I. De Moortel

How to Channel Photospheric Oscillations into the Corona

There are now many observations of waves in the solar corona with periods around 5 minutes. The source of these waves is uncertain, although global p-modes in the photosphere are an obvious candidate, given the similarity of the dominant periods. However, p-modes are traditionally considered evanescent in the upper photosphere, and it has been unclear how they could propagate through the chromosphere into the corona. Using a numerical model, we show that photospheric oscillations with periods around 5 minutes can actually propagate into the corona so long as they are guided along an inclined magnetic flux tube. The nonverticality of the flux tube increases the acoustic cutoff period to values closer to the dominant periods of the photospheric oscillations, thus allowing tunneling or even direct propagation into the outer atmosphere. The photospheric oscillations develop into shocks, which drive chromospheric spicules and reach the corona. We suggest that Transition Region and Coronal Explorer (TRACE) observations of propagating magnetoacoustic waves in the corona represent these shocked and tunneled photospheric oscillations. We also explore how seismology of these waves could be exploited to determine the connectivity between photosphere and corona.

Coupled Alfvén and Kink Oscillations in Coronal Loops

Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. However, there is ongoing discussion regarding their interpretation as kink or Alfven 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 Alfven mode. The decay of the propagating kink wave as energy is transferred to the local Alfven 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 Alfven 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.

Observation of Higher Harmonic Coronal Loop Oscillations

A sequence of TRACE 171 A observations taken on 2001 May 13 shows evidence of flare-induced, transverse coronal loop oscillations. We revisit this particular data set and present evidence of the presence of spatially resolved higher harmonics in the transverse loop displacements. The oscillations are identified as the second-harmonic, fast MHD kink waves (periods of 577-672 s), with higher harmonics (250-346 s) also present. The apparent absence of the fundamental mode and the fact that it is the second harmonic (P2) that dominates the oscillatory behavior of this particular loop may shed more light on either the excitation and/or the damping mechanism(s) of flare-induced, transverse loop oscillations.

The damping of slow MHD waves in solar coronal magnetic fields - II. The effect of gravitational stratification and field line divergence

This paper continues the study of De Moortel & Hood ([CITE]) into the propagation of slow MHD waves in the solar corona. Firstly, the damping due to optically thin radiation is investigated and compared to the effect of thermal conduction. In a second stage, gravitational stratification is included in the model and it is found that this increases the damping length significantly. Finally, the effect of different magnetic field geometries on the damping of the slow waves is investigated. As a first approximation, a purely radial magnetic field is considered and although the amplitudes of the perturbations decrease due to the divergence of the field, the effect is small compared to the effect of thermal conduction. A more realistic local geometry, estimated from the observations, is investigated and it is demonstrated that a general area divergence can cause a significant, additional, decrease of the amplitudes of the perturbations. The results of numerical simulations, incorporating the effects of gravitational stratification, the magnetic field geometry and thermal conduction are compared with TRACE observations of propagating waves in coronal loops. It is found that a combination of thermal conduction and (general) area divergence yields detection lengths that are in good agreement with observed values.

An overview of coronal seismology

The idea of exploiting observed oscillations as a diagnostic tool for determining the physical conditions of the coronal plasma was first suggested several decades ago (Roberts et al. 1984 Astrophys. J. 279, 857). Until recently, the application of this idea has been very limited by a lack of high-quality observations of coronal oscillations. However, during the last few years, this situation has changed dramatically, especially due to space-based observations by the Solar and Heliospheric Observatory and the Transition Region and Coronal Explorer and waves and oscillations have now been observed in a wide variety of solar structures, such as coronal loops, polar plumes and prominences. This paper will briefly summarize MHD wave theory, which forms the basis for coronal seismology, as well as present an overview of the variety of recently observed waves and oscillations in the solar corona. The present state of coronal seismology will also be discussed. Currently, the uncertainty associated with the obtained parameters is still considerable and, hence, the results require a cautious interpretation. However, these examples do show that coronal seismology is rapidly being transformed from a theoretical possibility to a viable technique.

Propagating coupled Alfvén and kink oscillations in an arbitrary inhomogeneous corona

Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform three-dimensional numerical simulations of footpoint-driven transverse waves propagating in a low β plasma. We consider the cases of distorted cylindrical flux tubes and a randomly generated inhomogeneous medium. When density structuring is present, mode coupling in inhomogeneous regions leads to the coupling of the kink mode to the Alfven mode. The decay of the propagating kink wave is observed as energy is transferred to the local Alfven mode. In all cases considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localized Alfven modes. We have demonstrated that mode coupling efficiently couples propagating kink perturbations to Alfven modes in an arbitrary inhomogeneous medium. This has the consequence that transverse footpoint motions at the base of the corona will deposit energy to Alfven modes in the corona.

Periodic spectral line asymmetries in solar coronal structures from slow magnetoacoustic waves

Recent spectral observations of upward moving quasi-periodic intensity perturbations in solar coronal structures have shown evidence of periodic line asymmetries near their footpoints. These observations challenge the established interpretation of the intensity perturbations in terms of propagating slow magnetoacoustic waves. We show that slow waves inherently have a bias toward enhancement of emission in the blue wing of the emission line due to in-phase behavior of velocity and density perturbations. We demonstrate that slow waves cause line asymmetries when the emission line is averaged over an oscillation period or when a quasi-static plasma component in the line of sight is included. Therefore, we conclude that slow magnetoacoustic waves remain a valid explanation for the observed quasi-periodic intensity perturbations.

Review Article: MHD Wave Propagation Near Coronal Null Points of Magnetic Fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a β=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.

Spatial damping of propagating kink waves due to mode coupling

Aims. We investigate the damping process for propagating transverse velocity oscillations, observed to be ubiquitous in the solar corona, due to mode coupling. Methods. We perform 3D numerical simulations of footpoint-driven transverse waves propagating in a low β coronal plasma with a cylindrical density structure. Mode coupling in an inhomogeneous layer leads to the coupling of the kink mode to the Alfven mode, observed as the decay of the transverse kink oscillations. Results. We consider the spatial damping profile and find a Gaussian damping profile of the form exp(−z/Lg) to be the most congruent with our numerical data, rather than the exponential damping profile of the form exp(−z/Ld) used in normal mode analysis. Our results highlight that the nature of the driver itself will have a substantial influence on observed propagating kink waves. Conclusions. Our study suggests that this modified damping profile should be taken into account when using coronal seismology to infer local plasma properties from observed damped oscillations.

Joint observations of propagating oscillations with SOHO/CDS and TRACE

Joint Observing Program (JOP) 83 Solar and Heliospheric Observatory/Coronal Diagnostic Spectrometer (SOHO/CDS) and Transition Region and Coronal Explorer (TRACE) data is analysed for evidence of propagating intensity oscillations along loop structures in the solar corona. A propagating intensity oscillation with a minimum estimated speed of 50-195 km s 1 is observed within a TRACE 171 A coronal loop using a running dierence method. Co-spatial and co- temporal CDS and TRACE observations of this loop are analysed using a wavelet analysis method. The TRACE data shows a propagating oscillation with a period of300 s. This period is also observed with CDS suggesting propagating oscillations at chromospheric, transition region and coronal temperatures in the He i ,O v and Mgix lines.