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

Ding Yuan Department of Physics

University of WarwickCoventry CV4 7AL, UK

Ding.Yuan@warwick.ac.uk

With thanks to R. Sych, V. Reznikova, V.M Nakariakov.

Contents

• Introduction to sunspot waves• Dataset• Methods• Results• Conclusions

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.

DST observations in H_alpha3-min standing wavesFrequency ~ 6.5 mHz

5-min running penumbral wavesFrequency ~3 mHzPhase speed ~13 km/sChristopoulou et al 2000Georgakilas et al 2000

Yuan et al 2012 A&A letter

Yuan et al 2013 A&A

3-min power map 5-min power map

Shock wave formation

Temporal variation of Stokes V

photosphere Chromosphere 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

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

Acoustic resonator in the choromospherewaves 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

TRACE observation of magneto-acoustic cut-off frequency

McIntosh & Jefferies 2006, Theory: Bel & Mein 1971, Bel & Leroy 1977

Energy flux spectrum (0.4 Mm) carried by magneto-acoustic waves at various frequency bands

Jefferies et al 2006 Fontenla 1993

HMI and AIA FOV

AR11330 （ 27 Oct 2011 ）

AR11131 （ 08 Dec 2010 ）

Pixelised Wavelet Filtering

Sych & Nakariakov 2008

Data format in polar coordinate

Magnetic inclination reconstruction

Bel & Leroy 1977

1D case for symmetric sunspot 08 Dec 2010

2D case for asymmetric sunspot 27 Oct 2011

Typical narrow-band power maps304 A

2 min 3 min 4 min 5 min

6 min 7 min 8 min 10 min

Typical narrow-band power maps1600 A

2 min 3 min 4 min 5 min

6 min 7 min 8 min 10 min

Typical narrow-band power maps1700 A

2 min 3 min 4 min 5 min

6 min 7 min 8 min 10 min

1D MAG cut-off frequency and magnetic inclination reconstruction

304A

1D MAG cut-off frequency and magnetic inclination reconstruction

1600 A

1D MAG cut-off frequency and magnetic inclination reconstruction

1700 A

2D MAG cut-off frequency and magnetic inclination reconstruction

304 A

2D MAG cut-off frequency and magnetic inclination reconstruction

1600 A

2D MAG cut-off frequency and magnetic inclination reconstruction

1700 A

Potential field extrapolation

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.

2D inclination reconstruction

304 A

1600 A

1700 A

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)

Diagnostics of the minimum temperatures and local sound speeds

Temperature profiles and Solar cycles

08 Dec 2010 @ 0.08 T_sc27 Oct 2011 @ 0.17 T_sc

Maltby-E @ 0.1 T_scMaltby-M @ 0.5 T_scMaltby-L @ 0.9 T_scSee Maltby et al 1986

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.