. Some of these brightenings show significant blueshifts in the Si iv line at 1402.77 A (logT[K] = 4.9). Such blueshifts cannot be reproduced by coronal loop models assuming heating by thermal conduction only, but are consistent with electron beam heating, highlighting for the first time the possible importance of non-thermal electrons in the heating of non-flaring active regions. Here we report on the coron…
The expansion of coronal loops in the transition region may considerably influence the diagnostics of the plasma emission measure. The cross sectional area of the loops is expected to depend on the temperature and pressure, and might be sensitive to the heating rate. The approach here is to study the area response to slow changes in the coronal heating rate, and check the current interpretation in terms of steady heating models. We study the area response with a time-dependent 2D MHD loop model, including the description of the expanding magnetic field, coronal heating and losses by thermal co…
2.5-dimensional magnetohydrodynamic (MHD) simulations are performed with high spatial resolution in order to distinguish between competing models of the coronal heating problem. A single coronal loop powered by Alfvén waves excited in the photosphere is the target of the present study. The coronal structure is reproduced in our simulations as a natural consequence of the transportation and dissipation of Alfvén waves. Further, the coronal structure is maintained as the spatial resolution is changed from 25 to 3 km, although the temperature at the loop top increases with the spatial resolution.…
Strongly damped Doppler shift oscillations are observed frequently associated with flarelike events in hot coronal loops. In this paper, a review of the observed properties and the theoretical modeling is presented. Statistical measurements of physical parameters (period, decay time, and amplitude) have been obtained based on a large number of events observed by SOHO/SUMER and Yohkoh/BCS. Several pieces of evidence are found to support their interpretation in terms of the fundamental standing longitudinal slow mode. The high excitation rate of these oscillations in small- or micro-flares sugge…
Recent observational and numerical studies show a variety of thermal structures in the solar chromosphere. Given that the thermal interplay across the transition region is a key to coronal heating, it is worth investigating how different thermal structures of the chromosphere yield different coronal properties. In this work, by MHD simulations of Alfvén-wave heating of coronal loops, we study how the coronal properties are affected by the chromospheric temperature. To this end, instead of solving the radiative transfer equation, we employ a simple radiative loss function so that the chromosphe…
Spectroscopic and stereoscopic imaging observations of slow magnetoacoustic wave propagation within a coronal loop are investigated to determine the decay length scale of the slow magnetoacoustic mode in three dimensions and the density profile within the loop system. The slow wave is found to have an e-folding decay length scale of $20,000^{+4000}_{-3000}$km with a uniform density profile along the loop base. These observations place quantitive constraints on the modelling of wave propagation within coronal loops. Theoretical forward modelling suggests that magnetic field line divergence is t…
Most solar flares demonstrate a prolonged, hourlong post-flare (or gradual) phase, characterized by arcade-like, post-flare loops (PFLs) visible in many extreme ultraviolet (EUV) passbands. These coronal loops are filled with hot -- $\sim 30 \,\mathrm{MK}$ -- and dense plasma, evaporated from the chromosphere during the impulsive phase of the flare, and they very gradually recover to normal coronal density and temperature conditions. During this gradual cooling down to $\sim 1 \,\mathrm{MK}$ regimes, much cooler -- $\sim 0.01 \,\mathrm{MK}$ -- and denser coronal rain is frequently observed ins…
Slow magnetosonic waves associated with flares were observed in coronal loops by SOHO/SUMER, SDO/AIA in various EUV bandpasses, and other instruments. The excitation and damping of slow magnetosonic waves provides information on the magnetic, temperature, and density structure of the loops. Recently, it was found using 1.5D models that the thermal conduction is suppressed and compressive viscosity is enhanced in hot (T>6 MK) flaring coronal loops. We model the excitation and dissipation of slow magnetosonic waves in hot coronal loops with realistic magnetic geometry, enhanced density, and temp…
Ponderomotive acceleration has been asserted to be a cause of the First Ionization Potential (FIP) effect, the by now well known enhancement in abundance by a factor of 3-4 over photospheric values of elements in the solar corona with FIP less than about 10 eV. It is shown here by means of numerical simulations that ponderomotive acceleration occurs in solar coronal loops, with the appropriate magnitude and direction, as a "byproduct" of coronal heating. The numerical simulations are performed with the HYPERION code, which solves the fully compressible three-dimensional magnetohydrodynamic equ…
The standing slow magneto-acoustic oscillations in cooling coronal loops are investigated. There are two damping mechanisms which are considered to generate the standing acoustic modes in coronal magnetic loops namely thermal conduction and radiation. The background temperature is assumed to change temporally due to optically thin radiation. In particular, the background plasma is assumed to be radiatively cooling. The effects of cooling on longitudinal slow MHD modes is analytically evaluated by choosing a simple form of radiative function that ensures the temperature evolution of the backgro…
Self-Consistent Heating of the Magnetically Closed Solar Corona: Generation of Nanoflares, Thermodynamic Response of the Plasma and Observational Signatures
We observed rapid variability ($\lesssim 60$ s) at the footpoints of transient hot ($\sim 8-10$ MK) coronal loops in active region cores, with the Interface Region Imaging Spectrograph (IRIS). The high spatial ($\sim 0.33$ arcsec) and temporal ($\lesssim 5$-10 s) resolution is often crucial for the detection of this variability. We show how, in combination with 1D RADYN loop modeling, these IRIS spectral observations of the transition region (TR) and chromosphere provide powerful diagnostics of the properties of coronal heating and energy transport (thermal conduction and/or non-thermal electr…
Observations show that the coronal X-ray emission of the Sun and other stars depends on the surface magnetic field. Using power-law scaling relations between different physical parameters, we build an analytical model to connect the observed X-ray emission to the magnetic flux. The basis for our model are the scaling laws of Rosner, Tucker \& Vaiana (RTV) that connect the temperature and pressure of a coronal loop to its length and energy input. To estimate the energy flux into the upper atmosphere, we use scalings derived for different heating mechanisms, e.g. for field-line braiding or Alfve…
We have demonstrated that the Transition Region Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, successfully removing the influence of numerical resolution on the coronal density response to impulsive heating. This is achieved by adjusting the parallel thermal conductivity, radiative loss, and heating rates to broaden the transition region (TR), below a global cutoff temperature, so that the steep gradients are spatially resolved even when using coarse numerical grids. Implementing the original 1D formulation of TRAC …
Propagating slow waves in coronal loops exhibit a damping which depends upon the frequency of the waves. In this study we aim to investigate the relationship of the damping length (L$_d$) with the frequency of the propagating wave. We present a 3-D coronal loop model with uniform density and temperature and investigate the frequency dependent damping mechanism for the four chosen wave periods. We include the thermal conduction to damp the waves as they propagate through the loop. The numerical model output has been forward modelled to generate synthetic images of SDO/AIA 171 Å and 193 Å channe…
It is extremely difficult to simulate the details of coronal heating and also make meaningful predictions of the emitted radiation. Thus, testing realistic models with observations is a major challenge. Observational signatures of coronal heating depend crucially on radiation, thermal conduction, and the exchange of mass and energy with the transition region and chromosphere below. Many magnetohydrodynamic simulation studies do not include these effects, opting instead to devote computational resources to the magnetic aspects of the problem. We have developed a simple method of accounting appr…
The heating of the solar chromosphere and corona to the observed high temperatures, imply the presence of ongoing heating that balances the strong radiative and thermal conduction losses expected in the solar atmosphere. It has been theorized for decades that the required heating mechanisms of the chromospheric and coronal parts of the active regions, quiet-Sun, and coronal holes are associated with the solar magnetic fields. However, the exact physical process that transport and dissipate the magnetic energy which ultimately leads to the solar plasma heating are not yet fully understood. The …
We investigate the heating of an erupting prominence and loops associated with a coronal mass ejection and X-class flare. The prominence is seen in absorption in EUV at the beginning of its eruption. Later the prominence changes to emission, which indicates heating of the erupting plasma. We find the densities of the erupting prominence using the absorption properties of hydrogen and helium in different passbands. We estimate the temperatures and densities of the erupting prominence and loops seen as emission features using the differential emission measure method, which uses both EUV and X-ra…
This Letter reports scaling laws of free magnetic energy stored in a solar emerging flux region which is a key to understanding the energetics of solar active phenomena such as solar flares and coronal mass ejections. By performing 3-dimensional magnetohydrodynamic simulations that reproduce several emerging flux regions of different magnetic configurations, we derive power law relationships among emerged magnetic flux, free magnetic energy and relative magnetic helicity in these emerging flux regions. Since magnetic flux is an observable quantity, the scaling law between magnetic flux and fre…
One proposed resolution to the long-standing problem of solar coronal heating involves the buildup of magnetic energy in the corona due to turbulent motions at the photosphere that braid the coronal field, and the subsequent release of this energy via magnetic reconnection. In this paper the ideal relaxation of braided magnetic fields modelling solar coronal loops is followed. A sequence of loops with increasing braid complexity is considered, with the aim of understanding how this complexity influences the development of small scales in the magnetic field, and thus the energy available for he…
Coronal loops are the basic building block of the upper solar atmosphere. Comprehending how these are energized, structured, and evolve is key to understanding stellar coronae. Here we investigate how the energy to heat the loop is generated by photospheric magneto-convection, transported into the upper atmosphere, and how the internal structure of a coronal loop forms. In a 3D magnetohydrodynamics (MHD) model, we study an isolated coronal loop rooted with both footpoints in a shallow layer within the convection zone using the MURaM code. To resolve its internal structure, we limited the compu…
Slow MHD waves are important tools for understanding the coronal structures and dynamics. In this paper, we report a number of observations, from X-Ray Telescope (XRT) on board HINODE and SDO/AIA of reflecting longitudinal waves in hot coronal loops. To our knowledge, this is the first report of this kind as seen from the XRT and simultaneously with the AIA. The wave appears after a micro-flare occurs at one of the footpoints. We estimate the density and the temperature of the loop plasma by performing DEM analysis on the AIA image sequence. The estimated speed of propagation is comparable or …
Magnetic reconnection in the corona results in contracting flare loops, releasing energy into plasma heating and shocks. The hydrodynamic shocks so produced drive thermal conduction fronts (TCFs) which transport energy into the chromosphere and drive upflows (evaporation) and downflows (condensation) in the cooler, denser footpoint plasma. Observations have revealed that certain properties of the transition point between evaporation and condensation (the "flow reversal point" or FRP), such as temperature and velocity-temperature derivative at the FRP, vary between different flares. These prope…
We investigate the propagation of MHD waves in a homogenous, magnetized plasma in a weakly stratified atmosphere, representing hot coronal loops. In most of earlier studies a time-independent equilibrium is considered. Here we abandon this restriction and allow the equilibrium to develop as function of time. In particular, the background plasma is assumed to be cooling due to thermal conduction. The cooling is assumed to be on a time scale greater than the characteristic travel times of the perturbations. We investigate the influence of cooling of the background plasma on the properties of mag…
We study a 2D cellular automaton (CA) model for the evolution of coronal loop plasmas. The model is based on the idea that coronal loops are made of elementary magnetic strands that are tangled and stressed by the displacement of their footpoints by photospheric motions. The magnetic stress accumulated between neighbor strands is released in sudden reconnection events or nanoflares that heat the plasma. We combine the CA model with the Enthalpy Based Thermal Evolution of Loops (EBTEL) model to compute the response of the plasma to the heating events. Using the known response of the XRT telesco…
Rapidly decaying long-period oscillations often occur in hot coronal loops of active regions associated with small (or micro-) flares. This kind of wave activity was first discovered with the SOHO/SUMER spectrometer from Doppler velocity measurements of hot emission lines, thus also often called "SUMER" oscillations. They were mainly interpreted as global (or fundamental mode) standing slow magnetoacoustic waves. In addition, increasing evidence has suggested that the decaying harmonic type of pulsations detected in light curves of solar and stellar flares are likely caused by standing slow-mo…
We develop and analyze a simple cellular automaton (CA) model that reproduces the main properties of the evolution of soft X-ray coronal loops. We are motivated by the observation that these loops evolve in three distinguishable phases that suggest the development, maintainance, and decay of a self-organized system. The model is based on the idea that loops are made of elemental strands that are heated by the relaxation of magnetic stress in the form of nanoflares. In this vision, usually called "the Parker conjecture" (Parker 1988), the origin of stress is the displacement of the strand footp…
Standing long-period (with the periods longer than several minutes) oscillations in large hot (with the temperature higher than 3 MK) coronal loops have been observed as the quasi-periodic modulation of the EUV and microwave intensity emission and the Doppler shift of coronal emission lines, and have been interpreted as standing slow magnetoacoustic (longitudinal) oscillations. Quasi-periodic pulsations of shorter periods, detected in thermal and non-thermal emissions in solar flares could be produced by a similar mechanism. We present theoretical modelling of the standing slow magnetoacoustic…
Observations reveal a correspondence between chromospheric type II spicules and bright upwardly moving fronts in the corona observed in the EUV band. However, theoretical considerations suggest that these flows are unlikely to be the main source of heating in coronal magnetic loops. We investigate the propagation of high-speed chromospheric flows into coronal magnetic flux tubes, and the possible production of emission in the EUV band. We simulate the propagation of a dense $10^4$ K chromospheric jet upwards along a coronal loop, by means of a 2-D cylindrical MHD model, including gravity, radi…
