A numerical study of the afterglow emission from GRB

double-sided jets

Collaborators Y. F. Huang, S. W. Kong

Xin WangXin Wang

Department of Astronomy, Nanjing University, China

Contents

1. Introduction

2. Model

3. Numerical Results

4. Comparisons

5. Conclusion

The Standard Fireball Model

Inter-StellarMedium

~108 kmγ~1000

internalshocks

progenitor

e+, e- γp

R~10 kmE>1052 ergsM<10-5 Msun

promptemission

externalshock

~1011 kmγ>>1

afterglows

Schematic GRB from a massive stellar progenitor

Beaming effect: achromatic break in afterglow LCs, polarization, energy crisis, orphan afterglow

Introduction

X

O

~1013 cm>1016 cm

Mészáros 2001

Detailed numerical investigation on the counter-jet emission is still lacking

Model We use the convenient generic dynamical model

advanced by Huang et al (2000). The physical picture is that the homogeneous

double-sided jet expands into a homogeneous interstellar medium (ISM).

Dynamics:

2

2

2

2

( 1)

2 (1 cos )

( 1)1

1

2(1 )

p

s

ej

dRc

dtdm

R nmdR

cd da

dt R dt R

d

dm M m m

)3/()14(ˆ

(the adiabatic index)

22s )1(ˆ1

1)1)(1ˆ(ˆ cc

(comoving sound speed)

shock radius

photon arrival timeejecta mass

half-opening angle

bulk Lorentz factor

Radiation: synchrotron radiation & self-absorption (SSA)

electron distribution function

synchrotron radiation power

optical depth of SSA

observed flux density

observer’s time

Numerical Results

1. Dynamic evolution of the receding jet2. Total equal arrival time surface (EATS)3. The overall light curves (LCs) including the

contribution from the receding jet component4. The effects of various parameters on the

receding jet component5. Peak time of receding component

The parameters of the “standard” condition are defined as follows: 3 53

0,iso j 01/ cm , 10 ergs, 0.1, 0, 300n E 2

e B obs L0.1, 0.01, 2.5, 0, =1 ( =6634.3 Mpc)p z d

Dynamic evolution of the receding jetin a rather long observer’s time (t ～ 100 d), γ of the receding jet remains almost constant

the emission from the receding jet will be very weak in this period, since it is highly beamed backwardly.

for the large circum-burst medium density case (n=1000/cm3), the receding jet is decelerated more rapidly

the emission from the receding jet will peak earlier than that under the standard condition.

EATS for the receding jet branch has

•much smaller typical radius

•much flatter curvature

•much smaller area

as compared with those for the forward jet branch at the same observer time.

Total equal arrival time surface (EATS)

Due to speed of light is not infinite, photons received at an observer’s time tobs are emitted from a distorted ellipsoid not simultaneously, which is determined by

1obst dR

c

Exemplar surfaces for a “standard” double-sided jet of ten equal arrival times, i.e. 100 d (red), 200 d (orange), 400 d (yellow), 600 d (olive),

800 d (cyan), 1000 d (blue), 1250 d (purple), 1500 d (pink), 1750 d (dark cyan), and 2000 d (grey).

(c)

(d)

The overall light curves

LCs of the double-sided jet with two parameters altered compared with the “standard” condition, i.e. n=1000/cm3 and z=0.1 (dL=454.8 Mpc).

The effects of various parameters

1/320,iso jRJ RJ

peak NR 2p

35

2 4

Et t

c nm c

All 8.46 GHz LCs

Peak time of receding component

1/320,iso jRJ RJ

peak NR 2p

35

2 4

Et t

c nm c

Fig. 3 Multiband afterglow light curves considering the contribution from the receding jet component. The total light curves at various observing frequencies, i.e. 109 (red), 1010 (orange), 1011 (yellow), 1012 (olive), 1013 (cyan), 1014 (blue), 1015 (purple), 1016 (pink), 1017 (black) Hz, are represented by solid lines, while the counter-jet emission by dashed lines. The dotted line marks the peak time of the receding jet component at 1 GHz. We can see that this peak time does not remain constant over a wide range of frequency, from radio, to optical, then to X-ray, and the plateau is not always formed in the late time light curves.

Li & Song (2004)

Comparisons

with analytical derivations with other numerical results with observations

Zhang & MacFadyen (2009)

Our results are consistent with other colleagues’.

radio afterglow LCs of GRB 980703

The emission of the receding jet is unable to constitute the radio data at late time. So we agree that the observed late-time flux density is mainly from the host galaxy emission (Berger+ 01; Frail+ 03; Kong+ 10, see SW’s talk)

1. According to our results, the contribution from the receding jet is quite weak and only manifests as a plateau ( ～ 0.3 at 1 GHz). At lower frequency, the relative intensity of the receding jet component becomes stronger, as compared with the peak of the forward jet.

2. Generally, our result is consistent with Zhang & MacFadyen’s and Li & Song’s. However the subtle difference between ours and Li & Song’s is ascribed to the EATS effect as well as the deceleration of the external shock, while the difference between ours and Zhang & MacFadyen’s is due to the SSA effect.

3. Contribution from the receding jet can be greatly enhanced if the circum-burst environment is very dense and/or the micro-physics parameters of receding jet is different and/or the burst has a low redshift.

4. The SSA effect is important for deciding the peak time of the counter-jet emission in radio bands. When the medium density is high, SSA tends to postpone the peak time at higher observing frequencies and decrease the peak flux.

5. We have studied the radio afterglow of GRB 980703. It is found that the counter-jet emission is much lower than the host galaxy level, and is completely submerged by the host galaxy emission.

ConclusionJy

Thanks for your patience!

The effects of various parameters (2) - Different characteristics for twin jets

8.46GHz LCs. In each panel, the solid line is plotted under the “standard” condition, i.e., the parameters are completely the same for the twin jets (but we have evaluated as 0.01 and as 10-4 here). For other LCs, one or two parameters are changed for the receding jet only.

2Be