1. OBSERVATION OF MICROWAVE OSCILLATIONS WITH SPATIAL RESOLUTION V.E. Reznikova 1, V.F. Melnikov 1, K. Shibasaki 2, V.M. Nakariakov 3 1 Radiophysical Research Institute, Nizhny Novgorod, Russia 2 Nobeyama Radio Observatory, NAOJ, Japan 3 University of Warwick, UK NRO, 17 - March, 2005

2. Quasi-periodical pulsations with short periods 1-20 s Observations without spatial resolution: Kane et al. 1983, Kiplinger et al. 1983, Nakajima 1983, Urpo et al. 1992. Only a few observations with spatial resolution: Asai A. et al. 2001, Melnikov et al. 2002, Grechnev V.V. et al. 2003. Nobeyama Radioheliograph Frequency: 17 GHz, 34 GHz Spatial resolution: 10" (17GHz) 5" (34GHz) Temporal resolution: 0.1 sec

3. The flare of 12-Jan-2000

4. Time profile of total fluxes and spectrum (NoRP)

5. Microwave time profiles (NoRH ) (a,c) NoRH time profiles of the averaged correlation amplitude:  (t) (b, d) Modulation depth :  0 – slowly varying component of the emission, obtained by 10-s smoothing the observed signal  (t)

6. Fourier spectra Radio pulsation analysis (NoRH) - 2 P 1 = 14 - 17 s P 2 = 8 - 11 s

7. Analysis of HXR emission pulsation (WBS/Yohkoh) Fourier spectra

8. Spatial structure of microwave and XR-sources L = 2.5  10 9 cm (~ 34") d = 6  10 8 cm (~ 8") L = 2.5  10 9 cm (~ 34") d = 6  10 8 cm (~ 8")

9. Pulsations in different parts of the loop Two main spectral components: P 1 = 14 - 17 s (more pronounced at the apex ) P 2 = 8 - 11 s (relatively stronger at the loop legs) ∆F/F = [F(t)- F 0 ]/F 0

10. Phase shift between oscillations in different parts of the loop LT NFP SFP

11. Results of analysis: Pulsations in microwaves and HXR without spatial resolution are synchronous Observations with spatial resolution show pulsations to exist everywhere in the source they are synchronous at two frequencies 17 and 34 GHz two dominant spectral components with periods P 1 = 14-17 s and P 2 = 8-11 s are clearly seen everywhere in the source pulsations at the legs are almost synchronous with the quasi- period P 2 = 8-11 s at the loop apex the synchronism with the legs’ pulsations is not so obvious, but definitely exists on the larger time scale, P 1 = 14-17 s phase shift between oscillations from 3 different sources is very small for the P 1 component, less than 0.5rad or 1.3s. However it is well pronounced for the P 2 spectral component.

12. Spectrum slope in different parts of the loop  = ln (F 34 /F 17 ) / ln (34/17) Near footpoints  0

13. What is the origin of the depression of radiation at 17 GHz in the upper part of the loop? Cyclotron absorption? Gyrosinchrotron self-absorption? Razin suppression?

14. What is the reason for low frequency depression in the upper part of the loop? Cyclotron absorption? - MDI/SOHO: at the photosphere level В ≤ 100G around SFP В ≤ 400G around NFP => f b ~ 1 GHz ↓↓ f peak ~ 20 GHz => spectral peak was at least at s = f peak / f b ~ 20 No!

15. What is the reason for low frequency depression in the upper part of the loop? Gyrosinchrotron absorption? If τ > 1 at 17 GHz => -the modulation depth of the emission is expected to be much less pronounced at 17 GHz; -time profiles of the emission intensity would be smoother than at 34 GHz;

16. If the modulation of the flux is due to temporal magnetic field variations : f < f peak ( thick ) : f > f peak ( thin ) : -the oscillations of the flux at low frequencies (optically thick case) and high frequencies (optically thin case) would be in anti-phase; I ν  В 0.90  -0.22  В 4 I ν  В –0.5-0.085   В -0.9 Dulk & Marsh, 1982

17. The observations show just opposite: - modulation depth at 17 GHz is even higher than at 34 GHz; - oscillations are in phase at both frequencies; - observable Тв is less than it is expected from theory; ↓↓ Gyrosinchrotron absorption - No!

18. Computed Тв(f) dependence for the optically thick source:  =5.3;  =75  ; Using Dulk, 1985 17GHz 34GHz B= 100 G B=400 G B=750 G

19. Razin suppression (Razin 1960) in the medium, where n ν f B ) peak frequency depends on the Razin frequency: in solar flaring loops: Melnikov, Gary and Nita, 2005 (in press)

20. Microwave diagnostic of physical parameters inside the loop Model simulation of gyrosynchrotron spectrum Model simulation of gyrosynchrotron spectrum: ~ 10 11 сm -3 N ~ 10 11 сm -3 B Loop apex: B  70 G B Loop legs: B  100 G ~ 10 11 сm -3 N ~ 10 11 сm -3 B Loop apex: B  70 G B Loop legs: B  100 G LT FP

21. Electron’s life time in the loop: (for E e > 160 keV) Decay time scales: n o = 10 11 сm -3 ; L = 2.5  10 9 сm;  =3÷5 E e = 1 MeV =>  l ~ 26 s;  dec ~ 4÷5 s High value of N 0 => short decay time scales (2÷5 s) for burst sub peaks

22. SXR - diagnostic at the time of burst maximum (GOES)

23. SXR- diagnostic at the later stage of the burst (Yohkoh/SXT) Column emission measure per pixel:

24. Observable shift of the brightness peaks between 17 and 34 GHz 17 GHz 34 GHz

25. Cross-section spatial profiles of the intensity for a model flaring loop 34 GHz 17 GHz plasma high energy electrons

26. Most probable mechanisms for the quasi-periodic microwave pulsations: Aschwanden, 1987 (for a review) oscillation of В in the loop; variation of angle between В and line of sight; variation of mirror ratio in the loop, modulating the loss cone condition; quasi periodical regime of acceleration / injection itself; P~10 s => important role of МHD- oscillations in coronal loop during the flare

27. Amplitude of magnetic field perturbations Assuming the pulsations are produced by variations of the value В in flaring loop:  I/I  15 %, if  = 5 => relative perturbation of B  B/B  3  4% variations of the viewing angle  between the B and the line-of-sight: if   80 ,  =5    12  15  I ν  В -0.22+0.90  I ν  (sin  ) -0.43+.65  Dulk & Marsh, 1982

28. Possible MHD-modes of magnetic tube oscillations in coronal conditions: “sausage” Zaitsev & Stepanov, 1975 Edwin & Roberts, 1983 Mihailovsky, 1981 “kink” “ballooning“ m – azimuthal mode number

29. Dispersive curves of MHD modes Using the loop parameters derived from microwave & X-ray diagnostics: C A0 = 600 km/s C Ae = 3,300 km/s C s0 = 340 km/s C se = 200 km/s sausage (m=0) - solid ; kink (m=1) - dotted ; ballooning (m=2) - dashed (m=3) - dashed-dotted } } } } } } l = 1 l = 2 l = 3 l = 4 l = 5 l = 6

30. Interpretation of the pulsations with Р 1 in terms of the Global Sausage Mode: P 1 =16s & λ=2L k = 2π/λ ω=2 π/P ↓↓ V ph = ω/k = 3130 km/s corresponding normalised longitudinal wave number ka ≈ 0.54 => a ≈ 4.3 Mm

31. Interpretation of the pulsations with Р 1 = 14÷17s in terms of the Global Sausage Mode: Nakariakov, Melnikov & Reznikova – 2003 ( A&A 412, L7) ~ 14 s lower limit: ~ 17 s ~ 17 s upper limit: (from existence condition)

32. Interpretation of the pulsations with Р 2 in terms of the kink mode (2 d and 3 d harmoniks) P 2 = 9 s λ = L λ = L/2

33. Conclusions Interpretation of quasi-periodic 16s radio pulsations in terms of the Global Sausage Mode (with the nodes at the footpoints) explains all the observational findings for P 1 component The second periodicity P 2 = 9s can be associated with several modes: - Kink mode (2 d or 3 d longitudinal harmonic) - Ballooning mode (2 d longitudinal harmonic)

34. Thank you for the attention!

35. What about f-f absorption? N = 10 11 cm -3 B = 50 G d = 6×10 8 cm T = 3×10 6 K Θ = 80°

36. Pressure balance equation

37. I =  /   (1  e  ) Transfer equation solution: 1) τ =   L << 1- optically thin source I (t) ≈  (t) L;   (t) ∞ n (t) => I = I(t);  =   (t);   =    (t) I (t) ∞ n (t) 2) τ =   L >> 1- optically thick source I (t) ≈  (t) /  (t);   (t) ∞ n (t),  ∞ n (t) => I (t) ∞ γ  n (t) / n (t) = γ I (t) ∞ γ

38. Influence of high plasma density: Razin effect at 17 GHz

39. Maximum gyrofrequency in the source: If B=400 G f B = 2.8 x 10e6 x 400 = 1.120 GHz Maximum plasma frequency in the source: If N=10 11 cm -3 f p = 9 x 10e3 x 3.3 x 10e5 = 29.7 10e8 = 2.9 GHz

41. V a = B/(4πnm p ) 1/2 V s = (3kT/m p ) 1/2