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OBSERVATION OF MICROWAVE OSCILLATIONS WITH SPATIAL RESOLUTION

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

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OBSERVATION OF MICROWAVE OSCILLATIONS WITH SPATIAL RESOLUTION

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  1. OBSERVATION OF MICROWAVE OSCILLATIONS WITH SPATIAL RESOLUTION V.E. Reznikova1, V.F. Melnikov1, K. Shibasaki2, V.M. Nakariakov3 1Radiophysical Research Institute, Nizhny Novgorod, Russia 2Nobeyama Radio Observatory, NAOJ, Japan 3University 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 fluxesand spectrum(NoRP)

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

  6. Radio pulsation analysis (NoRH) - 2 Fourier spectra P1 = 14 - 17 s P2 = 8 - 11 s

  7. AnalysisofHXRemissionpulsation(WBS/Yohkoh) Fourier spectra

  8. Spatial structure of microwaveand XR-sources L = 2.5109cm (~34") d =6108cm (~8")

  9. Pulsations in different parts of the loop ∆F/F = [F(t)- F0]/F0 Two main spectral components: P1 = 14 - 17 s(more pronounced at the apex ) P2 = 8 - 11 s (relatively stronger at the loop legs)

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

  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 P1 = 14-17 s and P2 = 8-11 s are clearly seen everywhere in the source • pulsations at the legs are almost synchronous with the quasi-period P2 = 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, P1 = 14-17 s • phase shift between oscillations from 3 different sources is very small for the P1 component, less than 0.5rad or 1.3s. However it is well pronounced for the P2 spectral component.

  12. Spectrum slope in different parts of the loop  = ln(F34/F17)/ln(34/17) Near footpoints< 0, near apex> 0

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

  14. What is the reason for low frequency depression in the upper part of the loop? • Cyclotronabsorption? - MDI/SOHO: at the photosphere level В ≤ 100G around SFP В ≤ 400G around NFP => fb ~ 1 GHz ↓↓ fpeak ~ 20 GHz => spectral peak was at least at s = fpeak /fb ~ 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 : Dulk & Marsh, 1982 • f < fpeak (thick ) : • f > fpeak (thin ) : • the oscillations of the flux at low frequencies (optically thick case) and high frequencies (optically thin case) would be in anti-phase; Iν В –0.5-0.085  В-0.9 Iν В 0.90 -0.22  В4

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

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

  19. Razin suppression (Razin 1960) • inthe medium, wherenν< 1 (f p > fB) • peak frequency depends on the Razin frequency: • in solar flaring loops: Melnikov, Gary and Nita, 2005 (in press)

  20. LT FP Microwave diagnostic of physical parameters inside the loop Modelsimulation of gyrosynchrotron spectrum: N~ 1011 сm-3 Loop apex:B 70 G Loop legs:B 100 G

  21. High value of N0 => short decay time scales (2÷5 s) for burst sub peaks Electron’s life time in the loop: (forEe >160 keV) Decay time scales: no = 1011 сm-3; L = 2.5109сm;=3÷5 Ee = 1 MeV =>  l ~ 26 s;  dec ~ 4÷5 s

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

  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 Вand 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- oscillationsin 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 viewinganglebetween the B and the line-of-sight: if  80, =5  1215 Iν В -0.22+0.90 Dulk & Marsh, 1982 Iν(sin ) -0.43+.65

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

  29. } } } } } } Dispersive curves of MHD modes Using the loop parameters derived from microwave & X-ray diagnostics: CA0 = 600 km/s CAe= 3,300 km/s Cs0 = 340 km/s Cse = 200 km/s l = 6 l = 5 l = 4 l = 3 • sausage (m=0) -solid; • kink(m=1) - dotted; • ballooning • (m=2) - dashed • (m=3) -dashed-dotted l = 2 l = 1

  30. Interpretation of the pulsations withР1in terms of the GlobalSausage Mode: P1=16s & λ=2L k = 2π/λω=2 π/P ↓↓ Vph = ω/k = 3130 km/s corresponding normalised longitudinal wave numberka ≈ 0.54 => a ≈ 4.3 Mm

  31. upperlimit: (from existence condition) ~ 17 s Interpretation of the pulsations withР1 = 14÷17s in terms of the GlobalSausage Mode: lowerlimit: ~ 14 s Nakariakov, Melnikov & Reznikova – 2003 ( A&A 412, L7)

  32. P2 = 9 s λ = L λ = L/2 Interpretation of the pulsations withР2in terms of the kink mode (2d and 3d harmoniks)

  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 P1 component • The second periodicity P2= 9s can be associated with several modes: - Kink mode (2d or 3d longitudinal harmonic) - Ballooning mode(2dlongitudinal harmonic)

  34. Thank you for the attention!

  35. What about f-f absorption? • N = 1011cm -3 • B = 50 G • d = 6×108 cm • T = 3×106 K • Θ= 80°

  36. Pressure balance equation

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

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

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

  40. Va =B/(4πnmp)1/2 • Vs =(3kT/mp) 1/2

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