Determination of the Spiral Pattern Speed in the Milky Way from Young Open Star Clusters

We have estimated the spiral pattern speed in the Galaxy \(\Omega_{p}\) from a large sample of young open star clusters (OSCs). For this purpose, we have used 2494 OSCs younger than 50 Myr. Their mean proper motions, line-of-sight velocities, and distances were calculated by Hunt and Reffert (2023) based on data from the Gaia DR3 catalogue. Three methods have been applied to estimate \(\Omega_{p}\). They all are based on the linear Lin–Shu spiral density wave theory. We have obtained an estimate of \(\Omega_{p}=24.26\pm 0.52\) km s\({}^{-1}\) kpc\({}^{-1}\) by the first method, which is most reliable in our view, using the velocity perturbations \(f_{R}\) and \(f_{\theta}\) found through a spectral analysis of the radial, \(V_{R}\), and residual rotation, \(\Delta V_{\rm circ}\), velocities. Using the second method, we have found the velocity perturbations \(f_{R}\) and \(f_{\theta}\) by solving the basic kinematic equations together with the Galactic rotation parameters and obtained an estimate of \(\Omega_{p}=23.45\pm 0.53\) km s\({}^{-1}\) kpc\({}^{-1}\). We have found \(\Omega_{p}=28.9\pm 2.8\) km s\({}^{-1}\) kpc\({}^{-1}\) by the third method based on an analysis of the position angles of OSCs at their birth time \(\theta_{\rm birth}\).