Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Seismology of the Solar Atmosphere HELAS Roadmap Workshop, OCA Nice Wolfgang Finsterle, PMOD/WRC, Davos, Switzerland

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Seismology of the Solar Atmosphere ● Conceptual ideas  Traveling waves  Wave travel times  Many different types of waves (MAG, Alfvén, etc.) ● Techniques  Multi-height observations  “Doppler”-grams  Cross-correlation analysis ● Scientific potential  Dispersion relation of the solar atmosphere  Diagnostics of magnetic fields  Chromospheric heating

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere The Atmospheric Wave Field ● Solar eigenmodes oscillate in phase at all heights in the solar atmosphere ● Traveling waves produce a relative phase shift which is characteristic to the observation height and depends on the sound speed structure

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Acoustic Probing of the Sun's Lower Atmosphere ● By cross-correlating the wave fields at different heights, we can estimate the wave paths and sound speed between the observed heights ● The results naturally link to the solar interior, where seismic models are well established ● Sound waves interact with magnetic fields (absorption, wave conversion/transmission)

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Basic Model for Sound Waves observe Waves propagate when  >  0 Standing waves Traveling waves Wave equation d 2  /dt 2 = v 2 d 2  /dz 2 -  0 2  (where v has dimensions of velocity) Solution  = Re{A exp[i(  t-kz)]} Dispersion relation  2 =c 2 k 2 +  0 2 (  0 is the cut-off frequency) Acoustic pressure: v 2 ~ P/  Magnetic pressure: v 2 ~ B 2 /4 

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Multi-height Observations MOTH observations: time Fit correlation using: time series FT -1 Na K FT  Power  filter cross correlate Power

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Group Travel Time K→Na Group time (t g ) Green “islands” coincident with magnetic regions “ ➢ “ Quiet Sun”: ➢ Eveanescent-like behaviour for  <  0 ➢ upward propagating waves for  >  0 ➢ “Mangetic Regions” ➢ “islands” of evanescent-like behaviour ➢ Upward propagating waves for  <  0

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Phase Travel Time K→Na Phase time (t p ) Qualitatively the same structures as in the group travel time, but numerically much more stable, hence less noisy.

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Quiet Sun - Dispersion Relation t g : group travel time (model) t p : phase travel time (model) T g : group travel time (measured) T p : phase travel time (measured) Dispersion relation  2 =c 2 k 2 +  0 2 (  0 is the cut-off frequency),,

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Phase Travel Time MDI magnetogram

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere T p (B,ν) phase time 1.Acoustic “portals”: Lower acoustic cut-off in magnetized regions 2.Plasma-ß canopy: Wave reflection at the boundary layer between “thermal” and “magnetic” atmosphere 3.What are we looking at? Possible Explanation:

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere 1. Acoustic “Portals” ● Inclined magnetic field lines at the boundaries of supergranules locally lower the acoustic cut-off frequency ➔ Acoustic portals for low-frequency waves (<5 mHz) to propagate into the solar atmosphere ➔ Chromospheric heating Jefferies et al. 2006, ApJ 648, L151

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere 2. The Plasma-ß Canopy Rosenthal et al. (2002, ApJ 564, 508) time Below magnetic canopy: propagating wave Above magnetic canopy: evanescent tail

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Height of the ß Canopy reflecting surface MOTH Na Doppler Power MOTH K Doppler Power MDI Ni Doppler Power Potential Field Extrapolation

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere cross phase contours Height of the ß Canopy

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere Height of the ß Canopy K→Na Ni→Na

Wolfgang finsterle, September 26, 2006 Seismology of the Solar atmosphere 3. What are we looking at? Some Thoughts about “Doppler”-Grams ● Line-of-sight velocities of the observed medium introduce Doppler shifts ● Dopplergrams filter for anti-parallel intensity changes in the red and blue wings of absorption lines ● The red- and blue-wing probes observe different heights in the solar atmosphere ● At high frequencies, the acoustic wavelengths become comparable to this separation ● → Frequency-dependent “Doppler”-grams