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Model comparison for the density structure across solar coronal waveguides  

Inigo Arregui   Submitted: 2015-09-09 02:50

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 Alfvén 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.

Authors: I. Arregui, R. Soler, A. Asensio Ramos
Projects: None

Publication Status: ApJ, accepted.
Last Modified: 2015-09-09 09:49
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Model comparison for the density structure along solar prominence threads  

Inigo Arregui   Submitted: 2015-05-14 03:52

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.

Authors: I. Arregui & R. Soler
Projects: None

Publication Status: A&A, accepted
Last Modified: 2015-05-14 14:49
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Wave heating of the solar atmosphere  

Inigo Arregui   Submitted: 2015-01-28 03:28

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.

Authors: I. Arregui
Projects: None

Publication Status: Accepted for publication in Royal Society of London Philosophical Transactions Series A
Last Modified: 2015-01-28 12:46
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Determination of the cross-field density structuring in coronal waveguides using the damping of transverse waves  

Inigo Arregui   Submitted: 2014-04-03 03:12

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 inhomogeneity 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.

Authors: I. Arregui and A. Asensio Ramos
Projects: None

Publication Status: accepted
Last Modified: 2014-04-07 10:55
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Determination of transverse density structuring from propagating MHD waves in the solar atmosphere  

Inigo Arregui   Submitted: 2013-04-26 08:36

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.

Authors: I. Arregui, A. Asensio Ramos, D. J. Pascoe
Projects: None

Publication Status: ApJL, accepted
Last Modified: 2013-04-26 10:15
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Bayesian Analysis of Multiple Harmonic Oscillations in the Solar Corona  

Inigo Arregui   Submitted: 2013-02-15 02:00

The detection of multiple mode harmonic kink oscillations in coronal loops enables to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic flux tube expansion, under each of the hypotheses. Then, the two models are compared using a Bayesian model comparison scheme to assess how plausible each one is, given our current state of knowledge.

Authors: I. Arregui, A. Asensio Ramos, A. J. Diaz
Projects: None

Publication Status: accepted, ApJL
Last Modified: 2013-02-15 02:00
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Inversion of physical parameters in solar atmospheric seismology  

Inigo Arregui   Submitted: 2012-03-14 04:38

Magnetohydrodynamic (MHD) wave activity is ubiquitous in the solar atmosphere. MHD seismology aims to determine difficult to measure physical parameters in solar atmospheric magnetic and plasma structures by a combination of observed and theoretical properties of MHD waves and oscillations. This technique, similar to seismology or helio-seismology, demands the solution of two problems. The direct problem involves the computation of wave properties of given theoretical models. The inverse problem implies the calculation of unknown physical parameters, by means of a comparison of observed and theoretical wave properties. Solar atmospheric seismology has been successfully applied to different structures such as coronal loops, prominence fine structures, spicules, or jets. However, it is still in its infancy. Far more is there to come. We present an overview of recent results, with particular emphasis on the inversion procedure.

Authors: I. Arregui
Projects: None

Publication Status: Review paper to appear in Astrophysics and Space Science Proceedings
Last Modified: 2012-03-14 14:08
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Prominence seismology  

Inigo Arregui   Submitted: 2012-02-01 10:38

Given the difficulty in directly determining prominence physicalparametersfrom observations, prominence seismology stands as an alternativemethod toprobe the nature of these structures. We show recent examples of theapplication ofmagnetohydrodynamic (MHD) seismology techniques to infer physicalparameters inprominence plasmas. They are based on the application of inversiontechniques usingobserved periods, damping times, and plasma flow speeds of prominencethread oscillations.The contribution of Hinode to the subject has been of centralimportance.We show an example based on data obtained with Hinode's Solar OpticalTelescope.Observations show an active region limb prominence, composed by amyriad of thinhorizontal threads that flow following a path parallel to thephotosphere and displaysynchronous vertical oscillations. The coexistence of waves and flowscan be firmlyestablished. By making use of an interpretation based on transverseMHD kink oscillations,a seismological analysis of this event is performed. It is shown thatthe combinationof high quality Hinode observations andproper theoretical models allows flowsand waves to become two useful characteristics for our understanding ofthe nature ofsolar prominences.

Authors: I. Arregui, J. L. Ballester, R. Oliver, R. Soler, J. Terradas
Projects: None

Publication Status: 4th Hinode Science Meeting: Unsolved Problems and New Insights ASP Conference Series, Vol. 455, pp. 211-218 (2012)
Last Modified: 2012-02-01 12:07
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Bayesian magnetohydrodynamic seismology of coronal loops  

Inigo Arregui   Submitted: 2011-07-21 01:41

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 Alfvén travel time and the transverse inhomogeneity length-scale. The obtained estimates for the Alfvén 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.

Authors: Inigo Arregui, Andres Asensio Ramos
Projects: None

Publication Status: ApJ, accepted
Last Modified: 2011-07-21 08:42
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Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads  

Inigo Arregui   Submitted: 2010-11-30 01:48

We analyze the oscillatory properties of resonantly damped transverse kink oscillations in two-dimensional prominence threads. The fine structures are modeled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary non-uniformly in both the transverse and the longitudinal directions. We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. The relevant parameters are the length of the dense part and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extend the damping ratios. This information is complemented with the analysis of the spatial distribution of perturbations and the energy flux at the resonances that allow us to explain the obtained damping times. Implications for prominence seismology are discussed in connection to the fact that observations may allow us to measure the length of the thread, while the supporting magnetic flux tube is not even observed and the density in the evacuated part of the tube is also difficult to estimate.

Authors: I. Arregui, R. Soler, J. L. Ballester, A. N. Wright
Projects: None

Publication Status: submitted
Last Modified: 2010-12-01 10:54
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Damping mechanisms for oscillations in solar prominences  

Inigo Arregui   Submitted: 2010-02-19 01:15

Small amplitude oscillations are a commonly observed feature in prominences/filaments. These oscillations appear to be of local nature, are associated to the fine structure of prominence plasmas, and simultaneous flows and counterflows are also present. The existing observational evidence reveals that small amplitude oscillations, after excited, are damped in short spatial and temporal scales by some as yet not well determined physical mechanism(s). Commonly, these oscillations have been interpreted in terms of linear magnetohydrodynamic (MHD) waves, and this paper reviews the theoretical damping mechanisms that have been recently put forward in order to explain the observed attenuation scales. These mechanisms include thermal effects, through non-adiabatic processes, mass flows, resonant damping in non-uniform media, and partial ionization effects. The relevance of each mechanism is assessed by comparing the spatial and time scales produced by each of them with those obtained from observations. Also, the application of the latest theoretical results to perform prominence seismology is discussed, aiming to determine physical parameters in prominence plasmas that are difficult to measure by direct means.

Authors: I. Arregui, J.L. Ballester
Projects: None

Publication Status: SSR (submitted)
Last Modified: 2010-02-19 08:55
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Damping of Fast Magnetohydrodymanic Oscillations in Quiescent Filament Threads  

Inigo Arregui   Submitted: 2008-06-18 02:46

High-resolution observations provide evidence about the existence of small-amplitude transverse oscillations in solar filament fine structures. These oscillations are believed to represent fast magnetohydrodynamic (MHD) waves and the disturbances are seen to be damped in short timescales of the order of 1 to 4 periods. In this Letter we propose that, due to the highly inhomogeneous nature of the filament plasma at the fine structure spatial scale, the phenomenon of resonant absorption is likely to operate in the temporal attenuation of fast MHD oscillations. By considering transverse inhomogeneity in a straight flux tube model we find that, for density inhomogeneities typical of filament threads, the decay times are of a few oscillatory periods only.

Authors: Inigo Arregui, Jaume Terradas, Ramon Oliver, Jose Luis Ballester
Projects: None

Publication Status: ApJ Letters, accepted
Last Modified: 2008-09-23 20:59
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Subject will be restored when possible  

Inigo Arregui   Submitted: 2008-04-24 04:00

We present an analytic approximate seismic inversion scheme for damped transverse coronal loop oscillations based on the thin tube and thin boundary approximation for computing the period and the damping time. Asymptotic expressions for the period and damping rate are used to illustrate the process of seismological inversion in a simple and easy to follow manner. The inversion procedure is formulated in terms of two simple functions, which are given by simple closed expressions. The analytic seismic inversion shows that an infinite amount of 1-dimensional equilibrium models can reproduce the observed periods and damping times. It predicts a specific range of allowable values for the Alfvén travel time and lower bounds for the density contrast and the inhomogeneity length scale. When the results of the present analytic seismic inversion are compared with those of a previous numerical inversion, excellent agreement is found up to the point that the analytic seismic inversion emerges as a tool for validating results of numerical inversions. Actually it helped us to identify and correct inaccuracies in a previous numerical investigation.

Authors: M. Goossens, I. Arregui, J.L. Ballester, T.J. Wang
Projects: None

Publication Status: A&A, accepted
Last Modified: 2008-09-23 21:09
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Subject will be restored when possible  

Inigo Arregui   Submitted: 2008-02-08 09:38

There is not as yet full agreement on the mechanism that causes the rapid damping of the oscillations observed by TRACE in coronal loops. It has been suggested that the variation of the observed values of the damping time as function of the corresponding observed values of the period contains information on the possible damping mechanism. The aim of this Letter is to show that, for resonant absorption, this is definitely not the case unless detailed a priori information on the individual loops is available.

Authors: Inigo Arregui, Jose Luis Ballester, Marcel Goossens
Projects: None

Publication Status: ApJL, in press
Last Modified: 2008-02-08 12:16
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Subject will be restored when possible  

Inigo Arregui   Submitted: 2008-02-08 09:38

There is not as yet full agreement on the mechanism that causes the rapid damping of the oscillations observed by TRACE in coronal loops. It has been suggested that the variation of the observed values of the damping time as function of the corresponding observed values of the period contains information on the possible damping mechanism. The aim of this Letter is to show that, for resonant absorption, this is definitely not the case unless detailed a priori information on the individual loops is available.

Authors: Inigo Arregui, Jose Luis Ballester, Marcel Goossens
Projects:

Publication Status: ApJL, 676, L77-L80
Last Modified: 2008-03-10 02:50
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Subject will be restored when possible  

Inigo Arregui   Submitted: 2007-08-28 07:26

The theory of magnetohydrodynamic (MHD) waves in solar coronal slabs in a zero-eta configuration and for parallel propagation of waves does not allow the existence of surface waves. When oblique propagation of perturbations is considered both surface and body waves are able to propagate. When the perpendicular wave number is larger than a certain value, the body kink mode becomes a surface wave. In addition, a sausage surface mode is found below the internal cut-off frequency. When non-uniformity in the equilibrium is included, surface and body modes are damped due to resonant absorption. In this paper, first, a normal-mode analysis is performed and the period, the damping rate, and the spatial structure of eigenfunctions are obtained. Then, the time-dependent problem is solved, and the conditions under which one or the other type of mode is excited are investigated.

Authors: I. Arregui, J. Terradas, R. Oliver, J.L. Ballester
Projects: None

Publication Status: Solar Physics. Accepted
Last Modified: 2007-08-30 21:46
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The resonant damping of fast magnetohydrodynamic oscillations in a system of two coronal slabs  

Inigo Arregui   Submitted: 2007-08-09 04:38

Observations of transversal coronal loop oscillations very often show the excitation and damping of oscillations in groups of coronal loops rather than in individual and isolated structures. We present results on the oscillatory properties (periods, damping rates, and spatial distribution of perturbations) for resonantly damped oscillations in a system of two inhomogeneous coronal slabs and compare them to the properties found in single slab loop models. A system of two identical coronal loops is modeled, in Cartesian geometry, as being composed by two density enhancements. The linear magnetohydrodynamic (MHD) wave equations for oblique propagation of waves are solved and the damping of the different solutions, due to the transversal inhomogeneity of the density profile, is computed. The physics of the obtained results is analyzed by an examination of the perturbed physical variables. We find that, due to the interaction between the loops, the normal modes of oscillation present in a single slab split into symmetric and antisymmetric oscillations when a system of two identical slabs is considered. The frequencies of these solutions may differ from the single slab results when the distance between the loops is of the order of a few slab widths. Oblique propagation of waves weakens this interaction, since solutions become more confined to the edges of the slabs. The damping is strong for surface-like oscillations, while sausage body-like solutions are unaffected. For some solutions, and small slab separations, the damping in a system of two loops differs substantially from the damping of a single loop.

Authors: Inigo Arregui, Jaume Terradas, Ramon Oliver, Jose Luis Ballester
Projects:

Publication Status: Submitted
Last Modified: 2007-08-10 11:00
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The influence of the internal structuring of coronal loops on the properties of their damped transverse oscillations  

Inigo Arregui   Submitted: 2007-02-08 07:37

The geometry and physical conditions in solar coronal loops are complicated and still not well understood. Recent high resolution observations, obtained with TRACE, indicate the existence of sub-resolution transverse structuring, not accessible to direct observation. This ingredient has not yet been taken into account in previous theoretical models used for the study of transversal coronal loop oscillations and their damping due to resonant conversion of energy. This study aims to assess the effect of the possibly unresolved internal structure of a coronal loop on the properties of its transverse oscillations and on the efficiency of resonant absorption as a damping mechanism of these oscillations. The equilibrium configuration of a single coronal loop with internal density structuring is modelled by considering the loop as being composed by two very close parallel identical coronal slabs in Cartesian geometry. The period of the oscillation and the damping time, for the resonantly damped fundamental kink mode, are computed. These quantities are then compared to those obtained for two models for a single equivalent slab without internal density structuring. We find that the period and the damping time of a coronal loop with internal density structuring change by less than 15%, when compared to the same oscillatory properties of a single coronal loop with either the same density contrast or a single coronal loop with the same total mass. Therefore the internal density structuring of a coronal loop does not affect very much its oscillatory properties. However, the sub-resolution structuring of a coronal loop, with different densities in its components or with different widths could vary these results.

Authors: I. Arregui, J. Terradas, R. Oliver, & J.L. Ballester
Projects:

Publication Status: A&A, Vol. 466, 1145-1151 (2007)
Last Modified: 2007-04-26 02:46
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MHD seismology of coronal loops using the period and damping of quasi-mode kink oscillations  

Inigo Arregui   Submitted: 2006-11-23 01:45

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. 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. 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 Alfvén speed (or Alfvén 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, Alfvén speed or Alfvén travel time). The projection of these solutions onto the Alfvén speed axis is found to be constrained to a rather limited interval. Upper limits to the internal Alfvén speed are derived for 9 of the 11 analysed events.

Authors: I. Arregui, J. Andries, T. Van Doorsselaere, M. Goossens, S. Poedts
Projects:

Publication Status: Published, A&A, Vol 463, 333-338
Last Modified: 2007-01-30 05:20
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Abstracts by Author
Model comparison for the density structure across solar coronal waveguides
Model comparison for the density structure along solar prominence threads
Wave heating of the solar atmosphere
Determination of the cross-field density structuring in coronal waveguides using the damping of transverse waves
Determination of transverse density structuring from propagating MHD waves in the solar atmosphere
Bayesian Analysis of Multiple Harmonic Oscillations in the Solar Corona
Inversion of physical parameters in solar atmospheric seismology
Prominence seismology
Bayesian magnetohydrodynamic seismology of coronal loops
Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads
Damping mechanisms for oscillations in solar prominences
Damping of Fast Magnetohydrodymanic Oscillations in Quiescent Filament Threads
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible
The resonant damping of fast magnetohydrodynamic oscillations in a system of two coronal slabs
The influence of the internal structuring of coronal loops on the properties of their damped transverse oscillations
MHD seismology of coronal loops using the period and damping of quasi-mode kink oscillations

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