1. Multi-level observations of magneto- acoustic cut-off frequency Ding Yuan Department of Physics University of Warwick Coventry CV4 7AL, UK Ding.Yuan@warwick.ac.uk With thanks to R. Sych, V. Reznikova, V.M Nakariakov.

2. Contents Introduction to sunspot waves Dataset Methods Results Conclusions

3. Reference to my publications Yuan et al 2011: Leakage of long-period from the chromosphere to the corona. 553(2011) A116 Yuan & Nakariakov 2012 ： Yuan & Nakariakov 543 (2012) A9 Yuan et al 2012 A&A letter: Detection of high-order azimuthal modes in sunspot Yuan et al 2012 A&A: Multi-level observations of sunspot waves and oscillations with SDO/AIA. I. Field line reconstruction with magneto-acoustic cut-off. Yuan et al 2013 A&A: Multi-level observations of sunspot waves and oscillations with SDO/AIA. II. Phase, coherence and correlative properties of 3- and 5-min oscillations.

4. DST observations in H_alpha 3-min standing waves Frequency ~ 6.5 mHz 5-min running penumbral waves Frequency ~3 mHz Phase speed ~13 km/s Christopoulou et al 2000 Georgakilas et al 2000 Yuan et al 2012 A&A letter Yuan et al 2013 A&A 3-min power map 5-min power map

5. Shock wave formation Temporal variation of Stokes V photosphereChromosphere Chromosphere Zoomed LOS velocity variation Centeno et al 2006, 2009 Shock waves indicates the existence of cut-off effect at certain height. or non-linear interactions

6. The exclusion of non-linear effect Phase spectrum between the LOS velocity of Si I and He II Coherency level, the dashed line indicates the acceptance level. Amplitude variation with frequency. Red solid line, theoretical linear wave mode with radiative cooling term Felipe et al 2010

7. Acoustic resonator in the choromosphere waves between a density gradient and magneto- acoustic cut-off Botha et al 2011,Zhugzhda 1983,2008 3-min EUV propagating disturbances in the corona 3-min standing wave in sunspot umbra Yuan & Nakariakov 2012 Yuan et al 2013 A&A

8. TRACE observation of magneto- acoustic cut-off frequency McIntosh & Jefferies 2006, Theory: Bel & Mein 1971, Bel & Leroy 1977

9. Energy flux spectrum (0.4 Mm) carried by magneto-acoustic waves at various frequency bands Jefferies et al 2006 Fontenla 1993

10. HMI and AIA FOV AR11330 （ 27 Oct 2011 ） AR11131 （ 08 Dec 2010 ）

11. Pixelised Wavelet Filtering Sych & Nakariakov 2008

12. Data format in polar coordinate

13. Magnetic inclination reconstruction Bel & Leroy 1977 1D case for symmetric sunspot 08 Dec 2010 2D case for asymmetric sunspot 27 Oct 2011

14. Typical narrow-band power maps 304 A 2 min3 min4 min5 min 6 min7 min8 min10 min

15. Typical narrow-band power maps 1600 A 2 min3 min4 min5 min 6 min7 min8 min10 min

16. Typical narrow-band power maps 1700 A 2 min3 min4 min5 min 6 min7 min8 min10 min

17. 1D MAG cut-off frequency and magnetic inclination reconstruction 304A

18. 1D MAG cut-off frequency and magnetic inclination reconstruction 1600 A

19. 1D MAG cut-off frequency and magnetic inclination reconstruction 1700 A

20. 2D MAG cut-off frequency and magnetic inclination reconstruction 304 A

21. 2D MAG cut-off frequency and magnetic inclination reconstruction 1600 A

22. 2D MAG cut-off frequency and magnetic inclination reconstruction 1700 A

23. Potential field extrapolation

24. 1D inclination reconstruction Red diamond: reconstructions with the theoretical cut-off frequency \nu_0=5.2 mHz Blue diamond: reconstructions with observational cut-off frequency for each bandpasses \nu_\lambda Shade asterisk: the inclination obtained from the potential field extrapolation [0: 90 ] degree Green asterisk: the return flux corrected to [0:90] degree. Dashed line: the umbra and penumbra borders Cross-hatched region: the measurements close to detection limit.

25. 2D inclination reconstruction 304 A 1600 A 1700 A

26. Correlation between cut- off and peak frequencies Diamonds: data obtained from sunspot AR11131 (08 Dec 2010) Dots: data obtained from sunspot AR11330 (27 Oct 2011)

27. Diagnostics of the minimum temperatures and local sound speeds

28. Temperature profiles and Solar cycles 08 Dec 2010 @ 0.08 T_sc 27 Oct 2011 @ 0.17 T_sc Maltby-E @ 0.1 T_sc Maltby-M @ 0.5 T_sc Maltby-L @ 0.9 T_sc See Maltby et al 1986

29. Conclusions 5-min oscillation is likely to originate from a level below the photosphere, where the magnetic field is medium in strength and inclined about 20-50 degrees to solar normal.( Cally2003, Schunker&Cally 2006 ) 3-min oscillations is generated in the chromosphere, in consistent with the acoustic cavity model ( Botha et al 2011, Zhugzhda 1993,2008 ) The cut-off and peak frequency shows very good correlation, match well with a linear model. ( Bogdan2006,Tziotziou et al 2006 ) Return flux was found at 0.8rp to 1.2 rp. More return flux are found to distribute in a lower atmosphere. This is in agreement with return flux sunspot model ( Fla et al 1982, Osherovich et al 1982). The cut-off frequency are observed to be lowered by the inclined magnetic field lines ( Bel & Leroy 1977 ), but the field line inclination only accounts for 60%-80% of the total lowering. The observation of the cut-off frequency is also a tool to diagnose the local minimum temperature, and sunspot dynamics and solar cycle variation. It awaits for a more systematic study.