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


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