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تسجيل مستخدم جديدIntrisic Dispersion of Correlations among Ep, Lp, and Eiso of Gamma Ray Bursts depends on the quality of Data Set
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We reconsider correlations among the spectral peak energy ($E_p$), 1-second peak luminosity ($L_p$) and isotropic energy (Eiso), using the database constructed by citet{yonetoku10} which consists of 109 Gamma-Ray Bursts (GRBs) whose redshifts are known and $E_p$, $L_p$ and Eiso are well determined. We divide the events into two groups by their data quality. One (gold data set) consists of GRBs with peak energies determined by the Band model with four free parameters. On the other hand, GRBs in the other group (bronze data set) have relatively poor energy spectra so that their peak energies were determined by the Band model with fixed spectral index (i.e. three free parameters) or by the Cut-off power law (CPL) model with three free parameters. Using only the gold data set we found the intrinsic dispersion in $log L_p$ ($=sigma_{rm int}$) is 0.13 and 0.22 for tsutsui correlation ($T_L equiv E_{rm iso}/L_p$) and yonetoku correlation, respectively. We also find that GRBs in the bronze data set have systematically larger $E_p$ than expected by the correlations constructed with the gold data set. This means that the intrinsic dispersion of correlations among $E_p$, $L_p$, and Eiso of GRBs depends on the quality of data set. At present, using tsutsui correlation with gold data set, we would be able to determine the luminosity distance with $sim 16%$ error, which might be useful to determine the nature of the dark energy at high redshift $z > 3$.
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We collect and reanalyze about 200 GRB data of prompt-emission with known redshift observed until the end of 2009, and select 101 GRBs which were well observed to have good spectral parameters to determine the spectral peak energy ($E_p$), 1-second p
eak luminosity ($L_p$) and isotropic energy ($E_{rm iso}$). Using our newly-constructed database with 101 GRBs, we first revise the $E_p$--$L_p$ and $E_p$--$E_{rm iso}$ correlations. The correlation coefficients of the revised correlations are 0.889 for 99 degree of freedom for the $E_p$--$L_p$ correlation and 0.867 for 96 degree of freedom for the $E_p$--$E_{rm iso}$ correlation. These values correspond to the chance probability of $2.18 times 10^{-35}$ and $4.27 times 10^{-31}$, respectively. It is a very important issue whether these tight correlations are intrinsic property of GRBs or caused by some selection effect of observations. In this paper, we examine how the truncation of the detector sensitivity affects the correlations, and we conclude they are surely intrinsic properties of GRBs. Next we investigate origins of the dispersion of the correlations by studying their brightness and redshift dependence. Here the brightness (flux or fluence) dependence would be regarded as an estimator of the bias due to the detector threshold. We find a weak fluence-dependence in the $E_p$--$E_{rm iso}$ correlations and a redshift dependence in the $E_p$--$L_p$ correlation both with 2 $sigma$ statistical level. These two effects may contribute to the dispersion of the correlations which is larger than the statistical uncertainty. We discuss a possible reason of these dependence and give a future prospect to improve the correlations.
We study the possible effects of selection biases on the Ep-Liso correlation caused by the unavoidable presence of flux-limits in the existing samples of Gamma Ray Bursts (GRBs). We consider a well defined complete sample of Swift GRBs and perform Mo
nte Carlo simulations of the GRB population under different assumptions for their luminosity functions. If we assume that there is no correlation between the peak energy Ep and the isotropic luminosity Liso, we are unable to reproduce it as due to the flux limit threshold of the Swift complete sample. We can reject the null hypothesis that there is no intrinsic correlation between Ep and Liso at more than 2.7 sigma level of confidence. This result is robust against the assumptions of our simulations and it is confirmed if we consider, instead of Swift, the trigger threshold of the Batse instrument. Therefore, there must be a physical relation between these two quantities. Our simulations seem to exclude, at a lower confidence level of 1.6 sigma, the possibility that the observed Ep-Liso correlation among different bursts is caused by a boundary, i.e. such that for any given Ep, we see only the largest Liso, which has a flux above the threshold of the current instruments.
Context. In the context of an in-depth understanding of GRBs and their possible use in cosmology, some important correlations between the parameters that describe their emission have been discovered, among which the Ep,i-Eiso correlation is the most
studied. Because of this, it is fundamental to shed light on the peculiar behaviour of a few events, namely GRB 980425 and GRB 031203, that appear to be important outliers of the Ep,i-Eiso correlation. Aims. In this paper we investigate if the locations of GRB 980425 and GRB 031203, the two (apparent) outliers of the correlation, may be due to an observational bias caused by the lacking detection of the soft X-ray emissions associated with these GRBs, from respectively the BATSE detector on-board the Compton Gamma-Ray Observer and INTEGRAL, that were operating at the epoch of the observations. We analyse the observed emission of other similar sub-energetic bursts (GRBs 060218, 100316D and 161219B) observed by Swift and whose integrated emissions match the Ep,i-Eiso relation. We simulate their integrated and time-resolved emissions as would have been observed by the same detectors that observed GRB 980425 and GRB 031203, aimed at reconstructing the light curve and spectra of these bursts. Results. If observed by old generation instruments, GRB 060218, 100316D and 161219B would appear as outliers of the Ep,i-Eiso relation, while if observed with Swift or WFM GRB 060218 would perfectly match the correlation. We also note that the instrument BAT alone (15-150 keV) actually measured 060218 as an outlier. Conclusions. We suggest that if GRB 980425 and GRB 031203 would have been observed by Swift and by eXTP they may have matched the Ep,i-Eiso relation. This provides strong support to the idea that instrumental biases can make some events in the lower-left corner of the Ep,i-Eiso plane appearing as outliers of the Amati relation.
I investigate the origin of the observed correlation between a GRBs nuFnu spectral peak Epk and its isotropic equivalent energy Eiso through the use of a population synthesis code to model the prompt gamma-ray emission from GRBs. By using prescriptio
ns for the distribution of prompt spectral parameters as well as the populations luminosity function and co-moving rate density, I generate a simulated population of GRBs and examine how bursts of varying spectral properties and redshift would appear to a gamma-ray detector here on Earth. I find that a strong observed correlation can be produced between the source frame Epk and Eiso for the detected population despite the existence of only a weak and broad correlation in the original simulated population. The energy dependance of a gamma-ray detectors flux-limited detection threshold acts to produce a correlation between the source frame Epk and Eiso for low luminosity GRBs, producing the left boundary of the observed correlation. Conversely, very luminous GRBs are found at higher redshifts than their low luminosity counterparts due to the standard Malquest bias, causing bursts in the low Epk, high Eiso regime to go undetected because their Epk values would be redshifted to energies at which most gamma-ray detectors become less sensitive. I argue that it is this previously unexamined effect which produces the right boundary of the observed correlation. Therefore, the origin of the observed correlation is a complex combination of the instruments detection threshold, the intrinsic cutoff in the GRB luminosity function, and the broad range of redshifts over which GRBs are detected. These simulations serve to demonstrate how selection effects caused by a combination of instrumental sensitivity and the cosmological nature of an astrophysical population can act to produce an artificially strong correlation between observed properties.
We study the distribution of long Gamma Ray Bursts in the Ep-Eiso and in the Ep,obs-Fluence planes through an updated sample of 76 bursts, with measured redshift and spectral parameters, detected up to September 2007. We confirm the existence of a st
rong rest frame correlation Ep ~ Eiso^0.54+-0.01. Contrary to previous studies, no sign of evolution with redshift of the Ep-Eiso correlation (either its slope and normalisation) is found. The 76 bursts define a strong Ep,obs-Fluence correlation in the observer frame (Ep,obs ~ F^0.32+-0.05) with redshifts evenly distributed along this correlation. We study possible instrumental selection effects in the observer frame Ep,obs-Fluence plane. In particular, we concentrate on the minimum peak flux necessary to trigger a given GRB detector (trigger threshold) and the minimum fluence a burst must have to determine the value of Ep,obs (spectral analysis threshold). We find that the latter dominates in the Ep,obs-Fluence plane over the former. Our analysis shows, however, that these instrumental selection effects do not dominate for bursts detected before the launch of the Swift satellite, while the spectral analysis threshold is the dominant truncation effect of the Swift GRB sample (27 out of 76 events). This suggests that the Ep,obs-Fluence correlation defined by the pre--Swift sample could be affected by other, still not understood, selection effects. Besides we caution about the conclusions on the existence of the Ep,obs-Fluence correlation based on our Swift sample alone.
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