The imaging telescope on board the Transition Region and Coronal Explorer (TRACE) spacecraft observed the decaying transversal oscillations of a long [(130 +/- 6) x 10(exp 6) meters], thin [diameter (2.0 +/- 0.36) x 10(exp 6) meters], bright coronal loop in the 171 angstrom Fe-IX emission line. The oscillations were excited by a solar flare in the adjacent active region. The decay time of the oscillations is 12.1 +/- 6.7 minutes for an oscillation with a frequency 3.90 +/- 0.13 millihertz The coronal dissipation coefficient is estimated to be eight to nine orders of magnitude larger than the theoretically predicted classical value. The larger dissipation coefficient may solve existing difficulties with wave heating and reconnection theories.

https://science.sciencemag.org/content/sci/285/5429/862.full.pdf

TRACE observation of damped coronal loop oscillations: implications for coronal heating

We report here, for the —rst time, on spatial oscillations of coronal loops, which were detected in extreme-ultraviolet wavelengths (171 with the T ransition Region and Coronal Explorer, in the tem- Ae ) perature range of MK. The observed loop oscillations occurred during a —are that began at T e B 1.0¨1.5 1998 July 14, 12:55 UT and are most prominent during the —rst 20 minutes. The oscillating loops connect the penumbra of the leading sunspot to the —are site in the trailing portion. We identi—ed —ve oscillating loops with an average length of L \ 130,000 ^ 30,000 km. The transverse amplitude of the oscillations is A \ 4100 ^ 1300 km, and the mean period is T \ 280 ^ 30 s. The oscillation mode appears to be a standing wave mode (with —xed nodes at the footpoints). We investigate diUerent MHD wave modes and —nd that the fast kink mode with a period q \ 205(L /1010 cm~3)1@2 cm)(n e /109 (B/10 G)~1 s provides the best agreement with the observed period. We propose that the onset of loop oscillations in distant locations is triggered by a signal or disturbance that propagates from the central —are site with a radial speed of B700 km s~1. Because the observed loop oscillation periods are compa- rable to photospheric 5 minute oscillations, a resonant coupling between the two systems is possible. We further —nd evidence for global extreme-UV dimming in the entire active region possibly associated with a coronal mass ejection. Subject headings: Sun: coronaSun: —aresSun: oscillationsSun: UV radiation

/pdf/coronal-loop-oscillations-observed-with-the-transition-41fi88x5lh.pdf

Coronal Loop Oscillations Observed with the Transition Region and Coronal Explorer

Motivated by recent Transition Region and Coronal Explorer (TRACE) observations of damped oscilla- tions in coronal loops, we consider analytically the motion of an inhomogeneous coronal magnetic tube of radius a in a zero-� plasma. An initially perturbed tube may vibrate in its kink mode of oscillation, but those vibrations are damped. The damping is due to resonant absorption, acting in the inhomogeneous regions of the tube, which leads to a transfer of energy from the kink mode to Alfven (azimuthal) oscillations within the inhomogeneous layer. We determine explicitly the decrement � (decay time � � 1 ) for a coronal flux tube whose plasma density varies only in a thin layer of thickness  on the tube boundary. The effect of viscosity is also considered. We show that, in general, the problem involves two distinct timescales, � � 1 and ! � 1 k R 1=3 , where R is the Reynolds number and !k is the frequency of the kink mode. Under coronal conditions (when � � 1 5 ! � 1 k R 1=3 ), the characteristic damping time of global oscillations is � � 1 . During this time, most of the energy in the initial perturbation is transferred into a resonant absorption layer of thickness of order  2 =a, with motions in this layer having an amplitude of order a= times the initial amplitude. We apply our results to the observations, suggesting that loop oscillations decay principally because of inhomogeneities in the loop. Our theory suggests that only those loops with density inhomogeneities on a small scale (confined to within a thin layer of order a�=! k in thickness) are able to support coherent oscillations for any length of time and so be observable. Loops with a more gradual density variation, on the scale of the tube radius a, do not exhibit pronounced oscillations. Subject headings: MHD — plasmas — Sun: corona — waves

/pdf/the-damping-of-coronal-loop-oscillations-55x721hery.pdf

The Damping of Coronal Loop Oscillations

The flow of energy through the solar atmosphere and the heating of the Sun's outer regions are still not understood. Here, we report the detection of oscillatory phenomena associated with a large bright-point group that is 430,000 square kilometers in area and located near the solar disk center. Wavelet analysis reveals full-width half-maximum oscillations with periodicities ranging from 126 to 700 seconds originating above the bright point and significance levels exceeding 99%. These oscillations, 2.6 kilometers per second in amplitude, are coupled with chromospheric line-of-sight Doppler velocities with an average blue shift of 23 kilometers per second. A lack of cospatial intensity oscillations and transversal displacements rules out the presence of magneto-acoustic wave modes. The oscillations are a signature of Alfven waves produced by a torsional twist of ±22 degrees. A phase shift of 180 degrees across the diameter of the bright point suggests that these torsional Alfven oscillations are induced globally throughout the entire brightening. The energy flux associated with this wave mode is sufficient to heat the solar corona.

/pdf/alfven-waves-in-the-lower-solar-atmosphere-4gzxvudpuz.pdf

Alfvén waves in the lower solar atmosphere.

Wave and oscillatory activity of the solar corona is confidently observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands, and interpreted in terms of magnetohydrodynamic (MHD) wave theory. The review reflects the current trends in the observational study of coronal waves and oscillations (standing kink, sausage and longitudinal modes, propagating slow waves and fast wave trains, the search for torsional waves), theoretical modelling of interaction of MHD waves with plasma structures, and implementation of the theoretical results for the mode identification. Also the use of MHD waves for remote diagnostics of coronal plasma - MHD coronal seismology - is discussed and the applicability of this method for the estimation of coronal magnetic field, transport coefficients, fine structuring and heating function is demonstrated.

/pdf/coronal-waves-and-oscillations-3na3kp3xre.pdf

Coronal Waves and Oscillations

The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvenic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvenic-type, oscillations arise only in high density (strictly, low Alfven velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.

Wave propagation in a magnetic cylinder

On coronal oscillations

Analogies of fast MHD waves propagating along a dense coronal structure are exploited to examine how the size and shape of the inhomogeneity affect the properties of the Love- and Pekeris-type waves. The profile's shape determines the dispersive nature of the waves. Excited impulsively, magnetic Love and Pekeris waves give rise to quasi-periodic oscillations with a duration and time scale that depend on the cross-sectional area and strength of the inhomogeneity. More diffuse coronal inhomogeneities support impulsively generated periodic oscillations, with the quasi-periodic signature being absent.

Employing analogies for ducted MHD waves in dense coronal structures

A model for ion-acoustic waves in the solar atmosphere is presented In the limit of strongly magnetized plasma this model leads to the Zakharov-Kuznetsov equation which possesses a flat solitary wave solution An initial-value problem for this equation is solved numerically to show a transition of the flat solitary waves into spherical solitary waves The paper suggests further developments of an ion-acoustic wave theory that may improve our knowledge of ion-acoustic waves and lead to the possibility of their being detected in the solar atmosphere

Ion-acoustic waves in the solar atmosphere

The distances over which magnetohydrodynamic waves will propagate in a non-ideal, magnetic, compressible medium, representing the solar corona structured by the presence of loops of denser material, are considered. The waves are damped by ion viscosity and electron heat conduction in a radiating, optically thin atmosphere. Waves which lose their energy of propagation in distances of less than our criterion value of 4 × 109 cm are regarded as candidates for contributing towards coronal heating. Alfvenic-type waves only dissipate in this way in weak (≲ 15 G) magnetic fields and when they have periods of a few seconds (2∓10 s). Acoustic-type waves can also be dissipated and we give typical values of magnetic field strength, density and temperature for which the dissipation could occur. Dissipating acoustic-type waves have periods that range from tens to hundreds of seconds (15–225 s).

P. M. Edwin

Papers

Wave propagation in a magnetic cylinder

On coronal oscillations

Employing analogies for ducted MHD waves in dense coronal structures

Ion-acoustic waves in the solar atmosphere

Dissipating the energy of magnetoacoustic waves in a structured atmosphere