The Primary Output of GRBs

David Eichler

My collaborators:

Amir Levinson

Jonathan Granot

Hadar Manis

Don Ellison (if time)

Which came first, -rays or baryonic jet?

“Slow” sheath of Baryons

Ultrarelativistic fireball

e.g. Levinson and Eichler 1993

Prompt Gamma Rays

1/Γ(t) Afterglow Cone

baryons

Offset observer sees kinematically dimmed, softened emission

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.

Eiso- peak correlation (Amati et al 2002, Atteia et al 2003)

Eiso proportional to peak2

Butler et al 2007

threshold

Horizontal purple line is Amati relation

Observer outside of extended beam – offset angle less than or comparable to opening angle of beam - sees diminished Eiso and peak 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.

X-ray flashes predicted to be as frequent as GRB if beam has a non-trivial morphology

e.g. annulus.

Off-axis Viewing as Grand Eiso- peak Correlate

Viewer outside annulus

Pencil beam

annulus

Inside annulus

Choosing an annulus with outer opening angle

about 0.1 radians ,

thickness about 0.03, and ~ 102 ,

and standard cosmology

gives a distribution of ( cosmological redshift

uncorrected ) Epeak that is flat, as observed

(Eichler and Levinson 2004).

1 MeV10 KeV

GRB’sXRF’s

Apparent Gamma ray efficiencies (i.e. apparent gamma ray energy E to . apparent blast energy EK)

Plotting gamma ray efficiency E/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 E/EB ~ 7, much

higher than estimate without a viewing angle

correction.

The other - 5 outliers of total sample of 22 (pre-Swift) GRB’s with known redshifts - has E/EB ~102. (Even higher)

Note that all outliers have E/EB >> 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.

So viewing angle correction, assuming universality among primary GRB output,

a) reduces scatter in Eprompt,/EK

b) raises its value

20% “expected” from inner shocks

Efficiencies with viewing angle correction

Without viewing angle correction, the scatter in gamma ray efficiency is much larger

Outside 1/afterglow cone

Iuside 1/afterglow cone

Inside 1/ prompt emission cone

Apparent

E/7.1Ek

Head-on

Ek estimate from X-ray afterglow depends on time of X-ray measurement

Apparent

Why is the Ghirlanda relation different from the Amati relation?

Eisoproportional to E2peak

E proportional to E1.5peak

Inferred opening angle (x-axis) overbiased for soft GRB?

If afterglow theory is correct INFERRED opening

angle is overestimated for off-beam viewing by peak1/4

.

This explains the peak1/2 difference between the Amati

and Ghirlanda relations (Levinson and Eichler 2005).

Eiso- peak2 correlation (Amati et al 2002, Atteia et al 2003)

Eigmma - peak1.5 (Ghirlanda et. al 2004)

= 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 peak1/2. which is

exactly the difference between the Amati and

Ghirlanda relations!.

Does this support the physical interpretations of

=K tb3/8EB

-1/8 and Eiso/ peak2 ?

What we know is that Eiso [K tb3/8Eiso

-1/8 ]2 and

Eiso/ peak2 each have considerably less scatter than

Eiso, peak2 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 peak1/2

What we know is that (Frail) Eiso [K tb3/8Eiso

-1/8 ]2, (i.e.

tb3/4Eiso

3/4 ) and (Amati et al) Eiso/peak2 (Eiso

3/4/peak3/2 ) each

have considerably less scatter than Eiso, peak2 separately. If

you believe each separately, then you probably have to

believe the Ghirlanda relation, tb3/4Eiso

3/4 /peak3/

2 .

.

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.

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.

Viewing angle proponents should be happy that

no ad hoc intrinsic dependence of peak needs to

be invoked to understand Amati et al relations

and the like.

Why is X-ray afterglow almost always seen within several hours?

Because the 1/ 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.

Off set viewer sees slower decline (or possibly rise) in X-ray afterglow during several minutes to hours than on beam viewer. (Eichler 2005)

High E/EK outlier

ENTER SWIFT

Eichler and Granot, 2006

Eichler and Granot, 2006

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.

Observer

Fast Rise, Slow Decay Subpulses from scattering off slow, accelerating baryonic clouds.

Τ(t1)

1

Cloud accelerated by photons pressure of Poynting flux

Observer

FRED’s

Τ(t2)

1

Later,

Observer

FRED’s

Τ(t3)

1

Still later…

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14L(abs) function of

L(ab

s)

= 15

Optically thin scattering cloud

Observer

Sharply rising FRED’s

Optically thick cloud?

Backscattered radiation in frame of cloud.

Shadow in frame of cloud

FRED’s

Observer

Τ(t1)

1

Optically thick cloud accelerated by photon pressure of Poynting flux

Backscattered radiation relativistically beamed in observer frame

shadow

FRED’s

Observer

Τ(t1)

1

Optically thick cloud accelerated by photon pressure of Poynting flux

Backscattered radiation relativistically beamed in observer frame

shadow

FRED’s

Observer

Τ(t1)

1

Optically thick cloud accelerated by photon pressure of Poynting flux

Backscattered radiation relativistically beamed in observer frame

shadow

Optically thick cloud

Blocked by high optical depth

Switches on just when = 1/.

Why are prompt emission and baryon KE consistently so close to each other in energy?

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

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.

Butler et al 2007

Short duration GRB harder, less frequent, less inferred total energy

“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 614:827

Ryde 2004

Spectral evolution of spikes scales as:

Epeak t-2/3

Signature of Acceleration of Source?

Lorentz factor of the accelerating blob scales as:

R1/3

Spectral peak photon energy is E* in source frame, E*/ in blob frame, and in observer’s frame:

Epeak = E* / 2 (1 - cos)

When < 1/i.e. before break (forward or side scattering), T roughly constant or slightly decreasing

When >> 1/i.e. after break, (backward scattered) t R

(1 – cos is approximately 2/2

Epeak -2 R -2/3 t -2/3

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.

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?)

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?)

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?)

Possibly 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.

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.

cc/3

Downstream frame

Condition for diffusive acceleration:

sin θ >1/3 in downstream frame.

mfp = 20

mfp = 50

mfp = 100

mfp = 10

0 = 20

B0 = 60o

20

mfp = 50mfp = 100

mfp = 10

p4

.23 f

(p)

Fra

ctio

n o

f p

arti

cles

ab

ove

p

mfp gr

Superluminal shock

B0 = 20o

B0 = 60o

B0 = 80o

cri

t

Shock Lorentz factor, 0

strong scat.

weak scat.

Values of crit below the

lines (strong scattering) produce spectra harder

than E-2.5

= crit rg yields E-2.5

spectrum

Stochastic but not diffusive shock acceleration

mfp

0 = 10

Portion of B0-mfp space where spectra harder

than E-2.5 can occur

strong scat.

weak scat.

Shock obliquity, B0 [deg]

= crit rg yields E-2.5

spectrum

crit

Diffusive SA regime

mfp

0 = 10

strong scat.

weak scat.

Shock obliquity, B0 [deg]

= crit rg yields E-2.5

spectrum

crit

Shock obliquity, B0 [deg]

mfp 0 = 3

ConclusionsBaryon 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.

.

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.

Non-simple jet topology (e.g. annulus) gives best fit to data on relative XRF , GRB rate.

FRED’s 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.