1 太陽雑誌会 (main) 2003.05.26 takako t. ishii ( 石井 ) flare occurrence rate and modeling of...

1

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

2

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

3

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

4

Flare occurrence rate (Observation) Peak flux

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

5

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

6

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]

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 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)

8

Avalanche model

Avalanche !

Critical state = Power-law distribution

Cell

Cellular automaton modelSelf-organized criticality

9

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

10

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

11

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

12

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 ?

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

Flu

x

Flux

Pro

babi

lity

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