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太陽雑誌会 (Main) 2003.05.26Takako T. Ishii ( 石井 )

Flare occurrence rate and modeling of soft X-ray light curves

1. Introduction 2. Model description3. Results4. Summary and future works

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Introduction

Flare occurrence rate ・ Flare occurrence rate, power-law slope α

・ α > 2 → small scale flare dominate α < 2 → large scale flare dominate

kEdE

dN

21

total 2E

kdEkEdE

dE

dNEE

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Flare occurrence rate (Observation)

・ Count-up flares from observational data

α Wavelength Reference1.5 – 1.7 Yohkoh SXT Shimizu 1995,19972.3 SMM Hard-X Porter et al. 19953 Radio* Mercier & Trottet 19971.88 GOES Soft-X* Feldman et al. 19972.3 – 2.6 SoHO EIT (QR) Krucker & Benz 19981.7 ± 0.4 Yohkoh SXT* Shimojo & Shibata 19992.0 – 2.6 TRACE EUV Parnell & Jupp 20001.8 TRACE EUV Aschwanden et al. 20003 – 7 BATSE Hard-X Lin et al. 20012.9 ±0.1 SoHO SUMER Winebarger et al. 20022.03±0.09 GOES Soft-X* Veronig et al. 2002

* peak flux

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Flare occurrence rate (Observation) Peak flux

Aschwanden et al.1998 ApJ, 497, 972Table 1

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Flare occurrence rate (Observation)

Aschwanden et al.2000 ApJ, 535, 1047Fig. 10

Flare Energy1024 erg 1032 erg

Fla

re f

requ

ency

kEdE

dN

α 1.5

α 2.5

α 1.8

α 1.7

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Flare occurrence rate (Observation)

・ Note: Filter response function (Temperature bias) Aschwanden & Charbonneau 2002 ApJLα biased 1.8 → non-biased 1.4

ex. Loop-length distribution

3.01

Mm50.1

LTe

Original data

ObservationT [1.1 – 1.6 MK]

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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 rateAnalogous 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 : 1.8Duration: 1.8 (Lu et al. 1993)

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Avalanche model

Avalanche !

Critical state = Power-law distribution

Cell

Cellular automaton modelSelf-organized criticality

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Flare occurrence rate (Model)

Aschwanden et al. 1998Logistic avalanche modelFrequency distribution of elementary time structuresduring individual flares.

Longcope & Noonan 2000 Minimum current corona model :

slow buildup and sudden releasecf. Lu & Hamiltion : magnetic relaxation

no MHD equationsPower-law index:

Energy: 1.34, Peak: 1.48, Duration: 1.53

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Flare occurrence rate (Model)

Kashyap et al. 2002 ApJ, 580, 1118

・ Stellar flare α : 2.6, 2.7, 2.0 ( for 3 stars)・ Flare occurrence:

Assume power-law distributiontotal flux = flare + backgroundFlare : 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

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Flare occurrence rate (Model)

・ Flare occurrence: Poisson process

Frontera & Fuligni 1979Hard X-ray flare observation (balloon flight)Power spectral density distributionshot-noise process → spikes (bursts) in hard X-ray

Wheatland et al. 1998, Wheatland 2000 Waiting time (time between flares) distributionHard X-ray burstsGOES flares ( 25 years)Time-dependent Poisson process

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Flare decay time scale

・ Flare duration: Impulsive < 60 min. ?LDE (long duration event) several hours ?

・ Modeling of light curves: Decay time scale: τBi-modal ? (impulsive & LDE)Power-law distribution ?

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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

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Flare occurrence rate

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Example light curve of a flare

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Characteristics of light curves

・ Probability density distribution function of flux

Time

Flu

x

Flux

Pro

babi

lity

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Observational light curve

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Flux distribution function

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3. Result Model light curve

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Flux distribution function (Single τ)

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Flux distribution function (Mixed τ)

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Flux distribution function (Mixed τ& Single τ)

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Model light curves (with constant base flux)

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Flux distribution function (with base-flux)

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Model light curves (with modulated p_intensity)

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Flux distribution function (with modulated p_int)

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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