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Register a new userAlfven Wave Solar Model (AWSoM): Coronal Heating
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We present a new version of the Alfven Wave Solar Model (AWSoM), a global model from the upper chromosphere to the corona and the heliosphere. The coronal heating and solar wind acceleration are addressed with low-frequency Alfven wave turbulence. The injection of Alfven wave energy at the inner boundary is such that the Poynting flux is proportional to the magnetic field strength. The three-dimensional magnetic field topology is simulated using data from photospheric magnetic field measurements. This model does not impose open-closed magnetic field boundaries; those develop self-consistently. The physics includes: (1) The model employs three different temperatures, namely the isotropic electron temperature and the parallel and perpendicular ion temperatures. The firehose, mirror, and ion-cyclotron instabilities due to the developing ion temperature anisotropy are accounted for. (2) The Alfven waves are partially reflected by the Alfven speed gradient and the vorticity along the field lines. The resulting counter-propagating waves are responsible for the nonlinear turbulent cascade. The balanced turbulence due to uncorrelated waves near the apex of the closed field lines and the resulting elevated temperatures are addressed. (3) To apportion the wave dissipation to the three temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating. (4) We have incorporated the collisional and collisionless electron heat conduction. We compare the simulated multi-wavelength EUV images of CR2107 with the observations from STEREO/EUVI and SDO/AIA instruments. We demonstrate that the reflection due to strong magnetic fields in proximity of active regions intensifies the dissipation and observable emission sufficiently.
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Observations have shown that magnetohydrodynamic waves over a large frequency range are ubiquitous in solar prominences. The waves are probably driven by photospheric motions and may transport energy up to prominences suspended in the corona. Dissipation of wave energy can lead to heating of the cool prominence plasma, so contributing to the local energy balance within the prominence. Here we discuss the role of Alfven wave dissipation as a heating mechanism for the prominence plasma. We consider a slab-like quiescent prominence model with a transverse magnetic field embedded in the solar corona. The prominence medium is modelled as a partially ionized plasma composed of a charged ion-electron single fluid and two separate neutral fluids corresponding to neutral hydrogen and neutral helium. Friction between the three fluids acts as a dissipative mechanism for the waves. The heating caused by externally-driven Alfven waves incident on the prominence slab is analytically explored. We find that the dense prominence slab acts as a resonant cavity for the waves. The fraction of incident wave energy that is channelled into the slab strongly depends upon the wave period, $P$. Using typical prominence conditions, we obtain that wave energy trapping and associated heating are negligible when $P gtrsim 100$ s, so that it is unlikely that those waves have a relevant influence on prominence energetics. When $1$ s $lesssim P lesssim 100$ s the energy absorption into the slab shows several sharp and narrow peaks, that can reach up to 100%, when the incident wave frequency matches a cavity resonance of the slab. Wave heating is enhanced at those resonant frequencies. Conversely, when $P lesssim 1$ s cavity resonances are absent, but the waves are heavily damped by the strong dissipation. We estimate that wave heating may compensate for about 10% of radiative losses of the prominence plasma.
Physical processes which may lead to solar chromospheric heating are analyzed using high-resolution 1.5D non-ideal MHD modelling. We demonstrate that it is possible to heat the chromospheric plasma by direct resistive dissipation of high-frequency Alfven waves through Pedersen resistivity. However this is unlikely to be sufficient to balance radiative and conductive losses unless unrealistic field strengths or photospheric velocities are used. The precise heating profile is determined by the input driving spectrum since in 1.5D there is no possibility of Alfven wave turbulence. The inclusion of the Hall term does not affect the heating rates. If plasma compressibility is taken into account, shocks are produced through the ponderomotive coupling of Alfven waves to slow modes and shock heating dominates the resistive dissipation. In 1.5D shock coalescence amplifies the effects of shocks and for compressible simulations with realistic driver spectra the heating rate exceeds that required to match radiative and conductive losses. Thus while the heating rates for these 1.5D simulations are an overestimate they do show that ponderomotive coupling of Alfven waves to sound waves is more important in chromospheric heating than Pedersen dissipation through ion-neutral collisions.
The solar atmosphere may be heated by Alfven waves that propagate up from the convection zone and dissipate their energy in the chromosphere and corona. To further test this theory, we consider wave heating in an active region observed on 2012 March 7. A potential field model of the region is constructed, and 22 field lines representing observed coronal loops are traced through the model. Using a three-dimensional (3D) reduced magneto-hydrodynamics (MHD) code, we simulate the dynamics of Alfven waves in and near the observed loops. The results for different loops are combined into a single formula describing the average heating rate Q as function of position within the observed active region. We suggest this expression may be approximately valid also for other active regions, and therefore may be used to construct 3D, time-dependent models of the coronal plasma. Such models are needed to understand the role of thermal non-equilibrium in the structuring and dynamics of the Suns corona.
A three-dimensional MHD model for the propagation and dissipation of Alfven waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100 km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfven waves using the reduced MHD approximation. The increase of Alfven speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheric and chromospheric parts of the flux tube. Part of the wave energy is transmitted through the TR and produces turbulence in the corona. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfven wave turbulence, provided the small-scale footpoint motions have velocities of 1-2 km/s and time scales of 60-200 s. The heating rate per unit volume in the chromosphere is 2 to 3 orders of magnitude larger than that in the corona. We construct a series of models with different values of the model parameters, and find that the coronal heating rate increases with coronal field strength and decreases with loop length. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfvenic turbulence.
There is observational evidence of the presence of small-amplitude transverse magnetohydrodynamic (MHD) waves with a wide range of frequencies in the threads of solar prominences. It is believed that the waves are driven at the photosphere and propagate along the magnetic field lines up to prominences suspended in the corona. The dissipation of MHD wave energy in the partially ionized prominence plasma is a heating mechanism whose relevance needs to be explored. Here we consider a simple 1D model for a non-uniform thin thread and investigate the heating associated with dissipation of Alfven waves. The model assumes an ad hoc density profile and a uniform pressure, while the temperature and ionization degree are self-consistently computed considering either LTE or non-LTE approximations for the hydrogen ionization. A broadband driver for Alfven waves is placed at one end of the magnetic field line, representing photospheric excitation. The Alfvenic perturbations along the thread are obtained by solving the linearized MHD equations for a partially ionized plasma in the single-fluid approximation.We find that wave heating in the partially ionized part of the thread is significant enough to compensate for energy losses due to radiative cooling. A greater amount of heating is found in the LTE case because the ionization degree for core prominence temperatures is lower than that in the non-LTE approximation. This results in a greater level of dissipation due to ambipolar diffusion in the LTE case. Conversely, in the hot coronal part of the model, the plasma is fully ionized and wave heating is negligible. The results of this simple model suggest that MHD wave heating can be relevant for the energy balance in prominences. Further studies based on more elaborate models are required.
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