Humps on the Profiles of the Radial-Velocity Distribution and the Age of the Galactic Bar

Abstract

We studied the model of the Galaxy with a bar which reproduces well the distributions of the observed radial, \(V_{R}\), and azimuthal, \(V_{T}\), velocities derived from the Gaia DR3 data along the Galactocentric distance \(R\). The model profiles of the distributions of the velocity \(V_{R}\) demonstrate a periodic increase and the formation of a hump (elevation) in the distance range of 6–7 kpc. The average amplitude and period of variations in the velocity \(V_{R}\) are \(A=1.76\pm 0.15\) km s\({}^{-1}\) and \(P=2.1\pm 0.1\) Gyr. We calculated angles \(\theta_{01}\), \(\theta_{02}\), and \(\theta_{03}\) which determine orientations of orbits relative to the major axis of the bar at the time intervals: 0–1, 1–2, and 2–3 Gyr from the start of simulation. Stars whose orbits change orientations as follows: \(0^{\circ}<\theta_{01}<45^{\circ}\), \(-45^{\circ}<\theta_{02}<0^{\circ}\), and \(0^{\circ}<\theta_{03}<45^{\circ}\), make a significant contribution to the hump formation. The fraction of orbits trapped into libration among orbits lying both inside and outside the outer Lindblad resonance (OLR) is 28\(\%\). The median period of oscillations of librating orbits is 2.0 Gyr. The median period \(P\) of long-term variations in the angular momentum and total energy of stars increases as the Jacobi energy approaches the values typical for the OLR but then sharply drops. The distribution of model stars over the period \(P\) has two maxima located at \(P=0.6\) and \(1.9\) Gyr. Stars with orbits lying both inside and outside the corotation radius (CR) concentrate to the first maximum. The distribution of stars whose orbits lie both inside and outside the OLR depends on their orientation: orbits elongated perpendicular to the bar concentrate to the first maximum but those stretched parallel to the bar concentrate to the second maximum. The fact that the observed profile of the \(V_{R}\)-velocity distribution derived from the Gaia DR3 data does not show a hump suggests that the age of the Galactic bar, counted from the moment of reaching its full power, must lie near one of two values: \(2.0\pm 0.3\) or \(4.0\pm 0.5\) Gyr.