Spectral Analysis of Spectral Analysis of Decimetric Solar Bursts VariabilityDecimetric Solar Bursts Variability

R. R. Rosa2,

F. C. R. Fernandes1, M. J. A. Bolzan1, H. S. Sawant3 and M. Karlický4

1Instituto de Pesquisa e Desenvolvimento (IP&D)Universidade do Vale do Paraíba (UNIVAP)

São José dos Campos, SP, Brazil

2Laboratório Associado de Computação e Matemática Aplicada (LAC)3Divisão de Astrofísica

Instituto Nacional de Pesquisas Espaciais (INPE)São José dos Campos, SP, Brazil

reinaldo.rosa@pq.cnpq.br

4Astronomical InstituteAcademy of Sciences of the Czech Republic

Ondrejov, Czech Republic

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

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 UThttp://www.das.inpe.br/fmi/intranet/news.php

•Ondrejov Radio Observatory (Czech Republic) 3GHz, 10ms, 4MHzhttp://www.asu.cas.cz/~radio/

1.6-2.0 GHz

SF

U

Starting 17:13:51.48 UT 25/9/2001

SF

U

June 06 200016:34:00 UT

SF

U

3GHz

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

log

P(w

)

α=2(1-H) (Mandelbrot, 1985)

H αH

Non-homogeneous scaling ptocess

Non-homogeneous Stochastic Process H and C(L)

Var[C(L)] = (1/N)i (Ci - C)2

Estimating a more robust H …

C(L) L-

H = 1-(/2)

Peitgen, Jurgen & SaupeChaos and Fractals, Springer1993

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)kH

H : Wavelet Transform Modulus Maxima (WTMM)

“Singularity Spectrum”

(H)

where αH (t0) 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 0.51/f2 0.089 0.6 1/f1.66 0.034 0.8Lorenz 0.025 0.4Multip 0.020 1.1

N=1024

p-Model: 1<H(L)<3

Characterizes Non-homogeneous multi-scaling process: p-Model

Dynamical Process Var(C)(5%) H (1%)

White Noise 0.002 0.501/f2 0.089 0.60 1/f1.66 0.034 0.80Lorenz 0.025 0.40Multip 0.020 1.10pModel 0.015 1.20

1.6 GHz 0.012 1.222.0 GHz 0.010 1.223.0 GHz 0.079 1.22

N=L=1024

1.6GHz

2GHz

3GHz

1.6GHz and 2.0 GHz (6 TS)3 GHz (1 TS)

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

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

Var[C(L)] = (1/N)i (Ci - C)2

1min before the flare

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.org www.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)

V=9

g=9

=16

=20

Time Series Analysis (High sensitivity): Gradient Pattern Analysis

“Asymmetry Coefficient”: G= ( - g)/g and Limg G=2

Assireu et al, Physica D 168(1):397, 2002.

G=1.87 G=1.82

Escala global

Escala local

G= ( - g)/gG(ℓ)

• 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)

Gradient Spectra for Turbulent-like Short Time Series

G = 1/N [Gi (ℓ)-G(ℓ]