Ok, it makes a lot of sense that the gravity of the disc of the Milky Way is pulling stars up and down as they go about their circum-galactic orbit. But this wouldn't explain why recent 3-D observations of the nearest stars using the FLAMES-GIRAFFE spectrograph on ESO’s Very Large Telescope and the IMACS spectrograph at the Las Campanas Observatory showed a definite wave-structure in the motions of stars orbiting the Galactic plane. In other words, most of the stars in the disc are following each other in a chain or train, as if they are bobbing up and down on a CURRENT. Which means they most certainly are oscillating on a current. And this was predicted in 1978!
Our Sun produces a magnetic field stretching out along the equatorial plane in the heliosphere. This field stretches throughout the Solar System where it is called the “Interplanetary Magnetic Field”. In 1965 John M., Wilcox and Norman F. Ness published their finding of the “Heliospheric Current Sheet” which showed that the Sun’s rotating magnetic field is constantly producing waves in the plasma of the interplanetary medium.
These waves form a “Parker Spiral” and are described in terms of an electromagnetic current but they are also mechanical waves which cause the planets themselves to oscillate up and down as they orbit the Sun. In 1978 Hannes Alfven and Per Carlqvist suggested that there is a similar “Galactic Current Sheet” carrying an electric current of 10^17 to 10^19 amperes through the plane of symmetry of the Galaxy.
Ok? That pretty much solves the mystery of the oscillation of the Milky Way's stars. But the problem here is that (ahem, cough cough) OUR SOLAR SYSTEM IS NOT PART OF THE MILKY WAY. In 1994 it was discovered that we are actually part of the Sagittarius Dwarf Elliptical Galaxy, or Sag-DEG for short, which is in a 500 million year POLAR ORBIT around the Milky Way.
Have you ever wondered why they say our Solar Apex is near Vega, but Vega itself is moving towards us almost twice as fast as we are moving towards it??? Well, in the late 80's it was discovered that nearly all of the stars orbiting the Milky Way seem to be "raining" down on our position. Which could only mean that our Solar System is moving upwards, out of the Milky Way. Sorry to inform you guys, but even though the stars of the Milky Way oscillate up and down during their 250 million year orbit, we aren't part of that dance. Our own path will take us high above the Galaxy, with a spectacular view at apogalacticon, and then back down again.