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A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram

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 Added by Nan Liang
 Publication date 2008
  fields Physics
and research's language is English




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An important concern in the application of gamma-ray bursts (GRBs) to cosmology is that the calibration of GRB luminosity/energy relations depends on the cosmological model, due to the lack of a sufficient low-redshift GRB sample. In this paper, we present a new method to calibrate GRB relations in a cosmology-independent way. Since objects at the same redshift should have the same luminosity distance and since the distance moduli of Type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a GRB at a given redshift by interpolating from the Hubble diagram of SNe Ia. Then we calibrate seven GRB relations without assuming a particular cosmological model and construct a GRB Hubble diagram to constrain cosmological parameters. From the 42 GRBs at $1.4<zle6.6$, we obtain $Omega_{rm M}=0.25_{-0.05}^{+0.04}$, $Omega_{Lambda}=0.75_{-0.04}^{+0.05}$ for the flat $Lambda$CDM model, and for the dark energy model with a constant equation of state $w_0=-1.05_{-0.40}^{+0.27}$, which is consistent with the concordance model in a 1-$sigma$ confidence region.



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Relations linking the temporal or/and spectral properties of the prompt emission of gamma-ray bursts (hereafter GRBs) to the absolute luminosity are of great importance as they both constrain the radiation mechanisms and represent potential distance indicators. Here we discuss two such relations: the lag-luminosity relation and the newly discovered duration-luminosity relation of GRB pulses. We aim to extend our previous work on the origin of spectral lags, using the duration-luminosity relation recently discovered by Hakkila et al. to connect lags and luminosity. We also present a way to test this relation which has originally been established with a limited sample of only 12 pulses. We relate lags to the spectral evolution and shape of the pulses with a linear expansion of the pulse properties around maximum. We then couple this first result to the duration-luminosity relation to obtain the lag-luminosity and lag-duration relations. We finally use a Monte-Carlo method to generate a population of synthetic GRB pulses which is then used to check the validity of the duration-luminosity relation. Our theoretical results for the lag and duration-luminosity relations are in good agreement with the data. They are rather insensitive to the assumptions regarding the burst spectral parameters. Our Monte Carlo analysis of a population of synthetic pulses confirms that the duration-luminosity relation must be satisfied to reproduce the observational duration-peak flux diagram of BATSE GRB pulses. The newly discovered duration-luminosity relation offers the possibility to link all three quantities: lag, duration and luminosity of GRB pulses in a consistent way. Some evidence for its validity have been presented but its origin is not easy to explain in the context of the internal shock model.
Thanks to their enormous energy release, Gamma Rays Bursts (GRBs) have recently attracted a lot of interest to probe the Hubble diagram (HD) deep into the matter dominated era and hence complement Type Ia Supernovae (SNeIa). We consider here three different calibration methods based on the use of a fiducial LCDM model, on cosmographic parameters and on the local regression on SNeIa to calibrate the scaling relations proposed as an equivalent to the Phillips law to standardize GRBs finding any significant dependence. We then investigate the evolution of these parameters with the redshift to obtain any statistical improvement. Under this assumption, we then consider possible systematics effects on the HDs introduced by the calibration method, the averaging procedure and the homogeneity of the sample arguing against any significant bias.
In this paper, we present a model-independent approach to calibrate the largest quasar sample. Calibrating quasar samples is essentially constraining the parameters of the linear relation between the $log$ of the ultraviolet (UV) and X-ray luminosities. This calibration allows quasars to be used as standardized candles. There is a strong correlation between the parameters characterizing the quasar luminosity relation and the cosmological distances inferred from using quasars as standardized candles. We break this degeneracy by using Gaussian process regression to model-independently reconstruct the expansion history of the Universe from the latest type Ia supernova observations. Using the calibrated quasar dataset, we further reconstruct the expansion history up to redshift of $zsim 7.5$. Finally, we test the consistency between the calibrated quasar sample and the standard $rm{Lambda}CDM$ model based on the posterior probability distribution of the GP hyperparameters. Our results show that the quasar sample is in good agreement with the standard $rm{Lambda}CDM$ model in the redshift range of the supernova, despite of mildly significant deviations taking place at higher redshifts. Fitting the standard $rm{Lambda}CDM$ model to the calibrated quasar sample, we obtain a high value of the matter density parameter $Omega_m = 0.382^{+0.045}_{-0.042}$, which is marginally consistent with the constraints from other cosmological observations.
With the understanding that the enigmatic Gamma-Ray Burts (GRBs) are beamed explosions, and with the recently discovered ``Ghirlanda-relation, the dream of using GRBs as cosmological yardsticks may have come a few steps closer to reality. Assuming the Ghirlanda-relation is real, we have investigated possible constraints on cosmological parameters using a simulated future sample of a large number of GRBs inspired by the ongoing SWIFT mission. Comparing with constraints from a future sample of Type Ia supernovae, we find that GRBs are not efficient in constraining the amount of dark energy or its equation of state. The main reason for this is that very few bursts are available at low redshifts.
206 - H.L. Xiao , W. Hajdas , T.W. Bao 2015
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