# What are evidences of stationarity of rotation of galaxies

Recently I have found the article Does There Really Exist the Problem of the Dark Matter in Spiral Galaxies? which states that dark matter does not exist because astronomers are wrong assuming stationarity of galaxy rotation.

According to them Doppler measurements give only one component of speed which is insufficiebt to restore full three dimensional vector. So they claim that stars in galaxies are on escape tragectories but reproduce correst rotational curves if we assume stationarity of rotation.

What are evidences that this is not true, what about measurements of proper motions, not doppler shifts only?

• The premise there is incorrect. You know it's rotating, so you need only one component, which you get from the deprojected Doppler measurment. – AtmosphericPrisonEscape Aug 27 '17 at 14:16
• You probably have not understod the question: How do you know that a galaxy is in a STATIONARY rotaion: i.e. average trajectories of stars are circles. There is an infinite number of velocity distributions with non zero radial velocity components that give the same curves.based on dopler shifts. – Truffaldino Aug 27 '17 at 17:34
• Spiral galaxies are seen at a variety of inclination angles. So how do you propose that the cosmic conspiracy arranges to account for this? – ProfRob Aug 27 '17 at 19:59
• – Rob Jeffries: This is somehow explained in the article cited above: I confess I did not read it carefully, just took a quick look. To me "Dark matter" also looks as a cosmic conspiracy – Truffaldino Aug 27 '17 at 20:16

If stars were actually about to escape, they would do so on a so-called dynamical timescale: $$t_\mathrm{dyn} \sim \sqrt{\frac{R^3}{8GM}},$$ where $G$ is the gravitational constant, and $R$ and $M$ are the radius and the mass of the galaxy, respectively. For a Milky Way-sized galaxy, this is equates to roughly 30 million years$^\dagger$. But disk galaxies are observed over time spans of billions of years. If they had for some reason been gravitationally bound and then "unleashed", they would have to be so at times synchronized such that we, today, in all directions, observe them in a state that has a very short time span compared their lives throughout the history of the Universe. That is, distant galaxies (which are young because we look far back in time) were unleashed early in their lives, and nearby galaxies (which we see in the "old age" because we look less far back in time) were unleashed recently. This not only seems unlikely, but would also put us in a special place in the Universe.
$^\dagger$Since the roughly constant rotation speed of disk galaxies with galaxy mass (a few 100s of km/s) implies that $R$ grows approximately linearly with $R$ (and not with $R^3$ as one might expect), smaller galaxies — which exist in much larger numbers than large galaxies — have even shorter dynamical timescales.