Resonant Alfven waves in coronal arcades driven by footpoint motions (original) (raw)

The heating of the solar corona by the resonant absorption of alfven waves

Applied Mathematics Letters, 1993

In this paper, upward propagating Magnetoacoustic waves in an ideal atmosphere are considered. It is shown that the magnetic field creates a nonabsorbing reflecting layer. An equation for the resonance is derived, which shows that resonance may occur for many values of the magnetic field and of the frequency if the wavelength is matched to the strength of the magnetic field. At the resonance frequencies the values of the magnetic and kinetic energies will increase to very large values, and this may account for the heating process. Consequently, for large P-plasma the mechanism for coronal heating will be acoustic. The authors would like to express their sincere thanks to Michael Yanowitch for his support during the preparation of this work. We would also like to thank R. E. Bradley for his helpful comments concerning the exposition of this result. The benefit of the referee's comments is gratefully acknowledged.

High-frequency torsional Alfvén waves as an energy source for coronal heating

The existence of the Sun's hot atmosphere and the solar wind acceleration continues to be an outstanding problem in solar-astrophysics. Although magnetohydrodynamic (MHD) modes and dissipation of magnetic energy contribute to heating and the mass cycle of the solar atmosphere, yet direct evidence of such processes often generates debate. Ground-based 1-m Swedish Solar Telescope (SST)/CRISP, Hα 6562.8 Å observations reveal, for the first time, the ubiquitous presence of high frequency (~12–42 mHz) torsional motions in thin spicular-type structures in the chromosphere. We detect numerous oscillating flux tubes on 10 June 2014 between 07:17 UT to 08:08 UT in a quiet-Sun field-of-view of 60 " × 60 " (1 " = 725 km). Stringent numerical model shows that these observations resemble torsional Alfvén waves associated with high frequency drivers which contain a huge amount of energy (~10 5 W m −2) in the chromosphere. Even after partial reflection from the transition region, a significant amount of energy (~10 3 W m −2) is transferred onto the overlying corona. We find that oscillating tubes serve as substantial sources of Alfvén wave generation that provide sufficient Poynting flux not only to heat the corona but also to originate the supersonic solar wind. Continuous generation of radiation and supersonic wind from the Sun's chromosphere and corona requires a large input of energy (~10 2 –10 4 W m −2) to balance these losses 1. The role of magnetohydrodynamic (MHD) waves and small-scale magnetic reconnection causing nano-flare heating have been explored as primary candidates to energize the solar atmosphere. However, direct evidence of energy sources and their dissipation are not yet fully understood 2–4. In the era of high resolution space and ground-based observations, it is now revealed that energy and mass transport in the quiescent solar atmosphere are associated with localized static and flowing flux tubes (e.g., network & inter-network magnetic fields, spicules, vortices etc) possessing various plasma and wave processes 5–8. Here, we observe directly, for the first time, the ubiquitous presence of high frequency (~12–42 mHz) torsional oscillations at apparent surfaces composed of thin spicular-type structures rooted in the quiet-Sun magnetic network. These observations are described by torsional Alfvén waves associated with high frequency drivers transferring ~10 3 W m −2 energy into the overlying corona. These oscillating tubes serve as substantial sources of Alfvén wave generation providing sufficient Poynting flux to heat the solar corona and in originating the nascent solar wind. Quiet-sun magnetic networks are the locations where field lines fan out into the outer atmosphere supporting waves and exotic plasma dynamics 9,10. The magnetic skeleton of the bundle of fine structured small-scale flux tubes becomes visible when remnants of plasma flows (e.g., spicules, jets, surges) are confined within their boundaries. Various other similar structures are prevalent in the solar chromosphere and well resolved with modern day instruments, e.g., on-disk counterparts of type-II spicules, chromospheric counterparts of the transition region network jets, etc. 11,12. A tube with its fine structures, each 120–215 km wide, is observed using CRISP on the Swedish Solar Telescope (see yellow and green expanding cylinders in Fig. 1A.1,A.2, respectively). In an integrated view, the tube's projected height and width at the top are respectively ~4 Mm and ~1.5 Mm. Using visualization software, we measure the structure's length, while the width is an average of the values measured at

On the coronal heating mechanism by the resonant absorption of Alfven waves

International Journal of Mathematics and Mathematical Sciences, 1993

In this paper, we will investigate the heating of the solar corona by the resonant absorption of Alfven waves in a viscous and isothermal atmosphere permeated by a horizontal magnetic field. It is shown that if the viscosity dominates the motion in a high (low)-βplasma, it creates an absorbing and reflecting layer and the heating process is acoustic (magnetoacoustic). When the magnetic field dominates the oscillatory process it creates a non-absorbing reflecting layer. Consequently, the heating process is magnetohydrodynamic. An equation for resonance is derived. It shows that resonances may occur for many values of the frequency and of the magnetic field if the wavelength is matched with the strength of the magnetic field. At the resonance frequencies, magnetic and kinetic energies will increase to very large values which may account for the heating process. When the motion is dominated by the combined effects of the viscosity and the magnetic field, the nature of the reflecting la...

Theory of heating of hot magnetized plasma by Alfven waves. Application for solar corona

The heating of magnetized plasma by propagation of Alfven waves is calculated as a function of the magnetic field spectral density. The results can be applied to evaluate the heating power of the solar corona at known data from satellites' magnetometers. This heating rate can be incorporated in global models for heating of the solar corona and creation of the solar wind. The final formula for the heating power is illustrated with a model spectral density of the magnetic field obtained by analysis of the Voyager 1 mission results. The influence of high frequency dissipative modes is also taken into account and it is concluded that for evaluation of the total coronal heating it is necessary to know the spectral density of the fluctuating component of the magnetic field up to the frequency of electron-proton collisions.

On Coronal Loop Heating by Torsional Alfvén Waves

Solar Physics, 2001

Heating of coronal loops by linear resonant Alfvén waves, excited by the footpoints motions in the photosphere, has been studied. The analysis of single-layer heating is extended to multilayer heating, in semiempirical treatment. Heating and nonthermal velocities in different layers of loops in X-ray bright points, active regions, and large-scale structures are estimated. The average value of velocity is found

Estimating the contribution of Alfvén waves to the process of heating the quiet solar corona

We solve numerically the ideal magnetohydrodynamic equations with an external gravitational field in 2D in order to study the effects of impulsively generated linear and non-linear Alfvén waves into isolated solar arcades and coronal funnels. We analyse the region containing the interface between the photosphere and the corona. The main interest is to study the possibility that Alfvén waves triggers the energy flux transfer towards the quiet solar corona and heat it, including the case that two consecutive waves can occur. We find that in the case of arcades, short or large, the transferred fluxes by Alfvén waves are sufficient to heat the quiet corona only during a small lapse of time and in a certain region. In the case of funnels the threshold is achieved only when the wave is faster than 10 km s −1 , which is extremely high. We conclude from our analysis, that Alfvén waves, even in the optimistic scenario of having two consecutive Alfvén wave pulses, cannot transport enough energy as to heat the quiet corona.

Torsional Alfvén waves in small scale density threads of the solar corona

Astronomy and Astrophysics, 2008

The density structuring of the solar corona is observed at large scales (loops and funnels), but also at small scales (sub-structures of loops and funnels). Coronal loops consist of thin density threads with sizes down to (and most probably below) the resolution limit. We study properties of torsional Alfvén waves propagating in inhomogeneous cylindrical density threads using the two-fluid magnetohydrodynamic equations. The eigenmode solutions supported by such a structure are obtained and analysed. It is shown that the dispersive and dissipative effects become important for the waves localised in thin threads. In this case, the Alfvén wave continuum is replaced with a discrete spectrum of Alfvén waves. This mathematical model is applied to the waves propagating in coronal structures. In particular, we consider ∼1 Hz Alfvén waves propagating along density threads with a relatively smooth radial profile, where a density contrast of about 1.1 is attained at radial distances of about 0.1 km. We found that the dissipation distance of these waves is less than the typical length of hot coronal loops, 50 Mm. Torsional Alfvén waves are localised in thin density threads and produce localised heating. Therefore, these waves can be responsible for coronal heating and for maintenance of small-scale coronal structuring.

Alfvénic waves with sufficient energy to power the quiet solar corona and fast solar wind

Nature, 2011

Energy is required to heat the outer solar atmosphere to millions of degrees (refs 1, 2) and to accelerate the solar wind to hundreds of kilometres per second (refs 2-6). Alfvén waves (travelling oscillations of ions and magnetic field) have been invoked as a possible mechanism to transport magneto-convective energy upwards along the Sun's magnetic field lines into the corona. Previous observations 7 of Alfvénic waves in the corona revealed amplitudes far too small (0.5 km s 21 ) to supply the energy flux (100-200 W m 22 ) required to drive the fast solar wind 8 or balance the radiative losses of the quiet corona 9 . Here we report observations of the transition region (between the chromosphere and the corona) and of the corona that reveal how Alfvénic motions permeate the dynamic and finely structured outer solar atmosphere. The ubiquitous outward-propagating Alfvénic motions observed have amplitudes of the order of 20 km s 21 and periods of the order of 100-500 s throughout the quiescent atmosphere (compatible with recent investigations 7,10 ), and are energetic enough to accelerate the fast solar wind and heat the quiet corona.

On a source of Alfvén waves heating the solar corona

Astronomy and Astrophysics, 1998

Studies of the origin of coronal heating and acceleration of the solar wind invoke high-frequency Alfvén waves. Here we suggest a source for such waves associated with twisted magnetic loops emerging on the solar surface and reconnecting with the open field. We identify the loops with the ephemeral regions (small-scale bipoles) observed by ground-based instruments and by SOHO. To characterize the loops we employ the concept of a minimum energy state for topologically complex fields. Emerging loops release energy relaxing to the minimum state. Relaxation along the minimum state-due to a competition between footpoint twisting by photospheric motions and reconnections inside the loops-releases blinks of energy into the solar atmosphere. We estimate the power released and the range of wave frequencies.

Three-Dimensional Propagation of Magnetohydrodynamic Waves in Solar Coronal Arcades

Astrophysical Journal, 2010

We numerically investigate the excitation and temporal evolution of oscillations in a two-dimensional coronal arcade by including the three-dimensional propagation of perturbations. The time evolution of impulsively generated perturbations is studied by solving the linear, ideal magnetohydrodynamic (MHD) equations in the zero-β approximation. As we neglect gas pressure the slow mode is absent and therefore only coupled MHD fast and Alfvén modes remain. Two types of numerical experiments are performed. First, the resonant wave energy transfer between a fast normal mode of the system and local Alfvén waves is analyzed. It is seen how, because of resonant coupling, the fast wave with global character transfers its energy to Alfvénic oscillations localized around a particular magnetic surface within the arcade, thus producing the damping of the initial fast MHD mode. Second, the time evolution of a localized impulsive excitation, trying to mimic a nearby coronal disturbance, is considered. In this case, the generated fast wavefront leaves its energy on several magnetic surfaces within the arcade. The system is therefore able to trap energy in the form of Alfvénic oscillations, even in the absence of a density enhancement such as that of a coronal loop. These local oscillations are subsequently phase-mixed to smaller spatial scales. The amount of wave energy trapped by the system via wave energy conversion strongly depends on the wavelength of perturbations in the perpendicular direction, but is almost independent from the ratio of the magnetic to density scale heights.