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Rapid variability has been found in two active region coronal loops observed by the X-ray Polychromator (XRP) and the Hard X-ray Imaging Spectrometer (HXIS) onboard the Solar Maximum Mission (SMM). There appear to be surprisingly few observations of the short-time scale behavior of hot loops, and the evidence presented herein lends support to the hypothesis that coronal heating may be impulsive and driven by flaring.
Based on new observations, a theoretical model of magnetic-field related heating processes in the solar corona is given. In this model, field-aligned currents are induced along coronal loops in thin current sheaths. Excitation of instabilities involving magnetic reconnection converts the energy associated with the current-related magnetic field directly into particle energy, where the heating process proceeds via short bursts corresponding to an intermittent disruption of the current sheath configuration. Because of the relatively low transverse thermal conduction, only a small fraction of the loop volume is heated to a much higher temperature than the average value. This is consistent with experimental observations of low filling factors of hot plasmas in coronal loops. Thus the model involves a repeated sequence of dynamic events taking into account the observed loop topology, the differential emission measure distribution in the 10 exp 6 - 10 exp 7 K range, the energy balance requirements in the loop, and the probable duty cycles involved in the heating processes.
The physical and geometrical characteristics of solar coronal loop transients are described in an MHD model based on Archimedes' MHD buoyancy force. The theory was developed from interpretation of coronagraphic data, particularly from Skylab. The brightness of a loop is taken to indicate the electron density, and successive pictures reveal the electron enhancement in different columns. The forces which lift the loop off the sun surface are analyzed as an MHD buoyancy force affecting every mass element by imparting an inertial force necessary for heliocentrifugal motion. Thermal forces are responsible for transferring the ambient stress to the interior of the loop to begin the process. The kinematic and hydrostatic buoyancy overcome the gravitational force, and a flux rope can then curve upward, spiralling like a corkscrew with varying cross section around the unwinding solar magnetic field lines.
The radiative stability of thermally isolated coronal loops with free-flow boundary conditions by nonlinear numerical simulation are studied. A chromosphere-to-corona loop equilibrium (including the option of a deep chromosphere) is first established by following the nonlinear evolution from an initial isothermal state with rigid boundaries. The end conditions are then changed, to allow free flow and to fix the temperature, and investigate the response to nonisobaric perturbations. Within a family of loops of the same pressure, long hot loops to be stable and short cool loops to be unstable to the thermal chromospheric-expansion mode are found. The stable cases remain so, even when long chromospheric ends and/or gravity are added. In those cases which are unstable, the subsequent nonlinear evolution which exhibits swelling of the chromosphere until the entire loop becomes cool and dense are followed.
The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength.
Physical parameters measured from an observation of a coronal loop from Gupta et al. (2015) using Hinode/EIS and SDO/AIA were used as input for the hydrodynamic, impulsively heating NRLSOFM 1-d loop model. The model was run at eight different energy inputs and used the measured quantities of temperature (0.73 MK), density (10(sup 8.5)cm(sup -3) and minimum loop lifetime to evaluate the success of the model at recreating the observations. The loop was measured by us to have an unprojected length of 236 Mm and was assumed to be almost perpendicular to the solar surface (tilt of 3.5 degrees) and have a dipolar geometry. Our results show that two of our simulation runs (with input energies of 0.01 and 0.02 ergs cm(sup -3)S(sup -1) closely match the temperature/density combination exhibited by the loop observation. However, our simulated loops only remain in the temperature sensitive region of the Mg 278.4 Angstrom filter for 500 and 800 seconds respectively which is less than the 1200 seconds that the loop is observed for with EIS in order to make the temperature/density measurements over the loop's entire length. This leads us to conclude that impulsive heating of a single loop is not complex enough to explain this observation. Additional steady heating or a collection of additional strands along the line-of-sight would help to align the simulation with the observation.
The stability of the 'quasi-static' models of coronal loops was examined. It was found that all models in which the heat flux at the base of the loop is assumed to vanish are unstable to the growth of thermal perturbations. The growth rates and the profiles of the unstable modes indicate that the instability involves primarily the low-temperature, transition-region plasma. The models can be made stable only by assuming that the heat flux at the base of the loop is large, of the order of 13% of the maximum flux in the loop. The results imply that the transition region must be intrinsically dynamic.
Consequences are examined of the assumption that an observed coronal loop transient is a twisted rope of magnetic-field lines expanding and broadening in the background coronal plasma and magnetic field. It is shown that the expansion can be accounted for by the azimuthal component of the field; the observed broadening of the loop as it moves outward can be accounted for by the longitudinal component of the field. In order to have a net outward force and at the same time avoid a classical pinch (sausage) instability, the two components of the field must satisfy a certain inequality. It is predicted that, as the loop rises, the width (h) of its top portion should vary proportionally with distance (R) from the sun's center. This is in good agreement with measurements that show h is proportional to the 0.8 power of R. The prediction that the radius of curvature of the top portion of the loop should be proportional to R differs from the measured variation. The difference could be accounted for by a drag due to the background coronal field that flattens the loop's top.
During the past ten years, solar physicists have attempted to infer the coronal heating mechanism by comparing observations of coronal loops with hydrodynamic model predictions. These comparisons often used the addition of sub ]resolution strands to explain the observed loop properties. On July 11, 2012, the High Resolution Coronal Imager (Hi ]C) was launched on a sounding rocket. This instrument obtained images of the solar corona was 0.2 ]0.3'' resolution in a narrowband EUV filter centered around 193 Angstroms. In this talk, we will compare these high resolution images to simultaneous density measurements obtained with the Extreme Ultraviolet Imaging Spectrograph (EIS) on Hinode to determine whether the structures observed with Hi ]C are resolved.
The stability to thermal perturbation of static models of coronal loops is considered including the effects of cool, radiatively stable material at the loop base. The linear stability turns out to be sensitive only to the boundary conditions assumed on the velocity at the loop base. The question of the appropriate boundary conditions is discussed, and it is concluded that the free surface condition (the pressure perturbation vanishes), rather than the rigid wall (the velocity vanishes), is relevant to the solar case. The static models are found to be thermally unstable, with a growth time of the order of the coronal cooking time. The physical implications of these results for the solar corona and transition region are examined.
A quasi-static numerical model for coronal loops is considered for the case of a uniform energy input per unit volume into the loops. A line dipole model is used to represent the loop magnetic field, and the variations in loop cross section observed in X-ray photographs are parameterized by the ratio between the cross-sectional areas at the loop apex and base. The results of numerical modeling indicate that for an area ratio greater than unity, increases in the area ratio of a loop with a given length and apex area cause a general rise in electron density and a fall in the temperature gradient, leading to large increases in the differential emission factor at high temperatures. The differential function obtained is significantly different from that predicted by analytical models; however, analytical predictions for the temperature-electron density relations are comparable to numerical results. It is also concluded that even a symmetrical loop may have a maximum temperature away from the apex.
A discussion is presented of elementary aspects of the physics of coronal loops, in order to more securely approach the question of their existence. It is noted that the time-scales for pressure equilibration are far shorter than typical cooling times in loop structures, and that the loop structures are accordingly in pressure balance with their surroundings. Those surroundings, however, are dark, implying a decreased density and gas pressure outside the bright loops. It is deduced that the loop interiors must have a weaker magnetic field than the gas immediately outside them.
A numerical method is applied to treat the energy balance of quasi-static solar coronal loops, which have been observed to persist for periods much greater than the radiative cooling time. The quasi-static loop model employed takes into account gravity, density-, temperature- or position-dependent energy input, an accurate form of the radiative losses and variable loop cross-sectional area, under assumptions of energy input by coronal heating balanced by radiative and conductive losses, an optically thin plasma, energy conduction along the field lines only and hydrostatic equilibrium. Computations of an emission measure function for various distributions of the energy input and loop geometries are then presented which show that little information on the location of the energy input may be gained from spectral line intensity measurements integrated over a single loop.
The paper presents preliminary results of an investigation of thickness variations along coronal loops observed with the Yohkoh Soft X-ray Telescope (SXT), using observations from ten loops selected from the SXT data. The quantitative results indicate that coronal X-ray loops do not expand. This contradicts the expectation that, if plasma loops coincide with magnetic loops, many loops must be significantly broader at their tops than at their foot points. Possible interpretations of the obtained results are proposed.
It is pointed out that any theoretical demonstration that the solar corona can be heated by waves requires a demonstration that the required energies can actually be carried from the convection zone to the corona by waves. In addition, it must be shown that the waves can dissipate their energy into heat in the corona. The present investigation is concerned specifically with the heating of closed magnetic structures in the corona, taking into account coronal loops or active region loops. Attention is given to the MHD Alfven wave. It is shown analytically that coronal active region loops can behave much like interference filters. The coronal part of the loop acts like a resonant cavity for Alfven waves. When the resonances are excited, large energy fluxes can be carried into the loop by Alfven waves which are generated in the solar convection zone. It is estimated that the energy fluxes can power the observed loops.
This research studies the flow of plasma inside a coronal loop in which an injection of plasma through the lateral surface is permitted. The flow is assumed steady and polytropic. The problem covers two cases: (a) upflow at one footpoint, downflow at the other; (b) downflow at both footpoints. The first case can be shown to be quite similar to that of a mass-conserving flow with variable cross section; the second, instead, is characterized by solutions with a different type of topology; its main new feature is the obvious fact that all the solutions pass through a single point going from negative to positive velocities. In this second case the density ratio between footpoints and top can be much smaller than in a mass conserving flow. This can explain some properties of observed loops.
A model is presented for the acceleration of electrons in a flaring solar coronal loop. It is suggested that the primary energy release event in the flare establishes a spectrum of MHD waves within the loop which accelerate electrons by wave-particle resonant interactions. The nature of the MHD oscillations are described and numerical and analytic solution of the dispersion relation are examined. It is found that the behavior of a particle depends on whether or not it is in resonance with the wave spectrum. Resonant particles follow chaotic trajectories and can diffuse in velocity space between wave effective potentials, thereby gaining energy.
Context. Observations reveal a correspondence between chromospheric type II spicules and bright upward-moving fronts in the corona observed in the extreme-ultraviolet (EUV) band. However, theoretical considerations suggest that these flows are probably not the main source of heating in coronal magnetic loops. Aims. We investigate the propagation of high-speed chromospheric flows into coronal magnetic flux tubes and the possible production of emission in the EUV band. Methods. We simulated the propagation of a dense 104 K chromospheric jet upward along a coronal loop by means of a 2D cylindrical MHD model that includes gravity, radiative losses, thermal conduction, and magnetic induction. The jet propagates in a complete atmosphere including the chromosphere and a tenuous cool (approximately 0.8 MK) corona, linked through a steep transition region. In our reference model, the jet initial speed is 70 km per second, its initial density is 10(exp 11) per cubic centimeter, and the ambient uniform magnetic field is 10 G. We also explored other values of jet speed and density in 1D and different magnetic field values in 2D, as well as the jet propagation in a hotter (approximately 1.5 MK) background loop. Results. While the initial speed of the jet does not allow it to reach the loop apex, a hot shock-front develops ahead of it and travels to the other extreme of the loop. The shock front compresses the coronal plasma and heats it to about 10(exp 6) K. As a result, a bright moving front becomes visible in the 171 Angstrom channel of the SDO/AIA mission. This result generally applies to all the other explored cases, except for the propagation in the hotter loop. Conclusions. For a cool, low-density initial coronal loop, the post-shock plasma ahead of upward chromospheric flows might explain at least part of the observed correspondence between type II spicules and EUV emission excess.