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Register a new userWave heating in gravitationally stratified coronal loops in the presence of resistivity and viscosity
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Added by
Konstantinos Karampelas
Publication date
2019
fields
Physics
and research's language is
English
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In recent years, coronal loops have been the focus of studies related to the damping of different magnetohydrodynamic (MHD) surface waves and their connection with coronal seismology and wave heating. For a better understanding of wave heating, we need to take into account the effects of different dissipation coefficients such as resistivity and viscosity, the importance of the loop physical characteristics, and the ways gravity can factor into the evolution of these phenomena. We aim to map the sites of energy dissipation from transverse waves in coronal loops in the presence and absence of gravitational stratification and to compare ideal, resistive, and viscous MHD. Using the PLUTO code, we performed 3D MHD simulations of kink waves in single, straight, density-enhanced coronal flux tubes of multiple temperatures. We see the creation of spatially expanded Kelvin-Helmholtz eddies along the loop, which deform the initial monolithic loop profile. For the case of driven oscillations, the Kelvin-Helmholtz instability develops despite physical dissipation, unless very high values of shear viscosity are used. Energy dissipation gets its highest values near the apex, but is present all along the loop. We observe an increased efficiency of wave heating once the kinetic energy saturates at the later stages of the simulation and a turbulent density profile has developed. The inclusion of gravity greatly alters the dynamic evolution of our systems and should not be ignored in future studies. Stronger physical dissipation leads to stronger wave heating in our set-ups. Finally, once the kinetic energy of the oscillating loop starts saturating, all the excess input energy turns into internal energy, resulting in more efficient wave heating.
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We investigate the relaxation of braided magnetic loops in order to find out how the type of braiding via footpoint motions affects resultant heating of the loop. Two magnetic loops, braided in different ways, are used as initial conditions in resistive MHD simulations and their subsequent evolution is studied. The fields both undergo a resistive relaxation in which current sheets form and fragment and the system evolves towards a state of lower energy. In one case this relaxation is very efficient with current sheets filling the volume and homogeneous heating of the loop occurring. In the other case fewer current sheets develop, less magnetic energy is released in the process and a patchy heating of the loop results. The two cases, although very similar in their setup, can be distinguished by the mixing properties of the photospheric driver. The mixing can be measured by the topological entropy of the plasma flow, an observable quantity.
The effects of both elliptical shape and stage of emergence of the coronal loop on the resonant absorption of standing kink oscillations are studied. To do so, a typical coronal loop is modeled as a zero-beta longitudinally stratified cylindrical magnetic flux tube. We developed the connection formulae for the resonant absorption of standing transversal oscillations of a coronal loop with an elliptical shape, at various stages of its emergence. Using the connection formulae, the dispersion relation is derived and solved numerically to obtain the frequencies and damping rates of the fundamental and first-overtone kink modes. Our numerical results show that both the elliptical shape and stage of emergence of the loop alter the frequencies and damping rates of the tube as well as the ratio of frequencies of the fundamental and its first-overtone modes. However, the ratio of the oscillation frequency to the damping rate is not affected by the tube shape and stage of its emergence and also is independent of the density stratification parameter.
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 whose indexes range from Kolmogorov-like values ($sim 5/3$) up to $sim 3$. We briefly describe the bearing for coronal heating rates.
We study the signatures of different coronal heating regimes on the differential emission measure (DEM) of multi-stranded coronal loops by means of hydrodynamic simulations. We consider heating either uniformly distributed along the loops or localized close to the chromospheric footpoints, in both steady and impulsive conditions. Our simulations show that condensation at the top of the loop forms when the localized heating is impulsive with a pulse cadence time shorter than the plasma cooling time, and the pulse energy is below a certain threshold. A condensation does not produce observable signatures in the global DEM structure. Conversely, the DEM coronal peak is found sensitive to the pulse cadence time. Our simulations can also give an explanation of the warm overdense and hot underdense loops observed by TRACE, SOHO and Yohkoh. However, they are unable to reproduce both the transition region and the coronal DEM structure with a unique set of parameters, which outlines the need for a more realistic description of the transition region.
Context: The location of coronal heating in magnetic loops has been the subject of a long-lasting controversy: does it occur mostly at the loop footpoints, at the top, is it random, or is the average profile uniform? Aims: We try to address this question in model loops with MHD turbulence and a profile of density and/or magnetic field along the loop. Methods: We use the ShellAtm MHD turbulent heating model described in Buchlin & Velli (2006), with a static mass density stratification obtained by the HydRad model (Bradshaw & Mason 2003). This assumes the absence of any flow or heat conduction subsequent to the dynamic heating. Results: The average profile of heating is quasi-uniform, unless there is an expansion of the flux tube (non-uniform axial magnetic field) or the variation of the kinetic and magnetic diffusion coefficients with temperature is taken into account: in the first case the heating is enhanced at footpoints, whereas in the second case it is enhanced where the dominant diffusion coefficient is enhanced. Conclusions: These simulations shed light on the consequences on heating profiles of the complex interactions between physical effects involved in a non-uniform turbulent coronal loop.
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