Thursday, 23 July 2015

Characterisation of Modes for solar global oscillations

This post is a summary of our work to classify energy propagation into the solar atmosphere resulting from different modes of solar global oscillations.

The background to the work is described at
Dynamics of the Solar Atmosphere Generated by the Eigen Modes of Solar Global Oscillations

Theoretical background to this work is described in
Our Wobbling Star!

and

The Solar Global Eigenmodes of Oscillation

Source code used for the runs including the input files may be obtained from github https://github.com/mikeg64/smaug_pmode/

We have performed two series of simulations delivering the same quantity of energy into the solar atmosphere with the extended driver across the lower boundary of the model.

The series are;

  1. Normal modes for a given value for the speed of sound in the solar atmosphere
  2. Mode series for drivers corresponding to the 5 minute and 3 minute oscillation

The series for the normal modes are calculated from the following expressions for a given of the speed of sound c and a value for the length of the simulation box of 4Mm. The frequency is computed using


The series of normal modes are computed such that the modes satisfy the following condition
The speed of sound for the VALIIc solar atmosphere is shown in the plot below
Variation of Sound Speed with height above the Photosphere Calculated from the VALIIC and McWhirter Model of the Solar Atmosphere

The simulations are tabulated below. The tables indicate the mode, the period for the driver, the driver amplitude and the label used for each of the data sets (for the input files and the configuration outputs). Remember that for both series the amplitudes have been set so that the same amount of energy is delivered by the driver. For the normal modes we have

For sound speed 20km/s

Mode Driver Period (s) Amplitude (m/s) Label
(0,0) 282.84 500 spic_2p82_0_0_3d
(0,1) 200.0 200 spic_2p00_0_1_3d
(0,2) 133.33 100 spic_1p33_0_2_3d
(0,3) 100.0 58.8 spic_1p00_0_3_3d

 For sound speed 13km/s

Mode Driver Period (s) Amplitude (m/s) Label
(0,0) 435.1 500 spic_4p35_0_0_3d
(0,1) 307.7 200 spic_3p07_0_1_3d
(0,2) 205.1 100 spic_2p05_0_2_3d
(0,3) 153.8 58.8 spic_1p53_0_3_3d

 For sound speed 8.4km/s

Mode Driver Period (s) Amplitude (m/s) Label
(0,0) 673.4 500 spic_6p7_0_0_3d
(0,1) 425.9 200 spic_4p3_0_1_3d
(0,2) 301.2 100 spic_3p0_0_2_3d
(0,3) 147.1 58.8 spic_2p3_0_3_3d


 For sound speed 31.43km/s

Mode Driver Period (s) Amplitude (m/s) Label
(0,0) 179.98 500 spic_1p79_0_0_3d
(0,1) 127.27 200 spic_1p27_0_1_3d
(0,2) 84.84 100 spic_0p84_0_2_3d
(0,3) 63.63 58.8 spic_0p63_0_3_3d


The series for the five and three minute modes are as follows


Mode Driver Period (s) Amplitude (m/s) Label
(0,0) 300.0 1250 spic5b0_3d_rep_3d
(0,1) 300.0 500 spic5b0_1_3d
(0,2) 300.0 250 spic5b0_2_3d
(0,3) 300.0 147.06 spic5b0_3_3d


Mode Driver Period (s) Amplitude (m/s) Label
(0,0) 180.0 1250 spic6b0_3d_rep_3d
(0,1) 180.0 500 spic6b0_1_3d
(0,2) 180.0 250 spic6b0_2_3d
(0,3) 180.0 147.06 spic6b0_3_3d

 We present below distance-time plots, plots of the energy flux and the variation of the energy flux for the different modes.

The plots below compare the distance time plots for the vertical component of the plasma velocity with the (0,0),(0,1),(0,2) and (0,3) modes.
Distance Time plot for 180s Driver the d-t plot has been taken through a horizontal section through the model in the Chromosphere at 1.06Mm.

Distance Time plot for 180s Driver the d-t plot has been taken through a horizontal section through the model in the Transition Layer at 2Mm.

Distance Time plot for 180s Driver the d-t plot has been taken through a horizontal section through the model in the Solar Corona at 4.3Mm.

Distance Time plot for 180s Driver the d-t plot has been taken through a vertical section through the model in the x-direction (section is taken at the horizontal location corresponding to the maxima)

Distance Time plot for 180s Driver the d-t plot has been taken through a vertical section through the model in the y-direction (section is taken at the horizontal location corresponding to the maxima)

Distance Time plot for 300s Driver the d-t plot has been taken through a horizontal section through the model in the Chromosphere at 1.06Mm.

Distance Time plot for 300s Driver the d-t plot has been taken through a horizontal section through the model in the Transition Layer at 2Mm.

Distance Time plot for 300s Driver the d-t plot has been taken through a horizontal section through the model in the Solar Corona at 4.3Mm.

Distance Time plot for 180s Driver the d-t plot has been taken through a vertical section through the model in the x-direction (section is taken at the horizontal location corresponding to the maxima)

Distance Time plot for 180s Driver the d-t plot has been taken through a vertical section through the model in the y-direction (section is taken at the horizontal location corresponding to the maxima)

The plots below show the integrated energy across a section of the computational model for different heights through the solar atmosphere the variation with time is shown.

Integrated Energy Variation for 180s Driver

Integrated Energy Variation for 300s Driver


The plots below compare the integrated time averaged flux for the solar atmosphere and the transition layer. For each mode the plots illustrate the variation of the integrated flux with the driver period.
Time Averaged Flux Variation for the Solar Corona


Time Averaged Flux Variation for the Transition Layer
Although the contribution of individual modes is a relatively small contribution we observe that as the driver period increases

The full set of results (images) is available from the following link
http://bit.ly/1TUMfOf

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