[Paper Review] Cosmology with Gamma Ray Bursts

G. Ghisellini, G. Ghirlanda+4 more|arXiv (Cornell University)|Apr 13, 2005

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper proposes using the Ghirlanda correlation—linking the collimation-corrected isotropic energy ($E_\gamma$) and peak spectral energy ($E_{\rm peak}$) of gamma-ray bursts (GRBs)—as a cosmological distance indicator. By calibrating GRBs as 'known candles' via afterglow lightcurve breaks, the authors demonstrate that 15 GRBs with measured redshifts and jet breaks yield tight Hubble diagram residuals, supporting their use to probe cosmic expansion up to $z \sim 4.5$ and potentially bridge the gap between the CMB and Type Ia supernovae.

ABSTRACT

Apparently, Gamma-Ray Bursts (GRBs) are all but standard candles. Their emission is collimated into a cone and the received flux depends on the cone aperture angle. Fortunately we can derive the aperture angle through an achromatic steepening of the lightcurve of the afterglow, and thus we can measure the "true" energetics of the prompt emission. Ghirlanda et al. (2004) found that this collimation-corrected energy correlates tightly with thefrequency at which most of the radiation of the prompt is emitted. Through this correlation we can infer the burst energy accurately enough for a cosmological use. Using the best known 15 GRBs we find very encouraging results that emphasize the cosmological GRB role. Probing the universe with high accuracy up to high redshifts, GRBs establish a new insight on the cosmic expanding acceleration history and accomplish the role of "missing link" between the Cosmic Microwave Background and type Ia supernovae, motivating the most optimistic hopes for what can be obtained from the bursts detected by SWIFT.

Motivation & Objective

• To establish gamma-ray bursts (GRBs) as viable cosmological distance indicators despite their intrinsic luminosity dispersion.
• To address the 'circularity problem' in calibrating the Ghirlanda correlation by using high-redshift GRBs to avoid cosmology-dependent bias.
• To demonstrate that GRBs can probe cosmic expansion history at higher redshifts than Type Ia supernovae, extending the cosmological baseline.
• To motivate future use of GRBs in constraining dark energy and the equation of state parameter $w$.

Proposed method

• Measure the jet break time in GRB afterglow lightcurves to infer the jet opening angle, enabling correction of isotropic energy to true energy ($E_\gamma$).
• Use the achromatic break in the X-ray and optical afterglow lightcurve to determine the jet break time with high accuracy.
• Apply the Ghirlanda correlation, which links $E_\gamma$ and $E_{\rm peak}$, to derive a 'known candle' relation for cosmological distance estimation.
• Construct a Hubble diagram using 15 GRBs with known redshifts and collimation-corrected energies, comparing residuals to standard cosmological models.
• Simulate future constraints using 150 GRBs to project improvements in $\Omega_{\rm M}$ and $\Omega_{\Lambda}$ precision, assuming realistic error budgets.
• Use the method of fitting the Ghirlanda relation to high-redshift GRBs to avoid circularity in cosmological calibration.

Experimental results

Research questions

• RQ1 Can the Ghirlanda correlation between $E_\gamma$ and $E_{\rm peak}$ be used to calibrate GRBs as cosmological distance indicators despite their non-standard luminosity?
• RQ2 How do the Hubble diagram residuals of GRBs compare to those of Type Ia supernovae when using the Ghirlanda relation?
• RQ3 What is the impact of using high-redshift GRBs on the circularity problem in calibrating the Ghirlanda relation?
• RQ4 How will future GRB samples from SWIFT improve constraints on cosmological parameters like $\Omega_{\rm M}$ and $\Omega_{\Lambda}$?
• RQ5 Can GRBs provide tighter constraints on dark energy parameters than supernovae due to their higher average redshift?

Key findings

• The Ghirlanda correlation enables the derivation of collimation-corrected isotropic energies ($E_\gamma$) from $E_{\rm peak}$ and jet break time, transforming GRBs into 'known candles' for cosmology.
• With 15 GRBs, the Hubble diagram residuals show tight agreement with the concordance cosmological model ($\Omega_{\rm M}$ = 0.27, $\Omega_{\Lambda}$ = 0.73), supporting their cosmological utility.
• GRBs extend the redshift baseline to $z \sim 4.5$, significantly beyond the $z \sim 1.7$ limit of current Type Ia supernova samples.
• The simulated sample of 150 GRBs yields tighter constraints on $\Omega_{\rm M}$ and $\Omega_{\Lambda}$ than the current SN Ia gold sample, with confidence contours showing improved precision and reduced degeneracy.
• The confidence contours for GRBs are more vertically elongated than for SN Ia, indicating that high-redshift GRBs can better constrain $\Omega_{\rm M}$ and $\Omega_{\Lambda}$ due to their larger redshift leverage.
• The method avoids strong extinction effects and is robust to absorption, as the prompt emission's hard X-rays are minimally affected by intergalactic absorption.