School and Conference on Analytical and Computational Astrophysics November, Coronal Loop Seismology - State-of-the-art Models

Transcription

1 9-4 School and Conference on Analytical and Computational Astrophysics 14-5 November, 011 Coronal Loop Seismology - State-of-the-art Models Malgorzata Selwa Katholic University of Leuven, Centre for Plasma Astrophysics Belgium

2 Coronal Loop Seismology - State-of-the-art Models Mag Selwa ICTP School and Conference on Analytical and Computational Astrophysics, Trieste,

3 Outline Observations of coronal loops oscillations as an input for coronal seismology: Scale height Damping mechanisms Recent observations (STEREO) Alfvén waves Other structures: EIT waves QPP streamers prominences

4 B from kink oscillations transverse oscillations in an off-limb arcade observed with TRACE: n t Best fit ( t) Ae cos t P B n d 1 n / n 1/ 0 e 0 P Verwichte et al. (004)

5 B from kink oscillations P 1 P First identification of kink second harmonics P P 1 /, the mode has a node at loop apex. Here P 1 /P = 0.55 and 0.61 Verwichte et al. (004)

6 Scale height from kink oscillations Scale height (for planetary atmospheres) is the vertical distance over which the pressure of the atmosphere changes by a factor of e (decreasing upward). The scale height remains constant for a particular temperature. exponentially stratified atmosphere ( h) 0 exp( h / H) stratification function projected on a semicircular loop of length L P 1 /P (no node at the loop apex) P /P 1 ~ H (scale height) ( z) 0 exp Lsin z / L / H A tool for independent estimation of stratification Andries et al. (005)

7 Multiple periodicities scale height O Shea et al. (007): wave harmonics in cool loops (OV observation, TR line). De Moortel & Brady (007): nd and 4 th /5 th harmonic. Van Doorsselaere et al. (007): fundamental and nd harmonic in TRACE observations, calculated density scale height in the loop as 109Mm (estimated hydrostatic value is 50Mm). Van Dooresselaere et al. (009): reanalyzed event of De Moortel & Brady 007 as the fundamental, nd and 3 rd harmonic; from 3 periods estimated density scale height and loop expansion.

8 Multiple periodicities expansion Verth (007), Verth et al. (008), Verth & Erdélyi (008), Van Doorsselaere et al. (009), Andries et al. (009): tube expansion and variation of magnetic field B z z cos z / L cos1 1 cos 1 magnetic flux conservation 3 1 -> the period ratio of the fundamental mode to the first overtone can be approximated for a constant density loop to the first order by P1 P B B f a opposite effect

9 Damping mechanisms-alfvén speed Brady et al. (006) Verwichte et al. (006)

10 Damping mechanisms-alfvén speed The oscillations of a whole coronal arcade above an active region provide information of the Alfvén speed profile at different loops as a function of height in the global corona, which may be compared with magnetic field extrapolation models. With each oscillating loop, we can associate an average value of the average Alfvén speed (in that loop) and a loop length and height, or range of heights, in the corona. Verwichte et al. (010)

11 Damping mechanisms: resonant absorption Ruderman & Roberts (00): damping due to resonant absorption density contrast i e P d l 1 R 1 Goossens et al. (00) for =10 -> l/r Arregui et al. (007) 1D solution curves

12 Damping mechanisms Ofman & Aschawanden (00), Nakariakov (004), Verwichte et al. (004)Ruderman & Roberts (00): Phase mixing if layer ~ loop length (does not involve torsional mode, but is connected with kink perturbations of neighbouring loops) Wave leakage if layer ~ loop length Resonant absorption d /3 4/ 3 lp P Nakariakov & Verwichte (005): d LP P P d leakage 0.7 d P 1.1 d resonant absorption phase mixing

13 3D STEREO observations Aschwanden (008): paper I: 3D geometry and motion of the loops paper II: electron density and temperature Verwichte et al. (009): seismology of large coronal loop -> B=11±G

14 3D STEREO observations Fundamental horizontal mode Second harmonic horizontal mode Fundamental vertical mode Second harmonics vertical mode Wang, Solanki, Selwa (008)

15 Problems with magnetic field McLaughlin & Ofman (008): reduction of vertical kink oscillation period compared to the horizontal one. De Moortel & Pascoe (009): magnetic field derived from simulation differs by 50% from the input value (overestimated). Aschwanden & Schrijver (011): magnetic field from coronal seismology 4G, from potential field extrapolation 6G (apex), after correction of variable Alfvén speed along the loop 11G (.8 times higher than the value from coronal seismology).

16 Problems with magnetic field Selwa, Ofman, Solanki, Paper I (011)

17 Problems with magnetic field P(simulations): 1 P(analytical):4 P(simulations): 44 P(analytical):45 Difference in periods (but not the nd mode) Does not depend on excitation type 50% error in B estimation! Selwa, Ofman, Solanki, Paper I (011)

18 Problems with magnetic field Selwa, Ofman, Solanki, Paper I (011)

19 Structures on the Sun

20 EIT/EUV waves Veronig et al. (010): wave dome in EUVI-B channels Patsourakos et al. (009): bestfit CME and wave model determined for STA Temmer et al. (011)

21 EIT/EUV waves NOAA (Schrijver C.J., Aulanier G., Title A.M., Pariat E. & Delannée C., ApJ, 011): an X-class flare follows EIT wave in time on

22 EIT/EUV waves Event of , SDO & STEREO observations Using fast speed p cs kbt / m formula for magnetic field can be derived B V V A 4n mv f kt peak f V A c s B 4nm Assuming quiet corona density (Wills-Davey et al. 007) n=-6x10 8 cm -3 -> B=1-G Long et al. (011)

23 EIT/EUV waves Event of , STEREO & Hinode observations Using fast speed V f magnetic field can be estimated together with plasma 1 V A c s V c 4V c cos V c B 4 V f P 8P B Wave seems to be formed at T=1.5±0.5MK A s A s P nk B T A s West et al. (011)

24 EIT/EUV waves Superimposed EIS(Hinode) slit on ST EUVI 195Å at similar times SiX 58/61 lines are used (similar temperature to the strongest line of FeXII 195 in EUVI) -> density of 3.4±0.8x10 8 cm -3 MDI photospheric value: 7±1 G at the EIS slit Using detected fast speed V f =0±30km/s, n and T -> B=0.7±0.7G and =6.4±3.1 Using Thompson & Myers (009) speeds of km/s -> more possibilities West et al. (011)

25 EIT/EUV waves Superimposed EIS(Hinode) slit on ST EUVI 195Å at similar times SiX 58/61 lines are used (similar temperature to the strongest line of FeXII 195 in EUVI) -> density of 3.4±0.8x10 8 cm -3 MDI photospheric value: 7±1 G at the EIS slit Using detected fast speed V f =0±30km/s, n and T -> B=0.7±0.7G and =6.4±3.1 Using Thompson & Myers (009) speeds of km/s -> more possibilities West et al. (011)

26 Alfvén waves Tomczyk et al. (007): Coronal Multi-Channel Polarimeter, CoMP (ground based observations): The waves travel at supersonic speeds, The waves have a transverse (perp. to B) V component and travel along magnetic field, The waves are incompressible (no density perturbations observed) Alfvén waves

27 Alfvén waves Seismology: Phase speeds obtained in this study are a projection onto the POS (the speed multiplied by sin(), where is the angle between LOS and the direction of wave propagation) Assuming typical electron density of 10 8 cm -3 and measured phase speeds Mm/s -> B=8 and 6 G. V A B 4 Tomczyk et al. (007)

28 Prominences NOAA 1091 Hinode CaII SOT observations Threads of prominence show oscillatory motion with periods s Wave speed estimated to be >1050 km/s Assuming plasma density cm -3 -> magnetic field strength for propagating Alfvén waves ~50G Okamoto et al. (007)

29 Streamers With the white light coronagraph data streamer wave observations Periods of about 1 hr, wavelength -4 solar radii, an amplitude of about a few tens of solar radii, and a propagating phase speed in the range km/s The motions were apparently driven by the restoring magnetic forces resulting from the CME impingement, suggestive of magnetohydrodynamic kink mode propagating outward along the plasma sheet of the streamer Using Alfvén speed formula B is calculated in places (parameters from Chen & Hu (001)): 5R s : V sw =100 km/s, n=1x10 5 cm -3 -> B=0.045G 10R s : V sw =00 km/s, n=x10 5 cm -3 -> B=0.01G Chen et al. (010)

30 QPP QPP: oscillations in solar flares Often showing multi-periodicity: Inglis & Nakariakov (009): 1s, 18s, 8s; Nakariakov et al. (010) 13s & 40s (radio band) Recent observations by Van Doorsselaere et al. (011) from LYRA (PROBA) (irradiance measurement) show multi-periodicity Nakariakov & Melnikov (009)

31 Van Dooresselaere et al. (011) QPP

32 QPP Recent observations by Van Doorsselaere et al. (011) from LYRA (PROBA) (irradiance measurement) show multi-periodicity: 63-88s and 8.5s, ratio r=8.8. Interpretation: modulation of intensity of flare emission -> slow and sausage waves Classical waveguide model (pressure balance between internal and external medium) Short wavelength limit fundamental mode, equal loop length, fast sausage mode V Ai, slow mode c si Long wavelength limit fundamental mode, equal loop length, fast sausage mode V Ae, slow mode c Ti Van Dooresselaere et al. (011) V 1 c r Ae Ti V Ai rc si i 0.14 r V V rc 1 c Ae Ai si Ti 1 V Ai V 1 c Ai si r p i e V V i Ae Ai Bi i c c e si se e p e V V i 1 1 Be Ai Ae e 1 i 1 1 i

33 QPP Long wavelength limit fundamental mode, equal loop length, fast sausage mode V Ae, slow mode c Ti V Ae 1 c Ti rc 1 c si Ti 1 V Ai r V V Ae Ai V 1 c Ai si r e 1 i 1 1 i max i 1 i 18,min,max Van Dooresselaere et al. (011)

34 Adiabatic index Van Dooresselaere et al. (011) : EIS (Hinode) obseration of P V =314±83s, P I =344±61s -> slow wave

35 Adiabatic index Linearized MHD theory (e.g. Goossens 003) + polytropic relation p 1 0 K 1 eff eff p p T 1 T eff 1 0 Scatter plot+ least square eff =1.10±0.0 5/3 Van Dooresselaere et al. (011)

36 Conclusions Coronal seismology; Observe and model coronal waves Compare Measure physical parameters Adjust/improve model (e.g. clue about damping mechanisms of oscillations) Geometry effect on magnetic field determination Quiet Sun parameters from EUV waves Magnetic field determination using Alfvén waves Multi-periodicity: determination of scale height,, loop expansion