Multi-level observations of magneto-acoustic cut-off frequency

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 & Nakariakov2012：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 5-min running penumbral waves Frequency ~3 mHz Phase speed ~13 km/s 3-min standing waves Frequency ~ 6.5 mHz Christopoulou et al 2000 Georgakilas et al 2000 3-min power map 5-min power map Yuan et al 2013 A&A Yuan et al 2012 A&A letter

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

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 choromospherewaves between a density gradient and magneto-acoustic cut-off 3-min standing wave in sunspot umbra 3-min EUV propagating disturbances in the corona Yuan & Nakariakov 2012 Botha et al 2011,Zhugzhda 1983,2008 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 AR11131 （08 Dec 2010） AR11330 （27 Oct 2011）

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 maps304 A 2 min 3 min 4 min 5 min 6 min 7 min 8 min 10 min

15. Typical narrow-band power maps1600 A 2 min 3 min 4 min 5 min 6 min 7 min 8 min 10 min

16. Typical narrow-band power maps1700 A 2 min 3 min 4 min 5 min 6 min 7 min 8 min 10 min

17. 1D MAG cut-off frequency and magnetic inclination reconstruction304A

18. 1D MAG cut-off frequency and magnetic inclination reconstruction1600 A

19. 1D MAG cut-off frequency and magnetic inclination reconstruction1700 A

20. 2D MAG cut-off frequency and magnetic inclination reconstruction304 A

21. 2D MAG cut-off frequency and magnetic inclination reconstruction1600 A

22. 2D MAG cut-off frequency and magnetic inclination reconstruction1700 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.