京大天体核　 D3 山崎 了

共同研究者 : 井岡 邦仁 ( 阪大 ) 、中村 卓史( 京大 )

Ref. Yamazaki et al., astro-ph/0401044

Light Curves of XRFs & GRBs

X-ray band

γ- ray band

X-ray flash (XRF) γ-ray burst (GRB)

Spectral properties of XRFs and GRBs

Double power-low form fits spectra of XRFs and GRBs.

Photon indices α, β ( スペクトルの傾き ) は GRB と XRF で同じ。XRF の Ep (peak energy) は GRB のものよりも小さい。

Ep=126 keVEp=19 keV

XRF GRB

Rest frame Ep - Eiso relation

XRF

GRB

X-ray rich GRB

XRF(X-ray rich GRB) と GRB の　･ スペクトル以外の性質 (duration, event rate 等 )　 は同じ。　･ 観測量の分布は連続的。　⇒ 両者の起源は同一であると考えられている。

(1+z) Ep ∝ Eiso1/2

(for GRBs and XRFs with known redshifts)

Theoretical Models of the X-ray flash

1. High redshift GRBs (Heise et al. 2001)

2. External shocks with small Lorentz factors (Dermer et al. 1999; Rossi et al. 2001)

3. Internal shocks with high Lorentz factors (Mochkovitch et al. 2003)

4. Photosphere-dominated fireball (Meszaros et al. 2002; Drenkahn 2002)

5. Jets with wide opening angles (Lamb et al. 2003)

6. Off-Axis GRBs (Yamazaki et al. 2002, 2003)

’’

Ｏ ff-Axis Jet Model of XRFsThe X-ray flashes (and the soft GRBs) are the typical GRBs observed from off-axis viewing angle.

(γ ～ 100)

XRFs

GRBs

jet

X-ray band

νFν

　

ν

γ-ray band

relativistic Doppler　　 effect

rela

tivis

tic

beam

ing

eff

ect GRB

XRF

LOS

Ep - Eiso relation in off-axis jet model

ν0 : frequency in the jet-comoving frame

θ= θ ｖ - Δθ (<< 1 )γ= 100 : Lorentz factor of the jet

Ep ～ ν0δ

δ-1 = γ(1-βcosθ) ～ [1+ (γθ)2]/(2γ)

Eiso ∝δ1-α

α= -1 ～ -2 : photon index

⇒ Ep ∝ Eiso1/(1-α)

　　　 ～ Eiso1/3 ～ 1/2

Line of sight

Jet Emission Model (Yamazaki et al. 2003)・ Spontaneous emission from instantaneously thin shell. ・ Normalization of emissivity; isotropic γ-ray energy from the source with z = 1 and θ ｖ = 0 satisfies Eγ= Eiso (Δθ)2 /2 = 1×1051 ergs (Bloom et al. 2003)

where Eiso = 4πdL2 (1+z)-1 Sγ ( Sγ; obs. fluence )

・ Emission spectrum in the comoving frame

Maximum redshift to be detected by HETE

γ = 100

z max :

max

imum

reds

hift

Viewing angle θV / γ-1

α = -1

β = -2.5

γν’ ０ = 500 keV

Slim(2-400 keV)= 5×10-8 erg/cm2

Δθ/γ-1 = 5

Δθ/γ-1 =10

Input parameters　 (10,000 events)

for z=0, θV=0

zα β

Δθ

Result of Simulation : Ep – Eiso relation

obs. best fit

Soft events (<100 keV) are off-axis emissions!

HETE detects 288 events among 10000 simulated bursts.

79 off-axis events

209 on-axis events

62 GRBs192 XRR-GRBs

34 XRFs

× : detected by HETE (off-axis)

＋ : detected by HETE (on-axis)

･ : not detected by HETE

Summary

Off-axis emission from z ～ 1 can be observable. The Ep-Eiso relation may be reproduced by the off-axis jet model : off-axis emission represents large portion of the X-ray flash.

The Ep-Eiso relation, the Ep-distribution, the hardness distribution etc. depend on the unknown functional form of the opening angle distribution.

⇒ Ep-Eiso relation constrains the jet opening angle distribution, and therefore the ratio of GRBs to core-collapse SNe !!!