Generalized Microlensing Effective Timescale
The microlensing effective timescale t_eff=beta*t_E is used frequently in high-magnification (beta << 1) microlensing events, because it is better constrained than either the impact parameter beta or the Einstein timescale t_E separately. It also facilitates intuitive understanding of lightcurves prior to determination of a model. Similar considerations may apply to very low magnification events. I therefore provide a generalization of this quantity to all events: t_eff = beta*t_E*sqrt((1+beta^2/2)(1+beta^2/4)).