[Paper Review] Measuring the bulk Lorentz factors of gamma-ray bursts with Fermi

Qing-Wen Tang, Fang‐Kun Peng+2 more|arXiv (Cornell University)|Dec 10, 2014

Gamma-ray bursts and supernovae3 references3 citations

TL;DR

This study measures the bulk Lorentz factors of 8 gamma-ray bursts (GRBs) using high-energy spectral cutoffs detected by the Fermi/LAT, applying pair-production absorption models to infer relativistic jet speeds. It finds a strong positive correlation between Lorentz factors and isotropic gamma-ray luminosity, indicating more luminous GRBs have faster jets.

ABSTRACT

Gamma-ray bursts (GRBs) are powered by ultra-relativistic jets. Usually a minimum value of the Lorentz factor of the relativistic bulk motion is obtained based on the argument that the observed high energy photons ($\gg { m MeV}$) can escape without suffering from absorption due to pair production. The exact value, rather than a lower limit, of the Lorentz factor can be obtained if the spectral cutoff due to such absorption is detected. With the good spectral coverage of the Large Area Telescope (LAT) on extsl{Fermi}, measurements of such cutoff become possible, and two cases (GRB~090926A and GRB~100724B) have been reported to have high-energy cutoffs or breaks. We systematically search for such high energy spectral cutoffs/breaks from the LAT and the Gamma-ray burst monitor (GBM) observations of the prompt emission of GRBs detected since August 2011. Six more GRBs are found to have cutoff-like spectral feature at energies of $\sim10-500$~MeV. Assuming that these cutoffs are caused by pair-production absorption within the source, the bulk Lorentz factors of these GRBs are obtained. We further find that the Lorentz factors are correlated with the isotropic gamma-ray luminosity of the bursts, indicating that more powerful GRB jets move faster.

Motivation & Objective

• To identify high-energy spectral cutoffs in Fermi/LAT and GBM data from GRBs detected after August 2011.
• To determine the bulk Lorentz factors of GRB jets by modeling spectral cutoffs as due to pair-production absorption.
• To test correlations between Lorentz factors and intrinsic GRB properties such as isotropic luminosity and energy.
• To provide a more direct and reliable estimate of Lorentz factors compared to indirect methods based on afterglow or photospheric emission.
• To constrain central engine models by linking Lorentz factors to mass outflow rates and energy output.

Proposed method

• Performed joint spectral analysis of Fermi/GBM and LAT data for 28 GRBs detected between August 2011 and October 2014.
• Used RMFIT with CSTAT statistic to handle low-event statistics at high energies, fitting spectra with the Band function and identifying cutoff-like features.
• Applied a one-zone fireball model assuming that spectral cutoffs at 10–500 MeV are caused by $ au_{\gamma\gamma} \lesssim 1$ pair-production absorption.
• Calculated bulk Lorentz factors using the relation $\Gamma \gtrsim E_{\rm cut} / (2 m_e c^2)$, where $E_{\rm cut}$ is the observed cutoff energy.
• Tested correlations between $\Gamma$ and isotropic luminosity $L_{\gamma,\rm iso}$ and energy $E_{\gamma,\rm iso}$ using Pearson correlation and null hypothesis testing.
• Excluded bursts without redshift measurements to assess robustness of correlations in a smaller, more reliable sample.

Experimental results

Research questions

• RQ1 Do high-energy spectral cutoffs in the Fermi/LAT data of GRBs indicate pair-production absorption, enabling direct Lorentz factor measurement?
• RQ2 What is the distribution of bulk Lorentz factors for GRBs with detectable high-energy cutoffs in the Fermi era?
• RQ3 Is there a correlation between the bulk Lorentz factor and the isotropic gamma-ray luminosity of GRBs?
• RQ4 How do the measured Lorentz factors compare with those derived from afterglow or photospheric emission models?
• RQ5 What constraints do the observed $\Gamma$–$L_{\gamma,\rm iso}$ correlations place on central engine models and mass outflow rates?

Key findings

• Six additional GRBs (beyond GRB 090926A and GRB 100724B) were found to exhibit high-energy spectral cutoffs between ~10 MeV and ~500 MeV.
• The bulk Lorentz factors of these eight GRBs were derived under the pair-production absorption model, with values consistent with $\Gamma \gtrsim 100$.
• A significant positive correlation was found between Lorentz factors and isotropic gamma-ray luminosity: $\Gamma = 10^{1.65 \pm 0.20} L_{\gamma,\rm iso,51}^{0.52 \pm 0.13}$, with Pearson correlation coefficient $r = 0.844$ and null hypothesis probability of 0.008.
• The correlation remains significant when excluding bursts without redshift measurements, indicating robustness.
• A weaker but still notable correlation was found between $\Gamma$ and isotropic energy: $\Gamma = 10^{1.01 \pm 0.56} E_{\gamma,\rm iso,52}^{0.88 \pm 0.35}$, with $r = 0.707$ and null hypothesis probability of 0.050.
• The observed $\Gamma$–$L_{\gamma,\rm iso}$ correlation implies that mass outflow rates scale as $\dot{M} \propto L_{\gamma,\rm iso}^{0.48 \pm 0.13}$, constraining central engine models.