[Paper Review] Redshift indicators for gamma-ray bursts

J. L. Atteia|arXiv (Cornell University)|May 4, 2005

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper proposes redshift indicators for gamma-ray bursts (GRBs) using luminosity correlations—particularly the E_peak–E_iso and E_peak–E_rad relations—to estimate pseudo-redshifts without spectroscopic redshifts. It demonstrates that these indicators achieve a dispersion of σ_DL ≈ 0.11–0.15 dex, enabling rapid distance estimation and cosmological applications despite observational biases in redshift measurement.

ABSTRACT

The measure of the distances and luminosities of gamma-ray bursts (GRBs) led to the discovery that many GRB properties are strongly correlated with their intrinsic luminosity, leading to the construction of reliable luminosity indicators. These GRB luminosity indicators have quickly found applications, like the construction of 'pseudo-redshifts', or the measure of luminosity distances, which can be computed independently of the measure of the redshift. In this contribution I discuss various issues connected with the construction of luminosity-redshift indicators for gamma-ray bursts.

Motivation & Objective

• Address the critical lack of spectroscopic redshifts for most GRBs, which limits cosmological and physical understanding.
• Develop reliable redshift indicators based on prompt emission properties to overcome observational biases in redshift distribution.
• Enable rapid distance estimation for high-redshift GRBs (z > 5) to guide prompt follow-up observations.
• Calibrate luminosity indicators for use in cosmology and star formation rate studies beyond z ≈ 3–4.
• Assess the applicability of these indicators to X-ray flashes (XRFs) and short-hard GRBs, where redshift data remain scarce.

Proposed method

• Construct redshift indicators using luminosity correlations such as E_peak–E_iso, E_peak–L_iso, and E_peak–E_rad, derived from GRB spectral and light curve parameters.
• Use the Band function to model GRB spectra and extract E_peak, the energy at which νFν peaks.
• Apply the E_iso (isotropic-equivalent radiated energy) and E_rad (beaming-corrected radiated energy) as luminosity proxies.
• Define σ_DL as the dispersion in log(D_L^pred / D_L^meas) to quantify indicator performance, using measured redshifts as ground truth.
• Apply the indicators to BATSE and HETE-2 GRBs, including XRFs like 020903 and 040701, to test consistency.
• Use cosmological models to convert luminosity indicators into pseudo-redshifts, enabling independent distance estimation.

Experimental results

Research questions

• RQ1 Can luminosity indicators based on prompt emission properties reliably estimate redshifts for GRBs without spectroscopic redshifts?
• RQ2 What is the intrinsic scatter of redshift indicators, and how does it compare to the dispersion in peak luminosity?
• RQ3 Are the same luminosity correlations applicable to X-ray flashes (XRFs), and can they distinguish between nearby soft GRBs and high-redshift classical GRBs?
• RQ4 Can redshift indicators be used to infer the star formation rate beyond z ≈ 3–4, where spectroscopic redshifts are scarce?
• RQ5 To what extent can GRB luminosity indicators constrain cosmological parameters independently of redshift measurements?

Key findings

• The E_rad luminosity indicator exhibits a low intrinsic scatter of 0.35 dex in log(E_rad), approaching standard candle behavior.
• Luminosity indicators based on E_peak–E_iso and E_peak–E_rad relations achieve a dispersion of σ_DL ≈ 0.15 dex for 24 GRBs and σ_DL ≈ 0.11 dex for 13 HETE-2 GRBs.
• The E_peak–E_iso relation successfully predicts redshifts for XRFs 020903 (z = 0.25) and 040701 (z = 0.21), suggesting applicability to XRFs.
• High-redshift GRBs (z > 5) remain undetected in optical bands, and redshift indicators are critical to guide follow-up for such events.
• The variability-luminosity correlation, previously developed for BATSE, is directly applicable to SWIFT GRBs, enhancing indicator robustness.
• The lack of supernova signatures in some XRFs may indicate higher redshifts than predicted by indicators, suggesting potential tension or alternative interpretations.