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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. Outline 1- Luminosity Indicators 2- Data Sample 3- Earlier Work 4- Current Results 5- Conclusion.
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Evolution of the Epeak 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
Outline1- Luminosity Indicators2- Data Sample3- Earlier Work4- Current Results5- Conclusion
Energy Relations / Luminosity Indicators 1-Lag relation (L – lag) 2-Variability relation (L – V) 3-Amati relation (Ep – Eiso ) 4- Yonetoku relation (Ep – Liso) 5- Ghirlanda relation (Ep – E) 6- Liang-Zhang relation (Ep – Eiso – tb) 7- “Firmani” relation (Ep – Liso – T0.45) more to come …
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.
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).
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)
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 Epeak vs. L relation. • Data sample: 69 GRBs taken from Schaefer (2007).
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.
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.
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.
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.
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.
Current Study We write the Epeak vs. L relation in the form: log(L) = A + B log[Epeak (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.
Conclusion In this study, a sample consisting of 69 GRBs was used to investigate the possible evolution of the Epeak 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 Epeak–L relation does not seem to evolve in any systematic way with redshift.
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