Five minute solar oscillation power within magnetic elements Rekha Jain & Andrew Gascoyne School of Mathematics and Statistics (SoMaS) University of Sheffield (UK) Brad Hindman & Ben Greer JILA, University of Colorado at Boulder (USA)

Interaction 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: suppression Bright region: enhancement Jain and Haber (A&A, 2002) Tracked & Remapped Magnetogram mHz mHz SunspotsActive 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 data Large scale magnetic features & acoustic power

Na line (589 nm) 500 km K line (770 nm) 250 km Ni line (677 nm) 100 km 3 mHz4 mHz5 mHz6 mHz7 mHz8 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 field on 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

Key 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 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 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 findings

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.

suggest that a magnetic field shortens the attenuation length (or the skin depth) of the p-mode eigenfunction in the upper atmosphere where the wave is evanescent. Such a mechanism would reduce the observed power amplitude without a significant change in the energy carried by the mode. Quote Jain et al (1996)

The Model

Isothermal Polytrope f and p mode solutions

dispersion diagram Solutions to this equation determines the discrete eigenvalues that insures stress continuity at the interface between the two atmospheres. n=0 n=1

Isothermal Polytrope Sausage wave solutions

Vertical displacement of p modes (solid) & sausage waves  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 polytrope and isothermal regions are matched. Vertical displacement of p modes (solid) & sausage waves Real part: dash Imag. part: dot

Power ratio power of longitudinal (sausage) waves inside the tube to the (external) p mode power at a fixed height z R (from z photo )

Dependence of power ratio on β for 3 mHz waves measured at three different heights, z R in the isothermal region. Assuming same amplitude

But observationally measured power maps have no wavenumber discrimination & the power measured in any given pixel is the power in all modes at a given ω where P n is the power in the nth order mode. 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 obtained from helioseismic technique of ring-analysis as implemented in Greer et al. (2014) from theory from HMI/SDO POWER RATIO

f : black crosses P 1 : red asterisk P 2 : red asterisk P 3 : blue diamonds P 4: yellow triangles p 5, p 6, p 7 : turquoise

skin depth of the p-mode solution in the isothermal atmosphere Fractional power change as a function 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 form in 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