Five minute solar oscillation power Five minute solar oscillation power within magnetic elementswithin magnetic elements

Rekha Jain & Andrew GascoyneSchool of Mathematics and Statistics (SoMaS)

University of Sheffield (UK)

Brad Hindman & Ben GreerJILA, University of Colorado at Boulder (USA)

Interaction with magnetic fieldsInteraction with magnetic fields

• Energy loss

• Energy redistribution

(i.e scattering)

Absorption

Damping

Power suppression

Phase shift

Mode mixing

Far field

Near-field (acoustic jacket modes)

Fast Fourier Transform (FFT) in time

Velocity Power maps

Dark region: suppressionBright region: enhancement

Jain and Haber (A&A, 2002)

Tracked &

RemappedMagnetogram

2.0-4.0 mHz

5.5-7.5 mHz

Sunspots Active Region

Doppler power images (integrating over diff. freq. ranges) Power suppressed in strong mag. field regions Power halos in strong mag. field but still suppressed in regions of strongest field

Doppler velocity dataLarge scale magnetic Large scale magnetic features & acoustic power features & acoustic power

Na line (589 nm)500 km

K line (770 nm)250 km

Ni line (677 nm)100 km

3 mHz 4 mHz 5 mHz 6 mHz 7 mHz 8 mHz

Moretti et al. (A&A, 2007)Three filters: different heights

• The suppression depends on height and frequency. Power halos are present in the limited range of frequencies that depend on the height

• The spatial extent of the region of power suppression grows as the height increases

Chitta et al. (ApJ, 2011) investigated the effect of magnetic fieldon photosphere/lower chromospheric intensity and velocity oscillations at the site of small scale magnetic features (|B| < 500 G) in quiet Sun close to the disk centre.

They chose quiet Sun with isolated small scale magnetic regions from different days with and without any visible large scale magnetic field regions such as sunspots and plages.

Small scale magnetic features and acoustic power Small scale magnetic features and acoustic power

Key findingsKey findings Both high resolution intensity observed in G band & velocity oscillations are influenced by the presence of magnetic field. Intensity oscillations are suppressed at all frequencies in strong magnetic regions

Key findingsKey findings Doppler velocity oscillations in magnetic elements are suppressed in the frequency range 2-5 mHz: compared to the surroundings (checked with separate data from MDI & HMI)

p-band

high-ν band

Diamond: reduction by a factor of 3

Key findingsKey findings Doppler velocity oscillations in magnetic elements are suppressed in the frequency range 2-5 mHz: there is 20-30% drop in power compared to the surroundings (checked with separate data from MDI & HMI)

p-band

high-ν band

The observed similarities between plage & small magnetic elements suggests that irrespective of the size of the magnetic regions, the physical mechanism that is responsible for the observed reduction of acoustic power is the same.

It is unlikely that the collective effect of tightly packed magnetic concentrations (as is typical of plage) is responsible??!!

Key findingsKey findings

However…However…

Sources of possible errors are not known.(so caution is needed & independent checks are needed.)

Simultaneous high resolution observations in different layers of solar atmosphere with co-temporal & co-spatial magnetic field information is needed.

The ModelThe Model

Isothermal

Polytrope

f and p mode solutionsf and p mode solutions

Isothermal

Polytrope

Sausage wave solutionsSausage wave solutions

Vertical displacement Vertical displacement of p modes (solid) of p modes (solid) & sausage waves& sausage waves

Re dashed

Im dotted

normalised by square root of density, as a function of dimensionless depth s. The vertical dotted line shows the position of the interface where the polytrope & isothermal regions are matched.

normalised by square root of density, as a function of dimensionless depth s. The vertical dotted line shows the position of the interface where the polytropeand isothermal regions are matched.

Vertical displacement of p modes (solid) & sausage wavesVertical displacement of p modes (solid) & sausage waves

Real part: dash

Imag. part: dot

Power ratioPower ratio

power of longitudinal (sausage) waves inside the tube to the (external) p mode power at a fixed height zR (from zphoto )

2

2

( )( )

( ),

v

nvz e

ws w

w

Dependence of power ratio on β for 3 mHz waves measured atthree different heights, zR in the isothermal region.

Assuming same amplitude

But observationally measured power maps have noBut observationally measured power maps have nowavenumber discrimination & the power measured inwavenumber discrimination & the power measured inany given pixel is the power in all modes at a given any given pixel is the power in all modes at a given ωω

where Pn is the power in the nth order mode.

( ) ( )n

n

P Pw w

( )magn

P w( )p

nP w

( )sn

P w sausage wave power

p-mode power

where

power in a magnetised pixel

f : filling factor

Power ratio

Since the fraction of p-mode power that is contained in any given order n is

( )( )

( )

pn

n pm

m

Pp

P

ww

w

obtained from helioseismic technique of ring-analysis as implemented in Greer et al. (2014)

1 1( ) [ ( )]n n

n

f r ps w

from theory

from HMI/SDO

POWER RATIO

f : black crossesP1: red asteriskP2: red asteriskP3: blue diamondsP4: yellow triangles

p5, p6, p7: turquoise

2

2

e

e

( )/ ( )

( )/ ( )

( )( , )

( )

HMI R n

HMI R m

z zHMIn

n R z zHMIm

m

pp z

p

a w

a w

ww

w

skin depth of the p-mode

solution in the isothermal atmosphere

Fractional power change as a Fractional power change as a function of height in the atmospherefunction of height in the atmosphere

Spectral lines are formed at different heights in magnetic and non-magnetic region - there will be some systematic error in the fractional power ratios.

We have investigated other data sets and our preliminary results suggest that the suppression in acoustic power at small scales, just like large-scale fields, is independent of the spectral line and instrument. However, caution is needed at this stage as observations at a very high spatial resolution can always open possibilities to deal with many of the questions we are trying to address in a much more effective way.

Suppression of intensity oscillations have been seen in Ca II K (which formin the lower to middle chromosphere). Since all Ca II K features have photospheric counterparts when observed in high-resolution G-band imaging, it remains to be seen if the intensity power suppression seen in the chromospheric Ca II K line is a result of already suppressed G-band intensity oscillations in the lower atmosphere.

centre to limb variation studies needed with different instruments & spectral lines