Recent observations have revealed that magnetohydrodynamic (MHD) waves and oscillations are ubiquitous in the solar atmosphere, with a wide range of periods. We give a brief review of some aspects of MHD waves and coronal seismology that have recently been the focus of intense debate or are newly emerging. In particular, we focus on four topics: (i) the current controversy surrounding propagating intensity perturbations along coronal loops, (ii) the interpretation of propagating transverse loop oscillations, (iii) the ongoing search for coronal (torsional) Alfvén waves, and (iv) the rapidly developing topic of quasi-periodic pulsations in solar flares.

Context. This paper extends the models of Craig & McClymont (1991, ApJ, 371, L41) and McLaughlin & Hood (2004, A&A, 420, 1129 to include finite β and nonlinear effects. Aims. We investigate the nature of nonlinear fast magnetoacoustic waves about a 2D magnetic X-point. Methods. We solve the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Arber et al. 2001, J. Comp. Phys., 171, 151) and consider an initial condition in u × B ·ẑ (a natural variable of the system). Results. We observe the formation of both fast and slow oblique magnetic shocks. The nonlinear wave deforms the X-point into a "cusp-like" point which in turn collapses to a current sheet. The system then evolves through a series of horizontal and vertical current sheets, with associated changes in connectivity, i.e. the system exhibits oscillatory reconnection. Our final state is non-potential (but in force balance) due to asymmetric heating from the shocks. Larger amplitudes in our initial condition correspond to larger values of the final current density left in the system. Conclusions. The inclusion of nonlinear terms introduces several new features to the system that were absent from the linear regime.

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Determining the heating mechanism (or mechanisms) that causes the outer atmosphere of the Sun, and many other stars, to reach temperatures orders of magnitude higher than their surface temperatures has long been a key problem. For decades, the problem has been known as the coronal heating problem, but it is now clear that 'coronal heating' cannot be treated or explained in isolation and that the heating of the whole solar atmosphere must be studied as a highly coupled system. The magnetic field of the star is known to play a key role, but, despite significant advancements in solar telescopes, computing power and much greater understanding of theoretical mechanisms, the question of which mechanism or mechanisms are the dominant supplier of energy to the chromosphere and corona is still open. Following substantial recent progress, we consider the most likely contenders and discuss the key factors that have made, and still make, determining the actual (coronal) heating mechanism (or mechanisms) so difficult.

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Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. However, there is ongoing discussion regarding their interpretation as kink or Alfvén waves. To investigate the nature of transverse waves propagating in the solar corona and their potential for use as a coronal diagnostic in MHD seismology, we perform three-dimensional numerical simulations of footpoint-driven transverse waves propagating in a low β plasma. We consider the cases of both a uniform medium and one with loop-like density structure and perform a parametric study for our structuring parameters. When density structuring is present, resonant absorption in inhomogeneous layers leads to the coupling of the kink mode to the Alfvén mode. The decay of the propagating kink wave as energy is transferred to the local Alfvén mode is in good agreement with a modified interpretation of the analysis of Ruderman & Roberts for standing kink modes. Numerical simulations support the most general interpretation of the observed loop oscillations as a coupling of the kink and Alfvén modes. This coupling may account for the observed predominance of outward wave power in longer coronal loops since the observed damping length is comparable to our estimate based on an assumption of resonant absorption as the damping mechanism.

Abstract. High cadence, 171Å, TRACE observations show that outward propagating intensity disturbances are a common feature in large, quiescent coronal loops. These oscillations are interpreted as propagating slow magnetoacoustic waves. Using a wavelet analysis, we found periods of the order of 282 ± 93 s. However, a careful study of the location of the footpoints revealed a distinct separation between those loops that support oscillations with periods smaller than 200 s and periods larger than 200 s. It was found that loops that are situated above sunspot regions display intensity oscillations with a period of the order of 172 ± 32 s, whereas oscillations in "non-sunspot" loops show periods of the order of 321 ± 74 s. We conclude that the observed longitudinal oscillations are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. This result suggests that the underlying oscillations can propagate through the transition region and into the corona.

Abstract.A theoretical description of slow MHD wave propagation in the solar corona is presented. Two different damping mechanisms, namely thermal conduction and compressive viscosity, are included and discussed in detail. We revise the properties of the "thermal" mode, which is excited when thermal conduction is included. The thermal mode is purely decaying in the case of standing waves, but is oscillatory and decaying in the case of driven waves. When thermal conduction is dominant, the waves propagate largely undamped, at the slower, isothermal sound speed. This implies that there is a minimum damping time (or length) that can be obtained by thermal conduction alone. The results of numerical simulations are compared with TRACE observations of propagating waves, driven by boundary motions, and standing waves observed by SUMER/SOHO, excited by an initial impulse. For typical coronal conditions, thermal conduction appears to be the dominant damping mechanism.