Transcript Document

Recent Advances in our Understanding
of GRB emission mechanism
Outline†
Pawan Kumar
♪
Constraints
on
radiation
mechanisms
•
• High energy emission from GRBs and
our understanding of Fermi data.
♪My goal is to generate a good discussion of this topic
Moscow, October 9, 2013
•
Understanding the radiation mechanism for ~10keV – 10 MeV band
is one of the most challenging problems in GRBs.
Emission in this band lasts for <102s, however it carries
a good fraction of the total energy release in GRBs.
And it offers the best link to the GRB central engine.
Jet energy dissipation
and γ-ray generation
relativistic
outflow
central engine
central engine  jet  -rays
External shock
radiation
• Conversion of jet energy to thermal energy
Internal/external shocks, magnetic reconnection etc.
Piran et al. ; Rees & Meszaros; Dermer;
Thompson; Lyubarsky; Blandford, Lyutikov;
Spruit…
• Radiation mechanism (sub-MeV photons)
1. Synchrotron 2. SSC (or IC of external photons)
3. photospheric mechanism…
Papathanassiou & Meszaros, 1996; Sari, Narayan & Piran, 1996; Liang et al. 1996;
Ghisellini et al. 2000; Thompson (1994); Lazzati et al. (2000); Medvedev (2000);
Meszaros & Rees 1992-2007; Totani 1998; Paczynski & Xu 1994; Zhang & Meszaros
2000;
Meszaros & Rees 1994; Pilla & Loeb 1996; Dermer et al. 2000; Wang et al. 2001 & 06;
Zhang & Meszaros 2001; Sari & Esin 01’; Granot & Guetta 2003; Piran et al. 2004; Fan
et al. 2005 & 08; Beloborodov 2005; Fan & Piran 2006; Galli & Guetta 2008; Pe’er et al.
06; Granot et al. 08; Bošnjak, Daigne & Dubus 09; Katz 1994; Derishev et al. 1999;
Bahcall & Meszaros 2000; Dermer & Atoyan 2004; Razzaque & Meszaros 2006; Fan &
Piran 2008; Gupta & Zhang 2008; Granot et al. 08; Daigne, Bošnjak & Dubus 2011 …
Energy dissipation: internal shocks (current paradigm)
(Prof. Bosnjak will talk about this model in detail)
Gehrels et al. (2002); Scientific American
Distance (Rs) of γ-ray source from the center of explosion
(This would help determine if radiation mechanism is photospheric or not)
1.
Steep decline of flux at end of GRB prompt phase
suggests: Rs ≈ 2c2δt ~ 1016cm
(Lyutikov; Lazzati & Begelman; Kumar et al.)
(Rs can be smaller if the steep decline is due to central
engine activity)
2. Prompt bright optical flash from GRBs:
16cm (GRB 080319B – Zou, Piran & Sari 2009)
Rs >
10
~
GRB 080319B: x-ray & optical LCs
t-5 (Too steep to be RS)
Kumar &
Panaitescu, 09
(RS)
Prompt -ray emission from
GRB 080319B also suggests
Rs >
~ 1016cm; Kumar & Narayan;
Racusin et al. 2008
Shen & Zhang (2009) provide a
limit on Rs from prompt optical
for a number of GRBs.
3. Detection of high energy -ray photons by Fermi/LAT
16cm
3  R = 2cΓ2δt
(GRB 080916C…)   >
10
10
>
s
~
~
However, Zou, Fan & Piran (2011), Hascoet et al. (2012) suggest Γ~300
This implies Rs~1015 cm, and that is still much larger than photospheric
radius (~1012 cm) – this is for MeV photon emission and δt ~ 0.1 s.
So the photospheric radiation is not the correct
mechanism for MeV γ-rays at least for some GRBs
GRB 080916C, a very bright Fermi burst, had a very stringent
upper limit on thermal component (Zhang & Pe’er, 2009).
Incidentally, Γ>103 would rule out baryonic and leptopic
thermal fireball model for GRBs since Γmax ~ 850 L521/4 R0,7-1/4;
where R0 the jet launching radius.
MeV γ-ray radiation mechanism
1. Synchrotron
• Synchrotron peak at ~102 kev  Bi2 ~ 2x1013
• Electron cooling
6mec(1+z)
tcool = ————— ~ (7x10−7 s) i33 2 « t ~ 0.1s
TB2i 
 f   −1/2 (or α = −1.5) which holds for only a small fraction of GRBs
This is basically Ghisellini et al. (2000) argument; Sari & Piran 1997
Note:
1. Synchrotron solutions with α = −2/3 is possible provided that Rs>1016cm,
and Γ> 300 –– Kumar & McMahon (2008), Beniamini & Piran (2013) ––
but in this case the variability time can’t be smaller than a few sec.
2. IC cooling in KN regime (Nakar, Ando & Sari, 2009;
Bosnjak et al.; Barniol Duran et al.) helps but not
enough..
3. Continuous acceleration of electrons can fix the low energy
spectral index problem.
(Ep)
• The spectral peak
4
for SSC: α γi so one
would expect a broad
distribution for Ep but
that is not what GRB
observations find
•
INTEGRAL: black
BATSE: violet
Fermi/GBM: red
Bosnjak et al. (2013)
2. Synchrotron-self-Compton solutions
It can be shown that for SSC solutions Ee α R3 and EB α R−4
 emission must be produced within a narrow range of R (factor ~2)
and that seems unlikely -- especially for the IS model.
• There is another problem with the SSC solution:
A lack of an excess in the Fermi/LAT band (100 MeV to
100 GeV), and absence of a bright optical flash severely
constrains the SSC model (e.g. Piran, Sari and Zou, 2009).
3. Thermal radiation + IC
(for prompt -rays)
Thompson (1994 & 06); Liang et al. 1997;
Ghisellini & Celloti 1999; Meszaros & Rees (2001);
Daigne & Mochkovitch (2002); Pe’er et al. (2006),
Beloborodov (2009)…
Observational constraints
•
Photospheric radius ~ 1012cm 3−3 Lj53; so the IC of thermal radiation is
expected to take place at a much smaller radius than Rs ~ 1016cm we are
finding.
•
Low energy spectrum should be fν  ν—ν2 which is rarely seen.
However, recent work of Burgess et al. (arXiv:1304.4628) claims to
see a thermal component for 5 out of 8 Fermi GRBs they analyzed.
Theoretical constraints
Vrum et al. (2013) & Asano & Meszaros (2013) provide general constraints
on photospheric models for MeV emission (Vrum’s talk on Monday)
They find that a large fraction of jet energy should be dissipated at a
radius of 1010–1011 cm –– optical depth ~10 –– and jet LF at this radius
should be order a few 10s, i.e. the dissipation should take place at a
high but not too large optical depth, i.e. some fine tuning needed.
Since GRB spectra are largely non-thermal, there are many
different proposals as to how to modify the photospheric
radiation so that the emergent spectrum is non-thermal.
Let us consider one particular photosphere model – n-p collision

Consider a baryonic jet consisting of n & p+. Neutrons accelerate with the
fireball expansion as long as they collide frequently with protons.

Eventually at some radius (Rnp) n & p+ decouple & hereafter n are no
longer accelerated whereas p+ Lorentz factor could continue to
increase with R as long as Γ(Rnp) < η.

The resulting differential velocity between n & p+ result in their
collision and conversion of a fraction of jet KE to thermal energy
below the photosphere.
 n–p decoupling radius is given by –
t R c 
'
np

2
4Rnp
m p c 2
 0L

Rnp
or
c
Rnp 
0 L
4 m p c 32
For n – p to develop differential velocity: Rnp < Rs = R0 η

  L 
0


3
 4m p c R0 
1
4
1/ 4
 485 L1/514 R0,7
Thus, GRB jets consisting of n & p & terminal Lorentz factor > 400 will
undergo n – p collisions below the Thomson photosphere & convert a

fraction of jet kinetic energy to radiation & e± thermal energy
(Beloborodov 2010; Vurm et al. 2011 & Meszaros & Rees 2011)
Beloborodov, 2010
n – p differential motion can also arise in internal shocks

Radius where internal collisions occur: Rcol = c Γ2 δt

And the radius where the probability of n-p
collisions drop below 0.5 is: Rnp α Γ-3


Rcol/Rnp α Γ5
For an efficient conversion of outflow kinetic energy
to thermal energy via n–p collisions these radii
should be approximately equal, and that requires:
50 < Γ < 102
Which does not appear to be consistent with GRB data.
Origin of high energy photons (>100 MeV)
Prompt phase: high energy photons during this phase might have
a separate origin than photons that come afterwards if rapid
fluctuations and correlation with MeV lightcurve is established.
Observers need to quantify the statistical significance of this!
• Hadronic processes: proton synchrotron, photo-meson …
Bottcher and Dermer, 1998; Totani, 1998; Aharonian, 2000; Mucke et al.,
2003; Reimer et al., 2004; Gupta and Zhang, 2007b; Asano et al., 2009;
Fan and Piran, 2008; Razzaque et al. 2010; Asano and Meszaros, 2012;
Crumley and Kumar, 2013….
Inefficient process – typically requires several order more
energy than we see in the MeV band (unless Γ were to be small,
of order a few hundred, which few people believe is the case for
Fermi/LAT bursts), e.g. Razzaque et al. 2010, Crumley &
Kumar 2013.
• Internal shock and SSC: e.g. Bosnjak et al. 2009, Daigne et al. 2011
Afterglow: external shock synchrotron, IC in forward or reverse shock of
prompt radiation or afterglow photons; IC of CMB photons by e± in
IGM; pair enrichment of external medium and IC…
Dermer et al., 2000; Zhang and Meszaros, 2001; Wang et al. 2001;
Granot and Guetta, 2003; Gupta and Zhang, 2007b; Fan and Piran,
2008; Zou et al., 2009; Meszaros and Rees 1994; Beloborodov 2005; Fan
et al., 200; Dai and Lu 2002; Dai et al. 2002; Wang et al. 2004; Murase et
al. 2009; Beloborodov 2013….
GRB 130427A (Perley et al. arXiv:1307.4401)
MeV duration (T90) = 138s, LAT duration (TGeV) > 4.3x103s; TGeV/T90 > 31
Highest energy photon (95 GeV) detected 242s after T0; z=0.34; Eγ,iso= 7.8x1053erg
GRB 110731A (Ackermann et al. 2013)
Kumar & Barniol Duran (2009) and Ghisellini, Ghirlanda & Nava
(2010) showed that high energy γ-ray radiation from GRBs, after the
prompt phase, are produced in the external-forward shock via the
synchrotron process. The reasoning for this will be described in the
next several slides.
Gehrels, Piro & Leonard: Scientific American, Dec 2002
Flux above νc is independent of density and almost independent of εB
• Consider GRB circumstellar medium density profile:   r s
• Blast wave dynamics follows from energy conservation:   r (3s)/ 2
• Observer frame elapsed time:
tobs  2cr 2  r 4 s
2
2
Comoving
magnetic
field
in
shocked
fluid:
B'




•
B

frequency:
• Synchrotron characteristic

• Observed flux at νm:
3 / 2
 m  B'  m2    1/B 2tobs
s/ 2
f m  1/B 2r
3 / 2 (3s4 )/ 2
Synchrotron
cooling
frequency:



r
•
c
B

. Observed flux
 at ν: f  f
..



m


 m ( p 1)/ 2  c p / 2
c

(3 p 2)/ 4
  (Bp 2)/ 4 tobs
The flux from the external shock above the cooling
frequency is given by:
0.2 mJy E55(p+2)/4 εep-1 εB(p-2)/4(1+z)(p+2)/4
fν =
_______________________________________
dL282(t/10s)(3p-2)/4 ν8p/2 (1+Y)
Y << 1 due to Klein-Nishina effect for electrons
radiating 102MeV photons.
Note that the flux does not depend on the external
medium density or stratification, and has a very
weak dependence on εB.
The expected decline of the >100 MeV lightcurve
according to the external shock model is t-(3p-2)/4.
For p=2.2 the expected decline is t-1.1 which is in
agreement with Fermi/LAT observations.
Temporal decay index in Fermi/LAT band; Ackermann et al. 2013
Table of expected and observed 100 MeV flux
Time (observer
Expected flux♪
Observed flux
z
E
frame in s)
from ES in nJy
(nJy)
γ,54
_____________________________________________________________
080916C
4.3
8.8
150
50
67
090510
0.9
0.11
100
9
14
090902B
1.8
3.6
50
300
220
110731A
2.83
0.6
100
8
~5
130427A
0.34
0.78
600
48
~40
♪We
have taken energy in blast wave = 3Eγ, εe=0.2, p=2.4, εB=10-5
According to the external shock model the LAT flux
should be proportional to E(p+2)/4 εep-1 or ~ (Eεe)
t-(3p-2)/4 ≈ t-1.1
(independent of n, ε )
B
Nava et al. 2013 -- arXiv:1308.5442
(E is proportional to Eγ,iso and PIC simulations suggest εe~0.1-0.2)
Long lived lightcurve for >102MeV (Abdo et al. 2009)
(GRB 080916C)
Abdo et al. 2009
Long lived lightcurve for >102MeV (Abdo et al. 2009)
Kumar & Barniol Duran (2009)
>102MeV data  expected ES flux in the X-ray and optical band
(GRB 080916C)
Abdo et al. 2009, Greiner et al. 2009, Evans et al. 2009
We can then compare it with the available X-ray and optical data.
Or we can go in the reverse direction…
> 100MeV
Optical
50 - 300keV
X-ray
Kumar & Barniol Duran (2009)
Assuming that the late (>1day) X-ray and optical flux are from ES,
calculate the expected flux at 100 MeV at early times
Abdo et al. 2009, Greiner et al. 2009, Evans et al.
2009
And that compares well with the available Fermi data.
A Brief Summary

The expected flux between 100 MeV and ~10 GeV
due to synchrotron emission in external shock is
within a factor 2 of the observed flux (as long as
electrons are accelerated as per Fermi mechanism).
The predicted flux is independent of ISM density
and εB. And hence the flux predictions are
robust.

An alternate mechanism to explain the >100 MeV flux
observed by Fermi/LAT would have to make a more
compelling case than the external shock model.
Let us look at one recent proposal…
According to the recent proposal of Beloborodov et al. (2013) –
IC scattering of MeV photons by e± produced in the external
medium – when R(1+z)/2cΓ2 (observer frame time for arrival of
IC photons) exceeds a few time T90 the GeV flux should decline
sharply. In other words this model suggests TLAT <
~ 3 T90,MeV
T90,MeV
TLAT (Power-law
TLAT/T90,MeV
(s)
decline part) in s
___________________________________________________________
080916C
60
>400
>7
090510
0.3
120
360
090902B
30
700
23
110731A
7.3
550
75
130427A
138
>4300
>30
•
There is little evidence for high density CBM required for this model to
work (A* ~ 0.5). Moreover, the high density is likely to over produce
100 keV flux at tobs< T90,MeV
•
The large optical flux according to this model (~1 Jy) could have
escaped detection. However, its IC scattering off of e± produces ~10
keV photons with flux ~ τ± fopt ~ a few mJy that is harder to hide.
What about 10 GeV – 95 GeV photons
detected from GRB 130427A?
Could these be produced by the synchrotron process?

Highest energy photon (95 GeV) was detected 242s after
the trigger (z=0.34, Eγ,iso= 7.8x1053erg) when Γ~ 102.

Highest possible energy for synchrotron photons is when
electrons lose half their energy in one Larmor time
(Because electrons gain energy by a factor ~2 in
shock acceleration in ~ a few Larmor time)

Larmor time =
me γe c
qB
Synchrotron
σT B2 γe2c
=
loss rate
6π
2
Larmor time x Synchrotro
<
m
γ
c
e
e
loss rate

νmax =
q γe2 ΓB
2π mec
<
9mec3 Γ
16π
q2
= 50 Γ MeV ~
< 10GeV
>10GeV photons might be due to IC in external shock, however,
perhaps the above limit could be violated by inhomogeneous B.
Summary
✫ The mechanism for generation of photons of energy
between ~10 keV and 10 MeV remains elusive.
✫ High energy photons (>100 MeV), after the prompt phase,
are produced by the simplest possible mechanism one could
imagine, i.e. synchrotron in external shock. However, it is
unclear how >10 GeV photons are produced.