The Primary Output of GRBs

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The Primary Output of GRBs David Eichler
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My collaborators Amir Levinson Jonathan
Granot Hadar Manis Don Ellison (if time)
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Which came first, g-rays or baryonic jet?
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Slow sheath of Baryons
Ultrarelativistic fireball
e.g. Levinson and Eichler 1993
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Offset observer sees kinematically dimmed,
softened emission
Prompt Gamma Rays
1/G(t) Afterglow Cone
baryons
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Hypothesis The primary output of GRB is gamma
rays and pairs. GRB spectra are intrinsically
similar peaking at about 1 MeV, and the
apparent difference is due to viewing angle
effects.
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Eiso- ?peak correlation (Amati et al 2002,
Atteia et al 2003) Eiso
proportional to ?peak2
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Butler et al 2007
threshold
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Horizontal purple line is Amati relation
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X-ray flashes predicted to be as frequent as GRB
if beam has a non-trivial morphology e.g.
annulus.
Observer outside of extended beam offset
angle less than or comparable to opening angle of
beam - sees diminished Eiso and npeak as per
the Amati et al relation, However, there must
be many such viewers. So consider a beam shape
that accommodates many such viewers by having
lots of perimeter relative to solid angle.e.g.
annulus.
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Off-axis Viewing as Grand Eiso- ?peak
Correlate Viewer outside annulus
annulus
Pencil beam ??????
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Inside annulus
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Choosing an annulus with outer opening angle
about 0.1 radians , thickness about 0.03, and G
102 , and standard cosmology gives a
distribution of ( cosmological redshift
uncorrected ) Epeak that is flat, as observed
(Eichler and Levinson 2004).
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GRBs
XRFs
1 MeV
10 KeV
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Apparent Gamma ray efficiencies (i.e. apparent
gamma ray energy E to .
apparent blast energy EK)
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Plotting gamma ray efficiency Eg/EB gamma ray
energy to inferred blast energy - with and
without viewing angle correction shows a
qualitative difference in the ordering of the
data. (Eichler and Jontof-Hutter 2005) With the
viewing angle correction the gamma ray
efficiencies separate into two classes. The
majority (17/22, pre-Swift) has Eg/EB 7, much
higher than estimate without a viewing angle
correction.
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The other - 5 outliers of total sample of 22
(pre-Swift) GRBs with known redshifts - has
Eg/EB 102. (Even higher) Note that all
outliers have Eg/EB gtgt 1. No outliers in the
other direction yet. So even though X-ray
afterglow is almost always seen, it does not
always show a baryonic output that compares in
total energy to the prompt gamma ray emission.

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• So viewing angle correction, assuming
  universality among primary GRB output,
• reduces scatter in Eprompt,g/EK
• raises its value

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20 expected from inner shocks
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Efficiencies with viewing angle correction


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Without viewing angle correction, the scatter in
gamma ray efficiency is much larger
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Iuside 1/G afterglow cone
Outside 1/G afterglow cone
Inside 1/G prompt emission cone
Head-on
Apparent Eg/7.1Ek
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Ek estimate from X-ray afterglow depends on time
of X-ray measurement
Apparent
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Why is the Ghirlanda relation different from the
Amati relation? Eiso proportional to E2peak Eg
proportional to E1.5peak
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Inferred opening angle (x-axis) overbiased for
soft GRB?
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If afterglow theory is correct INFERRED opening
angle is overestimated for off-beam viewing by
npeak1/4 . This explains the npeak1/2 difference
between the Amati and Ghirlanda relations
(Levinson and Eichler 2005).
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Eiso- ?peak2 correlation (Amati et al 2002,
Atteia et al 2003)
Eigmma - ?peak1.5 (Ghirlanda et. al
2004)
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q K tb3/8EB-1/8, so the beaming correction
made by Frail, K tb3/8Eiso-1/8 2, should be
proportional to (Eiso/EB)1/4 or npeak1/2. which
is exactly the difference between the Amati and
Ghirlanda relations!. Does this support the
physical interpretations of q K tb3/8EB-1/8
and Eiso/ npeak2 ? What we know is that Eiso
K tb3/8Eiso-1/8 2 and Eiso/ npeak2 each
have considerably less scatter than Eiso, npeak2
separately. If you believe that each has a
physical basis, then you probably have to believe
that the Ghirlanda relation differs from the
Amati one by npeak1/2
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• What we know is that (Frail) Eiso K
  tb3/8Eiso-1/8 2, (i.e. tb3/4Eiso3/4 ) and
  (Amati et al) Eiso/npeak2 (Eiso3/4/npeak3/2 )
  each have considerably less scatter than Eiso,
  npeak2 separately. If you believe each
  separately, then you probably have to believe
  the Ghirlanda relation, tb3/4Eiso3/4 /npeak3/
• 2 .

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Although this is a mathematical tautology, it
makes sense that opening angle (function of host
star?) and viewing angle should vary from one GRB
to the next, even if spectra and primary energy
output are universal. Accounting for each
reduces the scatter accounting for both reduces
scatter even more.
.
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So, with the viewing angle interpretation, most
everybody should be happy. Amati et al and
Ghirlanda et al should both be happy because
they are both right. Frail et al should be happy
that an additional effect, besides opening angle
correction, explains residual dispersion in Eiso.
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Viewing angle proponents should be happy that
no ad hoc intrinsic dependence of npeak needs
to be invoked to understand Amati et al relations
and the like.
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Why is X-ray afterglow almost always seen within
several hours?
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Because the 1/G spread in the afterglow emission
cone is wider, after several hours, than that of
the prompt emission, and is wide enough to cover
most relevant viewing angles.
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High E/EK outlier
Off set viewer sees slower decline (or possibly
rise) in X-ray afterglow during several minutes
to hours than on beam viewer. (Eichler 2005)
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ENTER SWIFT
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Eichler and Granot, 2006
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Eichler and Granot, 2006
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Many authors had predicted delayed afterglow for
offset viewers. The surprise from Swift was that
is came even when the gamma ray emission was
bright and hard (e.g. GRB 050315). One
interpretation Gamma-ray bright, baryon poor
line of sight (not expected if baryon KE is
primary). Supported by Dec. 27, 2004 giant flare
from SGR 1806-20. Prompt gamma rays could not
have been seen if they had been mixed in with the
baryons.
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Fast Rise, Slow Decay Subpulses from scattering
off slow, accelerating baryonic clouds.
Cloud accelerated by photons pressure of Poynting
flux
Observer
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FREDs
Later,
Observer
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FREDs
Still later
Observer
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Optically thin scattering cloud
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Sharply rising FREDs Optically thick cloud?
Observer
Backscattered radiation in frame of cloud.
Shadow in frame of cloud
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FREDs
Optically thick cloud accelerated by photon
pressure of Poynting flux
Observer
Backscattered radiation relativistically beamed
in observer frame
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FREDs
Optically thick cloud accelerated by photon
pressure of Poynting flux
Observer
shadow
Backscattered radiation relativistically beamed
in observer frame
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FREDs
Optically thick cloud accelerated by photon
pressure of Poynting flux
Observer
shadow
Backscattered radiation relativistically beamed
in observer frame
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Optically thick cloud
Blocked by high optical depth Switches on just
when q 1/G.
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Why are prompt emission and baryon KE
consistently so close to each other in energy?
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Why are prompt emission and baryon KE
consistently so close to each other in
energy? Because radially-combed, then scattered
radiation always imparts half its (momentum,
and therefore) energy to a relativistic
scattering cloud. So slow baryons and prompt
gamma rays get equal amounts
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Radiation scattered to very large viewing angles
by slow baryons is expected to some degree in
most GRB models. It produces scatter in Eiso
but without changing the spectrum, or the
observed break time (if there is one) so it
introduces one sided scatter in both the Frail
and Amati relations. The scatter is always in the
direction of hard or underluminous GRB. The
burst duration is biased toward shorter GRB.
Vmax is lower than for small viewing angles, so
these bursts should be less frequent.
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Butler et al 2007
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Short duration GRB harder, less frequent, less
inferred total energy
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We find that the pulses we study are consistent
with a thermal blackbody radiation throughout
their duration and that the temperature kT can be
well described by a broken power law as a
function of time, with an initially constant
temperature or weak decay (100 keV). After the
break, most cases are consistent with a decay
with index -2/3. Ryde 2004 ApJ 614827
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Ryde 2004
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• Spectral evolution of spikes scales as
• Epeak a t-2/3
• Signature of Acceleration of Source?
• Lorentz factor of the accelerating blob scales
  as
• a R1/3
• Spectral peak photon energy is E in source
  frame, E/G in blob frame, and in observers
  frame
• Epeak E / G2 (1 - bcosq)

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When G lt 1/q, i.e. before break (forward or
side scattering), T roughly constant or slightly
decreasing When G gtgt 1/q, i.e. after break,
(backward scattered) t a R (1 bcosq) is
approximately q2/2 Epeak a G -2 a R -2/3 a
t -2/3
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Are short bursts really short? Why should there
be two types of central engines? Maybe they
are just seen at large viewing angles and
scattered into line of sight by slow baryon
clouds.
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Are short bursts really short? Why should there
be two types of central engines? Maybe they
are just seen at large viewing angles and
scattered into line of sight by slow baryon
clouds. Search for (rare) orphan breakout
flashes? When GRB fireball is just clearing
away last of host star envelope. (Rare because
they are wide angle, low fluence events.
Coincidence with smothered neutrino burst?)
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Can dearth of early afterglow be because
ultrarelativistic shocks do not accelerate
particles diffusively? (If so, why does the Crab
Nebula which is both a termination shock AND an
ultrarelativistic shock, display such excellent
non-thermal particle acceleration?)
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Can dearth of early afterglow be because
ultrarelativistic shocks do not accelerate
particles diffusively? (If so, why does the Crab
Nebula which is both a Q-perp termination
shock AND ultrarelativistic, display such
excellent non-thermal particle accelerations?) Pos
sibly because of difference between diffusive
shock acceleration, where particles catch the
shock, and stochastic shock acceleration
(Schatzman 1962), where particles are scattered
WHILE in contact with the shock.
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Condition for thermal injection Q-parallel
geometry (Edmiston, Kennel and Eichler 1982) -
becomes condition for diffusive shock
acceleration for ultrarelativistic shocks,
because all particles must travel at most at c.
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c/3
c
Downstream frame
Condition for diffusive acceleration sin ? gt1/3
in downstream frame.
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?0 20 ?B0 60o
Superluminal shock
?mfp 10
p4.23 f(p)
?mfp 20
?mfp 50
?mfp 100
?mfp 10
Fraction of particles above p
20
?mfp 100
?mfp 50
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Stochastic but not diffusive shock acceleration
?B0 20o
weak scat.
?B0 60o
strong scat.
?crit
Values of ?crit below the lines (strong
scattering) produce spectra harder than E-2.5
?B0 80o
? ?crit rg yields E-2.5 spectrum
Shock Lorentz factor, ?0
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Diffusive SA regime
?0 10
Portion of ?B0-??mfp space where spectra harder
than E-2.5 can occur
?mfp
weak scat.
strong scat.
?crit
? ?crit rg yields E-2.5 spectrum
Shock obliquity, ?B0 deg
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?0 10
?mfp
weak scat.
?mfp
?0 3
strong scat.
?crit
? ?crit rg yields E-2.5 spectrum
Shock obliquity, ?B0 deg
Shock obliquity, ?B0 deg
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Conclusions
Baryon kinetic energy may be merely the tail
that gets wagged (contrary to the inner shock
model). The primary dog is electromagnetic.
(e.g. giant SGR flares.) The baryons are
sprinkled in and accelerated by the gamma
radiation, leading to diversity of individual GRB
fingerprints in light curves. The primary gamma
ray spectrum is a universal one, and variation
among GRB spectral peaks is attributable to
viewing angle effects. .
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• Implications of the viewing angle interpretation
• Most of emission is in gamma rays. Only about 15
  percent in blast. Gamma rays may energize
  baryons rather than the reverse. About 10 of
  energy goes into baryons.
• Sometimes only 10-2 or less in blast
  (baryon-poor line of sight?). At early times,
  when afterglow cone is narrow, this is not
  uncommon.
• Intrinsic spectrum peaks at 1 MeV, as expected
  from a pair annihilation photosphere (Levinson
  and Eichler 1999).
• Non-simple jet topology (e.g. annulus) gives
  best fit to data.

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Non-simple jet topology (e.g. annulus) gives best
fit to data on relative XRF , GRB rate. FREDs
can be explained as scattered radiation from
accelerating baryon clouds. Dearth of X-ray
afterglow at early times can be attributed to
viewer offset effect, or to failure of
ultrarelativistic shocks to accelerate particles
stochastically. Sharp X-ray flaring may be just
favorable fluctuations in the magnetic geometry.