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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

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Outline

1- Luminosity Indicators2- Data Sample3- Earlier Work4- Current Results5- Conclusion

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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 …

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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.

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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).

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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)

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• 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).

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Earlier ResultsThe 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.

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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.

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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.

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z no. events A B r

38 51.324 -0.82912 -0.8144

19 51.159 -0.91005 -0.844719 51.630 -0.65448 -0.7468

13 50.988 -0.98728 -0.899713 51.429 -0.70136 -0.715912 51.932 -0.54809 -0.8179

0.00 - 0.99 7 51.068 -0.61921 -0.78541.00 - 1.99 13 51.271 -0.89847 -0.84272.00 - 2.99 9 51.263 -0.95421 -0.85533.00 - 3.99 7 52.158 -0.29873 -0.7977

0.00 - 1.99 20 51.147 -0.90338 -0.83892.00 - 3.99 16 51.668 -0.63937 -0.7553

Binned by number into 3 bins

Entire set

Binned by number into 2 bins

Binned by z with z=1

Binned by z with z=2

Table 1: Correlation of log( lag /(1+z )) vs. log(L )

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z no. events A B r

51 54.797 1.46770 0.7140

26 54.652 1.38420 0.676125 53.808 0.80842 0.4705

17 54.320 1.23070 0.621717 54.841 1.48180 0.715517 53.330 0.43233 0.2978

0.00 - 0.99 14 53.690 0.94410 0.49021.00 - 1.99 15 55.142 1.62970 0.76172.00 - 2.99 9 55.274 1.75010 0.77123.00 - 3.99 7 52.779 0.16225 0.23204.00 - 4.99 5 53.093 0.22617 0.1619

0.00 - 1.99 29 54.636 1.38520 0.67462.00 - 3.99 16 53.849 0.87410 0.55024.00 - 5.99 5 53.093 0.22617 0.1619

Binned by z with z=2

Binned by number into 3 bins

Binned by z with z=1

Entire set

Binned by number into 2 bins

Table 2: Correlation of log(V (1+z )) vs. log(L )

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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.

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50.5

51

51.5

52

52.5

53

53.5

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-2.5 -2 -1.5 -1 -0.5 0 0.5 1

log(tlag)

log

(L)

Bin 1

Bin 2

Bin 3

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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.

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51

52

53

54

55

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-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1

log(V)

log

(L)

Bin 1

Bin 2

Bin 3

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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.

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run no. no. data z A B r

1 69 48.44 1.48 0.866

2 35 48.33 1.49 0.8953 34 49.09 1.26 0.75

4 23 48.46 1.41 0.9025 23 47.65 1.78 0.8486 23 49.91 0.99 0.704

Binned by number2 bins

3 bins

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7 18 48.36 1.46 0.9358 18 48.47 1.45 0.7649 18 48.63 1.43 0.727

10 15 50.06 0.92 0.742

11 14 48.41 1.41 0.92712 14 48.80 1.32 0.76213 14 47.66 1.77 0.78414 14 48.94 1.34 0.75415 13 50.42 0.80 0.663

16 12 48.26 1.50 0.93417 12 48.94 1.23 0.80818 12 47.74 1.77 0.85219 12 48.88 1.26 0.72620 12 48.59 1.53 0.83921 9 49.96 0.97 0.668

5 bins

6 bins

4 bins

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22 19 0.00 - 0.99 48.43 1.41 0.92123 18 1.00 - 1.99 48.33 1.52 0.824 14 2.00 - 2.99 48.02 1.66 0.80225 11 3.00 - 3.99 50.59 0.69 0.60526 5 4.00 - 4.99 50.37 0.87 0.514

27 37 0.00 - 1.99 48.34 1.49 0.89328 25 2.00 - 3.99 48.90 1.33 0.73329 5 4.00 - 5.99 50.37 0.87 0.514

30 51 0.00 - 2.99 48.28 1.53 0.87931 16 3.00 - 5.99 50.31 0.83 0.614

z=2

z=3

Binned by zz=1

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ConclusionIn 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.

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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