Heating of the Solar Corona by Alfvén Waves: Self-Induced Opacity

Abstract

Abstract. Static distributions of temperature and wind velocity at the transition region are calculated within the framework of magnetohydrodynamics (MHD) of completely ionized hydrogen plasma. The numerical solution of the derived equations gives the width of the transition layer between the chromosphere and the corona as a self-induced opacity of high-frequency Alfvén waves (AW). The domain wall is direct consequence of the self-consistent MHD treatment of AW propagation. The low-frequency MHD waves coming from the Sun are strongly reflected by the narrow transition layer, while the high-frequency waves are absorbed -that is why we predict considerable spectral density of the AW in the photosphere. The numerical method allows consideration of incoming AW with arbitrary spectral density. The idea that Alfvén waves might heat the solar corona belongs to Alfvén, we simply solved the corresponding MHD equations. The comparison of the solution to the experiment is crucial for revealing the heating mechanism. Alfvén model for corona heatingThe discovery of the lines of the multiply ionized iron in the solar corona spectrum [1] posed an important problem for the fundamental physics -what is the mechanism of the heating of the solar corona and why the temperature of the corona is 100 times larger then the temperature of the photosphere.The first idea by Alfvén [2] was that Alfvén waves (AW) [3] are the mechanism for heating the corona. AW are generated by the turbulence in the convection zone and propagate along the magnetic field lines. Absorption is proportional to ω 2 and the heating comes from highfrequency AW. Alfvén's idea for the viscous heating of plasma by absorption of AW was analyzed in the theoretical work by Heyvaerts [4]. In support of this idea is the work by Chitta [5] (Figures 8, 9 therein). The authors came to the conclusion that the spectral density of AW satisfies a power law with an index of 1.59. This gives a strong hint that this scaling can be extrapolated in the nearest spectral range for times less than 1 s and frequencies in the Hz range. Furthermore in the work by Tomczyk [6] it is stated that there exist very few direct measurements of the strength and orientation of coronal magnetic fields, meaning that the mechanisms responsible for heating the corona, driving the solar wind, and initiating coronal mass ejections remain poorly understood. After the launch of Hinode, however, the well-forgotten spatially and temporally ubiquitous waves in the solar corona [7] came again into the limelight and gave strong support for the idea of Alfvén. A clear presence of outward and inward propagating waves in the corona was noted. k − ω diagnostics revealed coronal wave power spectrum with an exponent of ≈ − 3 2 (cf. Fig. 2 of [6]). The observational data for the temperature profile of the solar corona show that the transition layer is extremely thin compared to the radius of the Sun [8]. The width of the transition layer λ may be evaluated using the logarithmic derivative of the temperature, λ = max( ...

Review of the Magnetohydrodynamic Waves and Their Stability in Solar Spicules and X-Ray Jets

“…However, spicules can be considered as Alfvén wave resonant cavities (Holweg, 1981;Leroy, 1981) and as Matsumoto & Shibata (Matsumoto & Shibata, 2010) claim, the waves of the period around 100-500 s can transport a large amount of wave energy to the corona. Zahariev & Mishonov (Zahariev & Mishonov, 2011) state that the corona may be heated through a self-induced opacity of high-frequency Alfvén waves propagating in the transition region between the chromosphere and the corona owing to a considerable spectral density of the Alfvén waves in the photosphere. Another trend in explaining the mechanism of coronal heating is the dissipation of Alfvén waves' energy by strong wave damping due to the collisions between ions and neutrals (Song & Vasyliūnas, 2011;Tsap et al, 2011).…”