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

Abstract

We have estimated the spiral pattern speed in the Galaxy $Ω_p$ 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 $Ω_p$. They all are based on the linear Lin-Shu spiral density wave theory. We have obtained an estimate of $Ω_p=24.26± 0.52$ km s${}^{-1}$ kpc${}^{-1}$ by the first method, which is most reliable in our view, using the velocity perturbations $f_R$ and $f_{θ}$ found through a spectral analysis of the radial, $V_R$, and residual rotation, $Δ V_circ$, velocities. Using the second method, we have found the velocity perturbations $f_R$ and $f_{θ}$ by solving the basic kinematic equations together with the Galactic rotation parameters and obtained an estimate of $Ω_p=23.45± 0.53$ km s${}^{-1}$ kpc${}^{-1}$. We have found $Ω_p=28.9± 2.8$ km s${}^{-1}$ kpc${}^{-1}$ by the third method based on an analysis of the position angles of OSCs at their birth time $θ_birth$.