Model-independent Multivariable Gamma-Ray Burst Luminosity Indicator and Its Possible Cosmological Implications

By E. Liang, Bing Zhang. 2005

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Without imposing any theoretical models and assumptions, we present a multivariable regression analysis to several observable quantities for a sample of 15 gamma-ray bursts (GRBs). The observables used in the analysis include the isotropic gamma-ray energy (Eγ,iso), the peak energy of the νFν spectrum in the rest frame (E), and the rest-frame break time of the optical afterglow light curves (t). A strong dependence of Eγ,iso on E and t is derived, which reads Eγ,iso/1052 ergs = (0.85 ± 0.21)(E/100 keV)1.94±0.17(t/1 day)-1.24±0.23 in a flat universe with ΩM = 0.28 and H0 = 71.3 km s-1 Mpc-1. We also extend the analysis to the isotropic afterglow energies in the X-ray and optical bands, respectively, and find that they are essentially not correlated with E and t. Regarding the Eγ,iso relationship as a luminosity indicator, we explore the possible constraints on the cosmological parameters using the GRB sample. Since there is no low-redshift GRB sample to calibrate this relationship, we weight the probability of using the relationship in each cosmology to serve as a standard candle by χ2 statistics and then use this cosmology-weighted standard candle to evaluate cosmological parameters. Our results indicate that 0.05 < ΩM < 0.50 at the 1 σ level, with the most probable value of ΩM being 0.28. The best value of ΩΛ is 0.64, but it is less constrained. Only a loose limit of ΩΛ < 1.2 is obtained at the 1 σ level. In the case of a flat universe, the 1 σ constraints are 0.13 < ΩM < 0.49 and 0.50 < ΩΛ < 0.85, respectively. The deceleration factor (q) and its cosmological evolution (dq/dz) are also investigated with an evolutionary form of q = q0 + z dq/dz. The best-fit values are (q0, dq/dz) = (-1.00, 1.12), with -2.23 < q0 < 0.26 and -0.07 < dq/dz < 3.48 at the 1 σ level. The inferred transition redshift between the deceleration and acceleration phases is 0.78 (1 σ). Through Monte Carlo simulations, we find that the GRB sample satisfying our relationship observationally tends to be a soft and bright one and that the constraints on the cosmological parameters can be much improved either by enlarging the sample size or by increasing the observational precision. Although the sample may not expand significantly in the Swift era, a significant increase of the sample is expected in the long-term future. Our simulations indicate that with a sample of 50 GRBs satisfying our multivariable standard candle, one can achieve a constraint to the cosmological parameters comparable to that derived from 157 Type Ia supernovae. Furthermore, the detections of a few high-redshift GRBs satisfying the correlation could greatly tighten the constraints. Identifying high-z GRBs and measuring their E and t are therefore essential for the GRB cosmology in the Swift era.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/d856c41ab5ed66f245d6077df4abced952d4d9d0

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Citations in the corpus

A complete sample of bright Swift long gamma-ray bursts: testing the spectral-energy correlations (2011, background): “…strongly correlates with (i) the isotropic energyEiso (Amati relation, Amati et al. 2002), (ii) the isotropic peak luminosity Liso (Yonetoku relation, Yonetoku et al. 2004) and (iii) the collimation– corrected energyEγ (Ghirlanda relation, Ghirlanda et al. 2004b; see also Liang & Zhang 2005).”
Gamma-Ray Bursts in the Swift Era (2007, background): “Starting with the assumption of constant energy reservoir of all events (as derived by Frail et al. 2001; Bloom et al. 2003 - but not confirmed by more systematic observations by Swift, e.g., Willingale et al. 2006; Burrows 2006; Zhang 2007), they drew the conclusion that GRBs have a typical opening”
The Ep,i–Eiso correlation in gamma-ray bursts: updated observational status, re-analysis and main implications (2006, methodology): “More intriguing, as will be discussed in Section 5, are the Ep,i – Eγ and Ep,i – Eiso – tb (tb is the achromatic afterglow light curve break time) correlations discovered by Ghirlanda, Ghisellini & Lazzati (2004) and Liang & Zhang (2005) basing on a limited sample of GRBs with known z, Ep,i and tb.”
Testing the Standard Fireball Model of Gamma-Ray Bursts Using Late X-Ray Afterglows Measured by Swift (2006, methodology): “…is likely that the end of the plateau phase, Ta, does depend on the total energy in the outflow, the collimation angle of the outflow and the density of the CSM and that the Eiso −Epeak − Ta correlation reported here is related to the Eiso −Epeak − tb,opt relation discussed by Liang & Zhang (2005).”
The physics of gamma-ray bursts & relativistic jets (2014, methodology): “Applying this relation to the cosmography study, Liang and Zhang (2005) found constraints on cosmological parameters similar to the one obtained using the Ghirlanda relation.”
Magnetic acceleration of ultrarelativistic jets in gamma-ray burst sources (2008, background): “…rate of jet breaks in the early afterglow light curves of GRB sources would prove to be more c© 0000 RAS, MNRAS 000, 000–000 at odds with the inference from a number of pre-Swift GRB sources of breaks of this type occurring on a time-scale of days (see e.g. Liang & Zhang 2005 for a compilation).”
Gamma-ray burst afterglows (2006, background): “…very early optical flashes have been discovered (e.g. GRB 990123, Akerlof et al. 1999; GRB 021004, Fox et al. 2003a; GRB 021211, Fox et al. 2003b; Li et al. 2003a), which are generally interpreted as emission from the reverse shock (Sari & Piran 1999a; Mészáros & Rees 1999; Kobayashi & Sari…”
On the Evolution of the Hubble Constant with the SNe Ia Pantheon Sample and Baryon Acoustic Oscillations: A Feasibility Study for GRB-Cosmology in 2030 (2022, background): “We here stress that this work can be also preparatory to the work of future application of GRBs as cosmological tools together with SNe Ia and Baryon Acoustic Oscillations (BAOs) through well-established correlations among the prompt variables, such as: the Amati relation [20], which connects the pe”
A Comprehensive Analysis of Swift XRT Data. II. Diverse Physical Origins of the Shallow Decay Segment (2007, background): “[7]), which is distinctly different from the Eiso,γ−E ′ p−t ′ b,opt relation discussed by Liang & Zhang (2005).”
Extremely energetic Fermi Gamma-Ray Bursts obey spectral energy correlations (2009, unknown): “In addition, it was found that by including the break time of the afterglow light curve, t b , either directly (Liang & Zhang 2005; Nava et al. 2006; Ghirlanda et al. 2007) or by using it to derive the jet opening angle and thus compute the collimation-corrected radiated energy E γ (Ghirlanda et…”
DISCERNING THE PHYSICAL ORIGINS OF COSMOLOGICAL GAMMA-RAY BURSTS BASED ON MULTIPLE OBSERVATIONAL CRITERIA: THE CASES OF z = 6.7 GRB 080913, z = 8.2 GRB 090423, AND SOME SHORT/HARD GRBs (2009, background): “When the optical afterglow light curve temporal break (topt) is included, a tighter correlation involving Ep and Eγ,iso is obtained (Ghirlanda et al. 2004; Liang & Zhang 2005) for some long duration GRBs.”
A Comprehensive Analysis of Swift XRT Data. III. Jet Break Candidates in X-Ray and Optical Afterglow Light Curves (2007, methodology): “…localized in the pre-Swift era with deep and long optical monitoring have a jetlike break in their optical afterglow light curves (see Frail et al. 2001; Bloom et al. 2003; Liang & Zhang 2005 and references therein), but the achromatism of these breaks was not confirmed outside of the optical band.”
A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram (2008, methodology): “Liang & Zhang (2005) constrained cosmological parameters and the transition redshift using theEisoEp-tb relation.”