Effect of a Radiation Cooling and Heating Function on Standing Longitudinal Oscillations in Coronal Loops

Abstract

Standing long-period (with the periods longer than several minutes) oscillations in large hot (with the temperature higher than 3 MK) coronal loops have been observed as the quasi-periodic modulation of the EUV and microwave intensity emission and the Doppler shift of coronal emission lines, and have been interpreted as standing slow magnetoacoustic (longitudinal) oscillations. Quasi-periodic pulsations of shorter periods, detected in thermal and non-thermal emissions in solar flares could be produced by a similar mechanism. We present theoretical modelling of the standing slow magnetoacoustic mode, showing that this mode of oscillation is highly sensitive to peculiarities of the radiative cooling and heating function. We generalised the theoretical model of standing slow magnetoacoustic oscillations in a hot plasma, including the effects of the radiative losses, and accounting for plasma heating. The heating mechanism is not specified and taken empirically to compensate the cooling by radiation and thermal-conduction. It is shown that the evolution of the oscillations is described by a generalised Burgers equation. Numerical solution of an initial value problem for the evolutionary equation demonstrates that different dependences of the radiative cooling and plasma heating on the temperature lead to different regimes of the oscillations, including growing, quasi-stationary and rapidly decaying. Our findings provide a theoretical foundation for probing the coronal heating function, and may explain the observations of decayless long-period quasi-periodic pulsations in flares. The hydrodynamic approach employed in this study should be considered with caution in the modelling of non-thermal emission associated with flares, as it misses potentially important nonhydrodynamic effects.

Undamped transverse oscillations of coronal loops as a self-oscillatory process

“…Müller et al 2003), and non-linear thermal overstability (e.g. Kumar et al 2016). Also, a class of quasi-periodic pulsations in flaring energy releases that are caused by spontaneous repetitive magnetic reconnection ("magnetic dripping", see e.g.…”

Very Long-Period Pulsations Before the Onset of Solar Flares

“…Some people suggested that such pulsations might be related to the slow-mode oscillations in large scale coronal loops (Svestka 1994), while other work suggested that the longperiod pulsations could be associated with gravitydriven solar interior modes and connected with the wave leakage of chromospheric oscillations (Yuan et al 2011). Another possible explanation of VLPs is the thermal overstability of standing slow magnetoacoustic waves in the magnetic flux loops (Kumar, Nakariakov, and Moon 2016), such as the SUMER oscillations with periods in the range of 5 -40 min and detected in long loops with lengths of 200 -300 Mm (Wang 2011).…”

Effect of Local Thermal Equilibrium Misbalance on Long-wavelength Slow Magnetoacoustic Waves

“…However, the damping caused by this term is independent of k. In the case R > 0, this term suppresses damping, and can even lead to the increase in the wave amplitude, the phenomenon known as thermal overstability (e.g. see Nakariakov et al 2000a;Kumar et al 2016, for this effect on magnetoacoustic waves). The critical value of R that separates the damping and over-stable regimes is…”

“…In the following we omit this subscript for the variables u and v. Following the procedure described in Afanasyev & Nakariakov (2015b) and Kumar et al (2016), we substitute expansion (7) in Eqs. (1-6) and, taking into account quadratically nonlinear terms everywhere except the terms on the right hand sides of Eqs.…”

“…The main attention was paid to the enhanced damping of the oscillations caused by the non-adiabatic effects and induced plasma condensation. For hotter plasma structures, it was recently shown that the cooling/heating misbalance could significantly modify the damping and non-linear evolution of standing slow magnetoacoustic waves in coronal loops (Kumar et al 2016). In the latter work the effects of the finite plasma-β were neglected.…”