Fast magnetoacoustic wave trains in magnetic funnels of the solar corona

Context: Fast magneto-acoustic waves are highly dispersive in waveguides, so they can generate quasi-periodic wave trains if a localised, impulsive driver is applied. Such wave trains have been observed in the solar corona and may be of use as a seismological tool since they depend upon the plasma structuring perpendicular to the direction of propagation. Aims. We extend existing models of magnetoacoustic waveguides to consider the effects of an expanding magnetic field. The funnel geometry employed includes a field-aligned density structure. Methods: We performed 2D numerical simulations of impulsively generated fast magneto-acoustic perturbations. The effects of the density contrast ratio, density stratification, and spectral profile of the driver upon the excited wave trains were investigated. Results: The density structure acts as a dispersive waveguide for fast magneto-acoustic waves and generates a quasi-periodic wave train similar to previous models. The funnel geometry leads to generating additional wave trains that propagate outside the density structure. These newly discovered wave trains are formed by the leakage of transverse perturbations, but they propagate upwards owing to the refraction caused by the magnetic funnel. Conclusions: The results of our funnel model may be applicable to wave trains observed propagating in the solar corona. They demonstrate similar properties to those found in our simulations

Transverse oscillations of two coronal loops

We study transverse fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma cylinders in a uniform magnetic field. The collective oscillatory properties of the system due to the interaction between the individual loops are investigated from two points of view. Firstly, the frequency and spatial structure of the normal modes are studied. The system supports four trapped normal modes in which the loops move rigidly in the transverse direction. The direction of the motions is either parallel or perpendicular to the plane containing the axes of the loops. Two of these modes correspond to oscillations of the loops in phase, while in the other two they move in antiphase. Thus, these solutions are the generalization of the kink mode of a single cylinder to the double cylinder case. Secondly, we analyze the time-dependent problem of the excitation of the pair of tubes. We find that depending on the shape and location of the initial disturbance, different normal modes can be excited. The frequencies of normal modes are accurately recovered from the numerical simulations. In some cases, because of the simultaneous excitation of several eigenmodes, the system shows beating and the phase lag between the loops is $\pi/2$.Comment: Accepted for publication in The Astrophysical Journa

On the Asymmetric Longitudinal Oscillations of a Pikelner's Model Prominence

We present analytical and numerical models of a normal-polarity quiescent prominence that are based on the model of Pikelner (Solar Phys. 1971, 17, 44 ). We derive the general analytical expressions for the two-dimensional equilibrium plasma quantities such as the mass density and a gas pressure, and we specify magnetic-field components for the prominence, which corresponds to a dense and cold plasma residing in the dip of curved magnetic-field lines. With the adaptation of these expressions, we solve numerically the 2D, nonlinear, ideal MHD equations for a Pikelner's model of a prominence that is initially perturbed by reducing the gas pressure at the dip of magnetic-field lines. Our findings reveal that as a result of pressure perturbations the prominence plasma starts evolving in time and this leads to the antisymmetric magnetoacoustic--gravity oscillations as well as to the mass-density growth at the magnetic dip, and the magnetic-field lines subside there. This growth depends on the depth of magnetic dip. For a shallower dip, less plasma is condensed and vice-versa. We conjecture that the observed long-period magnetoacoustic-gravity oscillations in various prominence systems are in general the consequence of the internal pressure perturbations of the plasma residing in equilibrium at the prominence dip.Comment: 24 Pages; 16 Figures; Solar Physic

New analytical and numerical models of solar coronal loop: I. Application to forced vertical kink oscillations

Aims. We construct a new analytical model of a solar coronal loop that is embedded in a gravitationally stratified and magnetically confined atmosphere. On the basis of this analytical model, we devise a numerical model of solar coronal loops. We adopt it to perform the numerical simulations of its vertical kink oscillations excited by an external driver. Methods. Our model of the solar atmosphere is constructed by adopting a realistic temperature distribution and specifying the curved magnetic field lines that constitute a coronal loop. This loop is described by 2D, ideal magnetohydro- dynamic equations that are numerically solved by the FLASH code. Results. The vertical kink oscillations are excited by a periodic driver in the vertical component of velocity, acting at the top of the photosphere. For this forced driver with its amplitude 3 km/s, the excited oscillations exhibit about 1.2 km/s amplitude in their velocity and the loop apex oscillates with its amplitude in displacement of about 100 km. Conclusions. The newly devised analytical model of the coronal loops is utilized for the numerical simulations of the vertical kink oscillations, which match well with the recent observations of decay-less kink oscillations excited in solar loops. The model will have further implications on the study of waves and plasma dynamics in coronal loops, revealing physics of energy and mass transport mechanisms in the localized solar atmosphere.Comment: 6 Pages; 5 Figures; A&

Does the Sun Shrink with Increasing Magnetic Activity?

We have analyzed the full set of SOHO/MDI f- and p-mode oscillation frequencies from 1996 to date in a search for evidence of solar radius evolution during the rising phase of the current activity cycle. Like Antia et al. (2000), we find that a significant fraction of the f-mode frequency changes scale with frequency; and that if these are interpreted in terms of a radius change, it implies a shrinking sun. Our inferred rate of shrinkage is about 1.5 km/y, which is somewhat smaller than found by Antia et al. We argue that this rate does not refer to the surface, but rather to a layer extending roughly from 4 to 8 Mm beneath the visible surface. The rate of shrinking may be accounted for by an increasing radial component of the rms random magnetic field at a rate that depends on its radial distribution. If it were uniform, the required field would be ~7 kG. However, if it were inwardly increasing, then a 1 kG field at 8 Mm would suffice. To assess contribution to the solar radius change arising above 4Mm, we analyzed the p-mode data. The evolution of the p-mode frequencies may be explained by a magnetic^M field growing with activity. The implications of the near-surface magnetic field changes depend on the anisotropy of the random magnetic field. If the field change is predominantly radial, then we infer an additional shrinking at a rate between 1.1-1.3 km/y at the photosphere. If on the other hand the increase is isotropic, we find a competing expansion at a rate of 2.3 km/y. In any case, variations in the sun's radius in the activity cycle are at the level of 10^{-5} or less, hence have a negligible contribution to the irradiance variations.Comment: 10 pages (ApJ preprint style), 4 figures; accepted for publication in Ap

Torsional Alfven Waves in Solar Magnetic Flux Tubes of Axial Symmetry

Aims: Propagation and energy transfer of torsional Alfv\'en waves in solar magnetic flux tubes of axial symmetry is studied. Methods: An analytical model of a solar magnetic flux tube of axial symmetry is developed by specifying a magnetic flux and deriving general analytical formulae for the equilibrium mass density and a gas pressure. The main advantage of this model is that it can be easily adopted to any axisymmetric magnetic structure. The model is used to simulate numerically the propagation of nonlinear Alfv\'en waves in such 2D flux tubes of axial symmetry embedded in the solar atmosphere. The waves are excited by a localized pulse in the azimuthal component of velocity and launched at the top of the solar photosphere, and they propagate through the solar chromosphere, transition region, and into the solar corona. Results: The results of our numerical simulations reveal a complex scenario of twisted magnetic field lines and flows associated with torsional Alfv\'en waves as well as energy transfer to the magnetoacoustic waves that are triggered by the Alfv\'en waves and are akin to the vertical jet flows. Alfv\'en waves experience about 5 % amplitude reflection at the transition region. Magnetic (velocity) field perturbations experience attenuation (growth) with height is agreement with analytical findings. Kinetic energy of magnetoacoustic waves consists of 25 % of the total energy of Alfv\'en waves. The energy transfer may lead to localized mass transport in the form of vertical jets, as well as to localized heating as slow magnetoacoustic waves are prone to dissipation in the inner corona.Comment: 12 pages; 12 Figures, Astron. Astrophys. (A&A); Comment : High-resolution images will be appeared with the final pape

Transverse oscillations of systems of coronal loops

We study the collective kinklike normal modes of a system of several cylindrical loops using the T-matrix theory. Loops that have similar kink frequencies oscillate collectively with a frequency which is slightly different from that of the individual kink mode. On the other hand, if the kink frequency of a loop is different from that of the others, it oscillates individually with its own frequency. Since the individual kink frequency depends on the loop density but not on its radius for typical 1 MK coronal loops, a coupling between kink oscillations of neighboring loops take place when they have similar densities. The relevance of these results in the interpretation of the oscillations studied by \citet{schrijver2000} and \citet{verwichte2004}, in which transverse collective loop oscillations seem to be detected, is discussed. In the first case, two loops oscillating in antiphase are observed; interpreting this motion as a collective kink mode suggests that their densities are roughly equal. In the second case, there are almost three groups of tubes that oscillate with similar periods and therefore their dynamics can be collective, which again seems to indicate that the loops of each group share a similar density. All the other loops seem to oscillate individually and their densities can be different from the rest