Start of orbit librations and the bar growth timescale

Abstract

We study a dynamical model of the Galaxy with an analytical bar that reproduces the radial velocity $V_R$ 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 $V_R$ 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 $T_g$. The temporal dependences of the radial velocity $V_R$ in the models with different $T_g$ 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 $T_g$ with the coefficient $k=0.54\pm 0.02$. Orbit librations do not start 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 $Q_b=0.314$, the librations start when the bar strength reaches $Q_b=0.170$.

13 pages, 12 figures