Transverse Inhomogeneity Length Scale Research Articles

Inference of magnetic field strength and density from damped transverse coronal waves

A classic application of coronal seismology uses transverse oscillations of waveguides to obtain estimates of the magnetic field strength. The procedure requires information on the density of the structures. Often it ignores the damping of the oscillations. We computed marginal posteriors for parameters such as the waveguide density, the density contrast, the transverse inhomogeneity length scale, and the magnetic field strength under the assumption that the oscillations can be modelled as standing magnetohydrodynamic (MHD) kink modes damped by resonant absorption. Our results show that the magnetic field strength can be properly inferred, even if the densities inside and outside the structure are largely unknown. Incorporating observational estimates of plasma density further constrains the obtained posteriors. The amount of information that is included a priori for the density and the density contrast influences their corresponding posteriors, but very little the inferred magnetic field strength. The decision to include or leave out the information on the damping and the damping timescales has a minimal impact on the obtained magnetic field strength. In contrast to the classic method, which provides numerical estimates with error bars or possible ranges of variation for the magnetic field strength, Bayesian methods offer the full distribution of plausibility over the considered range of possible values. The methods applied to available datasets of observed transverse loop oscillations can be extended to prominence fine structures or chromospheric spicules, and implemented to propagating waves in addition to standing oscillations.

MODEL COMPARISON FOR THE DENSITY STRUCTURE ACROSS SOLAR CORONAL WAVEGUIDES

The spatial variation of physical quantities, such as the mass density, across solar atmospheric waveguides governs the timescales and spatial scales for wave damping and energy dissipation. The direct measurement of the spatial distribution of density, however, is difficult and indirect seismology inversion methods have been suggested as an alternative. We applied Bayesian inference, model comparison, and model-averaging techniques to the inference of the cross-field density structuring in solar magnetic waveguides using information on periods and damping times for resonantly damped magnetohydrodynamic (MHD) transverse kink oscillations. Three commonly employed alternative profiles were used to model the variation of the mass density across the waveguide boundary. Parameter inference enabled us to obtain information on physical quantities such as the Alfv\'en travel time, the density contrast, and the transverse inhomogeneity length scale. The inference results from alternative density models were compared and their differences quantified. Then, the relative plausibility of the considered models was assessed by performing model comparison. Our results indicate that the evidence in favor of any of the three models is minimal, unless the oscillations are strongly damped. In such a circumstance, the application of model-averaging techniques enables the computation of an evidence-weighted inference that takes into account the plausibility of each model in the calculation of a combined inversion for the unknown physical parameters.

DETERMINATION OF TRANSVERSE DENSITY STRUCTURING FROM PROPAGATING MAGNETOHYDRODYNAMIC 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.

Damped kink oscillations of flowing prominence threads

Transverse oscillations of thin threads in solar prominences are frequently reported in high-resolution observations. Two typical features of the observations are that the oscillations are damped in time and that simultaneous mass flows along the threads are detected. Flows cause the dense threads to move along the prominence magnetic structure while the threads are oscillating. The oscillations have been interpreted in terms of standing magnetohydrodynamic (MHD) kink waves of the magnetic flux tubes which support the threads. The damping is most likely due to resonant absorption caused by plasma inhomogeneity. The technique of seismology uses the observations combined with MHD wave theory to estimate prominence physical parameters. This paper presents a theoretical study of the joint effect of flow and resonant absorption on the amplitude of standing kink waves in prominence threads. We find that flow and resonant absorption can either be competing effects on the amplitude or both can contribute to damp the oscillations depending on the instantaneous position of the thread within the prominence magnetic structure. The amplitude profile deviates from the classic exponential profile of resonantly damped kink waves in static flux tubes. Flow also introduces a progressive shift of the oscillation period compared to the static case, although this effect is in general of minor importance. We test the robustness of seismological estimates by using synthetic data aiming to mimic real observations. The effect of the thread flow can significantly affect the estimation of the transverse inhomogeneity length scale. The presence of random background noise adds uncertainty to this estimation. Caution needs to be paid to the seismological estimates that do not take the influence of flow into account.

BAYESIAN MAGNETOHYDRODYNAMIC SEISMOLOGY OF CORONAL LOOPS

We perform a Bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube and thin boundary approximations. For the inverse problem, we adopt a Bayesian approach to infer the most probable values of the relevant parameters, for given observed periods and damping times, and to extract their confidence levels. The posterior probability distribution functions are obtained by means of Markov Chain Monte Carlo simulations, incorporating observed uncertainties in a consistent manner. We find well localized solutions in the posterior probability distribution functions for two of the three parameters of interest, namely the Alfven travel time and the transverse inhomogeneity length-scale. The obtained estimates for the Alfven travel time are consistent with previous inversion results, but the method enables us to additionally constrain the transverse inhomogeneity length-scale and to estimate real error bars for each parameter. When observational estimates for the density contrast are used, the method enables us to fully constrain the three parameters of interest. These results can serve to improve our current estimates of unknown physical parameters in coronal loops and to test the assumed theoretical model.

SPATIAL DAMPING OF PROPAGATING KINK WAVES IN PROMINENCE THREADS

Transverse oscillations and propagating waves are frequently observed in threads of solar prominences/filaments and have been interpreted as kink magnetohydrodynamic (MHD) modes. We investigate the spatial damping of propagating kink MHD waves in transversely nonuniform and partially ionized prominence threads. Resonant absorption and ion-neutral collisions (Cowling's diffusion) are the damping mechanisms taken into account. The dispersion relation of resonant kink waves in a partially ionized magnetic flux tube is numerically solved by considering prominence conditions. Analytical expressions of the wavelength and damping length as functions of the kink mode frequency are obtained in the Thin Tube and Thin Boundary approximations. For typically reported periods of thread oscillations, resonant absorption is an efficient mechanism for the kink mode spatial damping, while ion-neutral collisions have a minor role. Cowling's diffusion dominates both the propagation and damping for periods much shorter than those observed. Resonant absorption may explain the observed spatial damping of kink waves in prominence threads. The transverse inhomogeneity length scale of the threads can be estimated by comparing the observed wavelengths and damping lengths with the theoretically predicted values. However, the ignorance of the form of the density profile in the transversely nonuniform layer introduces inaccuracies in the determination of the inhomogeneity length scale.

SEISMOLOGY OF STANDING KINK OSCILLATIONS OF SOLAR PROMINENCE FINE STRUCTURES

We investigate standing kink magnetohydrodynamic (MHD) oscillations in a prominence fine structure modeled as a straight and cylindrical magnetic tube only partially filled with the prominence material, and with its ends fixed at two rigid walls representing the solar photosphere. The prominence plasma is partially ionized and a transverse inhomogeneous transitional layer is included between the prominence thread and the coronal medium. Thus, ion-neutral collisions and resonant absorption are the considered damping mechanisms. Approximate analytical expressions of the period, the damping time, and their ratio are derived for the fundamental mode in the thin tube and thin boundary approximations. We find that the dominant damping mechanism is resonant absorption, which provides damping ratios in agreement with the observations, whereas ion-neutral collisions are irrelevant for the damping. The values of the damping ratio are independent of both the prominence thread length and its position within the magnetic tube, and coincide with the values for a tube fully filled with the prominence plasma. The implications of our results in the context of the MHD seismology technique are discussed, pointing out that the reported short-period (2 - 10 min) and short-wavelength (700 - 8,000 km) thread oscillations may not be consistent with a standing mode interpretation and could be related to propagating waves. Finally, we show that the inversion of some prominence physical parameters, e.g., Alfv\'en speed, magnetic field strength, transverse inhomogeneity length-scale, etc., is possible using observationally determined values of the period and damping time of the oscillations along with the analytical approximations of these quantities.

MHD seismology of coronal loops using the period and damping of quasi-mode kink oscillations

Aims. We combine the magnetohydrodynamic (MHD) theory of resonantly damped quasi-mode kink oscillations with observational estimates of the period and damping of transverse coronal loop oscillations to extract information on physical parameters in oscillating loops. Methods. A numerical study of the quasi-mode period and damping, in one-dimensional fully non-uniform flux tubes, is used to obtain equilibrium models that reproduce the observed periods and damping rates. This scheme is applied to 11 loop oscillation events. Results. When only the damping rate is used. the valid equilibrium models form a one-dimensional solution curve in the two-dimensional parameter space (density contrast, transverse inhomogeneity length-scale). Lower limits to the transverse inhomogeneity are obtained in the limit of high contrast loops. When both the period and the damping rate are used, the equilibrium Alfven speed (or Alfven travel time) comes into play. The valid equilibrium models then form a one-dimensional solution curve in the three-dimensional parameter space (density contrast, transverse inhomogeneity length-scale, Alfven speed or Alfven travel time). The projection of these solutions onto the Alfven speed axis is found to be constrained to a rather limited interval. Upper limits to the internal Alfven speed are derived for 9 of the 1 1 analysed events.