Estimation of the Galactic Spiral Pattern Speed from Cepheids

Abstract: To study the peculiarities of the Galactic spiral density wave, we have analyzed the space velocities of Galactic Cepheids with proper motions from the Hipparcos catalog and line-of-sight velocities from various sources. First, based on the entire sample of 185 stars and taking $R_0 = 8$ kpc, we have found the components of the peculiar solar velocity $(u_\odot,v_\odot,w_\odot)=(7.6,11.6,6.1)\pm(0.8,1.1,0.6)$ km s$^{-1}$, the angular velocity of Galactic rotation $\Omega_0 = -27.4\pm0.6$ km s$^{-1}$ kpc$^{-1}$ and its derivatives $\Omega^{'}_0 = +4.07\pm0.21,$ km s$^{-1}$ kpc$^{-2}$ and $\Omega^{"}_0 = -0.83\pm0.17,$ km s$^{-1}$ kpc$^{-3}$, the amplitudes of the velocity perturbations in the spiral density wave $f_R=-6.7\pm0.7$ and $f_\theta= 3.5\pm0.5$ km s$^{-1}$, the pitch angle of a two-armed spiral pattern (m = 2) $i=-4.5\pm0.1^\circ$ (which corresponds to a wavelength $\lambda=2.0\pm0.1$ kpc), and the phase of the Sun in the spiral density wave $\chi_\odot=-191\pm5^\circ$. The phase $\chi_\odot$ has been found to change noticeably with the mean age of the sample. Having analyzed these phase shifts, we have determined the mean value of the angular velocity difference $\Omega_p-\Omega$, which depends significantly on the calibrations used to estimate the individual ages of Cepheids. When estimating the ages of Cepheids based on Efremov's calibration, we have found $|\Omega_p-\Omega_0|=9\pm2$ km s$^{-1}$ kpc$^{-1}$. The ratio of the radial component of the gravitational force produced by the spiral arms to the total gravitational force of the Galaxy has been estimated to be $f_{r0} = 0.04$.