Luminosity-time correlationsfor GRBs afterglows

Maria Giovanna Dainotti Department of Astronomy, Stanford University, Stanford, California 

In collaboration withFirst part of the talkM. Ostrowski (Crakow Observatory, Krakow, Poland), S. Capozziello , V. F. Cardone (Naples University, Naples, Italy)and R. Willingale (Leicester University, Leicester, UK)And Second part of the talk Vahe’ Petrosian and Jack Singal (Stanford University, Stanford, California) Nikko, Japan, 15-03-2012

1

GRBs as possible cosmological tools?

Nikko, Japan, 15-03-20122

HoweverNotwithstanding the variety of their different peculiarities, some commonfeatures may be identified looking at their light curves.

A crucial breakthrough : the Swift satellite

•rapid follow-up of the afterglows in several wavelengths with better coverage than previous missions

•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)

•This provides the unprecedented opportunity to look for universal features that would allow us to recognize if GRBs are standard candles.

Nikko, Japan, 15-03-20123

Nikko, Japan, 15-03-2012 4

Therefore, studies of correlations between GRB observables are the attempts pursued in this direction

E_iso-E_peak (Lloyd & Petrosian 1999, Amatiet al. (2002,2009))

E_gamma,-E_peak (Ghirlanda et al. 2004, 2006)

L-E_peak (Schaefer 2003,Yonekotu et al. 2004)

L-V (Fenimore & Ramirez Ruiz 2000, Riechart et al. 2001, Norris et al. 2000,S03)

Lpeak- peak_width (Willingale et al. 2010)

Nikko, Japan, 15-03-2012 5

Definition of some physical quantitiesEiso isotropic energy integrated over T90 in the prompt emission.

Epeak the peak of the energy in vu*Fvu spectrum.

T90 time interval between the 5% of the total counts and the 95%. The 90% of the emission is associated to the duration of the event.

T45 time T45 is the time spanned by the brightest 45 % of the total counts above the background.

Tp time at the end of the prompt emission fitted within the Willingale et al. 2007 model.

Ta time at the end of the plateau phase

All the quantities presented in the talk are rescaled for the rest frame

Afterglow LuminosityTime correlation

- comparison between the well fitted by the Willingale model light curves vs

the irregular ones

Dainotti et al. ApJL, 722, L 215 (2010)

Nikko, Japan, 15-03-2012 6

Dainotti et al. MNRAS, 391, L 79D (2008)

Willin

gale

et

al.

W

illin

gale

et

al.

2007

2007

Phenomenological model with Phenomenological model with SWIFT lightcurvesSWIFT lightcurves

Nikko, Japan, 15-03-20127

Nikko, Japan, 15-03-2012

L*x(Ta) vs T*a distribution for the sample of 62 long afterglows

D’Agostini method (D’Agostini 2005 )

errors measurements on both x and y

8

aX TL *

Data and methodologySample : 77 afterglows, 66 long, 11 from IC class detected by Swift from January 2005 up to March 2009, namely all the GRBs with good coverage of data that obey to the Willingale model with firm redshift.

Redshifts : from the Greiner's web page http://www.mpe.mpg.de/jcg/grb.html.Redshift range 0.08 <z < 8.2 Spectrum for each GRB was computed during the plateau

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

Nikko, Japan, 15-03-2012 9

2/122 )()( TaLxE

If we had had a selection effect we would have observed the red points

only for the higher value of fluxes.

Is the tight correlation due to bias selection effects?

Nikko, Japan, 15-03-2012 10

The green triangles are XRFs, red points are the low error bar GRBs

Long GRBs:• for the sample of 62 GRBs out of 66 long the ρLT = -0.76 and the fit line values are • b = −1.06 ± 0.28 and log a = 51.06 ± 1.02

• for the well fitted GRB afterglows (red points) ρLT= -0.93 and the fit is b = -1.05 ± 0.20 and log a = 51.39 ± 0.90

We have conservatively decided to drop short GRBs from the analysis,

to deal with a physically more homogeneous sample of long GRBs (including also XRFs).

"Short" IC GRBs in the sample

• the fit line: b= −1.72 ± 0.22 and log a= 52.57±1.04

• a formally computed correlation coefficient for these 8 points ρLT = - 0.66.

Nikko, Japan, 15-03-2012 11

• LT correlation is highly significant even including the large error points, and it monotonously converges to a limiting value -0.93 for σ(E)<0.09

• The subsample of 8 small error GRBs has redshifts reaching the value z=2.75, the GRB with z=8.26 disappears after decreasing σ(E) below 0.25.

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), Bernardini et al. (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).

Remarks on Lx-Ta and its interpretations

12Nikko, Japan, 15-03-2012

A search for possible physical relations betweenthe afterglow characteristic luminosity L*a ≡Lx(Ta)

and the prompt emission quantities:

1.) the mean luminosity derived as <L*p>45=Eiso/T*45 2.) <L*p>90=Eiso/T*903.) <L*p>Tp=Eiso/T*p 4.) the isotropic energy Eiso

Nikko, Japan, 15-03-2012 13

Prompt – afterglow correlations

Dainotti et al., MNRAS, 418,2202, 2011

Nikko, Japan, 15-03-2012

L*a vs. <L*p>45 for 62 long GRBs (the σ(E) ≤ 4 subsample).

14

Nikko, Japan, 15-03-2012

(L*a, <L*p>45 ) - red (L*a, <L*p>90) - black (L*a, <L*p>Tp ) - green (L*a, Eiso ) - blue

Correlation coefficients ρ for for the long GRB subsamples with the varying error parameter u

15

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 Burstto 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, 775C - Cardone, V.F., Dainotti, M.G., Capozziello, S., and Willingale, R.

2010, MNRAS, 408, 1181C)

Conclusion I

16Nikko, Japan, 15-03-2012

Let’s go one step back

• Are the tests performed so far enough?• Maybe not!!!• 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?

• Namely, the LT correlation is actually intrinsic to GRBs, or is only apparent and is induced by observational limitations?

Nikko, Japan, 15-03-2012 17

Nikko, Japan, 15-03-2012 18

Update of the correlation with 100 GRBsρ=-0.73 (improved from the 77 sample)

a= 53.30b=-1.62±0.20 There is still compatibility in 1σ for the slope

why is the correlation slope changing?

• Therefore, it is imperative to first determine the true correlations among the variables

BEFORE • proceeding with any further

application to cosmology • Or using the luminosity-time

correlation as discriminant among theoretical models for the plateau emission

Nikko, Japan, 15-03-2012 19

Nikko, Japan, 15-03-2012 20

Division in redshift bins of the sample of 77 GRBs

(improved version of Dainotti et al. 2011, ApJ, 730, 135D )

Division in the same redshift bin of the updated sample 100 GRBs with firm redshft and plateau emission

Nikko, Japan, 15-03-2012 21

From a visual inspection it is hard to evaluate if there is redshift evolution or not.Therefore, we have applied the same test of Dainotti et al. 2011, ApJ, 730, 135D Namely we have checked that the slope of every redshift bin is consistent with every other, but it is not enough to answer definitely the question.

But for a more profound and rigorous understanding we apply:

The Efron & Petrosian method (EP) (ApJ, 399,

345,1992) •designed 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 evolution •has been already successfully applied to GRBs(Lloyd,N., & Petrosian, V. ApJ, 1999)

Nikko, Japan, 15-03-2012 22

The technique• Investigation whether the variables of the

distributions, L*X and T*a are correlated with redshift or are statistically independent.

• Namely, do we have luminosity and time evolution?

• If yes,• how to remove the evolution?By defining new and independent variables!

Nikko, Japan, 15-03-2012 23

Nikko, Japan, 15-03-2012 24

How the new variables are built?

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

Nikko, Japan, 15-03-2012 25

Luminosity vs z

Nikko, Japan, 15-03-2012 26

• 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 kL and kT for which τ L,z = 0 and τ T,z = 0 are the ones that best fit the luminosity and

time evolution respectively.

Nikko, Japan, 15-03-2012 27

τ L,z

Nikko, Japan, 15-03-2012 28

τ T,z

Nikko, Japan, 15-03-2012 29

The new approach:• Never applied in literature so far to find the

true slope in two dimensions• We consider again the method of the

associated set to find the slope of the uninvolved correlation:

• The slope computed with this method is compatible with observational results in 1 σ1.6<b<2.5

Nikko, Japan, 15-03-2012 30

Nikko, Japan, 15-03-2012 31

Ta*= Ta’ + α LOG10(Lx’/Lo)

Conclusion II

• The correlation still exists!!!!• The Conclusion of part I are

confirmed!• It can be useful as model

discriminator

Nikko, Japan, 15-03-2012 32