1. Sorting out GRB correlations with spectral peak David Eichler (presented by Jonathan Granot)

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

3. E iso - peak correlation (Amati et al 2002, Atteia et al 2003) E iso  peak 2

4. Observer outside of extended beam – offset angle less than or comparable to opening angle of beam - sees diminished E iso 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.

5. Off-axis Viewing as Grand E iso - peak Correlate Viewer outside annulus Pencil beam  annulus  Eichler & Levinson (2004)

6. Inside annulus  Eichler & Levinson (2004) E peak   -1, E iso   -    1+(  obs ) 2   2  /2 <  obs -  0 | ≲  0 (near edge)   3  obs ≳ 2  0 (point source limit) E peak   -1, E iso   -  where   1+(  obs ) 2   2 for  /2 < |  obs -  0 | ≲  0 (near edge)   3 for  obs ≳ 2  0 (point source limit)

7.  0  Choosing an annulus with half-opening angle  0  0.1 rad, thickness   0.03 rad, and  ~ 10 2, and standard cosmology gives a distribution of (cosmological redshift uncorrected) E peak that is flat, as observed (Eichler & Levinson 2004).

8. Eichler & Levinson (2004)  Different jet thicknesses  “on-axis” events at redshifts where most of the comoving volume resides obs obs from the jet symmetry axis at the maximal redshift out to which it could be detected (GRBs) “on-axis” (XRFs) “Off-axis”

9. 1 MeV10 KeV GRB’sXRF’s Different fluence detection thresholds

10. Why is the Ghirlanda relation, E   (E peak ) 1.5, different from the Amati relation, E iso  (E peak ) 2 ?

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

12. If afterglow theory is correct, INFERRED opening angle is overestimated for off-beam viewing by  p 1/4. This explains the  p 1/2 difference between the Amati and Ghirlanda relations Levinson and Eichler (2005).   2 E iso = f b -1 E  (E p /E p,max ) - , f b  (  out 2 -  in 2 )/2,   2  jet = 0.16[t jet,d /(1+z)] 3/8 (n 0   /E iso,52 ) 1/8  (E iso ) -1/8 f b,app   jet 2 /2   out 2 /2  (E iso ) -1/4  E p -  /4 E ,app = f b,app E iso  [1- (  in /  out ) 2 ] -1 E  (E p /E p,max ) -3  /4

13. E iso  peak 2 (Amati et al 2002, Atteia et al 2003) E   peak 1.5 (Ghirlanda et. al 2004)

14.  = K t b 3/8 E k,iso -1/8, then the beaming correction,  2 is proportional to E k,iso -1/4 or peak 1/2. So the true opening angle is confirmed, within the framework of this interpretation, to indeed be  E k,iso -1/8, as predicted by afterglow theory.

15. 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 E iso.

16. 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 E k,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.

17. 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?

18. 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.

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

20. Plotting gamma ray efficiency E  /E B – 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  /E B ~ 7

21. The other - 5 outliers of total sample of 22 GRB’s with known redshifts - has E  /E B ~10 2. Note that all outliers have E  /E B >> 1. No outliers in the other direction yet.

22. Efficiencies with viewing angle correction

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

25. Theoretical viewing angle correction

26. 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.