GRB afterglows in the Non-relativistic phase

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GRB afterglows in the Non-relativistic phase

• Y. F. Huang
• Dept Astronomy, Nanjing University
• Tan Lu
• Purple Mountain Observatory

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Outline

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

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The Physics of GRB Afterglows
Shock jump conditions
Energy of the shocked ISM
Adiabatic case E const
and
Highly radiative case
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Outline

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

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Why the non-relativistic phase is important?

• GRBs are impressive for their huge energies (Eiso
  1052 --- 1054 ergs) and ultra-relativistic
  motion ( 100 --- 1000)

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The deceleration of the shock is

• t -3/8
• (200 --- 400) (E52/n0)-1/8ts-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

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Theoretical afterglow light curve when
E1e52 erg, n1cm-3
Huang et al., 1998, MNRAS
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Observed afterglows
Kann et al. arXiv0804.1959
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Outline

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

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The evolution of external shocks
Highly radiative and when t lt n hours
Adiabatic when t gt n hours, and maybe
n days later
For highly radiative blastwave
For adiabatic blastwave
For Newtonian blastwave (Sedov solution)
We need a generic dynamical equation, that is
applicable in both relativistic phase and
non-relativistic phase.
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The evolution of external shocks
Highly radiative and when t lt n hours
Adiabatic when t gt n hours, and maybe
n days later
We need a generic dynamical equation, that is
applicable in both relativistic phase and
non-relativistic phase.
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A generic dynamical equation
Huang, Dai Lu 1999, MNRAS, 309, 513
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The equation is consistent with Sedov solution
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Outline

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

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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.

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Distribution function of e-
Problem t gt 1 --- 2 years, lt
1.5 (deep Newtonian phase)
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Our improvement
Huang Cheng (2003,MNRAS)
lg Ne
lg Ne
e5
o
lg e
0
lg ( e -1)
e5
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Numerical results (1)isotropic fireball
Huang Cheng, 2003,MNRAS
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Numerical results (2)conical jet
Huang Cheng, 2003,MNRAS
People usually use to
derive the jet break time tj .
However, in our calculation,
and gives a time of 4000 s.
But the break time is 40000 s.
The light curve does not break at
!
So, we should be careful in estimating the
beaming angle from the observed jet break time.
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Numerical results (3) cylindrical jet
Huang Cheng, 2003,MNRAS, 341, 263
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Application (1) GRB 980703
Radio light curve of GRB 980703 Frail et al.
2003, ApJ, 590, 992
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GRB 980703
See Kongs poster and references therein
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Application (2) GRB 030329
Density jump
Energy injection
2-component jet
Huang, Cheng Gao, 2006 Obs. data taken from
Lipkin et al. 2004
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Application (3) Failed GRBs
To produce a GRB successfully,we need A
stringent requirement !
i.e., for Eiso 1052 erg,we need Miso lt 10-5 Msun
There may be many fireballs with
We call themFailed GRBs They may manifest
asX-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
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a failed-GRB orphan
Jetted GRB orphan
How to distinguish a failed-GRB orphan afterglow
and a jetted but off-axis GRB orphan? It is not
an easy task.
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Conclusion

• 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.

Thank you!