1. GRB afterglows in the Non-relativistic phase Y. F. Huang Dept Astronomy, Nanjing University Tan Lu Purple Mountain Observatory

2. Outline 1.The importance of Non- relativistic phase 2.A generic dynamical model 3.The deep Newtonian phase 4.Numerical results

3. Energy of the shocked ISM: Adiabatic case: E ~ const and ： Highly radiative case: Shock jump conditions ： The Physics of GRB Afterglows

4. Outline 1.The importance of Non- relativistic phase 2.A generic dynamical model 3.The deep Newtonian phase 4.Numerical results

5. GRBs are impressive for their huge energies (Eiso ~ 10 52 --- 10 54 ergs) and ultra-relativistic motion ( ~ 100 --- 1000) Why the non-relativistic phase is important?

6.  t -3/8  (200 --- 400) (E 52 /n 0 ) -1/8 t s -3/8 t = 1 day  2.8 --- 5.6 t = 10 day  1.2 --- 2.4 t = 30 day  0.8 --- 1.6 t = 0.5 year  0.4 --- 0.8 t = 1 year  0.3 --- 0.6 The deceleration of the shock is:

7. Huang et al., 1998, MNRAS Theoretical afterglow light curve when E=1e52 erg, n=1cm -3

8. Kann et al. arXiv:0804.1959 Observed afterglows

9. Outline 1.The importance of Non- relativistic phase 2.A generic dynamical model 3.The deep Newtonian phase 4.Numerical results

10. We need a generic dynamical equation, that is applicable in both relativistic phase and non-relativistic phase. For adiabatic blastwave ： For highly radiative blastwave ： The evolution of external shocks ： Highly radiative and when t < n hours Adiabatic when t > n hours, and maybe n days later For Newtonian blastwave (Sedov solution) ：

11. We need a generic dynamical equation, that is applicable in both relativistic phase and non-relativistic phase. The evolution of external shocks ： Highly radiative and when t < n hours Adiabatic when t > n hours, and maybe n days later

12. A generic dynamical equation Huang, Dai & Lu 1999, MNRAS, 309, 513

13. The equation is consistent with Sedov solution

15. Outline 1.The importance of Non- relativistic phase 2.A generic dynamical model 3.The deep Newtonian phase 4.Numerical results

16. The deep Newtonian phase The generic dynamical equation can be used to describe the overall evolution of GRB shocks. However, to calculate the emission at very late stages, we meet another problem. It is related to the distribution function of shock-accelerated electrons.

17. Distribution function of e - Problem: t > 1 --- 2 years, < 1.5 (deep Newtonian phase)

18. Our improvement ： lg ( e -1) lg N e Huang & Cheng (2003,MNRAS) lg e lg N e 0 o e =5

19. Huang & Cheng, 2003,MNRAS Numerical results (1) ： isotropic fireball

20. Huang & Cheng, 2003,MNRAS Numerical results (2) ： conical jet People usually use to derive the jet break time t j. However, in our calculation, and gives a time of ~4000 s. But the break time is ~40000 s. So, we should be careful in estimating the beaming angle from the observed “jet break time”. The light curve does not break at !

21. Huang & Cheng, 2003,MNRAS, 341, 263 Numerical results (3): cylindrical jet

22. Radio light curve of GRB 980703 Frail et al. 2003, ApJ, 590, 992 Application (1): GRB 980703

23. GRB 980703 See Kong’s poster and references therein

24. Application (2): GRB 030329 Density jump 2-component jet Energy injection Huang, Cheng & Gao, 2006 Obs. data taken from Lipkin et al. 2004

25. To produce a GRB successfully ， we need: A stringent requirement ! i.e., for Eiso ~ 10 52 erg ， we need Miso < 10 -5 Msun There may be many fireballs with We call them ： Failed GRBs They may manifest as ： X-ray flashes, orphan afterglows Newtonian phase will be especially important in these cases. Huang, Dai, Lu, 2002, MNRAS, 332, 735 “Failed GRBs and orphan afterglows” Application (3): Failed GRBs

26. How to distinguish a failed-GRB orphan afterglow and a jetted but off-axis GRB orphan? It is not an easy task. a failed-GRB orphan Jetted GRB orphan

27. Although GRB fireballs are ultra-relativistic initially, they may become Newtonian in tens of days, and may enter the deep Newtonian phase in 1 --- 3 years. Conclusion Thank you!