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Seismology of Stellar Coronal Flares , 21-24 May 2013, Leiden

Seismology of Stellar Coronal Flares , 21-24 May 2013, Leiden. Quasi-Periodic Pulsations as a Feature of the Microwave Emission Generated by Solar Single-Loop Flares. 1. Introduction.

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Seismology of Stellar Coronal Flares , 21-24 May 2013, Leiden

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  1. Seismology ofStellar Coronal Flares, 21-24 May 2013, Leiden Quasi-Periodic Pulsations as a Feature of the Microwave Emission Generated by Solar Single-Loop Flares

  2. 1. Introduction Quasi-periodic pulsations (QPPs) during solar flares can be caused by the modulation of the intensity of radio emission or by the modulation of the acceleration of electrons. The periods of QPPs can be split into several bands, from sub-seconds up to tens of minutes. • ''Short'‘(sub-second) QPPs in the m-dm-cm radio emission : • kinetic processes caused by the dynamicinteraction of electromagnetic, plasma or whistler waves with energetic particles trapped in closedmagnetic fields during solar radio bursts. • Aschwanden, 1987, Solar Phys. 111, 113. • Fleishman et al., 2002, Astron. Astrophys.,385, 671. • ''Long'‘QPPs, with periods from several to tens of minutes : active region dynamics and global oscillations of the Sun • Gelfreikh et al., 1999, Solar Phys. 185, 177. • Shibasaki, 2001, Astrophys. J. 550, 1113. • O’Shea et al., 2001, Astron. Astrophys. 368, 1095. • McAteer et al. 2004, Astrophys. J. 602, 436

  3. 1. Introduction ''Medium period'‘(seconds toseveral minutes) QPPs detected in microwave, white light, EUVand X-ray emission : magnetohydrodynamic (MHD) processes insolar flaring loops. “Medium” QPPs are interesting dueto their possible association with the fundamental physical processes operating in flares:spontaneous and triggered energy releases, magnetic reconnection, thermodynamics, MHDoscillations, particle acceleration and other kinetic effects Observations with high spatial resolution give the possibility -- to define size of a flaring area, - to study a spatial structure of QPPs, and - to identify MHD mode of pulsations.

  4. Радиогелиограф в Нобеяме Nobeyama Radioheliograph Analysis of images Temporal resolution: 0.1 s Spatial resolution: 10’’ at 17 GHz 5’’ at 34 GHz 2009 г. 4

  5. Nobeyama Radiopolarimeters Frequencies: 1, 2, 3.75, 9.4, 17, 35, 80 GHz Analysis of full Sun fluxes with high temporal resolution (0.1 s).

  6. Integrated, or spatially unresolved, signal 1. We have used NoRP : the total flux density at f = 17 GHz and f = 35 GHz NoRH : the mean correlation amplitude at f = 17 GHz and f = 34 GHz 2. Spatial resolved signal – analysis of images NoRH: Analysis of images with high temporal (100 ms) and angular (5’’ and 10’’ at 34 GHz and 17 GHz) resolution.

  7. 2. Purpose of our study All of the events in previous studies were selected based on the visible presenceof well-indicated QPP patterns in the time profiles. The purpose is to carry out a statistically broader studybased upon the analysis of twelve well-resolved “single flaring loops”, seeking answers tothe following questions: 1. Is the presence of QPPs in a single flaring loops a common phenomenon? 2. How often may more than one spectral component occur in a single flaring loop, and ismulti-periodicity a common feature of QPPs? 3. What is the characteristic evolution of theQPPs spectrum during the flare?

  8. 3. Flares under study • The microwave sourceshould: • be well resolved by NoRH, that is, its length should be larger than the beamsize at 17 GHz; • have a single loop shape; • be located near the solar disk centre, orhave relatively small intensity if located near the limb, reducing the influence of positionalambiguity in the image synthesis. 14-Mar-2002 The visible presence or absence of QPPs in time profiles are not accounted for in the selection.

  9. modulation depth Fourier periodogram of R Auto-correlation function R( ) Set of spectral components: P and W Wavelet spectrum of Method of analysis of time profiles 4. We have used NoRP : the total flux density at f = 17 GHz and f = 35 GHz NoRH : the mean correlation amplitude at f = 17 GHz and f = 34 GHz This was done for a broad range of smoothing intervals τ form 5 s to 60 s, allowing us to understand whether the spectral peak found is real or produced by thesmoothing (filtering) procedure.

  10. Method of analysis of time profiles 4. • For the final analysis and classification, we have chosen only those oscillatory patternswhich satisfy the following criteria. • The oscillations should be well pronounced in thedata from both instruments (NoRH and NoRP) and have similar frequency-time behaviourof the wavelet spectra. • 2. They should be seen in periodograms of auto-correlationand cross-correlation functions at 17 and 34 GHz. • 3. The value of their period shouldnot depend upon the selected low frequency filter (the specific value of τ ), at least insidethe corresponding error bar. • 4. Thenumber of observed periods of QPPs should be at least three.

  11. is time: i = 0..N–1,N is number of points in time series Testing the method 5. Amount of tests is 500 Model function : s s s

  12. Testing the method 5. t = 15 s

  13. t = 20 s Testing the method 5.

  14. t= 25 s Testing the method 5.

  15. t= 30 s Testing the method 5.

  16. t= 40 s Testing the method 5.

  17. Testing the method 5.

  18. Testing the method 5. Results for period >90 % >96 % >99 % >99 %

  19. Results of analysis of QPPs in single flaring loops 6. • In ten out of the twelve events under study, at least one significant oscillation with a periodin the range from 5–60 s has been found. This means that QPPs is quite a common phenomenon in solar flares. • The quality of the oscillations is ratherlow; it mostly varies in the range 12 to 40, with an average of 25, in only one case thequality reaches 85. • Two oscillations were detected in two events, and one event was foundto have three pronounced oscillations. • In only two events significant periodicities, whichwould satisfy the imposed selection rules, were not found. Kupriyanova, Melnikov, Nakariakov, Shibasaki, 2010,Sol. Physics, 267, 329

  20. 2.5–5 min Reznikova, ShibasakiA&A 525, A112 (2011) Results of analysis of QPPs in single flaring loops 6.

  21. Results of analysis of QPPs in single flaring loops 6. • According to the timeevolution, we divide the QPPs into fourtypes: • those with stable mean periods in the range5 – 20 s (eight events); • those with spectral drift to shorter periods in the rise phase of theburst (two events); • those with drift to longer periods in the decay phase (two events); • those with an X-shaped drift between periods of 20 – 40 s (one event).

  22. 6. Results of analysis of QPPs in single flaring loops.Type 1 – QPPs with stable period 28 June 2002

  23. 6. Results of analysis of QPPs in single flaring loops.Type 1 – QPPs with stable period 18 Jule 2002

  24. 6. Results of analysis of QPPs in single flaring loops.Type 2 – QPPs with spectral drift to shorter periods 31 May 2002

  25. 6. Results of analysis of QPPs in single flaring loops.Type 3 – QPPs with spectral drift to longer periods 3 July 2002

  26. 6. Results of analysis of QPPs in single flaring loops.Type 4 – QPPs with X-shaped drift 21 May 2004

  27. Discussion 7. • Physical mechanisms of QPPs are • Periodic regimes of spontaneous magnetic reconnections • Magnetic reconnections, which induces periodically by external oscillations • Varying electric current in the equivalent RLC-contour • MHD-oscillations in an emitting plasma structures

  28. 2 L P = nvph L is loop length n isa harmonic number vph is the phase velocity Discussion 7. • MHD-oscillations in an emitting plasma structures. z Period of the standing MHD wave or of alfven wave: Dispersion equation of the MHD modes in the simplest magnetic tube: Preliminary restriction on the MHD mode (or modes) produces the QPPs observed. That is spatial distribution of amplitudes and phases of QPPs in a flaring loop?

  29. Integrated, or spatially unresolved, signal 1. We have used NoRP : the total flux density at f = 17 GHz and f = 35 GHz NoRH : the mean correlation amplitude at f = 17 GHz and f = 34 GHz 2. Spatial resolved signal – analysis of images NoRH: Analysis of images with high temporal (100 ms) and angular (5’’ and 10’’ at 34 GHz and 17 GHz) resolution.

  30. 1. Analysis of the integrated (spatially unresolved) signal. The flare on 3 July 2002 Inglis and Nakariakov, 2009, Astron. Astrophys., 493, 259 Kupriyanova, Melnikov, Nakariakov, Shibasaki, 2010,Sol. Physics, 267, 329 Kupriyanova, Melnikov, Shibasaki, 2013,Sol. Physics,284, 2, 559

  31. Modulation depth The methodology of analysis of images 2. • Stabilization of images; • study of the behaviour of the source; • data reduction; • data handling using the methods of autocorrelation, Fourier and wavelet analysis; • analysis of spatial features of QPPs; • identifying the oscillation modes which are able to produce observed QPPs.

  32. Single flaring loop Analysis of the spatial structure. Loop geometry 3. 1 pix = 2.5’’

  33. d Dynamics of the radio source 4.

  34. The analysis of the spatial structure of QPPs. 5. Set of 211 images, Dt = 1 s

  35. The analysis of the spatial structure of QPPs. 5. For each box: Set of 211 images, Dt = 1 s

  36. Search of an area with significant signal 5. For each box:

  37. Auto-correlation function R( ) Set of spectral components: P and W Wavelet spectrum of Where are an areas with maximal spectral powers ? Where are an areas with similar periods ? and Periodogram of R Spectral analysis of time profiles 5. For each box:

  38. 6. Positions of the sources of different spectral components.

  39. Modulation depth 6. Positions of the sources of different spectral components.

  40. Modulation depth Auto-correlation function 6. Positions of the sources of different spectral components.

  41. Wavelet Power Spectrum Global WPS Periodogram of auto-correlation function 6. Positions of the sources of different spectral components.

  42. 6. Positions of the sources of different spectral components.

  43. Wavelet Power Spectrum Global WPS Dynamics of the radio source 4.

  44. Five principal modes in a simplest coronal loop 7. sausage (|B|, r) kink torsional (incompressible) acoustic (r, V) flute (|B|, r)

  45. Five principal modes in a simplest coronal loop 7. • kink horizontal • sausage • kink vertical • acoustic (the second harmonic)

  46. 2 L P = nvph L is loop length n isa harmonic number PobsI ≈ 31.2 ± 2.5 s PAI ≈ 165 s a / L  1 / 5 Observable periods vph is the phase velocity • Acoustic mode PobsII ≈ 18.7 ± 1.0 s PAII ≈ 82 s T0 = 7106 K PAIII = 55 s PobsIII ≈ 11.5 ± 0.4 s 2. Sausage mode n0 = 1011 cm-3 B0 = 70 G PSI does not exist 4. Ballooning mode PKI = 31.7 s PBI = 30.6 s 3. Kink mode PSII = 26 s n0 = 51010 cm-3 n0 = 51010 cm-3 PBII = 15.7 s PKII = 16.8 s B0 = 180 G PSIII = 23 s B0 = 180 G PBIII = 10.8 s PKIII = 11.7 s Discussion of the oscillating modes 8. Period of the standing wave:

  47. S19W48 θ> 48° θ< 48° θ≈ 70° in the northern footpoint in the southern footpoint in the loop top Dulk and Marsh, 1982: ΔI /I ≈ 2–5 % Δ θ≈ 1.5–3° B ≈ const Horizontal kink oscillations 9. δ = 4.7 in the loop top and footpoints

  48. Aschwanden and Schrijver, 2011: is maximal at the loop top Dulk and Marsh, 1982: Vertical kink oscillations 10. Observations Fundamental mode Δθ<<1 δ = 4.7

  49. Vertical kink oscillations 10. B I a d

  50. Vertical kink oscillations 10. B I a d

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