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Modelling of early X-ray emission
from gamma-ray bursts
J.Dyks, Y.Z.Fan, B.Zhang
NCAC Hebrew Univ. Purple Mountain Obs.,
CAS National Astron. Obs., CAS UNLV
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Early X-ray lightcurves of GRBs
eg. OBrien et al.2006 Nousek et al. 2006
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Two components internal shocks/dissipation
external shocks
Paczynski Xu1994 Rees Meszaros 1994
Meszaros Rees 1997
?1 3-5 ?1 1-2
?2 0.2-0.8 ?2 0.7-1.2
?3 1.1-1.7 ?3 ?2
?4 2-3
t1
t2
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EARLY STEEP DECAY
OBrien et al.2006
very steep lasts for hundreds seconds smoothly
connected to prompt gamma rays
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X-ray tail of prompt emission
1. Cooling and/or 2. High latitude emission
VERIFICATION PROBLEMS a) zero time effect
gt steeper temporal slope b) admixture of
afterglow emission gt flatter slope c)
structured outflow gt flatter slope USEFUL
FOR i) determining of R_prompt ii)
determining of t_0 (assuming that 2 is correct)
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1. Cooling - very fast to account for the fast
variability of prompt gamma-ray emission If B
not far below equipartition gt ? 3 -
7 (Meszaros Rees 1999) gt the decay can easily
be dominated by the high latitude effect
(curvature effect)
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Curvature effect (high latitude effect)
Kumar Panaitescu 2000
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Zero time effect
fig. from Zhang et al. 2005
t_ejection 0, 1s and 10s
If zero of (log t)-axis lt t_ejection gt
t_ejection just ahead of spike
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Zero time effect turn negatives into positives
Liang et al. 2006
If the (blended) curvature effect is assumed
gt t0 just ahead of flares or last pulse in
prompt emission gt confirms curvature effect and
the internal origin of flares
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Structured outflow
Off-beam viewing required (? decreased by 1-2)
Dyks et al. 2005
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Important application Radius of prompt emission
Sari et al. 1999
Lazati Begelman 2006 Vaughan et al. 2006
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SLOW DECAY PHASE variations on the standard
afterglow model
Meszaros Rees (1997)
Adiabatic expansion of uniform relativistic
fireball into the (uniform) ISM medium,
impulsive injection, ? drops as r-3/2 or
t-3/8. Relativistic shocks transfer a fixed
fraction ?_e of internal energy e into a power
law distribution of electrons dNe/d? ??-p with
p gt 2 and a low energy cutoff at ?_m. Energy
density of B-field is a fixed fraction ?_B of
e. Synchrotron radiation is the main source of
observed photons and the main channel of electron
cooling. Inverse Compton scattering does not
contribute to the observed X-ray or optical
emission, although it may additionally cool
electrons (Y parameter).
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SLOW DECAY PHASE variations on the standard
afterglow model
Meszaros Rees (1997)
Sari et al.1998
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? (3p-2)/4 1.15 ? p/2 1.1 ?
(3?-1)/2
gt
tc is sensitive to ?B gt if ?B large (say 0.1)
gt
? 3(p-1)/4 0.9 ? (p-1)/2 0.6 ?
(3/2)?
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SLOW DECAY PHASE
1. Angular inhomogeneity (patchy shell) 2.
Density profile 3. Evolving shock parameters
eps_e, eps_B 4. Energy injection a) long
lived activity b) distribution of
?(E) 5. Magnetized outflow 6. Small zeta_e, 7.
reverse shock emission, etc...
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There is no spectral break at t_2 gt
hydrodynamical or geometrical origin of temporal
break at t_2
Off-beam viewing (Eichler Granot 2006) gt
Several problems, eg. a weaker and softer prompt
emission expected
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Partially Overlapping Patches (POP
geometry, Dyks 2006)
gt90 of kinetic energy must be reprocessed into
other forms (B-field, gamma-rays) in the region
that contains the line of sight
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GRB efficiency crisis?
Angular inhomogeneity (Kumar Granot 2000
Toma et al.2006)
The angular size of the causally connected region
1/? gt drastically nonuniform gamma-ray flux
and E_kin (natural possibility)
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Evolving shock parameters eps_e, eps_B
Shock strength-dependent ?e, ?B ?e ?
?-a ?B ? ?-b for ? gt ?0 ( few
tens)
Fan Piran 2006
Reproduces X-rays for a b 0.5 - 1.2. Cannot
explain both X-ray and optical emission (chromatic
t_2 breaks of GRB 050319 and GRB 050401)
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DENSITY PROFILE
n ? r-k, 0 ? k lt 3 k 0 gt uniform ISM k
2 gt wind
Generally not a good idea (no dependence on k)
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Energy injection to the forward shock (Rees
Meszaros 1998 Sari Meszaros 2000 Nousek et
al.2006 Zhang et al.2006 Granot Kumar
2006 Panaitescu et al.2006)
A) long lived activity problems smooth temporal
activity of the central source for
hours Einj(ltt)? tq, q 0.5 gt decelaration
slower than ?? t-3/8 dEinj/dt? t-0.5
too slow for models of the central engine B)
instantaneous injection of material with a
distribution of outflow Lorentz factor ?(E) (eg.
Nousek et al.2006 Granot Kumar 2006)
Fan Piran 2006
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DISTRIBUTION OF ?(E)
E(gt?) ? ?-a a 1 - 2.5
Fig. from Granot Kumar 2006
Nousek et al.2006 Granot kumar 2006
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Is there a GRB efficiency crisis?
Pre-Swift estimates of
Shallow phase requires 10?(E? /Ek)pre-Swift gt
efficiency gt 90?
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Is there a GRB efficiency crisis?
Pre-Swift estimates based on X-ray flux observed
10 days after GRB
Electron energy is a fixed fraction ?e of total
internal energy of shocked medium
(p-2)/(p-1) ignored gt ?m overestimated by a
factor of 30-40!
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Is there a GRB efficiency crisis?
gt no crisis efficiency lt50 even with the
energy injection included
Pre-Swift efficiency updated (Fan Piran 2006)
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Flares
Narrow ?T ltlt T and bright (F?F)/F 500 gt
internal origin, late activity of the central
engine (but why later flares are broader?)
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Eg. not due to collisions with clouds
Zhang et al.2006
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Nor due to off-(line of sight) subjets
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Conclusions
Fast decline - probably X-ray tail of prompt
(internal) emission high latitude emission
modified by the zero-time effect Slow
decline - possibly energy injection into the
external forward shock Flares - internal
origin, late central engine activity GENERALLY
strong support for the internal-external
shock model GRB efficiency
generally below 50 Central engine models
challenged
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Dzety w GRB
Sari et al. 1999
gt Eg Eg,iso (qj )2 / 2
Harrison et al. 1999
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SLOW DECAY PHASE variations on the standard
afterglow model
Meszaros Rees (1997)
Sari et al. 1996 Moderski et al.2000 Huang et
al. 2000 Salmonson 2003
const
const
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