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Register a new userDamping of slow magnetoacoustic oscillations by the misbalance between heating and cooling processes in the solar corona
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Rapidly decaying slow magnetoacoustic waves are regularly observed in the solar coronal structures, offering a promising tool for a seismological diagnostics of the coronal plasma, including its thermodynamical properties. The effect of damping of standing slow magnetoacoustic oscillations in the solar coronal loops is investigated accounting for the field-aligned thermal conductivity and a wave-induced misbalance between radiative cooling and some unspecified heating rates. The non-adiabatic terms were allowed to be arbitrarily large, corresponding to the observed values. The thermal conductivity was taken in its classical form, and a power-law dependence of the heating function on the density and temperature was assumed. The analysis was conducted in the linear regime and in the infinite magnetic field approximation. The wave dynamics is found to be highly sensitive to the characteristic time scales of the thermal misbalance. Depending on certain values of the misbalance time scales three regimes of the wave evolution were identified, namely the regime of a suppressed damping, enhanced damping where the damping rate drops down to the observational values, and acoustic over-stability. The specific regime is determined by the dependences of the radiative cooling and heating functions on thermodynamical parameters of the plasma in the vicinity of the perturbed thermal equilibrium. The comparison of the observed and theoretically derived decay times and oscillation periods allows us to constrain the coronal heating function. For typical coronal parameters, the observed properties of standing slow magnetoacoustic oscillations could be readily reproduced with a reasonable choice of the heating function.
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Slow magnetoacoustic waves are omnipresent in both natural and laboratory plasma systems. The wave-induced misbalance between plasma cooling and heating processes causes the amplification or attenuation, and also dispersion, of slow magnetoacoustic waves. The wave dispersion could be attributed to the presence of characteristic time scales in the system, connected with the plasma heating or cooling due to the competition of the heating and cooling processes in the vicinity of the thermal equilibrium. We analysed linear slow magnetoacoustic waves in a plasma in a thermal equilibrium formed by a balance of optically thin radiative losses, field-align thermal conduction, and an unspecified heating. The dispersion is manifested by the dependence of the effective adiabatic index of the wave on the wave frequency, making the phase and group speeds frequency-dependent. The mutual effect of the wave amplification and dispersion is shown to result into the occurrence of an oscillatory pattern in an initially broadband slow wave, with the characteristic period determined by the thermal misbalance time scales, i.e. by the derivatives of the combined radiation loss and heating function with respect to the density and temperature, evaluated at the equilibrium. This effect is illustrated by estimating the characteristic period of the oscillatory pattern, appearing because of thermal misbalance in the plasma of the solar corona. It is found that by an order of magnitude the period is about the typical periods of slow magnetoacoustic oscillations detected in the corona.
The processes of the coronal plasma heating and cooling were previously shown to significantly affect the dynamics of slow magnetoacoustic (MA) waves, causing amplification or attenuation, and also dispersion. However, the entropy mode is also excited in such a thermodynamically active plasma and is affected by the heating/cooling misbalance too. This mode is usually associated with the phenomenon of coronal rain and formation of prominences. Unlike the adiabatic plasmas, the properties and evolution of slow MA and entropy waves in continuously heated and cooling plasmas get mixed. Different regimes of the misbalance lead to a variety of scenarios for the initial perturbation to evolve. In order to describe properties and evolution of slow MA and entropy waves in various regimes of the misbalance, we obtained an exact analytical solution of the linear evolutionary equation. Using the characteristic timescales and the obtained exact solution, we identified regimes with qualitatively different behaviour of slow MA and entropy modes. For some of those regimes, the spatio-temporal evolution of the initial Gaussian pulse is shown. In particular, it is shown that slow MA modes may have a range of non-propagating harmonics. In this regime, perturbations caused by slow MA and entropy modes in a low-$beta$ plasma would look identically in observations, as non-propagating disturbances of the plasma density (and temperature) either growing or decaying with time. We also showed that the partition of the initial energy between slow MA and entropy modes depends on the properties of the heating and cooling processes involved. The obtained exact analytical solution could be further applied to the interpretation of observations and results of numerical modelling of slow MA waves in the corona and the formation and evolution of coronal rain.
Condensations in the more than 10^6 K hot corona of the Sun are commonly observed in the extreme ultraviolet (EUV). While their contribution to the total solar EUV radiation is still a matter of debate, these condensations certainly provide a valuable tool for studying the dynamic response of the corona to the heating processes. We investigate different distributions of energy input in time and space to investigate which process is most relevant for understanding these coronal condensations. For a comparison to observations we synthesize EUV emission from a time-dependent, one-dimensional model for coronal loops, where we employ two heating scenarios: simply shutting down the heating and a model where the heating is very concentrated at the loop footpoints, while keeping the total heat input constant. The heating off/on model does not lead to significant EUV count rates that one observes with SDO/AIA. In contrast, the concentration of the heating near the footpoints leads to thermal non-equilibrium near the loop top resulting in the well-known catastrophic cooling. This process gives a good match to observations of coronal condensations. This shows that the corona needs a steady supply of energy to support the coronal plasma, even during coronal condensations. Otherwise the corona would drain very fast, too fast to even form a condensation.
The rapid damping of slow magnetoacoustic waves in the solar corona has been extensively studied in previous years. Most studies suggest that thermal conduction is a dominant contributor to this damping, albeit with a few exceptions. Employing extreme-ultraviolet (EUV) imaging data from SDO/AIA, we measure the damping lengths of propagating slow magnetoacoustic waves observed in several fan-like loop structures using two independent methods. The dependence of the damping length on temperature has been studied for the first time. The results do not indicate any apparent decrease in damping length with temperature, which is in contrast to the existing viewpoint. Comparing with the corresponding theoretical values calculated from damping due to thermal conduction, it is inferred that thermal conduction is suppressed in hotter loops. An alternative interpretation that suggests thermal conduction is not the dominant damping mechanism, even for short period waves in warm active region loops, is also presented.
Slow magnetoacoustic waves are routinely observed in astrophysical plasma systems such as the solar corona. As a slow wave propagates through a plasma, it modifies the equilibrium quantities of density, temperature, and magnetic field. In the corona and other plasma systems, the thermal equilibrium is comprised of a balance between continuous heating and cooling processes, the magnitudes of which vary with density, temperature and magnetic field. Thus the wave may induce a misbalance between these competing processes. Its back reaction on the wave has been shown to lead to dispersion, and amplification or damping, of the wave. In this work the importance of the effect of magnetic field in the rapid damping of slow waves in the solar corona by heating/cooling misbalance is evaluated and compared to the effects of thermal conduction. The two timescales characterising the effect of misbalance are derived and calculated for plasma systems with a range of typical coronal conditions. The predicted damping times of slow waves from thermal misbalance in the solar corona are found to be of the order of 10-100 minutes, coinciding with the wave periods and damping times observed. Moreover the slow wave damping by thermal misbalance is found to be comparable to the damping by field-aligned thermal conduction. We show that in the infinite field limit, the wave dynamics is insensitive to the dependence of the heating function on the magnetic field, and this approximation is found to be valid in the corona so long as the magnetic field strength is greater than 10G for quiescent loops and plumes and 100G for hot and dense loops. In summary thermal misbalance may damp slow magnetoacoustic waves rapidly in much of the corona, and its inclusion in our understanding of slow mode damping may resolve discrepancies between observations and theory relying on compressive viscosity and thermal conduction alone.
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