1. 1 Nanjing June 2008 A universal GRB photon energy – luminosity relationship * Dick Willingale, Paul O’Brien, Mike Goad, Julian Osborne, Kim Page, Nial Tanvir arXiv:0710.3727 * except 980425/SN1998bw

2. 2 Nanjing June 2008 The End I will talk about: A new GRB Energy – Luminosity relationship The originating sample of 100 bursts, including short GRBs The introduction of a new robust burst duration metric The relationship to the Amati relation, and its connection to the Band function A response to the criticisms of Butler A hint at a thermal cause of the Band function How this new relationship cannot be used to measure redshift E wz ~ L iso 0.24

3. 3 Nanjing June 2008 The End GRB spectral – energy relationships: –Amati (2006) E pz ~ E iso 0.49 (41 GRBs) –Ghirlanda et al (2004) E pz ~ E γ 0.7 (37 GRBs) –Firmani et al (2006) * L iso ~ E pz 1.62 T 0.45 -0.49 (19 GRBs) –Nava et al (2006)E pz ~ E γ [wind only](18 GRBs) –Yonetoku et al (2004)L iso ~ E pz 2 (16 GRBs) * effectively retracted by Rossi et al. (arXiv:0802.0471) All exclude short GRBs Butler et al (2007) claim they are due to biased estimates New tight relationship: Includes short GRBs Pre-Swift and Swift bursts are the same E wz ~ L iso 0.24

4. 4 Nanjing June 2008 The End Band spectral parameters from the literature: BATSE, BeppoSAX, HETE-2, Konus/Wind, Swift (+Integral, K/W) 7 bursts with low energy photon index >2 excluded as no Ep measurable High energy photon index taken as 2.3 (BATSE mean) if not measured Sample is100 GRBs with redshift (incl 8 shorts & 7 XRFs) νF ν source frame spectra Symbols show isotropic energy density (times peak energy) at peak energy in the source frame Solid line shows observed bandpass Red = short Green = XRF E wz ~ L iso 0.24

5. 5 Nanjing June 2008 The End A new measure of burst length: Sorting intensity samples of a burst into descending order results in a common rate profile well fit by: f(t s )=f 0 [1-(t s /T E ) 1/C L ] C L +f E where T E is total duration, f E is the level at T E and C L is the luminosity index (>1) The profile is normalised to unity, so f 0 +f E =1/T L where T L is the luminosity time. (Peak flux)×T L = fluence, but more importantly in the source frame: L iso T Lz =E iso E wz ~ L iso 0.24

6. 6 Nanjing June 2008 The End E wz ~ L iso 0.24

7. 7 Nanjing June 2008 The End Comparison of T Lz and T 90z and the distribution of T Lz values E wz ~ L iso 0.24

8. 8 Nanjing June 2008 The End Factor E iso : E iso ≡ 4πd L 2 N tot I Band bol /(1+z) α+3 E iso = Q pz E wz Q pz is spectral energy density at peak of νFν source frame spectrum E wz is a characteristic energy of the source Band function E wz ≈ 4.3E pz, although photon indices α & β also contribute E wz ~ L iso 0.24

9. 9 Nanjing June 2008 E wz ~ L iso 0.24 We can approximate the characteristic energy in an empirical fit: E wz ~ E fit = E pz c 0 exp(c 1 -c 2 α-c 3 β) as E iso = Q pz E wz so E iso ~ Q pz E pz c 0 exp(c 1 -c 2 α-c 3 β) Thus some degree of correlation in the E iso – E pz Amati relation seems to be due to the shape of the Band function Understanding Amati means understanding the Band function

10. 10 Nanjing June 2008 The End Peak luminosity density of shorts ~ longs E wz ~ L iso 0.24 E wz Q pz Q pz /T Lz

11. 11 Nanjing June 2008 The prompt emission in the source frame is characterised by: E wz keV is a characteristic energy or colour of spectrum Q pz ergs/keV the spectral density at the peak energy E pz keV E iso = Q pz E wz ergs T LZ secs is a characteristic time it takes to emit E iso L iso ergs/sec is the peak luminosity or effective absolute magnitude L iso = E wz Q pz /T Lz So now we can look at the distribution in a colour-magnitude diagram E wz ~ L iso 0.24

12. 12 Nanjing June 2008 The End E wz /396keV = (L iso /10 50 erg) 0.24 for all bursts except GRB980425/SN1998bw (Pearson correlation coefficient = 0.77, 7.9σ) x E wz E wz ~ L iso 0.24 The main result E wz - Q pz /T Lz E wz - L iso

13. 13 Nanjing June 2008 The End K z ~E wz 0.97 L iso -0.24 is distance offset from best fit K z has very narrow range considering its dependencies: 90% of GRBs have 0.5< K z <2.0; real scatter is present, but is same for pre-Swift and Swift bursts K z is observed not to be a function of redshift E wz ~ L iso 0.24 Swift Pre- Swift

14. 14 Nanjing June 2008 This correlation is not an artifact due to use of correlated inputs Inputs are E p and spectral energy density at the peak (erg.cm -2.keV -1.s -1 ) These are not correlated The criticisms of Butler et al (2007) of the Amati relation do not apply because –All bursts satisfy the relationship –There is no difference between pre-Swift and Swift bursts (see Ghirlanda et al 2008 for a defence of the Amati relationship) The End E wz ~ L iso 0.24

15. 15 Nanjing June 2008 The new relationship would be consistent with the synchrotron internal shock model (which has E pz ~ Γ -2 t var -1 L 0.5, Zhang & Mészáros 2002) if Γ~L 1/8 and t var is the same for all bursts However, neither Γ~L 1/8 nor t var ~const seem natural If the energy peak is thermal, then relativistic expansion of the blackbody photosphere and integration of multiple temperatures gives rise to 10 7 Γ 0 /R 0 ~ K z 2 ~ 1, and so R 0 ~ 3x10 9 cm for Γ 0 ~ 300, ie the thermalisation radius estimated by Thompson, Mészáros & Rees (2007) E wz ~ L iso 0.24

16. 16 Nanjing June 2008 Finally… there’s a sting in the tail We can express K z as product of an observed ratio K and a redshift factor K z =K.C(z) For z>1.5 C(z) is only a very weak function of z. We use measured redshifts to produce the relationship E wz ~L iso 0.24 but K z is useless as a probe of high z (cf Li et al 2007, Schaefer & Collazzi 2007 for Amati) E wz ~ L iso 0.24

17. 17 Nanjing June 2008 Summary: New relationship covers 99 out of 100 bursts, short and long It relates source frame hardness to peak luminosity –a colour – magnitude relationship for GRBs The criticisms of Butler et al (2007) to the Amati relationship and others do not apply to this relationship This new relationship is suggestive of a thermal origin of the prompt emission It cannot be used to determine distance E wz ~ L iso 0.24

18. 18 Nanjing June 2008 The End Backup slides E wz ~ L iso 0.24

19. 19 Nanjing June 2008 The End E wz ~ L iso 0.24

20. 20 Nanjing June 2008 The End E wz ~ L iso 0.24

21. 21 Nanjing June 2008 The End E wz ~ L iso 0.24

22. 22 Nanjing June 2008 The End E wz ~ L iso 0.24

23. 23 Nanjing June 2008 The End E wz ~ L iso 0.24

24. 24 Nanjing June 2008 The End E wz ~ L iso 0.24

25. 25 Nanjing June 2008 The End E wz ~ L iso 0.24

26. 26 Nanjing June 2008 The End E wz ~ L iso 0.24

27. 27 Nanjing June 2008 The End E wz ~ L iso 0.24

28. 28 Nanjing June 2008 E wz ~ L iso 0.24 E iso ≡ 4πd L 2 N tot I Band bol /(1+z) α+3 E iso = Q pz E wz Q z = 4πd L 2 N tot exp[-(α+2)E pz -1 ]/(1+z) α+3 Q pz = Q z exp[(α+2)(E pz -1 -1)]E pz α+1 E wz = exp(α+2)I bol (E pz,α,β)E pz -(α+1)

29. 29 Nanjing June 2008 The End E wz ~ L iso 0.24

30. 30 Nanjing June 2008 The End E wz ~ L iso 0.24