Calculation of Spectral Darkening and Visibility Functions for Solar Oscillations

Calculations of spectral darkening and visibility functions for the brightness oscillations of the Sun resulting from global solar oscillations are presented. This has been done for a broad range of the visible and infrared continuum spectrum. The procedure for the calculations of these functions includes the numerical computation of depth-dependent derivatives of the opacity caused by p modes in the photosphere. A radiative-transport code was used for this purpose to get the disturbances of the opacities from temperature and density fluctuations. The visibility and darkening functions are obtained for adiabatic oscillations under the assumption that the temperature disturbances are proportional to the undisturbed temperature of the photosphere. The latter assumption is the only way to explore any opacity effects since the eigenfunctions of p-mode oscillations have not been obtained so far. This investigation reveals that opacity effects have to be taken into account because they dominate the violet and infrared part of the spectrum. Because of this dominance, the visibility functions are negative for those parts of the spectrum. Furthermore, the darkening functions show a wavelength-dependent change of sign for some wavelengths owing to these opacity effects. However, the visibility and darkening functions under the assumptions used contradict the observations of global p-mode oscillations, but it is beyond doubt that the opacity effects influence the brightness fluctuations of the Sun resulting from global oscillations

A New Look at Mode Conversion in a Stratified Isothermal Atmosphere

Recent numerical investigations of wave propagation near coronal magnetic null points (McLaughlin and Hood: Astron. Astrophys. 459, 641,2006) have indicated how a fast MHD wave partially converts into a slow MHD wave as the disturbance passes from a low-beta plasma to a high-beta plasma. This is a complex process and a clear understanding of the conversion mechanism requires the detailed investigation of a simpler model. An investigation of mode conversion in a stratified, isothermal atmosphere, with a uniform, vertical magnetic field is carried out, both numerically and analytically. In contrast to previous investigations of upward-propagating waves (Zhugzhda and Dzhalilov: Astron. Astrophys. 112, 16, 1982a; Cally: Astrophys. J. 548, 473, 2001), this paper studies the downward propagation of waves from a low-beta to high-beta environment. A simple expression for the amplitude of the transmitted wave is compared with the numerical solution.Comment: 14 pages, 6 figure

Propagation of Long-Wavelength Nonlinear Slow Sausage Waves in Stratified Magnetic Flux Tubes

The propagation of nonlinear, long-wavelength, slow sausage waves in an expanding magnetic flux tube, embedded in a non-magnetic stratified environment, is discussed. The governing equation for surface waves, which is akin to the Leibovich–Roberts equation, is derived using the method of multiple scales. The solitary wave solution of the equation is obtained numerically. The results obtained are illustrative of a solitary wave whose properties are highly dependent on the degree of stratification

Three Dimensional MHD Wave Propagation and Conversion to Alfven Waves near the Solar Surface. I. Direct Numerical Solution

The efficacy of fast/slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfven and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfven wave may couple to the magneto-acoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical ``scattering experiment'', placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvenic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfven waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfven fluxes are produced when the field is inclined 30-40 degrees from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60-80 degrees.Comment: Accepted for the HELAS II/ SOHO 19/ GONG 2007 Topical Issue of Solar Physic

Non-linear numerical simulations of magneto-acoustic wave propagation in small-scale flux tubes

We present results of non-linear, 2D, numerical simulations of magneto-acoustic wave propagation in the photosphere and chromosphere of small-scale flux tubes with internal structure. Waves with realistic periods of three to five minutes are studied, after applying horizontal and vertical oscillatory perturbations to the equilibrium model. Spurious reflections of shock waves from the upper boundary are minimized thanks to a special boundary condition. This has allowed us to increase the duration of the simulations and to make it long enough to perform a statistical analysis of oscillations. The simulations show that deep horizontal motions of the flux tube generate a slow (magnetic) mode and a surface mode. These modes are efficiently transformed into a slow (acoustic) mode in the vA < cS atmosphere. The slow (acoustic) mode propagates vertically along the field lines, forms shocks and remains always within the flux tube. It might deposit effectively the energy of the driver into the chromosphere. When the driver oscillates with a high frequency, above the cut-off, non-linear wave propagation occurs with the same dominant driver period at all heights. At low frequencies, below the cut-off, the dominant period of oscillations changes with height from that of the driver in the photosphere to its first harmonic (half period) in the chromosphere. Depending on the period and on the type of the driver, different shock patterns are observed.Comment: 22 pages 6 color figures, submitted to Solar Physics, proceeding of SOHO 19/ GONG 2007 meeting, Melbourne, Australi

Meridional Circulation and Global Solar Oscillations

We investigate the influence of large-scale meridional circulation on solar p-modes by quasi-degenerate perturbation theory, as proposed by \cite{lavely92}. As an input flow we use various models of stationary meridional circulation obeying the continuity equation. This flow perturbs the eigenmodes of an equilibrium model of the Sun. We derive the signatures of the meridional circulation in the frequency multiplets of solar p-modes. In most cases the meridional circulation leads to negative average frequency shifts of the multiplets. Further possible observable effects are briefly discussed.Comment: 14 pages, 5 figures, submittted to Solar Physics Topical Issue "HELAS

Transverse oscillations of coronal loops

On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this review we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist. An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube. Very often collective oscillations of an array of coronal magnetic loops are observed. It is natural to start studying this phenomenon from the system of two coronal loops. We describe very recent analytical and numerical results of studying collective oscillations of two parallel homogeneous coronal loops. The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations. In the last part of the review we summarise the most outstanding and acute problems in the theory of the coronal loop transverse oscillations

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review

Observation of solar low-l p-modes by the CORONAS-DIFOS experiment. The influence of turbulence on the solar p-mode frequencies

The CORONAS satellite, launched on 1994 March, 2 carried the DIFOS experiment to observe irradiance fluctuations due to global solar oscillations. The DIFOS experiment was working for almost 50 days near solar activity minimum. We present first results of the Fourier analysis of the full time series. The fine structure of the low-l p-modes can be seen clearly. Results of the wavelet analysis show strong variations of the p-modes with time. (orig.)SIGLEAvailable from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman