1. A numerical study of the afterglow emission from GRB double-sided jets Xin Wang Department of Astronomy, Nanjing University, China Collaborators Y. F. Huang, S. W. Kong

2. Contents • Introduction • Model • Numerical Results • Comparisons • Conclusion

3. The Standard Fireball Model external shock internal shocks prompt emission afterglows ~1011 km γ>>1 ~108 km γ~1000 progenitor Inter- Stellar Medium e+, e- γ p R~10 km E>1052 ergs M<10-5 Msun

4. >1016 cm ~1013 cm X O Detailed numerical investigation on the counter-jet emission is still lacking Introduction • Schematic GRB from a massive stellar progenitor • Beaming effect: achromatic break in afterglow LCs, polarization, energy crisis, orphan afterglow Mészáros 2001

5. 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: shock radius photon arrival time (comoving sound speed) ejecta mass half-opening angle (the adiabatic index) bulk Lorentz factor

6. Radiation: synchrotron radiation & self-absorption (SSA) electron distribution function synchrotron radiation power optical depth ofSSA observed flux density observer’s time

7. Numerical Results The parameters of the “standard” condition are defined as follows: • Dynamic evolution of the receding jet • Total equal arrival time surface (EATS) • The overall light curves (LCs) including the contribution from the receding jet component • The effects of various parameters on the receding jet component • Peak time of receding component

8. Dynamic evolution of the receding jet in a rather long observer’s time (t～100 d), γof 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.

9. 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 • 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.

10. 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).

11. (c) (d) 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 overall light curves

12. The effects of various parameters All 8.46 GHz LCs

13. Peak time of receding component

14. 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.

15. Zhang & MacFadyen (2009) Li & Song (2004) Comparisons radio afterglow LCs of GRB 980703 • with analytical derivations • with other numerical results • with observations The emission of the receding jetis 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) Our results are consistent with other colleagues’.

16. Conclusion m Jy • 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. • 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. • 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. • 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. • 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.

17. Thanks for your patience!

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