gamma0

Gamma0 is a notation used in physics to denote an initial or characteristic Lorentz factor in relativistic contexts. In special relativity, gamma0 refers to the Lorentz factor of a particle moving with speed v0 relative to an observer: gamma0 = (1 − v0^2/c^2)^{-1/2}. The corresponding energy is E0 = gamma0 m c^2 and the momentum is p0 = gamma0 m v0. The gamma factor encodes relativistic effects such as time dilation and energy-momentum relations, and gamma0 often serves as the starting value in problems involving acceleration, energy gain, or deceleration.

In astrophysics, gamma0 commonly denotes the initial bulk Lorentz factor of a relativistic outflow, such as a jet from a gamma-ray burst or an active galactic nucleus. Values typically span from the tens to the thousands. The choice of gamma0 influences how rapidly the jet decelerates as it sweeps up ambient material, the timing and brightness of afterglow emission, Doppler boosting of emitted photons, and the transparency of the outflow to high-energy photons. Observational constraints on gamma0 come from afterglow light curves, spectra, variability timescales, and, in some cases, radio scintillation studies.

Beyond GRBs, gamma0 appears in plasma physics and high-energy astrophysics as the initial Lorentz factor in simulations and scaling relations for relativistic shocks and winds. It is important to note that gamma0 is not universal; its definition is model-dependent and must be specified within a given context.