Bayesian Coronal Seismology

In contrast to the situation in a laboratory, the study of the solar atmosphere has to be pursued without direct access to the physical conditions of interest. Information is therefore incomplete and uncertain and inference methods need to be employed to diagnose the physical conditions and processes. One of such methods, solar atmospheric seismology, makes use of observed and theoretically predicted properties of waves to infer plasma and magnetic field properties. A recent development in solar atmospheric seismology consists in the use of inversion and model comparison methods based on Bayesian analysis. In this paper, the philosophy and methodology of Bayesian analysis are first explained. Then, we provide an account of what has been achieved so far from the application of these techniques to solar atmospheric seismology and a prospect of possible future extensions.Comment: 19 pages, accepted in Advances in Space Researc

Wave Heating of the Solar Atmosphere

Magnetic waves are a relevant component in the dynamics of the solar atmosphere. Their significance has increased because of their potential as a remote diagnostic tool and their presumed contribution to plasma heating processes. We discuss our current understanding on coronal heating by magnetic waves, based on recent observational evidence and theoretical advances. The discussion starts with a selection of observational discoveries that have brought magnetic waves to the forefront of the coronal heating discussion. Then, our theoretical understanding on the nature and properties of the observed waves and the physical processes that have been proposed to explain observations are described. Particular attention is given to the sequence of processes that link observed wave characteristics with concealed energy transport, dissipation, and heat conversion. We conclude with a commentary on how the combination of theory and observations should help us understanding and quantifying magnetic wave heating of the solar atmosphere.Comment: Accepted for publication in Royal Society of London Philosophical Transactions Series

Model comparison for the density structure along solar prominence threads

Quiescent solar prominence fine structures are typically modelled as density enhancements, called threads, which occupy a fraction of a longer magnetic flux tube. The profile of the mass density along the magnetic field is however unknown and several arbitrary alternatives are employed in prominence wave studies. We present a comparison of theoretical models for the field-aligned density along prominence fine structures. We consider Lorentzian, Gaussian, and parabolic profiles. We compare their theoretical predictions for the period ratio between the fundamental transverse kink mode and the first overtone to obtain estimates for the ratio of densities between the central part of the tube and its foot-points and to assess which one would better explain observed period ratio data. Bayesian parameter inference and model comparison techniques are developed and applied. Parameter inference requires the computation of the posterior distribution for the density gradient parameter conditional on the observable period ratio. Model comparison involves the computation of the marginal likelihood as a function of the period ratio to obtain the plausibility of each density model and the computation of Bayes Factors to quantify the relative evidence for each model, given a period ratio observation. A Lorentzian density profile, with plasma density concentrated around the centre of the tube seems to offer the most plausible inversion result. A Gaussian profile would require unrealistically large values of the density gradient parameter and a parabolic density distribution does not enable us to obtain well constrained posterior probability distributions. However, our model comparison results indicate that the evidence points to the Gaussian and parabolic profiles for period ratios in between 2 and 3, while the Lorentzian profile is preferred for larger period ratio values.Comment: 9 pages, 5 figures, accepted in A&

Determination of the cross-field density structuring in coronal waveguides using the damping of transverse waves

Time and spatial damping of transverse magnetohydrodynamic (MHD) kink oscillations is a source of information on the cross-field variation of the plasma density in coronal waveguides. We show that a probabilistic approach to the problem of determining the density structuring from the observed damping of transverse oscillations enables us to obtain information on the two parameters that characterise the cross-field density profile. The inference is performed by computing the marginal posterior distributions for density contrast and transverse inhomo- geneity length-scale using Bayesian analysis and damping ratios for transverse oscillations under the assumption that damping is produced by resonant absorption. The obtained distributions show that, for damping times of a few oscillatory periods, low density contrasts and short inho- mogeneity length scales are more plausible in explaining observations. This means that valuable information on the cross-field density profile can be obtained even if the inversion problem, with two unknowns and one observable, is a mathematically ill-posed problem.Comment: 5 pages, 3 figures, accepte

Determination of Transverse Density Structuring from Propagating MHD Waves in the Solar Atmosphere

We present a Bayesian seismology inversion technique for propagating magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The technique uses theoretical predictions for the spatial damping of propagating kink waves in transversely inhomogeneous coronal waveguides. It combines wave amplitude damping length scales along the waveguide with theoretical results for resonantly damped propagating kink waves to infer the plasma density variation across the oscillating structures. Provided the spatial dependence of the velocity amplitude along the propagation direction is measured and the existence of two different damping regimes is identified, the technique would enable us to fully constrain the transverse density structuring, providing estimates for the density contrast and its transverse inhomogeneity length scale

On the nature of transverse coronal waves revealed by wavefront dislocations

Coronal waves are an important aspect of the dynamics of the plasma in the corona. Wavefront dislocations are topological features of most waves in nature and also of magnetohydrodynamic waves. Are there dislocations in coronal waves? The finding and explanation of dislocations may shed light on the nature and characteristics of the propagating waves, their interaction in the corona and in general on the plasma dynamics. We positively identify dislocations in coronal waves observed by the Coronal Multi-channel Polarimeter (CoMP) as singularities in the Doppler shifts of emission coronal lines. We study the possible singularities that can be expected in coronal waves and try to reproduce the observed dislocations in terms of localization and frequency of appearance. The observed dislocations can only be explained by the interference of a kink and a sausage wave modes propagating with different frequencies along the coronal magnetic field. In the plane transverse to the propagation, the cross-section of the oscillating plasma must be smaller than the spatial resolution, and the two waves result in net longitudinal and transverse velocity components that are mixed through projection onto the line of sight. Alfv\'en waves can be responsible of the kink mode, but a magnetoacoustic sausage mode is necessary in all cases. Higher (flute) modes are excluded. The kink mode has a pressure amplitude that is smaller than the pressure amplitude of the sausage mode, though its observed velocity is larger. This concentrates dislocations on the top of the loop. To explain dislocations, any model of coronal waves must include the simultaneous propagation and interference of kink and sausage wave modes of comparable but different frequencies, with a sausage wave amplitude much smaller than the kink one.Comment: 11 pages. 5 figures. Accepted for publication in A&

Coronal cooling as a result of mixing by the nonlinear Kelvin–Helmholtz instability

This is the final version. Available from American Astronomical Society via the DOI in this recordRecent observations show cool, oscillating prominence threads fading when observed in cool spectral lines and appearing in warm spectral lines. A proposed mechanism to explain the observed temperature evolution is that the threads were heated by turbulence driven by the Kelvin–Helmholtz instability that developed as a result of wave-driven shear flows on the surface of the thread. As the Kelvin–Helmholtz instability is an instability that works to mix the two fluids either side of the velocity shear layer, in the solar corona it can be expected to work by mixing the cool prominence material with that of the hot corona to form a warm boundary layer. In this paper we develop a simple phenomenological model of nonlinear Kelvin–Helmholtz mixing, using it to determine the characteristic density and temperature of the mixing layer, which for the case under study with constant pressure across the two fluids are ρ_mixed=√ρ_1ρ_2 and T_mixed=√T_1T_2. One result from the model is that it provides an accurate, as determined by comparison with simulation results, determination of the kinetic energy in the mean velocity field. A consequence of this is that the magnitude of turbulence, and with it the energy that can be dissipated on fast time-scales, as driven by this instability can be determined. For the prominence-corona system, the mean temperature rise possible from turbulent heating is estimated to be less than 1% of the characteristic temperature (which is found to be T_mixed=10^5K). These results highlight that mixing, and not heating, are likely to be the cause of the observed transition between cool to warm material in Okamoto et al. (2015). One consequence of this result is that the mixing creates a region with higher radiative loss rates on average than either of the original fluids, meaning that this instability could contribute a net loss of thermal energy from the corona, i.e. coronal cooling.Science and Technology Facilities CouncilSpanish Ministerio de Ciencia, Innovacion y Universidade