V. M. Nakariakov

Determination of the coronal magnetic field by coronal loop oscillations

We develop a new method for the determination of the absolute value of the magnetic field strength in coronal closed magnetic structures, based on the analysis of flare-generated oscillations of coronal loops. Interpretation of the oscillations observed in terms of global standing kink waves allows to connect the period of the oscillations and the loops length with the magnetic field strength in the loops. For loop oscillations observed with TRACE on 14th July 1998 and 4th July 1999, we estimate the magnetic field strength as 4-30 G. Using TRACE 171 A and 195 A images of the loop, taken on 4th July 1999 to determine the plasma density, we estimate the magnetic field in the loop as 13 +- 9 G. Improved diagnostic of the loop length, the oscillation period, and the plasma density in the loop will significantly improve the methods precision.

Excitation of magnetospheric waveguide modes by magnetosheath flows

Standard models of the Earths outer magnetospheric waveguide assume that a perfectly reflecting magnetopause can trap energy inside the waveguide. In contrast, we show that the near-noon magnetopause often acts as a leaky boundary, wave trapping only being possible for large magnetosheath flow speeds. Moreover, for sufficiently fast flow speeds, we show how waveguide modes may be energized by magnetosheath flows via the overreflection mechanism. Unbounded simulations of the growth of surface waves via the development of a Kelvin-Helmholtz instability (KHI) vortex sheet show growth rates which increase without limit proportional to wavenumber (ky), until the assumption of a thin boundary is no longer valid. For a bounded magnetosphere, however, overreflected body type waveguide modes can introduce wavenumber selection, that is, generate modes with maximum linear growth rates at finite ky. A necessary condition is that the wave is propagating in the magnetosphere, that is, the waves turning point lies inside the magnetosphere. By developing a new description of both KHI and waveguide mode growth in terms of overreflection and the propagation of negative energy waves, we show how the maximum growth rate can be understood in terms of the reflection coefficient of waves incident upon the magnetopause. Our model can also explain the observed local time dependence of Pc5 field line resonance wave power, and can explain the observed correlation between high solar wind speeds and Pc5 wave power. Finally, we show how a waveguide with a free magnetopause boundary supports quarter-wavelength modes. These modes have lower frequencies than the standard (magnetopause velocity node) half-wavelength modes, perhaps generating the millihertz waveguide mode eigenfrequencies which appear to drive field line resonances in HF radar data.

Slow Magnetosonic Waves in Coronal Plumes

Recent observations of polar plumes in the southern solar coronal hole by the Extreme-Ultraviolet Imaging Telescope (EIT) on board the SOHO spacecraft show signatures of quasi-periodic compressional waves with periods of 10-15 minutes. The relative wave amplitude was found to increase with height in the plumes up to about 1.2 R☉. Using a one-dimensional linear wave equation for the magnetosonic wave, we show that the waves are propagating and that their amplitude increases with height. The observed propagation velocity agrees well with the expected sound velocity inside the plumes. We present the results of the first nonlinear, two-dimensional, magnetohydrodynamic (MHD) simulation of the magnetosonic waves in plumes for typical coronal conditions consistent with observations and gravitationally stratified solar corona. We find numerically that outward-propagating slow magnetosonic waves are trapped, and nonlinearly steepen in the polar plumes. The nonlinear steepening of the magnetosonic waves may contribute significantly to the heating of the lower corona by compressive dissipation.

Magnetohydrodynamic waves and coronal seismology: an overview of recent results

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.

Detection of waves in the solar corona : kink or Alfven?

Recently, the omnipresence of waves has been discovered in the corona using the CoMP instrument. We demonstrate that the observational findings can be explained in terms of guided kink magnetoacoustic modes. The interpretation of the observations in terms of Alfven waves is shown to be inconsistent with MHD wave theory. The implications of the interpretation in terms of kink waves are discussed.

Global sausage modes of coronal loops

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.

Coronal loop seismology using multiple transverse loop oscillation harmonics

Context. TRACE observations (23/11/1998 06:35:57−06:48:43 UT) in the 171 A bandpass of an active region are studied. Coronal loop oscillations are observed after a violent disruption of the equilibrium. Aims. The oscillation properties are studied to give seismological estimates of physical quantities, such as the density scale height. Methods. A loop segment is traced during the oscillation, and the resulting time series is analysed for periodicities. Results. In the loop segment displacement, two periods are found: 435.6 ± 4. 5sa nd 242.7 ± 6.4 s, consistent with the periods of the fundamental and 2nd harmonic fast kink oscillation. The small uncertainties allow us to estimate the density scale height in the loop to be 109 Mm, which is about double the estimated hydrostatical value of 50 Mm. Because a loop segment is traced, the amplitude dependence along the loop is found for each of these oscillations. The obtained spatial information is used as a seismological tool to give details about the geometry of the observed loop.

Quasi-periodic modulation of solar and stellar flaring emission by magnetohydrodynamic oscillations in a nearby loop

We propose a new model for quasi-periodic modulation of solar and stellar flaring emission. Fast magnetoacoustic oscillations of a non-flaring loop can interact with a nearby flaring active region. This interaction occurs when part of the oscillation situated outside the loop reaches the regions of steep gradients in magnetic field within an active region and produces periodic variations of electric current density. The modulation depth of these variations is a few orders of magnitude greater than the amplitude of the driving oscillation. The variations of the current can induce current-driven plasma micro-instabilities and thus anomalous resistivity. This can periodically trigger magnetic reconnection, and hence acceleration of charged particles, producing quasi-periodic pulsations of X-ray, optical and radio emission at the arcade footpoints.

Magnetic Kelvin-Helmholtz Instability at the Sun

Flows and instabilities play a major role in the dynamics of magnetized plasmas including the solar corona, magnetospheric and heliospheric boundaries, cometary tails, and astrophysical jets. The nonlinear effects, multi-scale and microphysical interactions inherent to the flow-driven instabilities, are believed to play a role, e.g., in plasma entry across a discontinuity, generation of turbulence, and enhanced drag. However, in order to clarify the efficiency of macroscopic instabilities in these processes, we lack proper knowledge of their overall morphological features. Here we show the first observations of the temporally and spatially resolved evolution of the magnetic Kelvin-Helmholtz instability in the solar corona. Unprecedented high-resolution imaging observations of vortices developing at the surface of a fast coronal mass ejecta are taken by the new Solar Dynamics Observatory, validating theories of the nonlinear dynamics involved. The new findings are a cornerstone for developing a unifying theory on flow-driven instabilities in rarefied magnetized plasmas, which is important for understanding the fundamental processes at work in key regions of the Sun-Earth system.

Dissipation of Slow Magnetosonic Waves in Coronal Plumes

Recently, slow magnetosonic waves were identified in polar plumes, at heights up to about 1.2 R☉ using the Extreme Ultraviolet Imaging Telescope (EIT) observations of quasi-periodic EUV intensity fluctuations, and higher in the corona using the Ultraviolet Coronagraph Spectrometer (UVCS) white-light channel. First, we derive the linear dispersion relation for the slow waves in the viscous plasma. Next, we derive and solve an evolutionary equation of the Burgers type for the slow waves, incorporating the effects of radial stratification, quadratic nonlinearity, and viscosity. Finally, we model the propagation and dissipation of slow magnetosonic waves in polar plumes using one-dimensional and two-dimensional MHD codes in spherical geometry. The waves are launched at the base of the corona with a monochromatic source. We find that the slow waves nonlinearly steepen as they propagate away from the Sun into the solar wind. The nonlinear steepening of the waves leads to enhanced dissipation owing to compressive viscosity at the wave fronts. The efficient dissipation of the slow wave by compressive viscosity leads to damping of the waves within the first solar radii above the surface. We investigate the parametric dependence of the wave properties.