Cosmology with GRBs. András Kovács 1. &

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1 Cosmology with GRBs András Kovács 1 andraspankasz@gmail.com & Z. Bagoly 1, P. Veres 1,2, I. Horváth 2, L.G. Balázs 3 1: Dept. Of Physics of Complex Systems, Eötvös University 2: Dept. Of Physics, Bolyai Military University 3: Konkoly Observatory Budapest IBWS Karlovy Vary, 2010.

2 Structure of the talk Theory of k-correction Data for the calculations Results and interpretation GRB Hubble diagram Estimation to the ΩM parameter

3 GRB spectra Parameters: E p e a k, α, β

4 GRB spectra Functions wherewith these spectras well-fitted: Band function, where E 0 =E p e a k (α+2): f E =A E/100 kev α exp E 2 +α Epeak Cutoff Power-law function (CPL): same to the 1 st part of Band, but no β due to the cutoff

5 k-correction Motivation: the energy one can measure with the gamma-ray detectors is not equal to the energy that the burst actually produced in its comoving system Goal: correcting the redshifted GRB spectra

6 k-correction Basic formula: Fluence: where E 1 &E 2 are the energies where D L : luminosity distance Including redshift: between S is calculable Meaning of k: where E 1 =1 kev E 2 =10000 kev Actually not this fluence is measured by the detector Finally:

7 k-correction What do we really have to calculate? S in an [E mi n, E ma x ] range is the measured fluence Measured redshift also necessary, because D L is easily calculable from z numerically

8 k-correction Interpretation: regard consequently this correction as a multiplication factor for the measured energy Important: this is an isotropic energy (not jet model) signed E i s o Follow trough: IDL code

9 The used data Gamma-ray Burst Coordinate Network Needed: z, E p e a k, S, E m i n, E m a x, α, β and of course the errors (the most importants are z & E p e a k ) Not every GRB has all of these, finally i've found 72 samples Most of them are Konus-WIND data

10 The used data I tried to use different data according to Amati In those publications, there are different values for the parameters Question: will the results be similar? LET'S SEE THEM...

11 Results of the corrections Histogram of k values The most frequented k value is ~ 1.2 Average deviation is ~20% from the measured data Some higher values: 1.5 < k < 3

12 Results of the corrections Logarithm of the k-corrected E i s o Most frequented value is ~ erg Only one peak

13 Error calculation Generated Gaussians, N=10000 Corrections also done with wrong parameters Example: α=σ ~ 1 order of magnitude less than E iso The error: α=σ

14 Amati relation Connection between (1+z) E p e a k & E i s o Checked in the past few years: [Amati el al. 2006, 2008] Valid only for long GRBs The correlation itself: There is a linear correlation between the mentioned quantities

15 My results & Amati's relation Outliers are short GRBs Outliers CPL type Band type

16 Intermediate group? IDEA: maybe they are separated... Long GRBs Overlap Intermediate GRBs

17 Comparison with other results Short GRBs My points Conclusions: - both follow the Amati relation - my points are a bit well-correlated Points from a publication based on Suzaku data

18 Comparison with other results Reasons for the differences: - different data from different satellites - diffrences between the calculations - the relative errors of the parameters are higher in the case of other calculations Summary: k-correction was successful, the data can be used for cosmology

19 GRB Hubble diagram Supernova Cosmology Projekt - accelerating expansion Former result: [Schaefer, B.E. 2007] Steps: Consider Amati relation real and fit a line Think the points are exactly on the line Equation of the line one can get DL D L distance modulus formula

20 GRB Hubble diagram - points are mostly over the theoretic curve - time-dilatation causes the same effect - some outliers maybe caused by relatively high errors

21 Estimation to the Ω M parameter By making the k-corrections, the result depends on the parameters of the Universe, because of D L : Change these Question: Amati relation also changes in which case can we get the highest correlation on the log(e i s o )-E p e a k *(1+z) plane?

22 Estimation to the Ω M parameter Calculations have been redone with so many values of Ω M ρ correlation coefficient Cause of 1/ρ to see a minimum value minimum by nearly 0.2

23 Estimation to the Ω M parameter Former results by Amati

24 Summary k-corrections were made for 72 GRBs The data was used for cosmological probes using Amati's relation Conclusions: Comparisons with former studies show good match, but i also have new data In some cases my calculations were more precise, produced better results

25 Thank you for your attention!