1. Spectral Analysis of Decimetric Solar Bursts Variability R. R. Rosa 2, F. C. R. Fernandes 1, M. J. A. Bolzan 1, H. S. Sawant 3 and M. Karlický 4 1 Instituto de Pesquisa e Desenvolvimento (IP&D) Universidade do Vale do Paraíba (UNIVAP) São José dos Campos, SP, Brazil 2 Laboratório Associado de Computação e Matemática Aplicada (LAC) 3 Divisão de Astrofísica Instituto Nacional de Pesquisas Espaciais (INPE) São José dos Campos, SP, Brazil reinaldo.rosa@pq.cnpq.br 4 Astronomical Institute Academy of Sciences of the Czech Republic Ondrejov, Czech Republic

2. Outline Decimetric Solar Bursts (DSB) DSB Spectral Analysis Classifying Variability Pattern Using the Var[C(L)] and  H A Case Study for Space Weather Concluding Remarks

3. Decimetric Solar Bursts Data (Time Series): Brazilian Solar Spectroscope (BSS) (INPE-São José dos Campos) 1-2.5 GHz, 3MHz, 3ms, 2-3 s.f.u, 100 channels, 11:00-19:00 UT http://www.das.inpe.br/fmi/intranet/news.php Ondrejov Radio Observatory (Czech Republic) 3GHz, 10ms, 4MHz http://www.asu.cas.cz/~radio/

4. 1.6-2.0 GHz SFU Starting 17:13:51.48 UT 25/9/2001

5. SFU June 06 2000 16:34:00 UT SFU 3GHz

6. Power spectra: 1/f  with 1.8 <   2  Complex scaling dynamics (hybrid components: plasma turbulence)   10% Previous Results from Spectral Analysis (Power Spectra) M. Karlický et al. A&A 375, 638-642 (2001) -2-1.92 Rosa et al. Adv Space Res 42 844–851(2008) Log f logP(w) α=2(1-H) (Mandelbrot, 1985) H  α H Non-homogeneous scaling ptocess

7. Non-homogeneous Stochastic Process  H and C(L) Var[C(L)] = (1/N)  i (C i -  C  ) 2 Estimating a more robust  H … C(L)  L -   H = 1-(  /2) Peitgen, Jurgen & Saupe Chaos and Fractals, Springer 1993 C(L) is the Auto-correlation function=> Non-stationary intermittent process Problem: Bias in  > 10% -1.92  H : “Holder exponent” Non-homogeneous scaling function w(1/L)  k  H

8.  H : Wavelet Transform Modulus Maxima (WTMM) “Singularity Spectrum” (H)(H) where α H (t 0 ) is the Holder exponent (or singularity strength). Halsey et al., PRA 33:1141, 1986; Arneodo et al; Physica A 213:232, 1995. Dynamical Process Var(C)(5%)  H White Noise 0.002 0.5 1/f 2 0.089 0.6 1/f 1.66 0.034 0.8 Lorenz 0.025 0.4 Multip 0.020 1.1 N=1024 p-Model: 1<  H (L)<3 Characterizes  Non-homogeneous multi-scaling process: p-Model

9. Dynamical Process Var(C)(5%)  H (1%) White Noise 0.002 0.50 1/f 2 0.089 0.60 1/f 1.66 0.034 0.80 Lorenz 0.025 0.40 Multip 0.020 1.10 pModel 0.015 1.20 1.6 GHz 0.012 1.22 2.0 GHz 0.010 1.22 3.0 GHz 0.079 1.22 N=L=1024 1.6GHz 2GHz 3GHz 1.6GHz and 2.0 GHz (6 TS) 3 GHz (1 TS)

10. Solar Flares are classified by their x-ray flux in the 1.0 - 8.0 Angstrom band as measured by the NOAA GOES-8 satellite. On June 6, 2000, two solar flares from active region 9026 registered as powerful X-class eruptions. http://science.nasa.gov/headlines/y2000/ast07jun_1m.htm A Case Study for Space Weather

11. June 6, 2000 solar flares (X2.3) 15:00-16:35 UT (NOAA AR 9026)

12. Var[C(L)] = (1/N)  i (C i -  C  ) 2  1min before the flare

13. Concluding Remarks: This advanced spectral analysis suggested the influence of both, nonlinear oscillations in the magnetic field (A) + turbulent interaction between electron beams and evaporation shocks (B), on the decimetric radio emission energy source (turbulent non-homogeneous MHD p-model cascade) Thank you for your attention. LAC - CTE http://epacis.orghttp://epacis.org www.lac.inpe.brwww.lac.inpe.br The results suggest Var[C( L)] or Var[C] x  H as a new metric for Solar radio flux monitoring VLADA (Virtual Lab for Advanced Data Analysis) (EMBRACE)

14. V=9 g=9 =16 =20 Time Series Analysis (High sensitivity): Gradient Pattern Analysis “Asymmetry Coefficient”: G= (  - g)/g and Lim g   G=2 Assireu et al, Physica D 168(1):397, 2002.

15. G=1.87 G=1.82

16. Escala global Escala local G= (  - g)/g  G(ℓ) 

17. There are 16 time series with 1024 points – square matrices 32x32 The signal is decompose by Daubechies Discrete Wavelet (Db8) (see an example for 512 points) Gradient Spectra G(f)

18. Gradient Spectra for Turbulent-like Short Time Series  G =  1/N  [ G i ( ℓ)-  G( ℓ  ]