2017MNRAS.464.4495G

The data of 223 stars within 4 kpc from the Sun and 400 pc from the plane are collected from Melnik et al., who listed photometric distances and velocities of 674 long-period Cepheids in the disc of our Galaxy. Both line-of-sight and transverse along the Galactic longitude velocities of the selected stars are analysed on the assumption that the system is the subject to Lin-Shu-type moderately unstable, low-amplitude, tightly wound and rigidly rotating density waves. Minimization of the least-squares estimator S of measured and modelled velocities of stars was performed in the geometrical parameters of waves. The wave structures defined from the two independent samples of velocities are nearly similar. Different radial scales (wavelengths) of velocity inhomogeneity of about 1, 2 and 4 kpc, which do not depend on the number of spiral arms m, were found. But for now it is unclear if one can identify these scales as fully independent global modes of collective oscillations or they are Fourier harmonics of a single wave, or they just reveal the segments of large-scale Orion, Sagittarius and Perseus arms. The dominant mode is the one-armed wave for the main minimum of all S considered. However, because the S values for fits with m = 1-4 are almost equal the latter conclusion must be regarded as tentative until more extensive data are available. High-precision Gaia observations could reveal in the near future whether the wave-like velocity fluctuations near the Sun reported here do indeed exist.