1 太陽雑誌会 (Main) Takako T. Ishii ( 石井 ) Flare occurrence rate and modeling of soft X-ray light curves 1. Introduction 2. Model description 3. Results 4. Summary and future works

2 Introduction Flare occurrence rate ・ Flare occurrence rate, power-law slope α ・ α > 2 → small scale flare dominate α < 2 → large scale flare dominate

3 Flare occurrence rate (Observation) ・ Count-up flares from observational data αWavelength Reference 1.5 – 1.7Yohkoh SXTShimizu 1995, SMM Hard-X Porter et al Radio*Mercier & Trottet GOES Soft-X*Feldman et al – 2.6 SoHO EIT (QR)Krucker & Benz ± 0.4Yohkoh SXT* Shimojo & Shibata – 2.6TRACE EUVParnell & Jupp TRACE EUVAschwanden et al – 7BATSE Hard-XLin et al ±0.1SoHO SUMERWinebarger et al ±0.09GOES Soft-X*Veronig et al * peak flux

4 Flare occurrence rate (Observation) Peak flux Aschwanden et al ApJ, 497, 972 Table 1

5 Flare occurrence rate (Observation) Aschwanden et al ApJ, 535, 1047 Fig. 10 Flare Energy erg erg Flare frequency α 1.5 α 2.5 α 1.8 α 1.7

6 Flare occurrence rate (Observation) ・ Note: Filter response function (Temperature bias) Aschwanden & Charbonneau 2002 ApJL α biased 1.8 → non-biased 1.4 ex. Loop-length distribution Original data Observation T [1.1 – 1.6 MK]

7 Flare occurrence rate (Model) ・ Avalanche model (Cellular-Automaton model) Lu & Hamilton 1991 Coronal magnetic field : self-organized critical state → Power-law dependence of flare occurrence rate Analogous to avalanches of sand → Same physical process (reconnection) The size of a given flare is determined by the number of elementary reconnection events. Simulated results: power-law slope Energy : 1.4, Peak flux : 1.8 Duration: 1.8 (Lu et al. 1993)

8 Avalanche model Avalanche ! Critical state = Power-law distribution Cell Cellular automaton model Self-organized criticality

9 Flare occurrence rate (Model) Aschwanden et al Logistic avalanche model Frequency distribution of elementary time structures during individual flares. Longcope & Noonan 2000 Minimum current corona model : slow buildup and sudden release cf. Lu & Hamiltion : magnetic relaxation no MHD equations Power-law index: Energy: 1.34, Peak: 1.48, Duration: 1.53

10 Flare occurrence rate (Model) Kashyap et al ApJ, 580, 1118 ・ Stellar flare α : 2.6, 2.7, 2.0 ( for 3 stars) ・ Flare occurrence: Assume power-law distribution total flux = flare + background Flare : Poisson process ・ Compare the modeled light curve with the observed light curve ( ＋ detector characteristics) parameter : power-law index α cf. observed light curve → construct dN/dE

11 Flare occurrence rate (Model) ・ Flare occurrence: Poisson process Frontera & Fuligni 1979 Hard X-ray flare observation (balloon flight) Power spectral density distribution shot-noise process → spikes (bursts) in hard X-ray Wheatland et al. 1998, Wheatland 2000 Waiting time (time between flares) distribution Hard X-ray bursts GOES flares ( 25 years) Time-dependent Poisson process

12 Flare decay time scale ・ Flare duration: Impulsive< 60 min. ? LDE (long duration event) several hours ? ・ Modeling of light curves: Decay time scale: τ Bi-modal ? (impulsive & LDE) Power-law distribution ?

13 2. Model description ・ Flare occurrence rate, power-law slope α(Peak flux) α = 2.3 ← One-year observation (2002) Construct ‘mock-flare data base’ (200,000 flares) ・ Flare decay time scale τ single τ, mixed τ etc. ( e.g. 10 min., 60 min.) ・ Monte Calro simulation (time, flux) Number of flares / time step : Poisson (p_intensity = 1) Time step : 5 min. Flux : exponential decay + flare peak flux

14 Flare occurrence rate

15 Example light curve of a flare

16 Characteristics of light curves ・ Probability density distribution function of flux Time Flux Probability

17 Observational light curve

18 Flux distribution function

19 3. Result Model light curve

20 Flux distribution function (Single τ)

21 Flux distribution function (Mixed τ)

22 Flux distribution function (Mixed τ& Single τ)

23 Model light curves (with constant base flux)

24 Flux distribution function (with base-flux)

25 Model light curves (with modulated p_intensity)

26 Flux distribution function (with modulated p_int)

27 4. Summary and future works ・ Flare : Poisson with modulated p_intensity Decay time scale τ: 10min. : 30min. = 1:1 (or 20min) ×Base-flux model Flux ←small scale flares ・ Extension : A-class flares α dependence