Thursday, 8 September 2016

Simulations of the Dynamics Generated by Solar Global OscillatingEigenmodes Generated in the Solar Atmosphere

This post continues a series of posts on global solar oscillation phenomena, we present results from Magneto Hydrodynamics simulations of solar oscillation phenomena in a gravitationally stratified atmosphere based on the VALIIIc model of the solar atmosphere.

The solar atmosphere exhibits a diverse range of wave phenomena, one of the earliest to be discovered was the five minute oscillation, the p-mode. The solar p modes are generated by global resonant oscillations and turbulent motions just beneath the photosphere. The aim of the work described here has been to investigate the dynamics in the solar atmosphere which are generated by solar global eigenmodes of oscillation. In addition we want to understand the mechanisms of leakage of these global oscillations into the atmosphere. It is also important for solar physicists to understand the conditions under which chromospheric dynamics evolve as a result of the 5 minute global oscillations - (spicules, waves).

There is increasing observational evidence of ubiquitous intensity oscillations and the detection of large scale solar oscillations in the solar corona. The Leakage of energy through the solar atmosphere (reference 1-5)i can be understood through theoretical studies of wave propagation through stratified atmospheres and by understanding the influence of the magnetic field on these motions. Great insight has been provided using studies of the solutions of the Klein-Gordon equation and by understanding the effect of the so called atmospheric cut-off and how this varies with atmospheric stratfication, more details are given in references 6-7.

For this work we have performed a range of numerical simulations of a model of the quiet solar atmosphere based on the VALIIc, the gravitationally stratified model has been excited by a periodic driver located at a position corresponding to the temperature minimum in the solar atmosphere. Full details of the procedure and the models performed are detailed at

http://solarwavetheory.blogspot.co.uk/2015/07/characterisation-of-modes-for-solar.html

Taking this work forward we have:
  1. Undertaken simulations for a greater range of wave modes
  2. Computed the energy flux through the solar atmosphere for drivers with different periods and for different wave modes.
Earlier simulations had been performed for the (0,0),(0,1),(0,2) and (0,3) modes as detailed in the earlier postings simulations were performed for normal modes and for driver period values of 180s, 300s and 30s. The latter periods correspond to the Chromospheric resonance, the five minute mode and a period below the cut off frequency.

For driver period 300s

Mode Amplitude (m/s) Label
(1,1) 175 spic5b1_1
(1,2) 137.28 spic5b1_2
(1,3) 110.7 spic5b1_3
(2,3) 99.0 spic5b2_3
(2,2) 116.7 spic5b2_2
(3,3) 87.5 spic5b3_3

For driver period 180s

Mode Amplitude (m/s) Label
(1,1) 175.3 spic6b1_1
(1,2) 137.5 spic6b1_2
(1,3) 110.9 spic6b1_3
(2,3) 99.2 spic6b2_3
(2,2) 116.9 spic6b2_2
(3,3) 87.7 spic6b3_3

Since we are investigating the leakage of energy into the solar atmosphere, for consistency it is necessary to ensure that for the different modes the driver amplitude is set to a value which provides the same total amount of energy over the model cross section and per unit time. The amplitudes for the (n,m) mode given in the above table are determined using the following relation.

 Where
Tm maximum period used for the simulations, T00 is the period used for the (0,0) mode with amplitude A00 here we used A00=500m/s.

For many of the earlier models we presented distance time-plots for the vertical component of the plasma velocity. Below we present the vertical component of the plasma velocity for the (2,3) mode 180s driver. At a height of  2.3Mm, a wave propagating across the transition zone can be observed.



The next movie shows the wave propagation at a height of 4.7Mm. At this height although the intensity of the plasma motion is reduced it is observed that there is a significant energy flux at this height. There appear to be two motions, one corresponding directly to the driver and the other motion which may be induced by reflections from the simulation box.




We compute the energy flux at different heights through the solar atmosphere using the following energy flux relation (see Bogdan ref. 8, quantities in the equations below subscripted with a b  are background variables.
The kinetic pressure is given by
The following plots display the energy flux at specific heights for the different modes and the driver periods

Energy Flux at 4Mm
Energy Flux at 5.5Mm

We noted that all the simulations were set with an amplitude resulting in a driver delivering the same quantity of energy over a specified amount of time. For some of the models we repeated the simulations but kept the amplitude for all drivers (i.e. all modes and driver frequencies) fixed at A=350m/s.

The next plots show the ratio of the energy flux for each of the driver periods and modes. In each case we have plotted the ratio of the flux for the fixed energy case to the flux for the fixed amplitude case.
Energy Flux Ratio at 4Mm
Energy Flux Ratio at 5.5Mm

The following bar charts show bar charts of the log10(energyFlux) for different modes. The cases for different driver periods are shown on different plots. We plot the energy flux at 4Mm and 5.5Mm i.e. the flux in the solar corona.

Energy Flux at 4Mm for 180s p-Mode Driver

Energy Flux at 5.5Mm for 180s p-Mode Driver

Energy Flux at 4Mm for 300s p-Mode Driver

Energy Flux at 5.5Mm for 300s p-Mode Driver

The energy  flux bar diagrams indicate that the fundamental mode delivers the maximum amount of energy. It is apparent that modes with odd numbers have a smaller energy flux  than for those cases with even mode numbers. The 180s driver delivers significantly more energy.

The energy flux ratio plots are interesting because they suggest that there is little variation in the flux ratio for drivers with different periods. Thus with a range of different drivers periods and modes we have a finite contribution to energy delivered to the solar atmosphere. The results of the simulations corroborate the ubiquity of the observed coronal intensity oscillations and naturally support  some of that characteristics alluded by theoretical modelling using the Klein-Gordon equation.

In further work we are currently undertaking simulations in which the oscillations are driven by configurations with magnetic fields, one such configuration is a thin 1kG vertical flux tube.
  1. Didkovsky, L.; Kosovichev, A.; Judge, D.; Wieman, S.; Woods, T., Variability of Solar Five-Minute Oscillations in the Corona as Observed by the Extreme Ultraviolet Spectrophotometer (ESP) on the Solar Dynamics Observatory/Extreme Ultraviolet Variability Experiment (SDO/EVE), Solar Physics, Volume 287, Issue 1-2, pp. 171-184 
  2. R. Erdelyi, R. Zheng, G. Verth, & P. H. Keys, Ubiquitous concurrent intensity oscillations in the solar atmosphere detected by SDO/AIA, 2016 submitted to ApJ 
  3. Marsh, M. S.; Walsh, R. W. p-Mode Propagation through the Transition Region into the Solar Corona. I. Observations, The Astrophysical Journal, Volume 643, Issue 1, pp. 540-548.
  4.  Freij, N et al, The Detection of Upwardly Propagating Waves Channeling Energy from the Chromosphere to the Low Corona, The Astrophysical Journal, Volume 791, Issue 1, article id. 61, 7 pp. (2014).
  5. Ireland, J.; McAteer, R. T. J.; Inglis, A. R., Coronal Fourier Power Spectra: Implications for Coronal Seismology and Coronal Heating, The Astrophysical Journal, Volume 798, Issue 1, article id. 1, 12 pp. (2015). 
  6. Taroyan, Y.; Erdélyi, R.; Malins, C. Propagation of p-modes into the solar atmosphere, Proceedings of SOHO 18/GONG 2006/HELAS I, Beyond the spherical Sun (ESA SP-624). 7-11 August 2006, Sheffield, UK. Editor: Karen Fletcher. Scientific Editor: Michael Thompson. 
  7. Malins, C.; Erdélyi, R. Direct Propagation of Photospheric Acoustic p Modes into Nonmagnetic Solar Atmosphere, Solar Physics, Volume 246, Issue 1, pp.41-52 
  8. Bogdan, T. J. et al, 2003 ApJ 599 626-660


Saturday, 23 April 2016

Dynamic Sun Conference: MHD waves in the Solar Atmosphere

In March I attended the dynamic sun conference, the theme of the conference was the study of MHD waves in the Solar Atmosphere. The purpose of the visit to this conference was fourfold
  1. Draw attention to work undertaken by IT services to support research needs of the solar physics community
  2. Publicise work on work investigating the  dynamics generated by the solar global oscillations
  3. Improve understanding of solar physics
  4. Network with the solar physics community and understand some of the research computing needs
Covering observational, theoretical and numerical studies of solar wave dynamics, the programme was excellent. The conference included  a visit to the sacred and iconic river Ganges. With so many good presentations, poster presentations and discussions it's challenging to cover everything in this relatively brief blog article.

The conference opened with  a discussion of wave coupling across the range of scale heights in the solar atmosphere and discussed the influence of magnetic field structures in opening windows channelling energy through the solar atmosphere. We hear how coupling was guided by 4 principles.
  1. The ramp effect - magnetoacoustic portal effect from inclined magnetic field
  2. Fast/slow mode wave conversion (Alfven speed matches acoustic wave speed)
  3. Fast wave reflection (horizontal wave speed same as acoustic wave speed)
  4. Fast/alfven mode conversion
The conversion of p-mode energy to fast modes and subsequent hypothesis of sunspot halos arising from the reflection of the fast modes higher in the atmosphere. This was followed by a discussion of methods for observing p-mode MHD wave generation in sunspots through helioseismology and vector polarimetry. Such observations are essential for explaining the uncertainties in the coupling and conversion mechanisms discussed above.

These topics are discussed in the following references
We heard about the preponderence of vortical motions in the solar atmosphere and how these drive the generation of Alfven waves thereby propagating energy efficiently to the upper layers of the chromosphere and the corona. A feature which clearly came across was the vortex motions generated by bumping and shear motions of the solar granular structures in the photsphere
We heard a presentation on Chromospheric heating. Mats Carlsson talked about models of the solar atmosphere. Because our models a good representation of the ever changing solar atmosphere, this was particularly interesting. Currently models are limited to the time averaged VAL3C model.

A discussion with Mats revealed a preference for the xeon-phi over omnipath for running large models using codes such as Bifrost. I also heard about the Bifrost implementation for handling boundaries using the method of characteristics for open end solutions.
Continuing the numerical simulation theme  there was fascinating discussion by a team from The University of Tokyo presented radiative MHD simulations of chromospheric jets. Visualisations of simulated  spicules were presented they claimed a dependence of jet length on coronal density. The simulation tool made use modelling thermal processes e.g. using radiative cooling and some ionization phenomena. Although the visualisations were compelling it was commented that it had overcomplicated the dominant physical processes responsible for spicule generation.  The MHD tool made use of the weighted essentilly non-oscillating  (WENO-Z) scheme for advancing the solutions. These are discussed in the following papers.
The conference excursions were excellent after a full day we enjoyed a Ganges boat trip to see the Agni Pujua (the worhsip to fire at ) Dashashwamedh Ghat. 
We also enjoyed a morning boat trip to observe the sunrise, what a fitting way to start another full day of solar physics.

Robertus provided an overview of MHD waves in localised magnetic structures. He started with an overview of models of the solar atmosphere and described how they have evolved as our knowledge has increased with improving observational, theoretical and computational understanding.



 The diagram above illustrates the sensitivity of different spectral regions for different parts of the atmosphere.
Studies have revealed the complex structures within the Chromosphere, such studies are dependent on developments in ground and space based instrumentation. We heard about a range of observatories in India and the forthcoming DKIST telescope based in Hawaii. With a primary mirror of 4.24m the DKIST solar telescope will be the largest in the world using adaptive optics to provide detailed imagery of the sun. We heard that it would have a 20km spatial resolution or 0.03" resolution at 500nm or 0.08" at 1.6micron.  Operations are expected to start in December 2019.

Bhola Dwivedi from Banares Hindu University closed the conference
Bhola talked about many things, he mentioned the Man-Mahal observatory which I visited on my final day in Varanasi.

Friday, 15 January 2016

Parallel, block-adaptive MHD simulations for solar coronal dynamics.


The SAC and SMAUG codes are based on the Versatile Advection Code we heard from one of the authors of the code about MPI-AMRVAC. This code is an advance on VAC,  the parallel scaling of the code exhibits weak scaling up to 30000 processors allowing to exploit modern peta-scale infrastructure. In particular the code has been developed to allow adaptive refinements of the computational mesh.

 The discussion focussed on solar physical applications modeled by the magnetohydrodynamic module of MPI-AMRVAC. The spatial discretizations available cover standard shock capturing finite volume algorithms, there are extensions to conservative high order finite difference schemes,  employing many flavors of limited reconstruction strategies. Multi-step explicit time stepping includes strong stability preserving high order Runge-Kutta steppers to obtain stable evolutions in multidimensional applications realizing up to fourth order accuracy in space and time.

 There was a discussion of the strategy for the AMR code. For a hypothetical grid arrangement exploiting 4 × 3 grid blocks at level l = 1, the left panel shows the global grid indices, while the right panel gives the tree representation with boolean variables indicating grid ‘leafs’.

Solar physics applications target the formation of flux rope topologies through
boundary driven shearing of magnetic arcades, following the in situ
condensation of prominences in radiatively controlled evolutions of arcades and
flux ropes, and the enigmatic phenomenon of coronal rain, where small-scale
condensations repeatedly form and rain down in thermodynamically structured
magnetic arcades.

The example above shows the density distribution at t = 3.01 × 105 yr after a supernova explosion. The entire domain is shown. Typical features such as the bow shock, the disturbed cloud with Richtmyer–Meshkov features on the front side, and a low-density region Rayleigh–Taylor instability behind the cloud are shown. The right hand image shows a zoomed-in look at the dust density distribution of species two in the cloud region. The dust can be seen to be tightly coupled to the dynamics of the cloud.

References

 `MPI-AMRVAC for solar and astrophysics', O. Porth, C. Xia, T. Hendrix, S.P. Moschou, & R. Keppens, 2014, ApJS 214, 4 (26pp) Full paper, doi:10.1088/0067-0049/214/1/4 )

`Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics', R. Keppens, Z. Meliani, A.J. van Marle, P. Delmont, A. Vlasis, & B. van der Holst, 2012, JCP 231, 718-744. Full paper, doi:10.1016/j.jcp.2011.01.020. Accepted for special topical issue, with R. Keppens as Associate Editor. See also the Editorial Preface: Computational Plasma Physics.

 https://gitlab.com/groups/mpi-amrvac
http://homes.esat.kuleuven.be/~keppens/

 `Three-dimensional prominence-hosting magnetic configurations: creating a helical magnetic flux rope', C. Xia, R. Keppens, & Y. Guo, 2014, ApJ 780, 130 (11pp) Full paper, doi:10.1088/0004-637X/780/2/130

`Simulating the in situ condensation process of solar prominences', C. Xia, R. Keppens, P. Antolin, & O. Porth, 2014, ApJ Letters 792, L38 (6pp) Full paper, doi:10.1088/2041-8205/792/2/L38

https://perswww.kuleuven.be/~u0016541/Pub.html
https://perswww.kuleuven.be/~u0016541/Cont.html
https://perswww.kuleuven.be/~u0016541/Teach.html