[Paper Review] Intrisic Dispersion of Correlations among Ep, Lp, and Eiso of Gamma Ray Bursts depends on the quality of Data Set

Ryo Tsutsui, T. Nakamura+3 more|arXiv (Cornell University)|Dec 14, 2010

Gamma-ray bursts and supernovae3 references3 citations

TL;DR

This study investigates how data quality affects intrinsic dispersion in E_p–L_p and E_p–T_L–L_p correlations among gamma-ray bursts (GRBs). By separating 109 GRBs into 'gold' (Band model with four free parameters) and 'bronze' (CPL or Band with fixed β) datasets, the authors find significantly lower intrinsic scatter in the gold sample (σ_int = 0.13 for E_p–T_L–L_p, 0.22 for E_p–L_p), indicating that spectral fitting method critically influences correlation tightness and cosmological utility.

ABSTRACT

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 $\log L_p$ ($=σ_{ m int}$) is 0.13 and 0.22 for sutsui correlation ($T_L \equiv E_{ m iso}/L_p$) 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 sutsui 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 $z > 3$.

Motivation & Objective

• To assess how the quality of spectral data affects the intrinsic dispersion in E_p–L_p and E_p–T_L–L_p correlations among GRBs.
• To investigate whether systematic biases from spectral fitting models (e.g., Band vs. CPL) contribute to observed scatter in empirical GRB correlations.
• To determine whether GRBs with higher-quality data (gold set) yield tighter, more cosmologically useful correlations than those with lower-quality data (bronze set).
• To evaluate the potential of the E_p–T_L–L_p correlation as a distance indicator for probing dark energy at z > 3.
• To identify and analyze outliers in the gold dataset that may arise from viewing angle effects or detection thresholds.

Proposed method

• The authors use a sample of 109 GRBs with known redshifts and well-determined E_p, L_p, and E_iso from Yonetoku et al. (2010).
• They classify GRBs into 'gold' and 'bronze' datasets based on spectral fitting quality: gold uses the full Band model (four free parameters), bronze uses CPL or Band with fixed β (three free parameters).
• Intrinsic scatter (σ_int) in log L_p is calculated for the E_p–T_L–L_p and E_p–L_p correlations using only the gold dataset.
• The authors compare the E_p values from bronze and gold datasets to assess systematic overestimation in the bronze set.
• Outliers in the gold dataset are identified and classified based on their position in E_p–T_L–L_p space to investigate possible physical origins.
• The cosmological utility of the E_p–T_L–L_p correlation is evaluated by estimating its luminosity distance precision (±16% error).

Experimental results

Research questions

• RQ1 Does the intrinsic dispersion in E_p–L_p and E_p–T_L–L_p correlations depend on the quality of spectral data used to determine E_p?
• RQ2 Are GRBs in the bronze dataset systematically overestimating E_p due to the use of the CPL model or Band model with fixed β?
• RQ3 Can the E_p–T_L–L_p correlation with gold-quality data serve as a reliable cosmological distance indicator at z > 3?
• RQ4 What causes the observed outliers in the gold dataset, and do they arise from viewing angle effects or detection thresholds?
• RQ5 To what extent do systematic errors from spectral fitting methods contribute to the scatter in empirical GRB correlations?

Key findings

• The intrinsic scatter in the E_p–T_L–L_p correlation is σ_int = 0.13 when calculated using only the gold data set, indicating a tight correlation.
• The intrinsic scatter in the E_p–L_p correlation is σ_int = 0.22 for the gold data set, significantly lower than previously reported values.
• GRBs in the bronze dataset have systematically higher E_p values than expected from the gold-based correlations, suggesting a bias from spectral fitting methods.
• The use of the CPL model or Band model with fixed β leads to overestimation of E_p by up to ~100 keV, as shown in simulations by Kaneko et al. (2006).
• Outliers in the gold dataset (e.g., 980425, 000131) may arise from viewing angle effects or detection thresholds, and their removal further tightens the correlation.
• The E_p–T_L–L_p correlation with gold data enables luminosity distance determination with ~16% error, making it a promising tool for probing dark energy at z > 3.