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 ${\mathrm{\Omega }}_p$ 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 ${\mathrm{\Omega }}_p$. They all are based on the linear Lin-Shu spiral density wave theory. We have obtained an estimate of ${\mathrm{\Omega }}_p=24.26\pm 0.52$~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, $\mathrm{\Delta }{V}_{\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}},$ 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 ${\mathrm{\Omega }}_p=23.45\pm 0.53$~km s${}^{-1}$ kpc${}^{-1}$. We have found ${\mathrm{\Omega }}_p=28.9\pm 2.8$~km s${}^{-1}$ kpc${}^{-1}$ by the third method based on an analysis of the position angles of OSCs at their birth time ${\theta }_{\mathrm{b}\mathrm{i}\mathrm{r}\mathrm{t}\mathrm{h}}$.