Different timescales in years: the timescale for binary-single encounters given by Eq. (2) (dashed lines) and gravitational radiation inspiral given by Eq. (3) (solid lines), considering a variation in the gas mass fraction between η_g = 0.0,  0.1,  0.3,  0.5,  1.0,  10.0, with the lowest value in the dashed blue line and the highest value in the violet. We also employed different values of the speed of light, from c = 10³ km/s (dashed brown line) to the real value of c = 3 × 10⁵ km/s (solid dark line). The vertical lines show the velocity dispersion given by v_∞ for different gas mass fractions.