2020 PDG seminars

A new seismology of the corona

The Coronal Multi-channel Polarimeter (CoMP) instrument has proved itself invaluable for the study of propagating kink waves in the corona.

After making the initial discovery back in 2007, CoMP has been able to provide a number of insights into the properties of the kink waves. The kink mode is found to be present throughout the corona and appears to be continuous. The widespread and reliable presence means that the propagating kink mode can make a fantastic tool for magneto-seismology.

While CoMP shows a persistent Doppler velocity signal related to the propagating kink mode, the continuous transverse motions of the coronal structures can also be detected with Solar Dynamics Observatory (SDO/AIA). However the scale of the displacements are at the edge of the SDO's capabilities, requiring careful measurements to be able to study them and exploit them for seismology.

In this talk, I discuss the new possibilities for coronal seismology using the propagating kink mode, demonstrating how we’ve used both CoMP and SDO/AIA to measure the young solar wind, the density structure in a coronal hole and provide the first estimates for the global coronal magnetic field.

Partial ionisation of hydrogen plasma in the solar atmosphere - a non-LTE modeler's view

Based on our extensive experience with the non-LTE radiative-transfer modelling of different atmospheric structures (chromosphere, flares, prominences, CME-cores), I will demonstrate the importance of partial hydrogen ionisation and review the most relevant atomic processes. I will also discuss the role of non-equilibrium ionisation of hydrogen.

A code that solves the equations of MHD coupled to radiation

Our code is based on a finite volume discretisation, and uses high-resolution shock-capturing flux formulae of the HLL class. Concerning the MHD part, we use the divergence cleaning method to preserve the non-monopoles constraint.

For radiation, at the moment, we use the M1 closure relation within the gray body approximation. The evolution equations for radiation become stiff for high opacities, for which we use an implicit-explicit evolution method, which allows the use of a standard integration time-step.

We present our code's status and mention the solar physics scenarios where we expect to produce some applications.

Bayesian coronal seismology

Coronal seismology is based on the remote diagnostics of physical conditions in the solar corona by comparison between model predictions and observations of wave activity.

Our lack of direct access to the physical system of interest makes information incomplete and uncertain so our conclusions are at best probabilities.

Bayesian inference is increasingly being employed in the area, following a general trend in solar and astrophysical research.

In this seminar, I first justify the use of a Bayesian probabilistic approach to seismology diagnostics and explain its philosophy and methodology. Then, I report on recent results that demonstrate its feasibility and advantage in applications to coronal loops, prominences and extended regions of the corona.

To finish, I suggest other areas of current interest where the use of Bayesian methods could contribute to improve our understanding on the structure, dynamics and heating of the corona.

Objective material barriers to the transport of momentum and vorticity

I discuss a recent theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active (ie, velocity-dependent) vector field, such as the linear momentum, the angular momentum or the vorticity, in three-dimensional unsteady flows.

These diffusion barriers provide physics-based, observer-independent boundaries of dynamically active coherent structures. Instantaneous limits of these Lagrangian diffusion barriers mark objective Eulerian barriers to short-term active transport.

I show how active diffusion barriers can be identified with active versions of Lagrangian coherent structure (LCS) diagnostics.

In comparison to their passive counterparts, however, active LCS diagnostics require no significant fluid particle separation and hence provide substantially higher-resolved Lagrangian and Eulerian coherent structure boundaries from shorter velocity data sets.

I illustrate these results on two-dimensional turbulence and three-dimensional wall-bounded turbulence.

Frequency power spectra of Alfvén waves in a solar coronal arcade: Discrete or continuous?

In this talk, I will present theoretically computed frequency power spectra for shear Alfvén waves excited in a solar coronal arcade.

I investigate two separate perturbations, a cosine-modulated Gaussian perturbation and an impulsive driver. The arcade is assumed to consist of potential magnetic field lines embedded in stratified plasma.

In principle, the nature of the frequency power spectra can constrain the size and the type of driver.

A new method for estimating global coronal wave properties from their interaction with solar coronal holes

Global coronal waves (CWs) and their interaction with coronal holes (CHs) result, among other effects, in the formation of reflected and transmitted waves. Observations of such events provide us with measurements of different CW parameters, such as phase speed and intensity amplitudes.

However, several of these parameters are provided with only intermediate observational quality, other parameters, such as the phase speed of transmitted waves, can hardly be observed in general.

We present a new method to estimate crucial CW parameters, such as density and phase speed of reflected as well as transmitted waves, Mach numbers and density values of the CH's interior, by using analytical expressions in combination with basic and most accessible observational measurements.

The transmission and reflection coefficients are derived from linear theory and subsequently used to calculate estimations for phase speeds of incoming, reflected and transmitted waves. The obtained analytical expressions are validated by performing numerical simulations of CWs interacting with CHs.

This new method enables us to determine in a fast and straightforward way reliable CW and CH parameters from basic observational measurements, which provides a powerful tool to better understand the observed interaction effects between CWs and CHs.

Modal decompositions: what are they, why should we use them and how?

The dynamics of natural systems are often complex and highly non-linear, understanding these procedures is difficult as their dynamics and complexities are usually intertwined and colluded.

Whilst we might be able to identify these systems using sets of nonlinear equations, determining the individual process is underlying a complex mechanism are non-trivial.

Over the past few decades, there has been much work to develop data driven methods to extract coherent features either in space or in time.

Two prominent methods are the proper orthogonal decomposition and the dynamic mode decomposition; in this seminar these two methods will be introduced, the underpinning mathematics and algorithms will be outlined, and variants of the algorithms and methods will also be described.

However, much of the seminar will focus on applying these methods, using them at all different scales from idealised small-scale laboratory experiments to large-scale real-world applications.

The primary aim of this seminar will be to equip you with an arsenal of spatially and temporally orthogonal tools which you can use to elucidate the complex features from your data sets.

Vortex flows in the solar atmosphere

Vortex flows exist over various spatial and temporal scales throughout the solar atmosphere and are of great importance due to their potential in twisting the magnetic field lines and hence facilitating Poynting flux transport.

Recent advances in both observational techniques and numerical simulations have enabled us to detect a multitude of small-scale vortices in the solar atmosphere.

Smaller vortices are suggested to play an important role in the solar atmospheric heating, however, their physical properties remain poorly understood due to limited resolution in observations. Hence, it is crucial to investigate them using high-resolution simulations since they are more abundant and faster rotating flows than the larger vortices.

Using MHD simulations, we explored the the relationship between vortex flows at different spatial scales, analyse their physical properties, and investigate their contribution to Poynting flux transport from the lower to the upper layers of the solar atmosphere.

We found that a large vortex, as seen at low spatial resolution, consists of a large number of smaller vortices, when seen at high spatial resolution. Statistically, they have higher densities and higher temperatures than the average values at the same geometrical height. Their Poynting flux contribution is more than adequate to compensate for the radiative losses in the chromosphere indicating their possible role in the solar atmospheric heating.

Ubiquituous hundred-Gauss magnetic fields in solar spicules

Even though they were observed for the first time in the 19th century, the nature of spicules is not well understood because they are are thin and elongated chromospheric jets. Therefore, their study is limited to the resolution of the instruments used.

Every time a step forward in the quality of the observations of the lower chromosphere is taken, the interest in spicules sparks. Most recently, the advent of the Hinode telescope provided high-resolution images of spicules that allowed for a better comprehension of their nature and behaviour. Studies regarding their magnetic field have been also undertaken, but most of them did not have the ideal spatial/temporal resolution needed to give definitive results.

This study is aimed to provide a step forward in this matter, with observations in the Ca II 854.2 nm line taken with the CRISP instrument at the Swedish 1-meter Solar Telescope in La Palma.

The sensitivity of the Ca II 854.2 nm line to the magnetic field is exploited and the Weak Field Approximation (WFA) is used to estimate the line-of-sight component of the magnetic field of spicules both off-limb and on the solar disk.

The WFA must be used carefully, since there are conditions that need to be met for it to be applicable. This consideration is assessed in every pixel, and a Bayesian approach is taken to infer the line-of-sight magnetic field component from the WFA equations.

It is established that magnetic fields over 100 G are abundant. The reason for the failure of previous studies to conclude this is carefully studied and is speculated to lie in the poor temporal/spatial resolution of the observations used.

Dynamics of the vortex tubes in the solar atmosphere

We use a state of the art vortex detection method, Instantaneous Vorticity Deviation, to define and locate three-dimensional vortices in magneto-convections simulations performed by the MURaM code.

The detected vortices extend from the photosphere to the low chromosphere. The dynamics across the vortical flows at different height levels are investigated through radial profiles.

We found that the vortices present similar dynamics at all height levels, with nonuniform angular rotational velocity and eddy viscosity effects. The vortices intensify the magnetic field, and in turn, the vortex dynamics are affected by the magnetic field.

On the other hand, our findings hint that kinematic vortices need to present high tangential velocities at different height levels to overcome the magnetic tension and generate magnetic vortices.

Numerical studies of jet formation in the solar atmosphere

Using the Newtonian CAFE MHD code to perform 2.5D and 3D resistive MHD simulations in the solar atmosphere, we show that magnetic reconnection may be responsible for the formation of jets with some characteristics of Type II spicules and cool coronal jets.

We numerically model the photosphere-corona region using the C7 atmosphere model. The initial magnetic configuration in the 2.5D case consists of two symmetric neighbouring loops with opposite polarity, used to support reconnection. In the 3D case, the initial magnetic configuration is extrapolated up to the solar corona region from a dynamic realistic simulation of the solar photospheric magnetoconvection model that mimics the quiet-Sun.

In the 2.5D simulations, we include the effect of the thermal conduction along the magnetic field lines to study some properties of spicule jets. In this case, we find that thermal conductivity affects morphology, velocity, and temperature of the jets. Also, the heat flux maps indicate the head of the jet and corona interchange energy more efficiently than the body of the jet.

In the 3D simulations, we have found that the formation of the jet depends on the Lorentz force, which helps to accelerate the plasma upward. The morphology, the upward velocity covering a range up to 130 km/s, and the timescale formation of the structure between 60 and 90 s, are similar to those expected for Type II spicules.

Additionally, we analyse various properties of the jet dynamics, and find that the structure shows rotational and torsional motions which may generate torsional Alfvén waves in the corona region.

Complex 3D dynamics of solar spicule structures

The sun’s outer atmosphere is a million degrees hotter than it’s visible surface, which is not understood with any of the known laws of thermodynamics and remains an intriguing problem for the astrophysics in general.

It is now believed that most of the energy dissipation phenomenon occurs at the interface region in between solar chromosphere and corona, which is a highly dynamic, gravitationally stratified, nonlinear, inhomogeneous environment.

Observed dynamics of thin magnetic fluxtube structures in this layer, reflects the confined magnetohydrodynamic (MHD) wave-modes (kink, sausage and torsional Alfven).

For the first time, the evolution of the resultant transverse displacement of the observed flux tube structures, estimated from perpendicular velocity components, is analysed along with cross-sectional width, photometric and azimuthal shear/torsion variations, to accurately identify the confined wave-mode(s).

In my talk, I will discuss the observational evidence of pulse-like nonlinear kink wave-mode(s), as indicated by the strong coupling in between kinematic observables, with a frequency-doubling, -tripling aspect, supported by mutual phase relations centred around 0 and +-180 (Sharma et al. 2018).

The 3D ensemble of the observed dynamic components revealed complexities pertinent to the accurate identification and interpretation of e.g. linear/nonlinear, coupled/uncoupled MHD wave-modes in the observed waveguides (spicules).

Waves in two-fluid gravitationally stratified plasmas

The temperature in the lower part of solar atmosphere is not high enough for a complete ionisation of the plasma. Therefore, this environment region is made up of electrons, positive ions and neutrals that interact through short and long range collisions in the presence of the magnetic field. Due to the low temperature, the gravitational scale-height is also short, meaning that perturbations will be affected by gravity.

Here, we study the spatial and temporal evolution of slow magnetoacoustics waves propagating in a stratified magnetic flux tube. In the two-fluid plasma, the dynamics of neutrals and charged species has to be studied separately.

Our analysis shows that the dynamic is described by a system of coupled Klein-Gordon equations that are solved in the strongly ionised limit. For the mentioned two species we study the changes in the cut-off frequency for a range of physical parameters. Asymptotic solutions to the governing equations are obtained for a harmonic driver.

Our results reveal that ion-acoustic and neutrals-acoustic slow modes show a different damping scale.

Identifying magnetohydrodynamic vortex tubes in the sun's photosphere

Vortex flows in the solar photosphere are fundamentally important for the generation of magnetohydrodynamic (MHD) waves which propagate to the upper layers of the solar atmosphere. Vortex tubes are formed as coherent magnetic field structures in the solar atmosphere, eg twisted magnetic flux tubes.

In this presentation, I will discuss the method of Lagrangian Averaged Vorticity Deviation (LAVD) developed by Haller (2016) to identify vortex flows, namely the centre of circulation and their boundary. 

Then, I will present the algorithmic technique I have developed to check whether a structure detected by the LAVD method is a true vortex or not and how to determine the rotational direction (clockwise or anticlockwise).

In addition, I will apply these methods to MURaM magneto-convection simulation data to detect and track the evolution of both 2D vortices and 3D vortex tubes in the solar photosphere.

Multi-faceted approach to decomposing and identifying individual magnetohydrodynamic (MHD) wave modes in sunspots and pores

High resolution observations of pores and sunspots show a rich and complex variety of oscillatory temporal and spatial behaviour. To decompose this data into individual magnetohydrodynamic (MHD) wave modes is non-trivial and requires a multi-faceted approach.

Here we take a three-pronged approach of combining Fourier analysis, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD).

The Fourier omega-k power spectrum provides us with a useful overall view of the particular temporal and spatial scales of interest but does not provide any cross-pixel correlation. In this regard, POD classifies modes that are orthogonal in space but places no restrictions on their frequencies. DMD has no such restrictions in space but classifies modes that are orthogonal in time, ie, identified modes cannot have the same frequency.

Each of these complementary techniques have their particular strengths which we will illustrate with synthetic data.

Vortex motions in the solar atmosphere

Solar photosphere vortices have the potential to form coherent magnetic field structures, eg twisted magnetic flux tubes and, therefore, may play a key role in the transport of energy and momentum from the lower atmosphere into the upper solar atmosphere.

In this talk, I will review existing methods for their identification and discuss our approach, which is based on Gamma detection and LAVD of inter-granular photospheric intensity vortices.

I will also present a new mechanism for the generation of magnetic waveguide from the lower solar atmosphere to the corona. This waveguide appears as the result of interacting perturbations (initially generated by photospheric vortex motions) in neighbouring magnetic flux tubes (modelled in the framework of self-similar approach).

Mode conversion of two-fluid shocks in a partially-ionised, isothermal, stratified atmosphere

The plasma of the lower solar atmosphere consists of mostly neutral particles, whereas the upper solar atmosphere is mostly ionised particles and electrons.

A shock that propagates upwards in the solar atmosphere therefore undergoes a transition where the dominant fluid is either neutral or ionised. An upwards propagating shock also passes a point where the sound and Alfven speed are equal. At this point the energy of the acoustic shock can separated into fast and slow components. How the energy is distributed between the two modes depends on the angle of magnetic field.

Two-fluid numerical simulations are performed of a wave steepening into a shock in an isothermal, partially-ionised atmosphere. The collisional coefficient is varied to investigate the regimes where the plasma and neutral species are weakly, strongly and finitely coupled.

The propagation speeds of the compressional waves hosted by neutral and ionised species vary, therefore velocity drift between the two species is produced as the plasma attempts to propagate faster than the neutrals. This is most extreme for a fast-mode shock.

We find that the collisional coefficient drastically changes the features present in the system, specifically the mode conversion height, type of shocks present, and the shock widths.

In the finitely-coupled regime fast-mode shock widths can exceed the pressure scale height leading to a new potential observable of two-fluid effects in the lower solar atmosphere.

Oscillation of coronal loops associated with flaring events

Loops are fascinating structures that bring us a lot of information about the exchange of energy in the solar atmosphere. Oscillations and waves represent one of the most fascinating events in the loops, which also plays a key role in the study of coronal seismology.

It is not clear how the disturbances are excited, however, there are several candidates, eg, flares, emerging flux, and eruptions.

In this talk, I present a summary of oscillations observed in different active regions in the presence of flares and other events.

This analysis has been done with data provided by IRIS, SDO and GOES-15 spacecraft. We have found excitation sources of some disturbances in lower heights of the solar atmosphere. This matches with oscillations found in the top and the footpoints of the coronal loops.

We used this information together with semi-empirical models to study the distribution of physical variables in the loops.

Magneto-acoustic waves in the lower solar atmosphere at high resolution

Fibrillar structures of different appearances and/or properties have ubiquitously been observed throughout the sun's chromosphere. They are often thought to map the magnetic fields, and are likely rooted in small-scale magnetic elements in the solar photosphere.

Here, we present properties of magnetohydrodynamic-wave dynamics in various fibrillar structures as well as in small magnetic elements in the low solar atmosphere, at high-spatial resolution, from the SUNRISE balloon-borne observatory as well as the Swedish Solar Telescope.

Our analysis reveals the prevalence of kink and sausage waves in both types of magnetic structures, propagating at similar high frequencies. The estimated energy flux carried by the observed waves is marginally enough to heat the chromosphere (and perhaps the corona).

Furthermore, such waves are compared with temperature fluctuations in the fibrils from high-temporal resolution observations with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Interface Region Imaging Spectrograph (IRIS) explorer, simultaneously observed at several millimetre and ultraviolet bands of, eg, ALMA 1.3 mm as well as IRIS Mg II h and k, Si IV, and C II spectral lines, from which, physical properties of the fibrillar structures are also discussed.