Abstract. Sufficiently thick and dense coronal loops can support global sausage magnetoacoustic modes. We demonstrate that the oscillation period of this mode, calculated in the straight cylinder approximation, is determined by the length of the loop, not by its diameter, as it was previously assumed. The existence condition for this mode is the ratio of the loop length to its diameter to be less than about a half of the square root of the density contrast ratio. This mode has a maximum of the magnetic field perturbation at the loop apex and nodes at the footpoints. We demonstrate that the 14−17 s quasi-periodic pulsations, oscillating in phase at a loop apex and at its legs, observed with the Nobeyama Radioheliograph, are interpreted in terms of the global sausage mode.

Abstract.A microwave burst with quasi-periodic pulsations was studied with high spatial resolution using observations with the Nobeyama Radioheliograph (NoRH). We found that the time profiles of the microwave emission at 17 and 34 GHz exhibit quasi-periodic (with two well defined periods P 1 = 14-17 s and P 2 = 8-11 s) variations of the intensity at different parts of an observed flaring loop. Detailed Fourier analysis shows the P 1 spectral component to be dominant at the top, while the P 2 one near the feet of the loop. The 14-17 s pulsations are synchronous at the top and in both legs of the loop. The 8-11 s pulsations at the legs are well correlated with each other but the correlation is not so obvious with the pulsations at the loop top. For this P 2 spectral component, a definite phase shift, P 2 /4 ≈ 2.2 s, between pulsations in the northern leg and loop top parts of the loop have been found. The length of the flaring loop is estimated as L = 25 Mm (≈34 ) and its average width at half intensity at 34 GHz as about 6 Mm (≈8 ). Microwave diagnostics shows the loop to be filled with a dense plasma with the number density n 0 ≈ 10 11 cm −3 , penetrated by the magnetic field changing from B 0 ≈ 100 G near the loop top up to B 0 ≈ 200 G near the north footpoint. A comparative analysis of different MHD modes of the loop demonstrates the possibility of the simultaneous existence of two modes of oscillations in the loop: the global sausage mode, with the period P 1 = 14-17 s and the nodes at the footpoints, and a higher harmonics mode (possibly with the radial wave number l > 1), with P 2 = 8-11 s.

We use images of high spatial and temporal resolution, obtained using both ground-and space-based instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a near-circular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the perioddistance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and force-free field extrapolations, we attribute this behaviour to the cut-off frequency imposed by the magnetic field geometry in this location. A rapid, localised inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cut-off frequency. For the first time we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magneto-hydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly-propagating magneto-acoustic waves generated in the photosphere.

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Context. The cut-off frequency of magnetoacoustic gravity (MAG) waves could be decreased by the inclined magnetic field, and therefore, low-frequency waves could penetrate into the upper atmosphere. Aims. We observe the distribution of the cut-off frequency of compressive waves at various heights and reconstruct the magnetic field inclination, according to the MAG wave theory in a stratified atmosphere permeated by a uniform magnetic field. Methods. We analysed the emission intensity oscillations of sunspot AR11131 (08 Dec. 2010) observed at the 1700 Å, 1600 Å, and 304 Å bandpasses of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO), and computed the narrow-band power maps with the pixelised wavelet filtering method. The distribution of the cut-off frequency was defined as the median contour in the azimuthally-averaged oscillation power. The magnetic field inclination was estimated with the local cut-off frequency according to the MAG wave theory in the low-β limit and was compared to the potential field extrapolation. Results. Shorter period oscillations dominate in the sunspot umbra, while longer period oscillations form an annular shape approximately concentric with the sunspot. Oscillations with longer periods are distributed further away from the sunspot centre. The 5 min oscillations appear to originate at or lower than the photosphere. The magnetic field inclinations determined with the cut-off frequency theory are about 30−40% larger than the values obtained by the potential field extrapolation. Conclusions. The oscillation power distribution in a sunspot atmosphere reflects its magnetic and thermal structure. The cut-off frequency could be used to probe the magnetic field inclination, however, other factors have to be included to fully understand this phenomenon. The existence of return magnetic flux at the outer penumbra was evidenced by the cut-off frequency distribution.