Role of Non-Ideal Dissipation with Heating-Cooling Misbalance on the Phase Shifts of Standing Slow Magnetohydrodynamic Waves

Abstract

We analyse the phase shifts of standing, slow magnetohydrodynamic (MHD) waves in solar coronal loops using a linear MHD model taking into account the role of thermal conductivity, compressive viscosity, radiative losses, and heating-cooling misbalance. We estimate the phase shifts in time and space of density and temperature perturbations with respect to velocity perturbations and also calculate the phase difference between density and temperature perturbations. The overall significance of compressive viscosity is found to be negligible for most of the loops considered in the study. For loops with high background density and/or low background temperature, the role of radiative losses (with heating-cooling misbalance) is found to be more significant. Also the effect of heating-cooling misbalance with a temperature- and density-dependent heating function is found to be more significant in the case of longer loop lengths ($L=500$\, Mm). We derived a general expression for the polytropic index [${\gamma }_{\mathrm{eff}}$] and found that under linear MHD the effect of compressive viscosity on polytropic index is negligible. The radiative losses with constant heating lead to a monotonic increase of ${\gamma }_{\mathrm{eff}}$ with increasing density whereas the consideration of an assumed heating function [$H(\rho ,T)\propto {\rho }^a{T}^b$, where $a=-0.5$ and $b=-3$] makes the ${\gamma }_{\mathrm{eff}}$ peak at a certain loop density. We also explored the role of different heating functions by varying the free parameters $a$ and $b$ for a fixed loop of ${\rho }_0=10^{-11}$\, kg ${\text{m}}^{-3}$, $T_0=6.3$\, MK and loop length $L=180$\, Mm. We find that the consideration of different heating functions [$H(\rho ,T)$] leads to a significant variation in the phase difference between density and temperature perturbations; however, the polytropic index remains close to a value of 1.66.

arXiv commentSolar Physics (in press)

References in corpus (29)

• Highly Efficient Modeling of Dynamic Coronal Loops
• Coronal heating by MHD waves
• Standing Slow-Mode Waves in Hot Coronal Loops: Observations, Modeling, and Coronal Seismology
• Kink oscillations of coronal loops
• Acoustic Oscillations in Solar and Stellar Flaring Loops
• The first observed stellar X-ray flare oscillation: Constraints on the flare loop length and the magnetic field
• Slow-Mode Magnetoacoustic Waves in Coronal Loops
• Determination of the Coronal Magnetic Field by Hot Loop Oscillations
• Statistical Properties of Quasi-Periodic Pulsations in White-Light Flares Observed With Kepler
• Evidence of thermal conduction suppression in a solar flaring loop by coronal seismology of slow-mode waves
• Formation of quasi-periodic slow magnetoacoustic wave trains by the heating/cooling misbalance
• Slow magnetosonic waves and fast flows in active region loops
• X-ray and EUV Observations of Simultaneous Short and Long Period Oscillations in Hot Coronal Arcade Loops
• Damping of slow magnetoacoustic oscillations by the misbalance between heating and cooling processes in the solar corona
• SDO/AIA Observations of a Reflecting Longitudinal Wave in a Coronal Loop
• Seismological constraints on the solar coronal heating function
• Oscillations in stellar superflares
• The polytropic index of solar coronal plasma in sunspot fan loops and its temperature dependence
• Observations of Solar Doppler Shift Oscillations with the EUV Imaging Spectrometer on Hinode
• Chromospheric Heating by MHD Waves and Instabilities
• The effect of magnetic field on the damping of slow waves in the solar corona
• Multi-instrument observations of a failed flare eruption associated with MHD waves in a loop bundle
• Effect of transport coefficients on excitation of flare-induced standing slow-mode waves in coronal loops
• Reflection Of Propagating Slow Magneto-acoustic Waves In Hot Coronal Loops : Multi-instrument Observations and Numerical Modelling
• Role of Compressive Viscosity and Thermal Conductivity on the Damping of Slow Waves in the Coronal Loops With and Without Heating-Cooling Imbalance
• Determination of transport coefficients by coronal seismology of flare-induced slow-mode waves: Numerical parametric study of 1D loop model
• Effect of Thermal Conductivity, Compressive Viscosity and Radiative Cooling on the Phase Shift of Propagating Slow Waves with and without Heating-Cooling Imbalance
• Evidence of Multiple Slow Acoustic Oscillations in the Stellar Flaring Loops of Proxima Centauri
• Excitation and Damping of Slow Magnetosonic Waves in Flaring Hot Coronal Loops: Effects of Compressive Viscosity

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