Spectrum of Lin-Shu-type density waves in the Galaxy: A number of discrete spiral modes of collective oscillations?

Measurements of great importance of photometric/trigonometric distances and velocities have recently done for 2859 open clusters and 103 masers associated with young high-mass stars in the disc of our Galaxy by Kharchenko et al. and Reid et al. We use these new high-precision data to determine the spectrum of Lin-Shu-type densitywaves in the system. The kinematics of 472 clusters and 65 masers selected within 4 kpc from the Sun is analysed on the assumption that the Galaxy is subject to moderately unstable, tightly-wound, small-amplitude density waves. For a given number of spiral arms, several minima of a least-squares estimator S of measured and predicted line-of-sight velocities of both clusters and masers with respect to the pitch angle p and the phase of the wave at the Sun's location are apparent from our calculation as |p| increases from 1° to 20°. The appearance of the minima of S is explained in terms of a number of discrete spiral modes of collective oscillations developing in the solar vicinity as suggested analytically by Lau, Lin & Mark, Bertin & Mark, Lau & Bertin and others in the late 1970s.