Light Curves of XRFs GRBs Xray flash XRF
Light Curves of XRFs & GRBs X-ray flash (XRF) γ-ray burst (GRB) X-ray band γ- ray band
Spectral properties of XRFs and GRBs Double power-low form fits spectra of XRFs and GRBs. XRF Ep=19 ke. V GRB Ep=126 ke. V 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。
Rest frame Ep - Eiso relation (for GRBs and XRFs with known redshifts) 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。 X-ray rich GRB ⇒ 両者の起源は同一であると考えられている。 XRF (1+z) Ep ∝ Eiso 1/2
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)
Ｏff-Axis Jet Model of XRFs The X-ray flashes (and the soft GRBs) are the typical GRBs observed from off-axis viewing angle. relativistic beaming effect νFν X-ray band γ-ray band XRFs GRBs XRF jet (γ～ 100) relativistic Doppler effect ν
Ep - Eiso relation in off-axis jet model Ep ～ ν 0δ ν 0 : frequency in the jet-comoving frame δ-1 = γ(1 -βcosθ) ～[1+ (γθ)2]/(2γ) γ= 100 : Lorentz factor of the jet θ= θｖ- Δθ (<< 1 ) Eiso ∝δ 1 -α α= -1～-2 : photon index ⇒ Ep ∝ Eiso 1/(1 -α) ～ Eiso 1/3～ 1/2 LOS
Jet Emission Model (Yamazaki et al. 2003) ・Spontaneous emission from instantaneously thin shell. Line of sight ・Normalization of emissivity; isotropic γ-ray energy from the source with z = 1 and θｖ= 0 satisfies Eγ= Eiso (Δθ)2 /2 = 1× 1051 ergs (Bloom et al. 2003) where Eiso = 4πd. L 2 (1+z)-1 Sγ ( Sγ; obs. fluence ) ・Emission spectrum in the comoving frame
zmax : maximum redshift Maximum redshift to be detected by HETE Δθ/γ-1 =10 γ = 100 α = -1 β = -2. 5 γν’０ = 500 ke. V Δθ/γ-1 = 5 Slim(2 -400 ke. V) = 5× 10 -8 erg/cm 2 Viewing angle θV / γ-1
Input parameters (10, 000 events) α β z Δθ for z=0, θV=0
Result of Simulation : Ep – Eiso relation HETE detects 288 events among 10000 simulated bursts. Soft events (<100 ke. V) are off-axis emissions! obs. best fit 209 on-axis events 79 off-axis events 62 GRBs 192 XRR-GRBs 34 XRFs ＋ : detected by HETE (on-axis) × : detected by HETE (off-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 !!!
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