Estimation of the Galactic Spiral Pattern Speed from Cepheids

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 $f_{r0} = 0.04$.