Connection between Energy-dependent Lags and Lorentz Factor in Gamma-ray Bursts

We suggest a connection between the pulse paradigm at gamma-ray energies and the recently demonstrated luminosity distribution in gamma-ray bursts: Spectral evolution of pulse structures is anticorrelated with quantities which may be expected to reflect the bulk relativistic Lorentz factor, Γ, and therefore intrinsic luminosity. We establish this relationship in two important burst samples using the cross-correlation lags between low (25–50 keV) and high (100–300 keV and > 300 keV) energy bands. For the set of six bursts (four with redshifts) observed by CGRO/BATSE and BeppoSAX which also have optical counterparts, the γ/X peak flux ratios (isotropic energies) are anti-correlated with spectral lag. For the 176 brightest BATSE bursts with durations longer than 2 s and significant emission above 300 keV, a similar anti-correlation is evident between gamma-ray hardness ratios, or peak flux, and spectral lag. We conjecture that a range in Lorentz factors – and therefore portion of observed wavefront – translates into the observed range in propagation times as a function of energy, with lower energy photons originating off-axis. The observed range of spectral lags is consistent with that expected for pulsed emission from a central engine produced in shells with radii ~ 10 13 cm and Γ ~ 100–3000.