The Energy Dependence of GRB Minimum Variability Timescales

Abstract

We constrain the minimum variability timescales for 938 GRBs observed by the Fermi /GBM instrument prior to July 11, 2012. The tightest constraints on progenitor radii derived from these timescales are obtained from light curves in the hardest energy channel. In the softer bands -or from measurements of the same GRBs in the hard X-rays from Swift -we show that variability timescales tend to be a factor 2-3 longer. Applying a survival analysis to account for detections and upper limits, we find median minimum timescale in the rest frame for long-duration and short-duration GRBs of 45 ms and 10 ms, respectively. Fewer than 10% of GRBs show evidence for variability on timescales below 2 ms. These shortest timescales require Lorentz factors ∼ > 400 and imply typical emission radii R ≈ 1×10 14 cm for long-duration GRBs and R ≈ 3×10 13 cm for short-duration GRBs. We discuss implications for the GRB fireball model and investigate whether GRB minimum timescales evolve with cosmic time.

Distinguishing short and longFermigamma-ray bursts

“…The data are taken from MacLachlan et al (2013a,b), and are complemented by Golkhou & Butler (2014); Golkhou, Butler & Littlejohns (2015). They consist of 46 long and 22 short GRBs detected by the Fermi satellite.…”

“…Examples are ε = Eγ,iso,52/E 5/3 p,z,2 (where Eγ,iso,52 is the isotropic gammaray energy given in 10 52 erg, and Ep,z,2 is the cosmic rest-frame spectral peak energy in units of 100 keV) unambiguously dividing short and long GRBs (Lü et al 2010), MVTS (Bhat 2013;MacLachlan et al 2012MacLachlan et al , 2013aGolkhou & Butler 2014;Golkhou, Butler & Littlejohns 2015) or HE (MacLachlan et al 2013b). However, providing a set of parameters that could classify GRBs with high accuracy remains a desired objective.…”

On the limit between short and long GRBs

“…Additional parameters have been defined and proposed for GRB classification as well. Examples are ε = E γ,iso,52 /E 5/3 p,z,2 (unambiguously dividing short and long GRBs) (Lü et al 2010), minimum variability timescale (MVTS) (Bhat 2013;MacLachlan et al 2012MacLachlan et al , 2013aGolkhou and Butler 2014;Golkhou et al 2015) or Hurst exponent (HE) (MacLachlan et al 2013b;Tarnopolski 2015c). Still, the most common criterion is the GRB duration, and its limitting value has been shown herein to be detector dependent.…”

Search for high-energy neutrinos from bright GRBs with ANTARES

“…As a consequence, default values are assigned to these inputs: the ratio fp between internal energy in protons and electrons (also called baryonic loading) is fixed to fp = 10; the fraction of internal energy in electrons e and that in magnetic field B are assumed equal because of energy equipartition, with e = B = 0.1; the average fraction of proton energy transferred to a pion is xp→π = 0.2; and the Lorentz factor of the overall jet, more commonly denoted as bulk Lorentz factor, is Γ = 316. Also, when not explicitly mentioned, the minimum variability time is assumed to be tvar = 0.01 s for long bursts: this parameter affects the evaluation of neutrino expectations, since it is directly related to the morphology of the internal source (Golkhou et al 2015). Below the selection of the γ-ray parameters, as collected from the Gamma-ray Coordinate Network (GCN) Circular Archive 1 and reported in Tab.…”