Kinematic analysis of spiral structures in the local disk

We present a method, based on the kinematic analysis of the Galactic disk stars near the Sun, to clarify whether the internal motions of the stellar system in spiral arms follow those expected in the density wave theory. The method is based on the linear relation between the phases of spatial positions and those of epicyclic motions of stars, as predicted by the theory. The application of the method to the 78 Galactic Cepheids near the Sun, for which accurate proper motions are available from the Hipparcos Catalogue, has revealed that these Cepheids show no correlation between both phases, mainly because of the large uncertainties in their spatial motions. This implies that previous studies for the calibration of the wave parameters using a similar sample to ours lack a clear physical basis: the currently available data of the Cepheids are still inaccurate to assess the presence of density waves in the solar neighborhood. We show the required accuracy for the astrometric data of the Cepheids to clarify the issue and future prospects are outlined.