1. 1 Evolution of the E peak vs. Luminosity Relation for Long GRBs W.J. Azzam & M.J. Alothman Department of Physics University of Bahrain Kingdom of Bahrain wjazzam@sci.uob.bh

2. 2 Outline 1- Luminosity Indicators 2- Data Sample 3- Earlier Work 4- Current Results 5- Conclusion

3. 3 Energy Relations / Luminosity Indicators 1- Lag relation (L –  lag ) 2- Variability relation (L – V) 3- Amati relation (E p – E iso ) 4- Yonetoku relation (E p – L iso ) 5- Ghirlanda relation (E p – E  ) 6- Liang-Zhang relation (E p – E iso – t b ) 7- “Firmani” relation (E p – L iso – T 0.45 ) more to come …

4. 4 The importance of these relations lies in: 1- Their potential use as cosmological probes. For instance, to constrain  M and   (Ghirlanda et al. 2006; Capozziello & Izzo 2008; Amati et al. 2008). 2- Insight into the physics of GRBs.

5. 5 Some generalized tests have been carried out to check the robustness of these relations (Schaefer & Collazi 2007) and in fact to produce a GRB Hubble diagram (Schaefer 2007).

6. 6 On the other hand, some studies have tried to deal with the problems of circularity and selection effects: Li et al. (2008) Butler et al. (2008) Ghirlanda et al. (2008) Nava et al. (2009)

7. 7 General purpose of our study: do some (or all) of these relations evolve with z ? In an earlier study (Azzam, Alothman, & Guessoum 2008) we looked at the possible evolution of: 1- the time-lag,  lag, relation 2- the variability, V, relation In this study we consider: possible evolution of the E peak vs. L relation. Data sample: 69 GRBs taken from Schaefer (2007).

8. 8 Earlier Results The entire data sample consists of 69 GRBs, of which 38 have  lag values and 51 have V values.The method consists of binning the data by redshift, z, then writing the time-lag relation in the form: log(L) = A + B log[  lag / (1+z)] and extracting the fit parameters A and B for each redshift bin.

9. 9 Likewise, for the variability relation, which we write in the form: log(L) = A + B log[V (1+z)]. The objective is then to see whether the fitting parameters A and B evolve in any systematic way with the redshift.

10. 10 Note that the binning was done in two ways for each of the two relations: Binning by number in which the number of bursts per bin was fixed. Binning by width in which the  z was fixed.

11. 11

12. 12

13. 13 Figure 1. The best fit lines for the three redshift bins (binning by number) that are presented in Table 1 for the lag-relation, showing a systematic variation of the A and B parameters with redshift.

14. 14 Figure 2. The best fit lines for the three redshift bins (binning by number) that are presented in Table 2 for the variability relation, showing no systematic variation of the A and B parameters with redshift.

15. 15 Current Study We write the E peak vs. L relation in the form: log(L) = A + B log[E peak (1+z)] Again, we bin the data, extract the fitting parameters A and B, and see whether they evolve in any systematic way with redshift.

16. 16

17. 17

18. 18

19. 19

20. 20

21. 21 Conclusion In this study, a sample consisting of 69 GRBs was used to investigate the possible evolution of the E peak vs. L relation. The data was binned in redshift, and the fit parameters A and B were extracted. The parameters A and B showed no systematic dependence on z, and hence the E peak – L relation does not seem to evolve in any systematic way with redshift.

22. 22 References Amati, L. et al. 2002, A&A, 390, 81 Amati, L. 2006, MNRAS, 372, 233 Amati, L. et al. 2008, (arXiv:0805.0377) Butler, N.R. et al. 2008, (arXiv:0802.3396) Capozziello, S. & Izzo, L. 2008, (arXiv:0806.1120) Fenimore, E.E., & Ramirez-Ruiz E. 2000, (astro-ph/0004176) Ghirlanda, G. et al. 2004, ApJ, 616, 331 Ghirlanda, G. et al. 2006, A&A, 452, 839 Ghirlanda, G. et al. 2008, (arXiv:0804.1675) Li, H. et al. 2008, ApJ, 680, 92 Liang, E. & Zhang, B. 2005, ApJ, 633, L611 Norris, J.P. et al. 2000, ApJ, 534, 248 Schaefer, B.E. 2007, ApJ, 660, 16 Schaefer, B.E. & Collazi, A.C. 2007, ApJ, 656, L53 Yonetoku, D. et al. 2004, ApJ, 609, 935