It has no sense that stars that have a bigger radius and apparently less angular speed($\omega$) goes faster than the ones near the center.


5 Answers 5


Short answer

The question is a bit ambiguous. If the question is

why do star velocity increase with distance close to the galactic centre ?

the answer is

because their orbit encompass more mass, and this corresponds to a stronger gravity pull.

If the question is

why does their velocity stays constant and does not decrease at big radii, where the star density decreases ?

the current consensus answer is

We have to add dark matter to observed stars to explain that.

Long answer

The curve B below (taken from wikipedia) plots the the observed star velocity as function of the distance from the galactic centre.

Galactic rotation

The curve A corresponds to the expected curve without dark matter. As you can see, beyond a given distance, the velocity is expected to decrease, but it actually stays roughly constant. Dark matter has been initially postulated as a solution to this discrepancy.

The increase of velocity close to the centre is independent to the presence of dark-matter or not. The velocity of a star on a circular orbit of radius $r$ in the galactic plane is given by a balance of the centrifugal acceleration and the gravity it feels: $$\begin{gather} \frac{v^2}r= G \frac{m(r)}{r^2}\\ v=\sqrt{ G\frac{m(r)}{r}} \end{gather}$$ where $m(r)$ is the mass of stars contained in a spheroid centred on the galactic centre of radius $r$ (see e.g. here for more details. And then adapt it to the geometry of a galaxy). If $r$ is smaller than the galaxy thickness, the number of star is proportional to the volume of the sphere, and we expect $$\begin{align} m(r)&\propto r^3& v&\propto r \end{align}$$ which is consistent with the initial increase.

When $r$ is bigger than the thickness, if the star density is constant, we have then $$\begin{align} m(r)&\propto r^2& v&\propto \sqrt r, \end{align}$$ and this still corresponds to a velocity increase.

When $r$ is big enough, the density of star decreases with $r$ upto a point where $m(r)< C r$ and this should give the decreasing curve A. On the other hand, the observed curve B is essentially constant, and this can bee seen as a measurement of $m(r)\propto r$. This is not consistent with the observed star repartition, but it is consistent with the presence of dark (i.e. not seen) matter with a radial density $\propto\frac1{r^2}$.

  • $\begingroup$ +1 for using mathcal :D. And for the interesting, detailed, answer. $\endgroup$ Apr 2, 2012 at 16:30
  • $\begingroup$ @Manishearth : Apparently, \mathcal was not standard (even if I learned it this way ;-) ), so Garmen1778 removed it. I hope the +1 stays anyway ! $\endgroup$ Jun 4, 2012 at 15:36

since no one mentioned it, i think its only fair to provide at least one answer about MOND (Modified Newtonian Dynamics).

Basically the galaxy rotation curve is the reason dark matter was proposed in the first instance. However, the dark matter explanation, putting aside for a moment other considerations as supersymmetric weakly coupled partners, is not very satisfying from a scientific point of view, since its an instance of adjusting parameters (i.e: unseen matter) in order to preserve a model. Think of Ptolomeus model of the solar system, with the epicyclic orbits postulated in order to preserve the earth in the center of the model.

MOND as an alternative explanation to dark matter is widely discredited, specially after the observation of gravitational lensing in the middle regions of the Bullet cluster, which suggests to some that a transparent source of gravity is causing the lensing effect.

However, despite this, the MOND hypothesis, at least as an heuristic to retrodict the galaxy rotation curves works extremely well. The hypothesis basically says that the gravitational mass coupling becomes weaker when accelerations drop below $a_0 \approx 10^{-10} m/s^2$. From that simple assumption, it is able to predict most of the galaxy rotation curves that are currently observed


The striking similarity of a galaxy and an hurricane .
a spiral galaxy field versus an hurricane force field
Do you need DM or SMBH in the hurricane ? Their force field is similar. The hurricane is governed by a vortex, then how can a galaxy be subjected to such a field that is more important than the central force at the centre of the galaxy ? I'm sure that there is a way.

Edit add
I will try to explain why there is a vortex :

All images were taken from outra Física CC.
In this PSE-link (anti gravity) I show with graphs and equations how the voids have to grow due to the gravitational field. All the mass that was previously inside them is now in the exterior shell of the voids.

When two voids intersect a we have :

void intersection and the field is like field at the intersection of two voids
To see the field of a vortex you need to remove the mean field the galactic vortex

As you see there is no need of DM neither SMBH. The only think that is needed is to follow the rules of physics (and a lot of imagination of my friend Alfredo that allow s me to see only physics as the true nature of Nature, when everybody else can only explain with a magical Dark Matter).

There are recent news (arxiv and cosmiclog) that DM probably has to have a two different composition/properties and the astronomers dont now how to justify the observed behaviour.
Of course one can continue the pursue of DM quest. I dont.

The resistence that the readers have to this kind of model, that only follows the laws of gravity, has to have with the fact that this asks for a different kind of beginning of the Universe. Why not? Ahh the BB and the Dark Energy, you say!

Then, the beginning of the Universe can be an infinite universe (or almost), homogeneous, and with temperature = 0. Temperature will grow, contradicting our deepest convictions that this is impossible.

If you want to understand clearer read that blog from the first to the last post (it is written, in portugueese, in such a way that any person can understand), or to focus only the present question you should start at O nascimento de uma Bolha until you arrive at As espirais Galácticas.

And the Dark Energy? You got rid of it, again with the help of my friend Alfredo, with his paper: A self-similar model of the Universe unveils the nature of dark energy. I posted a short math proof of his argument in this PSE link (are-the-rest-masses-of-fundamental-particles-certainly-constants). Why sould the particles be shrinking giving us the impression of a space expansion ? Their associated fields expand in space, the fields have energy, and are sourced by the particles. To preserve the total energy budget they must 'shrink'. Hey, in the lab I dont see that shrinking, how come? It is impossible to detect the phenomena locally because the lab, the instrumentation and yourself are shrinking, and above all no one likes to be shrinking.

I do realize that when DM was 'invented' was only a data fit. They have no model to justify the observations and instead of thinking harder they postulated its existence. Do we need GR in the cosmology if the space is flat arxiv-BAO-survey? No. That is why I invite the readers to pay attention to my friends paper, and be the first to say 'I spot an error'.

When I went to school I already 'knew' that the space is expanding, and the same with you. It is shocking if it is 'on the contrary'.

The bigest enemy we face in the search of the knowledge is our 'rooted beliefs'.

Now, that I took my precious time to write this long answer I kindly ask the downvoters to say in what particular points they beleive that I am mistaken.

  • $\begingroup$ -1 : It is not an answer about the velocity distribution. If you explicitely link you hurricane intuition with the increase of velocity, I may remove the -1 $\endgroup$ Apr 3, 2012 at 12:39
  • $\begingroup$ @Frédéric - the galacic vortex is in place. The outer regions have bigger speeds as you can see. $\endgroup$ Apr 3, 2012 at 19:14
  • $\begingroup$ I don't think this place is for original research. Your answer seems to be far from the scientific consensus. Maybe the consensus is wrong, but if you manage to convince a significant part of the astrophysics community that your explanation is the good one, I promise to remove my downvote, even if you will probably not care at this step. $\endgroup$ Apr 10, 2012 at 13:25
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    $\begingroup$ And I will not read your explanation on your blog beacause : 1. Even if I'm a professional physicist, I do not have enough knowledge in astrophysics to judge the relevance of arguments about the dark matter model. 2. I'm not any person, since I cannot understand Portuguese. Essayez en Français, pour que je puisse comprendre ;-) $\endgroup$ Apr 10, 2012 at 13:29

The stars in the galactic disk rotates with almost the same orbital velocity 200-230 km/s around the galactic center. Unlike a star system where the planets follow Kepler's third law. To explain the almost constant orbital speed of the stars in the galaxy, we have calculated dark matter, which is distributed in such a way, that it gives stars almost the same orbital speeds, which is an odd coincidence.

There could be an engine in the middle accelerating the stars, but such an engine is absurd, as we don't know how the energy can be transferred this way at this immense scale. I just proposed a hypothetical solution, where a binary black hole system in the middle of the galaxy, accelerate the stars in the galactic disk by gravitational waves. You might want to take a look at it: Is there a binary black hole system in the middle of the galaxy?

  • $\begingroup$ -1. I don't think this place is for original research. If you have a fantastic new solution to the dark matter “problem”, the best way of proceeding would be to publish it and have it accepted by (at least some) other professional astrophysicists. Then (but only then), referring to it in a physics.sx answer is a good idea. $\endgroup$ Feb 8, 2016 at 11:26
  • $\begingroup$ @FrédéricGrosshans What is original research is the dark matter research, where we have postulated dark matter without any observational evidence. The dark matter is again hypothesized to be perfectly placed so the galaxy rotates almost as one solid disk. That is in my opinion just too unlikely, and it should be space for alternative hypothetical explanations on the table. $\endgroup$
    – Enos Oye
    Feb 8, 2016 at 14:55

The dark matter or the dark energy.

We don't know at all what are they. We just know that they exist, but as I say, we don't have idea.

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    $\begingroup$ well dark energy isn't required to explain the flat rotation curves. And while we don't what DM is, we know what DM isn't, cf MACHOs $\endgroup$
    – Nic
    Apr 2, 2012 at 14:58
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    $\begingroup$ DM isnt that mysterious. Also, this doesn't really answer the question--you need to include the explanation as well. $\endgroup$ Apr 2, 2012 at 15:02
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    $\begingroup$ The wikipedia page on dark matter gives some details en.wikipedia.org/wiki/Dark_matter $\endgroup$ Apr 2, 2012 at 15:12

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