A numerical study of the afterglow emission from GRB double-sided jets Collaborators Y. F. Huang, S....
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Transcript of A numerical study of the afterglow emission from GRB double-sided jets Collaborators Y. F. Huang, S....
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