Slides for UK National Astronomy Meeting, Portsmouth, June 2014. Session "Energy Transfer through the Solar Atmosphere: waves and reconnection"

1. Simulations of the Dynamics Generated
in the Solar Atmosphere by Solar Global
Oscillating Eigenmodes
Michael Griffiths, Viktor Fedun, Robertus Erdélyi
The Solar Wave Theory Group
And Corporate Information and Computing Services
The University of Sheffield
National Astronomy Meeting
University of Portsmouth
June 2014

2. Outline
• Solar Global Oscillating Eigenmodes
• A model for studying dynamics in the
atmosphere
• Simulation
• Evidence of induced Dynamics
• Conclusion and Future Work

3. Dynamics in
the Solar Atmosphere
• Earliest observations of motions of
the solar surface around 1918,
(St.John C.E. et al, from Doppler Shift
when studying solar rotation).
• Leighton1960, Vertical motions 300-
400m/s,explained by Ulrich1970
• The solar p modes are generated by
global resonant oscillations and
turbulent motions just beneath the
photosphere.
• Modes trapped below the photosphere refracted
by sharp change in density
• Power peak at 5 – minutes p mode oscillations

4. l=4,m=2 l=10,m=4 l=20,m=2
Solar Global Eigen modes
of Oscillation
Hydrodynamic Waves Gravitating Slab
Quantization condition – l usually large
Spherical solution using spherical harmonics

5. • Demonstrate code validity by repeating earlier
hydrodynamic 2D models of Malins and Erdelyi
• Demonstrate cavity modes in the
Chromosphere
• Surface modes in the transition region
• Understand dynamics allowing mode tunnelling
and energy leakage into the corona
• Modes evanescent around photosphere – inhibit
propagation into corona
• Upper and lower turning points determined by
order
Objectives

6. Vertical driver to Induce
Dynamics in the
Solar Atmosphere
• Represent oscillation modes as a vibrating membrane
• Driver located at temperature minimum
• Deliver same amount of energy for different modes

7. • Fully stratified quiet solar
atmosphere based on VALIIIC
and McWhirter
• Model of the stratified solar
atmosphere
• Height upto 6Mm
• Cross section 4Mmx4Mm
• 128x128x128 computational
domain
• Local acoustic cut-off
• Propagation below cutoff
• Evanescence (above cutt-
off)
• Cutoff calculated in different ways
• Isothermal atmosphere
• Highly stratified
• Models with 30s,180s,300s
drivers
• 00,01 and 02 modes
• Run normal mode fixed energy
Computational Model

8. Stratified Magnetohydrodynamics
Accelerated
Using GPUs:SMAUG
• SMAUG is a novel fully non-
linear MHD code based on
SAC/VAC (Shelyag et al 2008)
• designed for simulations of
linear and non-linear wave
propagation
• with gravitationally strongly
stratified magnetised plasma.
• Version of SAC ported to GPU
(Graphical Processing Units)
• Single GPU
• 2.5xfaster than latest Intel
Xeon (using 8 cores)
• Multiple GPU version available

9. Validation of SMAUG
(Flux Tube with Torsional Driver)
128x128x128
1.5x2x2Mm
Fully
stratified
quiet solar
atmosphere
based on
VALIIIC
Flux tube
1000G
Driver
Amplitude
200km/s
Period
Also Orszag-
Tang, Brio-
Wu and
explosion
model
Fedun et Al., Astrophys. J. Lett 740:L46,2011 movie

10. Energy leakage and Evolution
• For each time step integrate the total
energy over the model cross section
• Plot the energies for the transition
region and into the Corona
• 180s and 300s modes provide
energy leakage with period the
same as that of the driver
• 30s driver is the least efficient at
coronal energy leakage.
• Evidence for non linear beahviour

11. Variation of Energy leakage
with Driver frequency
• Integrate perturbed energy over cross sectional and over either the
transition region or the corona
• Take average over the simulation time
• For the 02 mode 180s driver dominates

12. Variation of Energy leakage
with Driver frequency
Compute time averaged perturbation energy for the 00 and 01 modes
• fundamental mode 5 min driver (300s) effective for energy supply to the corona
region and 3 min driver effective for TR
• 01 mode 5 min nothing for corona and 3 min again effective for TR
• 02 mode 5 min nothing for corona and 3 min effective for corona

13. Distance Time Plots
For 0,1 mode from left to right 30s, 180s, 300s for the vertical component of
the velocity

14. Driver is 0,1 Mode with Period 300s
(z Component of Velocity)

15. • Mainly future work!
• GPU code performs well
• Results provide evidence for energy leakage into the corona
• fundamental mode 5 min driver (300s) effective for energy supply to the
corona region and 3 min driver effective for TR
• 01 mode 5 min nothing for corona and 3 min again effective for TR
• 02 mode 5 min nothing for corona and 3 min effective for corona
• Distance time plots illustrate cavity modes in the chromosphere
• For 300s and 180s drivers clear indication of induced dynamics in the corona
• Unexplained resonances e.g. for 30s driver probably resulting from non-linear
behaviour
• Further characterisation of the normal modes and run models with a greater
range of modes of oscillation
• Genuine MHD examples
• Vertical B field
• Horizontal B field
• Flux tubes
Conclusion and Future Work

16. • Thank you for Listening
• http://uk.virginmoneygiving.com/mikeg64

17. Driver is 0,1 Mode with Period 30s

18. Driver is 0,1 Mode with Period 180s