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

Introduction ''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,  O’Shea et al., 2001, Astron. Astrophys. 368,  McAteer et al. 2004, Astrophys. J. 602, 436 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 dynamic interaction of electromagnetic, plasma or whistler waves with energetic particles trapped in closed magnetic fields during solar radio bursts.  Aschwanden, 1987, Solar Phys. 111, 113.  Fleishman et al., 2002, Astron. Astrophys., 385,

''Medium period'‘ (seconds to several minutes) QPPs detected in microwave, white light, EUV and X-ray emission : magnetohydrodynamic (MHD) processes in solar flaring loops. “Medium” QPPs are interesting due to their possible association with the fundamental physical processes operating in flares: spontaneous and triggered energy releases, magnetic reconnection, thermodynamics, MHD oscillations, 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. 1. Introduction

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

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

Integrated, or spatially unresolved, signal 1. Spatial resolved signal – analysis of images 2. 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 NoRH: Analysis of images with high temporal (100 ms) and angular (5’’ and 10’’ at 34 GHz and 17 GHz) resolution.

Purpose of our study All of the events in previous studies were selected based on the visible presence of well-indicated QPP patterns in the time profiles. The purpose is to carry out a statistically broader study based upon the analysis of twelve well-resolved “single flaring loops”, seeking answers to the 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 is multi-periodicity a common feature of QPPs? 3. What is the characteristic evolution of the QPPs spectrum during the flare? 2.

Flares under study Mar-2002 The microwave source should: 1.be well resolved by NoRH, that is, its length should be larger than the beam size at 17 GHz; 2.have a single loop shape; 3.be located near the solar disk centre, or have relatively small intensity if located near the limb, reducing the influence of positional ambiguity in the image synthesis. The visible presence or absence of QPPs in time profiles are not accounted for in the selection.

Method of analysis of time profiles 4. Fourier periodogram of R Wavelet spectrum of Auto-correlation function R( )modulation depth 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 the smoothing (filtering) procedure. Set of spectral components: P and W

Method of analysis of time profiles 4. For the final analysis and classification, we have chosen only those oscillatory patterns which satisfy the following criteria. 1.The oscillations should be well pronounced in the data from both instruments (NoRH and NoRP) and have similar frequency-time behaviour of the wavelet spectra. 2. They should be seen in periodograms of auto-correlation and cross-correlation functions at 17 and 34 GHz. 3. The value of their period should not depend upon the selected low frequency filter (the specific value of τ ), at least inside the corresponding error bar. 4. The number of observed periods of QPPs should be at least three.

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

Testing the method 5.  = 15 s

 = 20 s Testing the method 5.

 = 25 s Testing the method 5.

 = 30 s Testing the method 5.

 = 40 s Testing the method 5.

Testing the method 5.

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

1.In ten out of the twelve events under study, at least one significant oscillation with a period in the range from 5–60 s has been found. This means that QPPs is quite a common phenomenon in solar flares. 2.The quality of the oscillations is rather low; it mostly varies in the range 12 to 40, with an average of 25, in only one case the quality reaches Two oscillations were detected in two events, and one event was found to have three pronounced oscillations. 4.In only two events significant periodicities, which would satisfy the imposed selection rules, were not found. Results of analysis of QPPs in single flaring loops 6. Kupriyanova, Melnikov, Nakariakov, Shibasaki, 2010, Sol. Physics, 267, 329

Results of analysis of QPPs in single flaring loops –5 min Reznikova, Shibasaki A&A 525, A112 (2011)

According to the time evolution, we divide the QPPs into four types: 1.those with stable mean periods in the range 5 – 20 s (eight events); 2.those with spectral drift to shorter periods in the rise phase of the burst (two events); 3.those with drift to longer periods in the decay phase (two events); 4.those with an X-shaped drift between periods of 20 – 40 s (one event). Results of analysis of QPPs in single flaring loops 6.

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

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

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

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

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

Discussion 7. Physical mechanisms of QPPs are 1.Periodic regimes of spontaneous magnetic reconnections 2.Magnetic reconnections, which induces periodically by external oscillations 3.Varying electric current in the equivalent RLC-contour 4.MHD-oscillations in an emitting plasma structures

Discussion 7. L is loop length n is a harmonic number v ph is the phase velocity Period of the standing MHD wave or of alfven wave: 4.MHD-oscillations in an emitting plasma structures. 2 L nv ph P = z 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?

Integrated, or spatially unresolved, signal 1. Spatial resolved signal – analysis of images 2. 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 NoRH: Analysis of images with high temporal (100 ms) and angular (5’’ and 10’’ at 34 GHz and 17 GHz) resolution.

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

The methodology of analysis of images 2. Modulation depth  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.

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

Dynamics of the radio source 4. d

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

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

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

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

Positions of the sources of different spectral components. 6.

Modulation depth Positions of the sources of different spectral components.

6. Modulation depthAuto-correlation function Positions of the sources of different spectral components.

6. Wavelet Power SpectrumGlobal WPSPeriodogram of auto-correlation function Positions of the sources of different spectral components.

6. Positions of the sources of different spectral components.

Dynamics of the radio source 4. Wavelet Power SpectrumGlobal WPS

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

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

L is loop length n is a harmonic number v ph is the phase velocity 2 L nv ph P = Period of the standing wave: Discussion of the oscillating modes 8. a / L  1 / 5 1. Acoustic mode T 0 = 7  10 6 K P A I ≈ 165 s P A II ≈ 82 s P A III = 55 s 2. Sausage mode n 0 = cm -3 B 0 = 70 G P S I does not exist P S II = 26 s P S III = 23 s 3. Kink mode n 0 = 5  cm -3 B 0 = 180 G P K I = 31.7 s P K II = 16.8 s P K III = 11.7 s 4. Ballooning mode n 0 = 5  cm -3 B 0 = 180 G P B I = 30.6 s P B II = 15.7 s P B III = 10.8 s P obs I ≈ 31.2 ± 2.5 s P obs II ≈ 18.7 ± 1.0 s P obs III ≈ 11.5 ± 0.4 s Observable periods

Horizontal kink oscillations 9. Dulk and Marsh, 1982: S19W48θ > 48° in the northern footpoint θ < 48° in the southern footpoint θ ≈ 70° in the loop top ΔI /I ≈ 2–5 % in the loop top and footpoints Δ θ ≈ 1.5–3° δ = 4.7 B ≈ const

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

d BI a 10. Vertical kink oscillations

BI a 10. Vertical kink oscillations d

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

1. Quasi-periodic pulsations (QPPs) with at least three simultaneously existing spectral components with periods about 30 s, 20 s and 10 s were detected during the decay phase of solar flare on 03 July 2002, observed with NoRH. 2. It is shown that the source of the QPPs with period 30 s has its maximum amplitude in the inner region of the loop, between the footpoints. QPPs with period 20 s are localized at the periphery of the loop, mainly in the outer parts of the footpoints. The spatial distribution of oscillations with period about 10 s contains three regions of high QPP amplitudes: two near the footpoints and one in the middle of the flaring region. 3. It is shown that the observed properties of the spectral components are most accurately described by the fundamental, second and third harmonics of the kink mode standing waves. This is the first identification of the kink mode in flare loops which is based on strict limitations derived from data on the spatial structure of a pulsating flare region. 11. Conclusions Kupriyanova, Melnikov, Shibasaki, 2013, Sol. Physics, 284, 2, 559 Kupriyanova, Melnikov, Shibasaki, 2013, PASJ, in press

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