[Paper Review] An independent estimate of the cosmological distance to GRB970228 and GRB970508

V. Lipunov, К. А. Постнов+1 more|ArXiv.org|Mar 27, 1997

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper presents an independent cosmological distance estimate for GRB970228 and GRB970508 using a standard-candle model based on binary neutron star mergers, leveraging BATSE GRB statistical properties. Assuming a flat Ω=1 universe with Λ=0.7, it derives redshifts of z=0.7±0.1 and z=1.9±0.1, respectively, for the two bursts, based on a spectral index s=−1.1±0.3 and a star formation redshift z*=3–10.

ABSTRACT

Assuming binary neutron star mergings as a standard-candle model for GRBs, an independent estimate is obtained for the redshift of GRB970228 and GRB970508 with optical counterparts, using mean statistical properties of GRBs observed by BATSE. We derive z=0.7\pm 0.1 and z=1.9\pm 0.1 for GRB970228 and GRB970508 respectively, depending on the power-law index of the GRB spectrum s=-1.1\pm 0.3 and the value of the redshift of the initial star formation z_*=3-10 in a flat Ω=1 Universe with a cosmological term Λ=0.7.

Motivation & Objective

• To provide an independent estimate of cosmological distances to GRB970228 and GRB970508 using a standard-candle model based on binary neutron star mergers.
• To test the consistency of GRB redshifts derived from statistical properties of BATSE-observed GRBs with known optical counterparts.
• To constrain the redshifts of these two GRBs under a flat Ω=1 cosmological model with a cosmological constant Λ=0.7.
• To assess the impact of spectral index s=−1.1±0.3 and initial star formation redshift z*=3–10 on the derived distance estimates.

Proposed method

• Assumes binary neutron star mergers as a standard-candle model for GRBs, with luminosity tied to statistical properties of BATSE-observed GRB populations.
• Uses the mean energy output and spectral properties of BATSE GRBs to calibrate the luminosity distance scale.
• Applies a power-law spectrum model with index s=−1.1±0.3 to relate observed fluence to intrinsic luminosity.
• Imposes a cosmological model with Ω=1 and Λ=0.7 to convert luminosity distance into redshift.
• Incorporates a star formation redshift z*=3–10 to model the progenitor population's redshift distribution.
• Derives redshift estimates by matching observed GRB fluences to the calibrated luminosity function under the assumed model.

Experimental results

Research questions

• RQ1 What is the cosmological redshift of GRB970228 based on a standard-candle model calibrated from BATSE GRB statistics?
• RQ2 What is the cosmological redshift of GRB970508 under the same standard-candle assumption and cosmological model?
• RQ3 How do uncertainties in the spectral index s=−1.1±0.3 affect the derived redshift estimates for these GRBs?
• RQ4 How sensitive are the redshift estimates to the assumed redshift of initial star formation z*=3–10?
• RQ5 What is the consistency of the derived redshifts with the observed fluences of GRB970228 and GRB970508 in a flat Ω=1, Λ=0.7 universe?

Key findings

• The redshift of GRB970228 is estimated to be z=0.7±0.1 using the binary neutron star merger standard-candle model and BATSE statistical properties.
• The redshift of GRB970508 is estimated to be z=1.9±0.1 under the same assumptions and cosmological model.
• The derived redshifts are consistent with a flat Ω=1 universe and a cosmological constant Λ=0.7.
• The spectral index s=−1.1±0.3 is a key input parameter that influences the luminosity calibration and thus the redshift estimate.
• The initial star formation redshift z*=3–10 is a critical assumption affecting the model's normalization and redshift predictions.
• The results represent an independent estimate of cosmological distances to these GRBs, distinct from other methods such as afterglow redshifts.