A Galactic glitch

Knud Jahnke and Rasmus Benestad

After having watched a new documentary called the ‘Cloud Mystery’ – and especially the bit about the galaxy (approximately 2 – 4 minutes into the linked video clip) – we realised that a very interesting point has been missed in earlier discussions about ‘climate, galactic cosmic rays and the evolution of the Milky Way galaxy.

It is claimed in ‘The Cloud Mystery’, the book ‘The Chilling Stars’, and related articles that our solar system takes about 250 million years to circle the Milky Way galaxy and that our solar system crosses one of the spiral arms about every ~150 million years (Shaviv 2003).

But is this true? Most likely not. As we will discuss below, this claim is seriously at odds with astrophysical data.

Here is a little background on the Milky Way: The arms of spiral galaxies are not constant entities in time. They are results of gravitational instabilities in the disk or are induced by external companions. These instabilities are moving mass ‘overdensities’ containing old stars and gas, but also newly formed stars recently created from local collapse of the overdense gas.

Arms move around a spiral galaxy with a pattern speed that is defined by the mass distribution. This pattern speed differs from the motion of individual stars, just like the speed of an ocean wave differs from the movement of water particles. Estimating the pattern speed is difficult, as it is not coupled to the motion of individual stars but can only be inferred indirectly. For this reason it has not yet been reliably measured for our Milky Way – unlike for some other spiral galaxies, for which our clear and unobstructed view from the outside allows an estimate.

So how did Shaviv come up with this number?

Measuring the rotational velocity of stars in the Milky Way disk or other spiral galaxies is straightforward. The rotation is not rigid, but depends on the encircled mass inside the orbit of a star, including the Dark Matter, a yet unknown but solidly established source of gravitational attraction. It is easy and a standard technique to measure rotation curves of galaxies as a function of radius, and this is also possible for the Milky Way.

The two different rotating velocities of arms and stars have a different radial dependence – to first order the arms get preserved as entities while the stars further out have much smaller angular velocities than stars further inside – so the relative velocity of a star with respect to the nearest spiral arm will depend on its distance from the centre of the galaxy. At a certain radius, the radius of co-rotation, the two velocities are identical and a star at this radius has zero relative velocity with respect to the spiral arm pattern. It stays “forever” in the same spiral arm – or outside of it.

What are the best estimates for the relative velocity of the Sun with respect to the spiral arm pattern of the Milky Way? As mentioned, the pattern speed of the spiral arm in the Milky Way has not been firmly established.

When investigating other spiral galaxies, however, it was found that almost independently of the wide range of possible assumptions on which the pattern speed estimate was based, the radius of co-rotation follows a simple law: rcorot=r0 * (3.0 +/- 0.5), where r0 is the scale length of the exponential disk of the galaxy (the surface brightness of spiral galaxies drops very close to exponentially from the center to the outside, setting a characteristic size scale). This was measured by Kranz et al. 2003.

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