Start of Orbit Librations and the Bar Growth Timescale

We study a dynamical model of the Galaxy with an analytical bar that reproduces the radial-velocity VR profiles as a function of the Galactocentric distance R obtained from the Gaia DR3 data. The model radial-velocity profiles show a periodic increase in VR caused by orbits trapped into libration near the outer Lindblad resonance (OLR). To determine the moment when the librations start, we built a set of additional models differing only in the bar growth time Tg . The temporal dependences of the radial velocity VR(t) in the models with different Tg retain their shape but are shifted relative to each other in time t . The shift providing the best agreement between the model dependences is proportional to Tg with the coefficient k=0.54± 0.02 . Orbit librations start not when the bar reaches its full strength, but when it attains only 54 $$%$$ of its maximum strength. Since the maximum bar strength in the models is Qb=0.314 , the librations start when the bar strength reaches Qb*=0.170 .