New results on the gamma-ray burst variability-luminosity relation

TL;DR

This study retests the variability–luminosity relation for long GRBs using $\sim$216–$~$212 bursts with robust $V_f$ and $L_{ m iso}$ estimates from Swift, Fermi, and Konus/WIND. It shows that the correlation is weaker than previously claimed, with significance largely eroded by smooth, luminous events; in contrast, the minimum variability timescale (MVT) remains more tightly linked to $L_{ m iso}$ and the jet Lorentz factor $Γ$. The authors discuss how photospheric smoothing and internal dissipation influence GRB light curves, propose external-shock origins for a subset of smooth, single-pulse GRBs, and identify a potential merger-indicator region characterized by high $V_f$, low $L_{ m iso}$, and short $MVT$. These results refine our understanding of GRB prompt variability, highlight the different physics captured by $V_f$ and MVT, and offer observational cues for identifying compact-binary merger events.

Abstract

At the dawn of the gamma-ray burst (GRB) afterglow era, a Cepheid-like correlation was discovered between time variability V and isotropic-equivalent peak luminosity Liso of the prompt emission of about a dozen long GRBs with measured redshift available at that time. Soon afterwards, the correlation was confirmed against a sample of about 30 GRBs, despite being affected by significant scatter. Unlike the minimum variability timescale (MVT), V measures the relative power of short-to-intermediate timescales. We aim to test the correlation using about two hundred long GRBs with spectroscopically measured redshift, detected by Swift, Fermi, and Konus/WIND, for which both observables can be accurately estimated. For all the selected GRBs, variability was calculated according to the original definition using the 64-ms background-subtracted light curves of Swift/BAT (Fermi/GBM) in the 15-150 (8-900) keV energy passband. Peak luminosities were either taken from literature or derived from modelling broad-band spectra acquired with either Konus/WIND or Fermi/GBM. The statistical significance of the correlation has weakened to <~2%, mostly due to the appearance of a number of smooth and luminous GRBs characterised by a relatively small V. At odds with most long GRBs, 3 out of 4 long-duration merger candidates have high V and low Liso. Luminosity is more tightly connected with shortest timescales measured by MVT rather than short-to-intermediate ones, measured by V. We discuss the implications on internal dissipation models and the role of the e+- photosphere. We identified a few, smooth GRBs with a single broad pulse and low V, that might have an external shock origin, in contrast with most GRBs. The combination of high variability (V>~0.1), low luminosity (Liso<~10^51 erg s^-1) and short MVT (<~ 0.1 s) could be a good indicator for a compact binary merger origin.

Figures (11)

• Figure 1: Illustrative example of how variability is calculated. Shown is the 15--150-keV light curve $\{r_i\}$ of GRB 080319B as observed with BAT. The orange line shows the smoothed profile $\{s_{f,i}\}$ obtained with a smoothing timescale of $T_f=18.43$ s, which collects a fraction $f=0.45$ of the total fluence of the GRB.
• Figure 2: Comparison between estimates of variability obtained with BAT in the 15--150 keV band vs. the GBM estimates in the 8--900 keV band, obtained for a common sample and assuming $f=0.45$ and $\beta=0.6$. Equality is shown by the solid line.
• Figure 3: Variability--luminosity correlation obtained for $f=0.8$ and $\beta=0.6$. This value of $f$ gives the highest degrees of correlation. Different symbols refer to the different detectors used to measure $V_f$. For BAT-GBM shared GRBs we used BAT values. Pentagons are long-duration merger candidates. The redshift information is also available through the colour-coded scale.
• Figure 4: Variability--luminosity correlation obtained for $f=0.45$ and $\beta=0.6$. In addition to the 184 GRBs analysed in the present work, also shown (stars) are GRBs from Guidorzi05b. Redshift is colour-coded. The shaded region shows a density map, obtained using a kernel density estimate, of the same data set (excluding the Guidorzi05b GRBs). The four GRBs with red pentagons are long-duration merger candidates (GRB 060614, GRB 191019A, GRB 211211A, and GRB 230307A) that were considered separately.
• Figure 5: Same plot as that of Figure \ref{['fig:VL_f0.45_beta0.6_z']}, except for the colour-code, which corresponds to five different classes of number of peaks.