Monday, 19 March 2018

p-mode oscillations in magnetic solar atmospheres

p-Mode Oscillations in Highly Gravitationally Stratified Magnetic Solar Atmospheres

Introduction

Observational, theoretical and computational studies of the sun reveal a diversity of  structures and complex dynamics. This is clearly revealed by imagery from solar telescopes, the AIA 171 angstrom image from SDO  illustrates this most clearly.


The culmination of studies of the dynamics of the coronal loop structures at different scales and heights in the solar atmosphere is illustrated by the sketch of the solar chromosphere by Wedemeyer-Bohm


This diversity of dynamics gives rise to a menagerie of waves providing powerful diagnostics to aid our understanding and advance our knowledge. One of the most famous oscillations is the p-mode oscillation we studied these to test our MHD code for gravitationally stratified atmospheres. Our initial models were hydrodynamic simulations of a realistically stratified model of the solar atmosphere representing its lower region from the photosphere to low corona. The objective was to model atmospheric perturbations, propagating from the photosphere into the chromosphere, transition region and low corona. The perturbations are caused by the photospheric global oscillations. The simulations use photospheric drivers mimicking the solar p-modes.

The studies revealed that.

  1. There is consistency between the frequency-dependence of the energy flux in the numerical simulations and power flux measurements obtained from SDO;
  2. energy propagation into the mid- to upper-atmosphere of the quiet Sun occurs for a range of frequencies and may explain observed intensity oscillations for periods greater than the well known 3-minute and 5-minute oscillations;
  3. energy flux propagation into the lower solar corona is strongly dependent on the particular wave modes;
  4. agreement between the energy flux predictions of our numerical simulations and that of the two layer Klein-Gordon model supports our interpretation of the interaction of solar global oscillations with the solar atmosphere.

Structures in the Solar Atmosphere

The 3-minute and 5-minute wave modes are influenced in various ways in the different regions of the solar atmosphere. Our initial studies were relevant for the quiet inter-network region of the non magnetic solar chromosphere. These are the regions between the magnetic flux concentrations. The quiet sun magnetic flux is typically in the range 5-10G . For the coronal holes these are cold regions of plasma  and  have open field lines allowing solar particles to escape during the solar minima these regions can cause space weather disturbances.

Regions of the magnetic chromosphere are referred to as the network or plage regions, these are bright areas near to sunspots, faculae and pores. Pores are smaller counterparts of sunspots upto a few Mm across. The faculae are bright spots forming in the canyons between solar granules, they constantly form and dissipate over time scales of several minutes. They are formed near magnetic field concentrations. The active network regions are plage like bright areas which extend away from the active regions. The magnetic fields in this area diffuse away into the quiet sun regions, they are constrained by the network boundaries.

The internetwork or inner network may contain super granules which are convective regions about 30Mm across with strong horizontal flows.  The field in the internetwork region is in the region of 100-300G for the mean photospheric field.  Solar active regions contain sunspots which have sizes from 1 to 50Mm. The solar active region 10652 comprised many features and extended beyond this this region produced many solar flares and had magnetic fields easily exceeding the normal range of 100-500G.

e.g. see solar monitor AR10652


 Given this variety of solar regions it is recognised that the 3 minute and 5 minute modes behave in different ways in the solar atmosphere network, inter network, plage and faculae regions. These differences have been summarised nicely by the tables presented by Khomenko et al in reference5 below. For each of these regions the wave periodicities
  • centre of magnetic elements
  • close surroundings
  • internetwork beyond the magnetic elements
For the faculae and plage oscillations they consider
  • the centre of the magnetic elements
  • close surroundings and
  • in the halo areas
These are considered for the photosphere, chromosphere and corona. What is striking is the varied behavour for different magnetic structures and the influence of reflecting layers such as the transition layer influencing upward and downward propagation. In summary, for the network and inter network regions short (3 minute) period waves ( 5−8 mHz) propagate from the photosphere to the chromosphere only in restricted areas of the network cell interiors,the spatial distribution of 3-minute chromospheric shocks is highly dependent on the local magnetic topology. The long (5 minute) period waves (ν1.2−4 mHz) propagate efficiently to the chromosphere in the close proximity of the magnetic network elements. These long-period network halos are most prominent in the photosphere, but are also present in the chromosphere; and are observed to be co-spatial with chromospheric “magnetic shadows” for 3 min waves. Plage and faculae regions possess more complex magnetic structures and exhibit a more complex pattern.  Observations show that the power of 5-min oscillations increase significantly in the chromosphere For example for the short (3 minute) period waves (5−8 mHz) there is an enhancement, both in the photosphere and in the chromosphere. These power enhancements are known as “halos” and have been widely reported.

Motivation

Before attempting to develop a model which we allege is a realistic representation of the solar atmosphere it is necessary to establish that our modelling tools give a consistent behaviour in idealised test cases bridging our theoretical understanding and computational tools.

In our earlier studies reported in reference 9 and this blog ( http://solarwavetheory.blogspot.co.uk/search/label/pmode ) we investigated the energy propagation into a model solar atmosphere using perturbed computational MHD for highly gravitationally stratified atmospheres. Simulation drivers were used in the model to represent p-mode oscillations with varying modes and periods. In this study we attempted to generate a more representative atmosphere by introducing uniform vertical magnetic fields. Simulations were run for different values for the magnitude of the magnetic field and the energy propagation into the corona examined.

For all the simulations we used a p-mode driver with period 300s and mode (2,2). The 300s driver  was used as this corresponds to the well known 5 minute mode. The (2,2) mode was used because our earlier study demonstrated its effectiveness with energy propagation.

The videos below show the solar plasma velocity in the vertical direction at different layers in the solar atmosphere. The first example shows the case when there is no magnetic field in this case we observe the pure acoustic modes of oscillation.


Magnetic field model for solar atmosphere
50G Maximum field

75G Maximum field
100G Maximum field








The case above corresponds to zero magnetic field.



The above case corresponds to a maximum vertical B-field of 50G at the centre of the simulation box.


The above case corresponds to a maximum vertical B-field of 75G at the centre of the simulation box.



The above case corresponds to a maximum vertical B-field of 100G at the centre of the simulation box.

For cases where there is a non zero magnetic field we observe  oscillation modes which are different in character from the purely acoustic mode. As the magnetic field is increased the vertical motion of the plasma is enhanced.




The plot above compares the sections through the model at a time of 76s (i.e. 1 quarter of the time period) for the different field cases (i.e. 50G, 75G and 100G from left to right respectively). The beta equal one isosurface is shown near the base of the model.




The plot above shows a vertical slice taken at the midpoint of the simulation box, it compares the energy flux at a time of 76s (i.e. 1 quarter of the time period) for the different field cases (i.e. 50G, 75G and 100G from left to right respectively).



The plot above compares the sections through the model at a time of 150s (i.e. half of the time period) for the different field cases (i.e. 50G, 75G and 100G from left to right respectively). The beta equal one isosurface is shown near the base of the model.






The plot above shows a vertical slice taken at the midpoint of the simulation box, it compares the energy flux at a time of 150s (i.e. half of the time period) for the different field cases (i.e. 50G, 75G and 100G from left to right respectively).




The plot above compares the sections through the model at a time of 225s (i.e.three quarters of the time period) for the different field cases (i.e. 50G, 75G and 100G from left to right respectively). The beta equal one isosurface is shown near the base of the model.





The plot above shows a vertical slice taken at the midpoint of the simulation box, it compares the energy flux at a time of 225s (i.e. three quarters of the time period) for the different field cases (i.e. 50G, 75G and 100G from left to right respectively).





The plot above compares the sections through the model at a time of 330s (i.e.more than one time period) for the different field cases (i.e.50G, 75G and 100G from left to right respectively). The beta equal one isosurface is shown near the base of the model.


The plot above shows a vertical slice taken at the midpoint of the simulation box, it compares the energy flux at a time of 330s (i.e. over one time period) for the different field cases (i.e. 50G, 75G and 100G from left to right respectively).

As well as influencing the motion of the plasma the field enhances the energy flux which is able to pass through the transition layer. After one period there is a reflection of energy from the top boundary.

The diagrams below show distance time plots taken at different vertical slices through the model. The first one shows a section taken through the middle of the box at 2Mm. The second one a section taken at 1Mm and the third one is a section taken at 0.5Mm. They show the different modes including purely acoustic modes for the 0G case and the magneto acoustic modes for the non-zero B field.

Distance time plot for section at 2Mm

Distance time plot for section at 1Mm

Distance time plot for section at 0.5Mm

From the distance time plot we computed the slopes and determined a propagation speed. These are tabulated below. The first table gives speeds computed from the trailing edge (trailing edge is on the left of the plot i.e. t=0 side). The results computed using the slope at the leading edge are shown in the second table.

position 0G 50G 75G 100G
2Mm 12.6 96.5 47.7 25.2
1Mm 10.1 64.1 44.4 45.4
0.5Mm 8.7 45.4 37.8 32.3
Trailing Edge Result Table

position 0G 50G 75G 100G
2Mm 13.2 194 15.6 17.0
1Mm 13.8 181.6 18.4 17.2
0.5Mm 12.8 169.2 16.6 9.4
Leading Edge Result Table

From these results, what is interesting in particular from the leading edge results is the observation that computed propagation speeds are higher for the reduced field value.


this
Alfven speed Computed for Different Heights and Sections for 50G(blue:0.5Mm, green:1Mm, red:2Mm)

Alfven speed Computed for Different Heights and Sections for 75G(blue:0.5Mm, green:1Mm, red:2Mm)

Alfven speed Computed for Different Heights and Sections for 100G(blue:0.5Mm, green:1Mm, red:2Mm)

Fast mode speed Computed for Different Heights and Sections for 50G(blue:0.5Mm, green:1Mm, red:2Mm)

Fast mode speed Computed for Different Heights and Sections for 75G(blue:0.5Mm, green:1Mm, red:2Mm)

Fast mode speed Computed for Different Heights and Sections for 100G(blue:0.5Mm, green:1Mm, red:2Mm)

Sound speed Computed for Different Heights and Sections for 50G(blue:0.5Mm, green:1Mm, red:2Mm)

Sound speed Computed for Different Heights and Sections for 75G(blue:0.5Mm, green:1Mm, red:2Mm)

Sound speed Computed for Different Heights and Sections for 100G(blue:0.5Mm, green:1Mm, red:2Mm)

Slow mode speed Computed for Different Heights and Sections for 50G(blue:0.5Mm, green:1Mm, red:2Mm)

Slow mode speed Computed for Different Heights and Sections for 75G(blue:0.5Mm, green:1Mm, red:2Mm)

Slow mode speed Computed for Different Heights and Sections for 100G(blue:0.5Mm, green:1Mm, red:2Mm)



References

  1. The Influence of the Magnetic Field on Running Penumbral Waves in the Solar Chromosphere http://adsabs.harvard.edu/abs/2013ApJ...779..168J
  2. Wave Damping Observed in Upwardly Propagating Sausage-mode Oscillations Contained within a Magnetic Pore, http://adsabs.harvard.edu/abs/2015ApJ...806..132G
  3. On the Source of Propagating Slow Magnetoacoustic Waves in Sunspots, http://adsabs.harvard.edu/abs/2015ApJ...812L..15K
  4. An Inside Look at Sunspot Oscillations with Higher Azimuthal Wavenumbers, http://adsabs.harvard.edu/abs/2017ApJ...842...59J
  5. Magnetohydrodynamic waves driven by p-modes
  6. Magnetohydrodynamic Waves in a Gravitationally Stratified Fluid
  7. The Frequency-dependent Damping of Slow Magnetoacoustic Waves in a Sunspot Umbral Atmosphere, http://adsabs.harvard.edu/abs/2017ApJ...847....5K
  8. High-frequency torsional Alfvén waves as an energy source for coronal heating, http://adsabs.harvard.edu/abs/2017NatSR...743147S
  9. Solar Atmosphere Wave Dynamics Generated by Solar Global Oscillating Eigenmodes
    1. https://doi.org/10.1016/j.asr.2017.10.053 


Saturday, 2 December 2017

Solar Atmosphere Wave Dynamics Generated by Solar Global Oscillating Eigenmodes

We have recently completed our work investigating the dynamics and upward propagation of waves which are generated by the solar global eigenmodes. A lot of the background work is documented on this blog under the pmode label.

In this post I describe a series of hydrodynamic simulations of a realistically stratified model of the solar atmosphere representing its lower region from the photosphere to low corona. The objective was to model atmospheric perturbations, propagating from the photosphere into the chromosphere, transition region and low corona. The perturbations are caused by the photospheric global oscillations. The simulations use photospheric drivers mimicking the solar p-modes. In this post I review the work and highlight some of the results. Finally we review future work to investigate how the mean magnetic field itself would change the coupling of the global solar acoustic modes to the overlaying magnetised atmosphere. 



The discovery of solar global oscillations is highly remarkable and has resulted in the technique of helioseismology which has revealed  Observations of William Herschel as early as 1778-1818 revealed a granular structure. Around 1904 studies by Pierre Janssen suggested these structures had a diameter of around 1500km. These were soon attributed to the convective cells. In the 1960's the spectrographic studies of Evans and Leighton were able to identify and measure the rising and falling motions of solar the solar atmosphere. Using  Doppler shifts for different spectral lines the average turbulent velocity was measured for different heights. Leighton employed a technique different to that of Evans his approach study the doppler shift for a single spectral line (Ca-K band) but to scan two images across the solar disk. The resulting dopplergrams were subtracted to reveal an oscillatory motion with a period of 300s and amplitude of 300-400m/s. It was realised that this was a global phenomena. A number of theories were suggested for example the granules  acted as a piston driving the acoustic osillations, in another theory (Lighthill and Lamb) it was suggested that the stratified solar atmosphere acts as a filter possessing characteristic cutoff frequencies. A third model, the resonant cavity model although it could maintain five minute modes the cut-off frequency at the temperature minimum of the solar atmosphere meant that the 5-minute modes could not escape into the solar atmosphere. Further observations (Frazier and Mein 1965) provided evidence that the oscillations were generated deep in the convective interior. In 1970 Ulrich's theory used a resonant cavity with its upper boundary just below the top of the convection zone. The theory provided a dispersion relation showing how waves of given frequency and wavenumber lay along define ridges. Initially these were not observed this was because it was necessary to observe the sun over a long time and a large area. With the rise of the global oscillations network and the big bear observatory  such observations were possible and spectra like that of Ulrich's phase diagram were observed e.g. see below, the new discipline of helioseismology had arrived and we were beginning to understand the nature of solar global oscillations. As a student I remember a lecture on stellar interiors, it was claimed that this was a good area of study because it's difficult to look inside a star to verify your theory, therefore you have a greater freedom. Perhaps this speaker knew about the developments in helioseisomology it has changed things for our own star it's a developing and exciting field and that comment years ago fueled my curiosity.  A well worthwhile read is the book Sunquakes: Probing the Interior of the Sun by Jack Zirker (see reference 12).


It was recognised that turbulence in the convection zone generates acoustic noise continuously with some waves reflected back into the cavity by the photosphere. Thus the photosphere is driven up and down by evanescent waves leaking through the upper boundry with a spectrum which has a peak at five minutes. Since the advent of coronal seismology  many space-based high-resolution solar observations e.g. SOHO, TRACE, SDO and IRIS (to name but a few) have provided evidence for wave phenomena in the solar atmosphere. The power spectra reveal strong 3-5-minute oscillations in all channels and in- clude some longer period modes too. Using SDO/AIA data we show in Figure (1) the power spectrum in nine AIA passbands for randomly selected single pixels in and Active Region (AR), Quiet Sun (QS), and a Coronal Hole (CH) on a randomly chosen day (22 August 2010) during solar minimum. The power spectra are derived by studying image sequences at solar minimum for the different solar regions e.g. AR, a typical QS region and a CH.

The power spectrum in nine AIA passbands for single pixels in AR (black solid), QS (red solid), and CH (blue solid).

These results demonstrate the ubiquity of the observed 3- and 5-minute oscillations in all channels and regions and may serve as evidence of a global excitation mechanism. These observations are our strong motivation to model whether global p-modes may penetrate in the atmosphere.

Numerical MHD Simulations

To investigate these phenomena we ran a range of numerical hydrodynamical simulations of a model solar atmosphere for the quiet sun. We studied both the motion and the energy propagation characteristics for a range of frequencies and mode numbers.  The different driver modes are illustrated below for a vibrating membrane. This model is oscillator is located at the base of the model and is coincident with the temperature minimum.




The solar global modes of oscillation can be understood from the gravitating slab model discussed in the blog post "Our Wobbling Star". The modes observed at the solar surface are characterised by two indices l and m. l is the number of nodes between the poles whilst the azimuthal mode number m is the number of modes around the circumference. There are many thousands of modes some of which are illustrated below.
l=1,m=0


l=2,m=2
l=2,m=0
l=4,m=2
l=4,m=4
l=10,m=4
l=20,m=2
l=20,m=0

Research-IT Services Used

The completion of this work has been dependent on a range of research-IT services hosted and supported by The University of Sheffield. Research support was required throughout the full lifecycle of the project.  This work was funded by the Science and Technology Facilities Council (STFC), UK this funding was crucial to develop the codes used to perform the simulations and the analysis.
The computational models were run using the smaug code using the GPUs hosted on the iceberg high performance computer. Reference 11 provides details about the development and implementation of the code. We used revision 257 of SMAUG which can be checked out from the ccpforge code repository, this was checked out using the following subversion command.

svn checkout -r 257 http://ccpforge.cse.rl.ac.uk/svn/sac/dev/smaug
(see comment below ccpforge due to retire end of 2018)

A record of the project  was maintained using the github repository
https://github.com/mikeg64/smaug_pmode
This was used for a number of things
  •  to monitor any code changes and modifications (which would be checked back into the main repository on ccpforge)
  • The different simulations that were performed
  • The analysis applications  for visualisation and post processing
  • The final paper
The HPC services we used are heavily dependent  on GPU technology
A range of different software packages were used

A subset of the final results was published on the research data archive service provided by The University of Sheffield.

Results of Numerical Simulation

Since we are interested in the propagation of energy into the solar corona we computed the energy flux for different times and for different sections through the model. We also used time-distance plots to  characterise the modes of oscillation. Since we ran a large number of simulations with different modes and frequencies we attempted to summarise the results by preparing a collection of videos.

Each video shows the value of the vertical component of the plasma velocity (z-component) along different slices through the simulation box. The scale shows the velocity value in m/s. The green vectors show the velocity directions along a single slice through the simulation. The green surface at a height of 3.5Mm is the 2MK temperature isosurface. The simulation box is 4Mmx4Mm along the base and the height of the box is 5.7Mm. The driver for the simulations is located at a height of 0.5Mm.

Each video is labelled using 3 numbers. The first number is the driver period in seconds. The following 2 integers are each of the mode indices for the x and y direction respectively. Details of the full set of simulations is given in reference 1 see also the link to the repository at;

Videos of Magnetohydrodynamics Simulations of Solar Atmosphere Wave Dynamics Generated by Solar Global Oscillating Eigenmodes


Conclusions

Our results support the notion that solar global oscillations may be a driver for a range of global dynamical phenomena resulting in chromospheric and low coronal Doppler and intensity oscillations which, after all, may contribute to the non-thermal energy present in the solar atmosphere. We would like to emphasise that these upper atmospheric ubiquitous wave phenomena may not arise solely from the photospheric p-modes. On the contrary, a range of sources including, turbulent motions from convective cells, local nano-flares, small-scale Kelvin-Helmholtz instabilities, or continuous reconnection events in the magnetic carpet may contribute to their excitation.
Among others, we found that.
  1. There is consistency between the frequency-dependence of the energy flux in the numerical simulations and power flux measurements obtained from SDO;
  2. energy propagation into the mid- to upper-atmosphere of the quiet Sun occurs for a range of frequencies and may explain observed intensity oscillations for periods greater than the well known 3-minute and 5-minute oscillations;
  3. energy flux propagation into the lower solar corona is strongly dependent on the particular wave modes;
  4. agreement between the energy flux predictions of our numerical simulations and that of the two layer Klein-Gordon model supports our interpretation of the interaction of solar global oscillations with the solar atmosphere.

Future work

 An important caveat of the present work is the modelling of the active response of the atmospheric magnetic field. Although the plasma-β may be very low in the low corona, this approximation may serve an appropriate initial insight, nevertheless one needs to relax this condition and analyse how perhaps the mean magnetic field itself would change the coupling of the global solar acoustic modes to the overlaying magnetised atmosphere. Here, an interesting question would be to investigate whether slow or fast MHD waves are the key stakeholders in the re-distribution of the convective kinetic energy.

It has been recognised that magnetic fields influence the propagation of solar acoustic modes in a variety of ways (reference 8).  Hindman (reference  5) demonstrated the frequency shift of p-modes in vertical fields of different strengths. Cally and Goosens demonstrated that in the region of the solar atmosphere where the alfven speed matches the sound speed there is a significant transfer of energy between the different modes (see reference 7). A study of wave propagation in sunspot umbrae (see reference 4 below) reveals a suppression of wave power. The complexity of modelling physical processes in the highly stratified and magnetised makes it challenging to understand global oscillation phenomena. We have undertaken initial simulations with a uniform vertical field and using a (2,2) mode 300s driver. Some of the simulations have resulted in high frequency oscillations, these simulation artifacts can be filtered e.g. see the method used in reference 4. Our simulations clearly demonstrated the blockage of the 30s p-mode due to the cut-off for a magnetic field free atmosphere (see reference 6 below). However early results of computational simulations of the 30s mode using a magnetised solar atmosphere clearly demonstrate a leakage of energy in the solar corona the observed speed of propagation of the leaked mode is suggestive of mode conversion. Khomenko and Collados review the modelling and observation of sunspot waves in reference 9.

Further work will be undertaken using larger domains with greater resolution using the smaug+ code described in reference 13.

References

  1. Solar Atmosphere Wave Dynamics Generated by Solar Global Oscillating Eigenmodes
    1. https://doi.org/10.1016/j.asr.2017.10.053 
  2. Videos of Magnetohydrodynamics Simulations of Solar Atmosphere Wave Dynamics Generated by Solar Global Oscillating Eigenmodes
  3.  A Fast MHD Code for Gravitationally Stratified Media using Graphical Processing Units: SMAUG
  4. Magneto-acoustic Waves in Sunspots: First Results From a New Three-dimensional Nonlinear Magnetohydrodynamic Code 
  5. Driven Acoustic Oscillations within a Vertical Magnetic Field 
  6. On wave equations and cut-off frequencies of plane atmospheres 
  7. Three Dimensional MHD Wave Propagation and Conversion to Alfven Waves near the Solar Surface. I. Direct Numerical Solution 
  8. Absorption of p-Modes by Slender Magnetic Flux Tubes and p-Mode Lifetimes
  9. Oscillations and Waves in Sunspots 
  10. On coronal oscillations
  11.  A Fast MHD Code for Gravitationally Stratified Media using Graphical Processing Units: SMAUG
  12. Sunquakes: Probing the Interior of the Sun Hardcover – 29 Oct 2003 by J. B. Zirker (Author) 
  13. MHD code using multi graphical processing units: SMAUG+ 
    1. https://doi.org/10.1016/j.asr.2017.10.027 






Friday, 24 November 2017

Coronal loops heated by transverse waves

This week we had a talk about solar coronal heating with a particular focus on transverse waves in coronal loops the speaker was Tom Van Doorsselaere who visited Sheffield. The talk was introduced with an overview of recent observations of transverse waves in the solar atmosphere. He highlighted a claim that there were no waves in the corona! The time distance plot below 


A good introduction to transverse wave in the solar corona is given by the Warwick centre for Fusion, Space and Astrophysics.

Coronal Transverse Waves

Tom talked about coronal heating and identified mechanisms for heating the solar corona as well as convective heating and radiative transfer i.e. direct coronal heating he noted the important contribution of waves.


Tom summarized the current equilibrium models for coronal loops and reviewed some of the recent results from numerical simulations run by their group, e.g. see, Observational Signatures of Transverse Magnetohydrodynamic Waves and Associated Dynamic Instabilities in Coronal Flux Tubes.

  
Tom showed that coronal loops driven by transverse waves form a turbulent structure, via the Kelvin-Helmholtz instability or uniturbulence. The cascade of the wave energy to the small scales is beneficial for heating of solar coronal loops by waves. Tom described how forward modelling  was used to make the connection of the wave models to the observations. These results were generated using the FoMO application.

 Snapshots of the emission line flux (in inverted grayscale colors) in Fe xii 193 for model 1 (left panels) and in Fe ix 171 for model 2 (right panels) with the velocity field overlaid in rainbow colors. The snapshots follow the formation of the first KHI vortices (named TWIKH rolls). The color scale for the velocity field incorporates the extrema over the entire simulation.
Time–distance diagrams of the intensities in the Fe ix (top panel) and Fe xii (middle panel) lines of model 1 and Fe ix line (bottom panel) of model 2 for a slit placed perpendicularly to the loop at the apex and with a LOS angle of 45° and at numerical (highest) spatial resolution.

It was fascinating to see how models of many thin flux tubes resulted in mixing giving rise to a single flux tube. It was good to hear about the FoMo code this is something that Robertus has encouraged us to do i.e. reconstruct observations using our simulation data, here's how you do it.

https://github.com/TomVeeDee/FoMo
http://iopscience.iop.org/article/10.3847/1538-4357/aa5eb2

Friday, 27 October 2017

Discoveries in the Great Solar Data Mountain

One of the key's to the discovery of the Higgs Boson by the Large Hadron Collider at CERN
was the recognition of the quantity of data required to reveal a signature of the Higgs Boson. This needed a novel approach to the analysis and storage of the mountain of data that would be generated by the Large Hardron Collider.... big data had arrived. Just as CERN was first with the world wide web it was also first with the recognition of the Big Data problem. The story started with the discovery of the neutral current (a.k.a. the Z boson) in 1973 by the Gargamelle bubble chamber. This was remarkable because three events were observed in over 1.4 million bubble chamber photographs taken over a two year period, we didn't have digital image processing back then! Now, research is massively dependent on digital image processing and it is fascinating to follow the enormous variety of research problems in the area of solar physics, these researchers make use of toolkits such as the IDL solar software library, the more recent SunPY project or even Matlab. Along with many disciplines, there are two massive problems in this research field
  1. Solar physics has a big data problem, how do researchers collaboratively analyse the mountain of data both historical and being generated by new satellites studying our nearest star.
  2. How do we ensure that the software we use continues to be fit for purpose?
One of the solutions to the first problem was addressed by two excellent talks to the solar physics group the first talk a couple of weeks ago was about deep learning for solar flare forecasting. Yudong Ye gave todays talk which was an introduction to machine learning and its application to space physics. Ye said that Machine learning is more and more useful in this data explosion era and could be a powerful tool to reveal hidden connections and pave the way to new discoveries.  Two quantities  noted currently are the Sloane Digital Sky survey  which holds 140TB of data for optical telescope sky surveys between 2000 and 2010. The NASA NCSS holds 32pB of climatological data covering the years upto 2013. Ye provided a clear introduction to machine learning covering its concepts, he identified the different categories and gave recent applications in space physics. With an example of deciding whether there is a strong geomagnetic storm (namely, the Dst index is less than -100) from ICME’s plasma and magnetic field parameters using a support vector machine. He explained step by step how a machine learning method was applied to the specific problem described above. Further details are in references 11-15 below.
 
The previous talk given by Xin Huang discussed a model for  deep learning based solar flare forecasting. Solar flares originate from the release of the energy stored in the non-potential magnetic field of active regions, the triggering mechanism for these flares, however, are still unknown. For this reason, conventional solar flare forecasting is probabilistic and based on the statistical relationship between the characteristic parameters of active regions and solar flares. In the deep learning method, forecasting patterns can be learned from the line-of-sight magnetograms of solar active regions. It is necessary to obtain observational data with sufficient size to train the forecasting model and test its performance. Huang described how a dataset was created from the line-of-sight magnetogarms of active regions observed by SOHO/MDI and SDO/HMI from April 1996 to October 2015 along with the corresponding soft X-ray solar flares observed by GOES. The MDI data was taken as the training set and the HMI data as the testing set. The experimental result indicated that (1) the forecasting patterns can be automatically reached with the training set and these patterns can also be applied to the testing set, which is reduced to be the MDI proxy data; (2) the performance of the deep learning forecasting model is not sensitive to the given forecasting periods (6 hour, 12 hour, 24 hour or 48 hour); (3) a reasonable forecasting model is achieved for solar flares with higher importance. Huang used a deep learning package called CAFFE and used a single NVIDIA GPU (see references 6-9) below. He described how a cascade of layers in a convolutional neural network were used for feature extraction. The trick with deep learning is to exploit readily trained networks and to make use of supervised learning.

This talk was rather inspirational I've known for a long time that the Matlab package provides machine learning toolbox. At the risk of a little knowledge being dangerous I decided to try one of the matlab deep learning demos with a GPU, which is a Demonstration of Image category classification using deep learning (ref 2). This was very easy to run and I attempted a simple image classification on a set of photographs, clearly this is very powerful. But this is open to all our users on the central HPC at the university of sheffield it's possible to run the matlab deep learning demos. ShARC features a range of deep learning and machine learning software which has been well used and tested by the RSE and machine learning groups at The University of Sheffield.

A further possibility for researchers is to use the new deep learning cluster, JADE, based at Oxford ( see reference 10 ). It is fortunate that The University of Sheffield is a partner in this project making access much easier for researchers to use this powerful and increasingly used technique to meet the challenge of the big data problem (see reference 19). We can look forward to some excellent adventures exploring the great solar data mountain! 
  1.  The discovery of the weak neutral currents
  2. Demonstration of Image category classification using deep learning with Matlab
  3. Neural network toolbox for Alexnet Network with Matlab  
  4. Neural network importer for CAFFE models
  5. Mathworks neural networks toolbox team
  6. CAFFE
  7. THEANO
  8. TORCH
  9. TENSORFLOW
  10. JADE
  11. Predicting Coronal Mass Ejections Using Machine Learning Methods
  12. Solar Flare Prediction Model with Three Machine-learning Algorithms using Ultraviolet Brightening and Vector Magnetograms 
  13. Space weather research group (Bradford)
  14. Automated Prediction of CMEs Using Machine Learning of CME – Flare Associations 
  15. AUTOMATIC SHORT-TERM SOLAR FLARE PREDICTION USING MACHINE LEARNING AND SUNSPOT ASSOCIATIONS  
  16. Studying imagery from solar dynamics 
  17. Application of Convolution Neural Network to the forecasts of flare classification and occurrence using SOHO MDI data
  18. Application of a deep-learning method to the forecast of daily solar flare occurrence using Convolution Neural Network
  19. GPU Computing Sheffield 

Friday, 3 February 2017

Heliseismology - Introduction

I remember attending a lecture many years ago about the physics of stellar interiors with particular emphasis on the sun. It is amusing that the lecturer noted that one of the reasons for his interest was his freedom to construct models in the knowledge that it was very difficult to come up with the experimental evidence to verify the models! The field of helioseisomology and neutrino observations are changing this idea and we are gleening more information about the interior of our nearest star and other stars too.

Reka Jain gave an excellent presentation, her experience in this area is great and covers many levels of expertise including information inspiring young people [ref. 6]. Reka provided an overview of Helioseismology and  briefly discussed some recent successes of global and local Helioseismology.

My interest  in this area relates to the link between excitations in the solar atmosphere and the solar global oscillations see reference 13 and 14.

Helioseismology is the study of wave oscillations in the Sun. Observations of acoustic wave oscillations are used to make helioseismic studies of the interior of the Sun even though helioseismic techniques operate slightly differently on different length scales.The diagram below illustrates the variety of reflections and refractions occuring when acoustic waves propagate in the solar interior.

The helioseismic vibrations arise from convective and turbulent motions within the solar interior. We can identify two types of modes, pressure driven p-modes and gravity driven g-modes. Solving spherically symmetric equations of hydrodynamics (see our wobbling star) the modes can be understood in terms of spherical harmonics illustrated in the figure below. The predicted power spectrum gives rise to a series of distinct ridges 200000  modes have been detected of a possible million.



Reka's talk was particularly interesting because not only did she provide a clear overview  we heard about exciting advances including applications of helioseismology for studying
  • sunspot growth and evolution,
  • flux tubes convecting to the surface and the study of
  • neutrino observations to determine characteristics of g-mode oscillations.
  • neutrino propagation in stellar interiors to determine the properties of dark matter
Deubner [ref. 7] explained the p-mode oscillations using  the phase and group velocity of fluctuations of different solar spectral lines. Agreement with theoretical estimates was shown for acoustic waves trapped in the sun. With increasingly accurate models of the sun from helioseismology it is possible to use this higher quality data to study the propagation of neutrinos such probes can be used in studies of the difficult to find g-mode oscillations. One possibility is to use the sun as a probe for fundamental physics and cosmology. An important idea is the detection of dark matter and to understand the impact that this has onthe formation of stars [ref 8


ref. 8 Neutrion propagation in the interior
The Sun as a probe of Fundamental Physics and Cosmology The high quality data provided by helioseismology, solar neutrino flux measurements, spectral determination of solar abundances, nuclear reactions rates coefficients among other experimental data, leads to the highly accurate prediction of the internal structure of the present Sun - the standard solar model. In this talk, I have discussed how the standard solar model, the best representation of the real Sun, can be used to study the properties of dark matter, for which two complementary approaches have been developed: - to limit the number of theoretical candidates proposed as the dark matter particles, this analysis complements the experimental search of dark matter, and - as a template for the study of the impact of dark matter in the evolution of stars, which possibly occurs for stellar populations formed in regions of high density of dark matter, such as stars formed in the centre of galaxies and the first generations of stars.

 ref. 9 Predictions of solar cycle  changes in p-mode frequencies change with the solar cycle
The Sun's activity measured through many of its proxies varies in a periodic manner with an average duration of about 11 years. The empirical relations based on the periodicity are considered as the first generation methods to predict the maximum amplitude of the next solar cycle. These methods which are statistical in nature fall into two different categories: precursor methods and extrapolation methods and has been widely used in the later part of the 20th century. Recent advances include predictions based on non-linear methods and dynamo models, where the later predicts not only the maximum amplitude of the solar cycle but also the timing of the activity maximum. In this review, we focus on different prediction methods and compare their outcome for previous cycles with an emphasis on cycle 24. We further analyze and compare various predictions for solar cycle 25 and beyond.


The figures above and below illustrate the variation of the meridional flow.


reference 11,12 helioseismic detection of supergranulation
We present measurements of the Sun’s sub-surface convective flows and provide evidence that the pattern of supergranulation is driven at the surface. The pattern subsequently descends slowly throughout the near-surface shear layer in a manner that is inconsistent with a 3D cellular structure. The flow measurements are obtained through the application of a new helioseismic technique based on traditional ring analysis. We measure the flow field over the course of eleven days and perform a correlation analysis between all possible pairs of depths and temporal separations. In congruence with previous studies, we find that the supergranulation pattern remains coherent at the surface for slightly less than two days and the instantaneous surface pattern is imprinted to a depth of 7 Mm. However, these correlation times and depths are deceptive. When we admit a potential time lag in the correlation, we find that peak correlation in the convective flows descends at a rate of 10-40 m s-1 (or equivalently 1-3 Mm per day). Furthermore, the correlation extends throughout all depths of the near-surface shear layer. This pattern-propagation rate is well matched by estimates of the speed of downflows obtained through the anelastic approximation. Direct integration of the measured speed indicates that the supergranulation pattern that first appears at the surface eventually reaches the bottom of the near-surface shear layer a month later. Thus, the downflows have a Rossby radius of deformation equal to the depth of the shear layer and we suggest that this equality may not be coincidental.

We present measurements of the Sun's sub-surface convective flows and provide evidence that the pattern of supergranulation is driven at the surface. The pattern subsequently descends slowly throughout the near-surface shear layer in a manner that is inconsistent with a 3-D cellular structure. The flow measurements are obtained through the application of a new helioseismic technique based on traditional ring analysis. We measure the flow field over the course of eleven days and perform a correlation analysis between all possible pairs of depths and temporal separations. In congruence with previous studies, we find that the supergranulation pattern remains coherent at the surface for slightly less than two days and the instantaneous surface pattern is imprinted to a depth of 7 Mm. However, these correlation times and depths are deceptive. When we admit a potential time lag in the correlation, we find that peak correlation in the convective flows descends at a rate of 10 - 30 m s-1 (or equivalently 1 - 3 Mm per day). Furthermore, the correlation extends throughout all depths of the near-surface shear layer. This pattern-propagation rate is well matched by estimates of the speed of down flows obtained through the anelastic approximation. Direct integration of the measured speed indicates that the supergranulation pattern that first appears at the surface eventually reaches the bottom of the near-surface shear layer a month later. Thus, the transit time is roughly equal to a solar rotation period and we suggest this equality may not be coincidental. 

References

  1. Helioseismology
  2. Lecture notes on stellar oscillations
  3. Introduction to helioseismology
  4. Leibacher, A New Description of the Solar Five-Minute Oscillation
  5. Ulrich, The Five-Minute Oscillations on the Solar Surface
  6. Junior introduction to Helioseismology 
  7. Deubner, F.-L., Acoustic waves and the geometric scale in the solar atmosphere  see also Some properties of velocity fields in the solar photosphere. V - Spatio-temporal analysis of high resolution spectra
  8. Lopes, The Sun as a probe of Fundamental Physics and Cosmology
  9. Tripathy, Predictions of solar cycle
  10. Jain K, Tripathy, Hill, Solar Activity in Cycle 24 - What do Acoustic Oscillations tell us? 
  11. Greer, Hindman and Toomre, Helioseismic Imaging of Supergranulation throughout the Sun’s Near-Surface Shear Layer 
  12. Hindman, Greer, Toomre, Helioseismic Imaging of Supergranulation throughout the Sun's Near-Surface Shear Layer 
  13. Solar wave theory blog: helioseismology 
  14. Solar wave theory blog: solar global oscillations 
  15. A Comparison Between Global Proxies of the Sun's Magnetic Activity Cycle: Inferences from Helioseismology