<p>If stars were actually about to escape, they would do so on a so-called <em>dynamical timescale</em>:
$$
t_\mathrm{dyn} \sim \sqrt{\frac{R^3}{8GM}},
$$
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.</p>

<p>Note also that the paper you link to is over 20 years old, non-refereed and has no citations (and that the author in general has very few citations). Of course this by no means implies that he's wrong, but it does give a hint that it's a good idea to be cautious of the conclusions of the paper. Since that paper was written, much more independent evidence for dark matter has been obtained.</p>

<hr>

<p>$^\dagger$<sub>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.</sub></p>

CC BY-SA 3.0
2017-08-27T20:56:52.253Z
This is a good argument
Truffaldino
CC BY-SA 3.0
2017-08-27T19:19:50.797Z
2017-08-28T11:42:15.673Z
2017-08-28T11:42:15.673Z
pela
<p>Recently I have found the article <a href="https://arxiv.org/abs/astro-ph/9511022" rel="nofollow noreferrer">Does There Really Exist the Problem of the Dark Matter in Spiral Galaxies?</a> which states that dark matter does not exist because astronomers are wrong assuming stationarity of galaxy rotation.</p>

<p>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.</p>

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

CC BY-SA 3.0
2017-08-27T14:16:22.557Z
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
CC BY-SA 3.0
2017-08-27T17:34:30.603Z
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
CC BY-SA 3.0
2017-08-27T19:59:46.050Z
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
CC BY-SA 3.0
2017-08-27T20:16:17.317Z
– 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
<galaxy><rotation><dark-matter><doppler-effect><spiral-arms>
What are evidences of stationarity of rotation of galaxies
Truffaldino
# What are evidences of stationarity of rotation of galaxies

(Asked by: username_0 on 2017-08-27)

Recently I have found the article [Does There Really Exist the Problem of the Dark Matter in Spiral Galaxies?](https://arxiv.org/abs/astro-ph/9511022) 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?

**Tags:** galaxy, rotation, dark-matter, doppler-effect, spiral-arms

> **Comments:**
> **username_1**: The premise there is incorrect. You know it's rotating, so you need only one component, which you get from the deprojected Doppler measurment.  
> **username_0**: 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.  
> **username_2**: Spiral galaxies are seen at a variety of inclination angles. So how do you propose that the cosmic conspiracy arranges to account for this?  
> **username_0**: – 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  

---

## 1 answers

### Answer by username_3 on 2017-08-27. Score: 5 | Accepted answer

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.

Note also that the paper you link to is over 20 years old, non-refereed and has no citations (and that the author in general has very few citations). Of course this by no means implies that he's wrong, but it does give a hint that it's a good idea to be cautious of the conclusions of the paper. Since that paper was written, much more independent evidence for dark matter has been obtained.

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$^\dagger$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.

> **Comments:**
> **username_0**: This is a good argument  

---

