1. SPATIALLY RESOLVED MINUTE PERIODICITIES OF MICROWAVE EMISSION DURING A STRONG SOLAR FLARE Kupriyanova E. 1,Melnikov V. 1, Shibata K. 2,3, Shibasaki K. 4 1 Pulkovo Observatory, Russia 2 Kyoto University, Japan 3 Kwasan and Hida Observatory, Japan 4 Nobeyama Solar Radio Observatory,Japan

2. 2 Until recent time, quasi-periodic pulsations (QPPs) with periods from 1 to 15 minutes have been observed in solar microwave emission above the sunspots only ( Gelfreikh et al., Solar Phys., V.185, P.177, 1999 ). Last time, QPPs with that periods became to appear during the flares also. In the microwaves. They was discribed in the papers: Zaitsev et al., Cosmic Research, V.46, P.301, 2008; Meszarosova et al., Astron. Astrophys., V.697, P. L108, 2009; Sych et al., Astron. Astrophys., V.505, P.791, 2009; Reznikova, Shibasaki, Astron. Astrophys., V.525, P.A112, 2011; Kim et al., The Astrophysical Journal Letters, V. 756, P. L36, 2012 In X-rays, minute QPPs were studied by Jakimiec and Tomczak (Solar Phys., V.261, P.233, 2010) Studies of these oscillations became especially topical in view of their possible relationship to flare energy release and heating of the solar corona: Nakariakov and Zimovets, Astrophys. J.L., V.730. P.L27, 2011; Zaitsev and Kislyakova, Radiophys. Quant. El., V.55. P.429. 2012. Introduction Study of the spatial structure of QPPs with periods of several minutes in the microwave emission of the solar flare on May 14, 2013. The aim 1. 2.

3. 3 Methodology. Analysis of QPPs in Time Profiles 3. 4. NoRH radio maps at 17 and 34 GHz are built (time cadence is 1 s); 5. small boxes are selected in a different parts of flaring area; 6. time profiles of the integrated fluxes are calculated for each box; 7. the time profiles are studied using the method discribed in items 1-3. Analysis of spatial structure of QPPs 1. Time profiles of high-frequency component are calculated for each box using formula (1) Here F (t) is original flux (Stokes I or Stokes V) from a whole box, F sm (t) is its low-frequency background obtained using method of running average with time intervals  = 30  500 s. 2. The time profiles  (  ) are studied using methods of correlation, Fourier and wavelet analysis. 3. For each  : auto-correletion functions R(  ) and their Fourier periodograms; wavelet spectra of .

4. 4 Integrated (spatially unresolved) time profiles Fig. 1 4.

5. 5 Cross-correlations of NoRH and NoRP signals The time profiles of the NoRH correlation amplitudes are well correlated with NoRP integrated flux Fig. 1. Their cross-correlation function at 17 GHz are shown in Fig. 2 (upper panel), and that for 34 GHz(35 GHz) (downer panel). The total time profiles (without detrending) of the NoRH correlation amplitudes are well correlated at frequences 17 GHz and 34 GHz (Fig. 3) with correlation coefficient r ≈ 1.0. The total time profiles (without detrending) of the NoRP fluxes are well correlated at frequences 17 GHz and 34 GHz (Fig. 3) with correlation coefficient r ≈ 0.8. Fig. 2Fig. 3

6. 6 Phase of flare maximum 01:06:30 – 01:08:00 UT. QPPs with period 50 s are well pronounced at both frequincies. The time profile at 34 GHz delays relatively to time profile at 17 GHz by 12 s Spectral properties of the integrated signal (correlation amplitudes) 5.

7. 7 Dynamic of the source of microwave emission 6. Time profiles of emission fluxes intergrated over the whole area

8. Dynamic of the source of microwave emission 6. N = 1800 from 01:00:00 to 01:29:59 UT Variance map Data cube is stable

9. 9 Analysis of spatial structure of QPPs 7. Flare maximum phase QPPs with P ≈1 min reveal obvious delays between time profiles from large loop relatively to time profile of the small loop

10. 10 Spectral analysis of QPPs 8.8. Period, s Spectral power From violet to orange lines  = 15, 30, 60, 90, 120, 150,180 s Periods detected: 50 s, 60 s, 100 s, 150 s

11. 11 Cross-correlation analysis of QPPs 9. Spectral power The fluxes from box 1, box 2, and box 3 in the big loop delay with respect to the flux from box 0 in the small loop by  t ≈ 36–40 s

12. Standing MHD modes trapped in magnetic tube. P obs ≈ 50–180 s Observed periods Kink mode P K I = 12–17 s P K II = 6–9 s P K III = 4–9 s T 0 = 5·10 6 ―2  10 7 K n 0 = 5·10 10 –10 11 cm -3 B 0 = 300 G L = 22 Mm P SMA I ≈ 61–120 s P SMA II ≈ 32–60 s P SMA III = 20–40 s Slow magneto- acoustic mode Sausage mode P S I does not exist P S II does not exist P S III = 3–4 s Discussion. MHD-oscillations Balloning mode P B I = 11–16 s P B II = 6–8 s P B III = 4–6 s 10. a/L ≈ 0.2

13. Standing MHD modes trapped in magnetic tube. P obs ≈ 50–180 s Observed periods Kink mode P K I = 65–92 s P K II = 34–48 s P K III = 24–33 s T 0 = 5·10 6 ―2  10 7 K n 0 = 5·10 10 –10 11 cm -3 B 0 = 100 G L = 40 Mm P SMA I ≈ 173–245 s P SMA II ≈ 87–122 s P SMA III = 58–82 s Slow magneto- acoustic mode Sausage mode P S I does not exist P S II does not exist P S III = 15–21 s Discussion. MHD-oscillations Balloning mode P B I = 63–89 s P B II = 32–45 s P B III = 22–31 s 10. a/L ≈ 0.2

14. 14 L — loop length n — harmonic number v ph — phase velocity The period of the standing MHD wave is: 2 L nv ph P = Dispersion equation for MHD mode in a simplest magnetic loop: L, N 0,B 0,T 0 N e, B e, T e The periods can be caused by SMA mode of MHD oscillations in a loop P obs ≈ 1 min Periods observed Discussion. MHD oscillations. Standing waves? But... L 2 = 22 MmL 1 = 40 Mm Period is the same in the both loops 10.

15. Induced oscillations 11. The small loop: T 0 = 5·10 6 K n 0 = 5·10 10 cm -3 B 0 = 300 G The fundamental P SMA I ≈ 61 s Second harmonic P SMA II ≈ 60 s T 0 = 2·10 7 K n 0 = 5·10 10 cm -3 B 0 = 300 G T 0 = 5·10 6 –10 7 K n 0 = 5·10 10 –10 11 cm -3 B 0 = 100–300 G v ph ≈ 330–510 km/s P obs ≈ 1 min Observed periods 15  t ≈ 40 s Delays The big loop:  L = v ph ·  t  L ≈ 16000 km SMA waves L = 22 Mm L = 40 Mm LL

16. 16 Conclusions Spatially resolved quasi-periodic pulsations (QPPs) periods P = 50, 60, 100, 155, 180 s are found in microwave emission during solar flare on May 14, 2013. Data of Nobeyama Radioheliograph (NoRH) and Radio Polarimeters (NoRP) at 17 GHz and 34 GHz are used. The QPPs with the same period of P ≈ 1 min originate from two flaring loops having different lengths L during the impulsive phase of the flare. These QPPs in the big loop delays over the QPPs from the small loop by  t ≈ 40 s. The periods QPPs in the small loop correspond to the standing SMA mode. QPPs in the large loop are induced by oscillation of the small loop.

17. Thank you for your attention !

18. 18 But... Slow magnetoacoustic waves in two-ribbon flares? 11. The loop in the middle appears after the border loops

22. 22 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 :

23. 23 Testing the method 5.  = 15 s

24. 24  = 20 s Testing the method 5.

25. 25  = 25 s Testing the method 5.

26. 26  = 30 s Testing the method 5.

27. 27  = 40 s Testing the method 5.

28. 28 Testing the method 5.

29. 29 Results for period > 90 % > 96 % > 99 % Testing the method 5.