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.


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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 


2 comments:

  1. see notes for future work at
    https://docs.google.com/document/d/1WdNKPciBvG7lqAA_0J0FdZRSLZ5-1TGdfL0eiMTQW1k/edit

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