# Presentation: 046011

## Sorting out GRB correlations with spectral peak

**David Eichler**
- (presented by **Jonathan Granot**)

## Hypothesis:  GRB spectra are intrinsically similar – peaking at ~ 1 MeV,  & the apparent differences are due to viewing angle effects. 

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

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

**E****iso  ********  ********peak****2**

## 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.

## Off-axis Viewing as Grand   Eiso- peak Correlate

- Off-axis Viewing as Grand   Eiso- peak Correlate
- Viewer outside annulus

- Pencil beam 

- annulus

- 

- Eichler & Levinson (2004)

## Inside annulus

- 

- Eichler & Levinson (2004)

- Epeak  -1, Eiso  - where   1+(obs)2    2 for /2 < |obs-0| ≲  0 (near edge)     3 for obs ≳ 20 (point source limit)

## Choosing an annulus with half-opening angle 0  0.1 rad, thickness   0.03 rad, and   ~ 102, and standard cosmology gives a distribution of  (cosmological redshift uncorrected)  Epeak that is  flat, as observed (Eichler & Levinson 2004).

## Eichler & Levinson (2004)

- Different jet thicknesses 

- “on-axis” events at redshifts where most of the comoving volume resides

- obs from the jet symmetry axis at the maximal redshift out to which it could be detected

- (GRBs)
- “on-axis”

- (XRFs)
- “Off-axis”

## 1 MeV

- 10 KeV

- GRB’s

- XRF’s

- Different fluence detection thresholds

## Why is the Ghirlanda relation, E  (Epeak )1.5, different from the Amati relation, Eiso (Epeak)2  ?

## Inferred opening angle (x-axis) over-biased for soft GRB?

## If afterglow theory is correct, INFERRED opening angle is overestimated for off-beam viewing by p1/4.

- This explains the  p1/2 difference between the Amati and Ghirlanda relations Levinson and Eichler (2005).
- Eiso = fb-1E(Ep/Ep,max)- , fb  (out2-in2)/2 ,   2
- jet = 0.16[tjet,d/(1+z)]3/8(n0/Eiso,52)1/8  (Eiso)-1/8
-  fb,app  jet2/2  out2/2  (Eiso)-1/4  Ep- /4
- E,app = fb,appEiso  [1- (in/out)2]-1E(Ep/Ep,max)-3/4

## Eiso  peak2  (Amati et al 2002, Atteia et al 2003)   E  peak1.5       (Ghirlanda et. al 2004)

- Eiso  peak2  (Amati et al 2002, Atteia et al 2003)   E  peak1.5       (Ghirlanda et. al 2004)

## = K  tb3/8Ek,iso-1/8,  then the beaming correction, 

- 2  is proportional to  Ek,iso-1/4 or peak1/2.
- So the true opening angle is confirmed, within the framework of this  interpretation, to indeed be
-  Ek,iso-1/8, as predicted by afterglow theory.

## So, with the viewing angle interpretation,  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.

## Afterglow theorists should be happy that break times are connected to opening angle. AND that the true opening angle is indeed “measured” to be proportional to Ek,iso-1/8.

- 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.

## Because the 1/ beaming cone of 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. 

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

## Off-beam viewer sees slower decline  (or possibly rise) in the X-ray afterglow light curve (compared to an on-beam viewer) during  the first several minutes to hours.

## Gamma ray efficiencies (i.e. gamma ray energy to blast energy)

## 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 & Jontof-Hutter 2005)

- With the viewing angle correction  the gamma ray efficiencies separate into two classes.  The majority (17/22)  has E/EB ~ 7

## The other  - 5 outliers of  total sample of 22 GRB’s with known redshifts - has E/EB ~102.

- Note  that all outliers  have E/EB >> 1. No outliers in the other direction yet.

## Efficiencies with viewing angle correction

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

## Slide 24

## Theoretical viewing angle correction

##     Implications of the viewing angle interpretation:

- Most of the energy is in gamma rays. Only ~15% of the energy is in the afterglow shock.  Gamma rays may energize baryons rather than the reverse.
- Sometimes only ~10-2 of the total energy is in the forward shock (baryon-poor line of sight?)
- Intrinsic spectrum peaks at ~1 MeV, as expected from a pair annihilation photosphere (Levinson & Eichler 1999).
- Non-simple jet topology (e.g. annulus) gives best fit to data.