2. Luminosity -time correlation Determination of The intrinsic nature of the Luminosity -time correlation in the X-ray afterglows of GRBs Maria Giovanna Dainotti Stanford University, Stanford, USA Jagellonian University, Krakow, Poland in collaboration with V. Petrosian, Singal,J., R. Willingale, Ostrowski M and Capozziello S., 1 GRB Symposium, Nashville, April 2013

3. Notwithstanding the variety of GRB’s different peculiarities, some common features may be identified looking at their light curves. A crucial breakthrough : a more complex behavior of the lightcurves, different from the broken power-law assumed in the past (Obrien et al. 2006,Sakamoto et al. 2007) A significant step forward in determining common features in the afterglow X-ray afterglow lightcurves of the full sample of Swift GRBs shows that they may be fitted by the same analytical expression (Willingale et al. 2007) 2 Phenomenological model with SWIFT lightcurves GRB Symposium, Nashville, April 2013

4. Lx(T*a) vs T*a distribution for the sample of 62 long afterglows 3 Firstly discovered in 2008 by Dainotti, Cardone, & Capozziello MNRAS, 391, L 79D (2008) Later uptdated by Dainotti, Willingale, Cardone, Capozziello & Ostrowski ApJL, 722, L 215 (2010) Dainotti et al. correlation GRB Symposium, Nashville, April 2013

5. Data and methodology  Sample : 77 afterglows, 66 long, 11 from IC class (short GRBs with extended emission) detected by Swift from January 2005 up to March 2009, namely all the GRBs with good coverage of data that obey to the Willingale et al. 2007 model with firm redshift.  Redshifts : from the Greiner's web page http://www.mpe.mpg.de/jcg/grb.html.http://www.mpe.mpg.de/jcg/grb.html  Redshift range 0.08 <z < 8.2  Spectrum for each GRB was computed during the plateau with the Evans et al. 2010 web page http://www.swift.ac.uk/burst_analyser/ For some GRBs in the sample the error bars are so large that determination of the observables (Lx, Ta ) is not reliable. Therefore, we study effects of excluding such cases from the analysis (for details see Dainotti et al. 2011, ApJ 730, 135D ). To study the low error subsamples we use the respective logarithmic errors bars to formally define the error energy parameter 4GRB Symposium, Nashville, April 2013

6. A search for possible physical relations between the afterglow characteristic luminosity L*a ≡Lx(Ta) and the prompt emission quantities: 1.) the mean luminosity derived as 45=Eiso/T*45 2.) 90=Eiso/T*90 3.) Tp=Eiso/T*p 4.) the isotropic energy Eiso GRB Symposium, Nashville, April 2013 5 Prompt – afterglow correlations Dainotti et al., MNRAS, 418,2202, 2011

7. L*a vs. 45 for 62 long GRBs (the σ(E) ≤ 4 subsample). 6 (L*a, 45 ) - red (L*a, 90) - black (L*a, Tp ) - green (L*a, Eiso ) - blue Correlation coefficients ρ for for the long GRB subsamples with the varying error parameter u The search for standard GRBs continues GRB Symposium, Nashville, April 2013

8. GRBs with well fitted afterglow light curves obey tight physical scalings, both in their afterglow properties and in the prompt-afterglow relations. We propose these GRBs as good candidates for the standard Gamma Ray Burst to be used both - in constructing the GRB physical models and -in cosmological applications -(Cardone, V.F., Capozziello, S. and Dainotti, M.G 2009, MNRAS, 400, 775C2009, MNRAS, 400, 775C -Cardone, V.F., Dainotti, M.G., Capozziello, S., and Willingale, R. 2010, MNRAS, 408, 1181C)2010, MNRAS, 408, 1181C Conclusion I 7GRB Symposium, Nashville, April 2013

9. Let’s go one step back BEFORE proceeding with any further application to cosmology or using the luminosity-time correlation as discriminant among theoretical models for the plateau emission We need to answer the following question: Is what we observe a truly representation of the events or there might be selection effect or biases? Is the LT correlation intrinsic to GRBs, or is it only an apparent one, induced by observational limitations and by redshift induced correlations? THEREFORE, at first one should determine the true correlations among the variables 8GRB Symposium, Nashville, April 2013

10. Division in redshift bins for the updated sample of 100 GRBs (with firm redshift and plateau emission) 9 From a visual inspection it is hard to evaluate if there is a redshift induced correlation. Therefore, we have applied the test of Dainotti et al. 2011, ApJ, 730, 135D to check that the slope of every redshift bin is consistent with every other. BUT for a quantitative analysis we turn to ….. ρ=-0.73 for all the distribution b= -1.32±0.20 1σ compatible with the previous fit GRB Symposium, Nashville, April 2013

11. The Efron & Petrosian method (EP) (ApJ, 399, 345,1992) to obtain unbiased correlations, distributions, and evolution with redshift from a data set truncated due to observational biases. corrects for instrumental threshold selection effect and redshift induced correlation has been already successfully applied to GRBs (Lloyd,N., & Petrosian, V. ApJ, 1999) The technique we applied Investigates whether the variables of the distributions, L* X and T* a are correlated with redshift or are statistically independent. do we have luminosity vs. redshift evolution? do we have plateau duration vs. redshift evolution? If yes, how to accomodate the evolution results in the analysis? By defining new independent variables! 10GRB Symposium, Nashville, April 2013 The Efron and Petrosian Method

12. GRB Symposium, Nashville, April 201311 How the new variables are built? The new variables will be uninvolved in redshift, namely they will be not affected by redshift evolution. The correction will be the following For luminosity: where the luminosity evolution For time where the time evolution We denote with ‘ the not evolved observables

13. How to compute g(z) and f(z)? The EP method deals with data subsets that can be constructed to be independent of the truncation limit suffered by the entire sample. This is done by creating 'associated sets', which include all objects that could have been observed given a certain limiting luminosity. We have to determine the limiting luminosity for the sample GRB Symposium, Nashville, April 201312

14. Luminosity vs 1+z GRB Symposium, Nashville, April 201313 The more appropriate Flux limit is the black dotted line Flux= In such a way we have 90 GRBs in total, but with an appropriate limiting flux

15. A specialized version of the Kendall rank correlation coefficient, τ a statistic tool used to measure the association between two measured quantities takes into account the associated sets and not the whole sample produces a single parameter whose value directly rejects or accepts the hypothesis of independence. The values of k L and k T for which τ L,z = 0 and τ T,z = 0 are the ones that best fit the luminosity and time evolution respectively. GRB Symposium, Nashville, April 201314

16. GRB Symposium, Nashville, April 2013 K L =-0.05 for 100 GRBs red line green 53 GRBs K T =-0.85

17. A new approach: Never applied in literature so far to find the true slope of correlation We consider again the method of the associated set to find the slope of the correlation not evolved with redshift : The slope computed with this method is 1 σ compatible with observational results in 1.5<b<2.0 α=b’ GRB Symposium, Nashville, April 201316 -1.24 <b< -0.93 For 100 GRBs The true slope:

18. Cumulative luminosity function and density function GRB Symposium, Nashville, April 201317 Log Phi can be fitted with a single polinomial, the sigma(z) with two polinomial for z 0.4 The red points show the correction with the Efron and Petrosian (1992) method Log sigma (z) = Sum (1+1/m(j)) where m(j) is the number of the associated sets in the sample For luminosity function the correction is Not relevant

19. The correlation La-Ta exists !!! It can be useful as model discriminator among several models that predict the Lx-Ta anti-correlation : energy injetion model from a spinning-down magnetar at the center of the fireball Dall’ Osso et al. (2010), Xu & Huang (2011), Rowlinson & Obrien (2011) Accretion model onto the central engine as the long term powerhouse for the X-ray flux Cannizzo & Gerhels (2009), Cannizzo et al. 2010 Prior emission model for the X-ray plateau Yamazaki (2009) and the phenomenological model by Ghisellini et al. (2009). For a correct cosmological use we should use the right sample !!!! Conclusions – part II 18GRB Symposium, Nashville, April 2013