Effect of Thermal Conductivity, Compressive Viscosity and Radiative Cooling on the Phase Shift of Propagating Slow Waves with and without Heating-Cooling Imbalance

Abstract

We study phase shifts of the propagating slow waves in coronal loops invoking the effects of thermal conductivity, compressive viscosity, radiative losses and heating-cooling imbalance. We derive a general dispersion relation and solve it to determine phase shifts of density and temperature perturbations relative to the velocity and their dependence on equilibrium parameters (${\rho }_0$, $T_0$). We estimate phase difference ($\Delta \varphi$) between density and temperature perturbations and its dependence on ${\rho }_0$ and $T_0$. The effect of viscosity on the phase shifts was found negligible. The role of radiative losses along with h/c imbalance for chosen specific heating function ($H(\rho ,T)\propto {\rho }^{-0.5}{T}^{-3}$) in determining phase shifts, is found to be significant for the high density and low temperature loops. The h/c imbalance can increase the phase difference ($\Delta \varphi \approx 140^{\circ }$) for low temperature loops compared to the constant heating case ($\Delta \varphi \approx 30^{\circ }$). We derive a general expression for the polytropic index. We find that in the presence of thermal conduction alone, the polytropic index remains close to its classical value for all the considered ${\rho }_0$ and $T_0$. However, it reduces to a value $1.2$ when loop density is decreased by an order of magnitude compared to its normal coronal value. We find that the inclusion of radiative losses, with or without h/c imbalance, cannot explain the observed polytropic index. The thermal ratio ($d$) needs to be enhanced by an order of magnitude, in order to explain its observed value $1.1\pm 0.02$ in the solar loops. We also explore the role of different heating functions for typical coronal parameters and found that although the polytropic index remains close to its classical value, the phase difference is highly dependent on the form of heating function (The abstract is restructured for arxiv).

arXiv comment32 Pages; 8 Figures; 1 Table; The final paper (arxiv version) as appeared in "Solar Physics" Journal after the editorial and proof correction (Prasad et al., Sol Phys., 296, 105 (2021))

References in corpus (30)

• 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
• Quasi-periodic Propagating Signals in the Solar Corona: The Signature of Magnetoacoustic Waves or High-Velocity Upflows?
• Hinode/EIS observations of propagating low-frequency slow magnetoacoustic waves in fan-like coronal loops
• The Spectroscopic Signature of Quasi-periodic Upflows in Active Region Timeseries
• Slow-Mode Magnetoacoustic Waves in Coronal Loops
• Propagating slow magnetoacoustic waves in coronal loops observed by Hinode/EIS
• 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
• Damping of slow magnetoacoustic oscillations by the misbalance between heating and cooling processes in the solar corona
• Wide-Spectrum Slow Magnetoacoustic Waves in Coronal Loops
• Propagating intensity disturbances in polar corona as seen from AIA/SDO
• Seismological constraints on the solar coronal heating function
• The polytropic index of solar coronal plasma in sunspot fan loops and its temperature dependence
• Coronal Seismology and the Propagation of Acoustic Waves Along Coronal Loops
• Waves in Solar Coronal Loops
• Vertical Propagation of Acoustic Waves in the Solar Inter-Network as Observed by IRIS
• Modelling of Reflective Propagating Slow-mode Wave in a Flaring Loop
• Intensity oscillations observed with Hinode near the south pole of the Sun: leakage of low frequency magneto-acoustic waves into the solar corona
• Measuring temperature - dependent propagating disturbances in coronal fan loops using multiple SDO/AIA channels and surfing transform technique
• Effect of transport coefficients on excitation of flare-induced standing slow-mode waves in coronal loops
• Observational Signatures of Waves and Flows in the Solar Corona
• 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
• Propagation of Waves above a Plage as Observed by IRIS and SDO
• Accelerating and Supersonic Density Fluctuations in Coronal Hole Plumes: Signature of Nascent Solar Winds
• Propagating Disturbances along fan-like coronal loops in an active region

Cited by in corpus (9)

• The solar corona as an active medium for magnetoacoustic waves
• Dispersion of Slow Magnetoacoustic Waves in the Active Region Fan Loops Introduced by Thermal Misbalance
• Excitation and Damping of Slow Magnetosonic Waves in Flaring Hot Coronal Loops: Effects of Compressive Viscosity
• Role of Non-Ideal Dissipation with Heating-Cooling Misbalance on the Phase Shifts of Standing Slow Magnetohydrodynamic Waves
• A new look at the frequency-dependent damping of slow-mode waves in the solar corona
• Dynamics of fast and slow magnetoacoustic waves in plasma slabs with thermal misbalance
• Bayesian evidence for two slow-wave damping models in hot coronal loops
• Impact of thermal misbalance on acoustic-gravity waves in the solar atmosphere
• Spectroscopic study of solar transition region oscillations in the quiet-Sun observed by IRIS using Si IV spectral line