# Talk:Galaxy rotation curve

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### Mass Distribution Models

Models of mass distribution show rotation curves calculated entirely according to Newtonoian formula that match observation. This should be included in the article. A uniform spherical distribution model shows a rotation curve that slopes steeply up from center. A uniform disk model shows a rotation curve that slopes less steeply. A disk with a bulge of increased mass in the middle model shows the rotation curve noted in the article. Rising steeply in the bulge like the uniform spherical distribution then flat in the disk. An all mass in the middle model like the solar system shows a rotation curve that slopes down as the "predicted" line in the diagram.

Since these models predict rotation curves that match observations in all cases they should be included. These models also predict luminant and opaque matter distributions that match observation.

98.164.89.190 (talk) 13:49, 24 May 2012 (UTC)

The equation

$\rho(r) = \frac{3 v(r)^2}{4 \pi G r^2}\quad (??)$

that claims to relate the mass density distribution to the rotation curve is not correct --- or it least it does not follow from Kepler's third law without some ascribing some unusual meaning to the "radial density profile". Asssuming spherical symmetry (is this reasonable?) a correct equation relating $\rho(r)$ to the velocity curve is surely

$v^2(R) = \frac{4\pi G_N}{R} \int_0^R r^2 \rho(r) dr$

I'd change the equation, but I'm not sure how the change would affect the rest of the section, which is confusing enough as it stands.

Mike Stone (talk) 15:13, 19 March 2013 (UTC)

I can only underline that Eq. (??) is wrong. I think the derivation of the correct formula is simple enough to be stated in the Wikipedia. It can be done in the first semester in the usual physics curriculum at universities.

The first important feature of Newtonian gravity, which is sufficient for this purpose, is that the gravitational force on a body moving in an extended radially symmetric (around a center) mass distribution that consitutes the gravitational field is given by

$\vec{F}=-\frac{G_N m M(r)}{r^2} \frac{\vec{r}}{r}, \qquad (1)$

where $G_N$ is Newton's gravitation constant, $m$ is the mass of the body, $\vec{r}$ is the position vector relative to the center of the mass distribution, and $M(r)$ is the total mass contained in a sphere around the center, i.e.,

$M(r)=4 \pi \int_{0}^{r} \mathrm{d} r' r'^2 \rho(r'). \qquad (2)$

To get the rotation curve, we make the simplifying assumption that the body runs on a circular orbit. Then you equate the centripetal force, necessary to keep the body on this orbit with the gravitational force, which gives

$\frac{m v^2(r)}{r}=\frac{G_N m M(r)}{r^2} \; \Rightarrow \; v(r)=\sqrt{\frac{G_N M(r)}{r}}. \qquad (3)$

From (3) and (2) we find the relation of the velocity profle to the density distribution as

$M(r)=\frac{r v^2(r)}{G_N} \; \Rightarrow \; \rho(r)=\frac{M'(r)}{4 \pi r^2}=\frac{1}{4 \pi G_N r^2} \frac{\mathrm{d}}{\mathrm{d} r} [r v^2(r)].$

Vanhees71 (talk) 08:57, 19 December 2013 (UTC)

The equation is correct (eg equation 3.20 on p. 100 of the Sparke & Gallagher 2000 textbook). What's confusing is that the Wikipedia article expresses the equation as $\rho(r) = M / (4/3 \pi r^3)$; rho is the average density within a sphere of radius r, not the local density at radius r. More commonly (including in Sparke & Gallagher), this equation is expressed using M(<r), the mass enclosed within a radius r. However, it is the mass enclosed, expressed either M(<r) or rho as in the current version of the Wikipedia article, which is relevant for Kepler's law. The local mass density is not relevant. —Alex (ASHill | talk | contribs) 03:37, 20 December 2013 (UTC)

## Refactored from Archived Discussion

### Elliptical orbits

One thing that I have never seen is an explanation of the galactic rotation curve that also explicitly takes into account the theory that the spiral arms are not in fact coherent but are a construct of the elliptical orbits of the stars that make them up, as explained by Image:Spiral galaxy arms diagram.png. The implication of this is that a star in a spiral arm is near the aphelion end of the ellipse, and so is going more slowly than a star on a circular orbit at that distance would be. If the ellipses themselves are turning and giving the illusion of the spiral arms rotating evenly, then the discrepancy could disappear. It seems unlikely that this has been overlooked, but I'd be interested to see a discusson that includes this aspect. PhilHibbs | talk 18:41, 23 Feb 2005 (UTC)

### Velocity vs Speed

The vertical axis of the graph really should be "Speed". I know that "Velocity" sounds more scientific, but velocity is a vector and that's not being represented on the graph, but only the magnitude, and the magnitude component of velocity is "speed". -- Ch'marr 15:29, 10 October 2005 (UTC) (the pedant)

Actually it would be correct to call it angular velocity, since that's what it is. 132.229.87.144 12:51, 4 August 2007 (UTC)

Not true. If it were angular velocity then it wouldn't be flat at large radii: v(r)~constant, but $\omega$(r)=v(r)/r$\propto$1/r. And angular velocity is also a vector, although the distinction isn't important for a rotating disk. Cosmo0 —Preceding signed but undated comment was added at 18:41, 20 September 2007 (UTC)

## Mysterious vs. Mundane Dark Matter

I've read in the past, either in "Light at the Edge of the Universe" or perhaps "The Whole Shebang" (I can't remember which) that the amount of matter required to explain the galaxy rotation curve effect was significantly less than the amount of matter required to explain the flat curvature of the universe in the FLRW metric. I should, I suppose, find the exact quote.

For the galaxy rotation curve, it was estimated that approximately 90% of the matter of the universe had to be "dark" which to me seems no great stretch of the imagination, just considering free hydrogen in a more-or-less smooth distribution. In the region of planets, of course, you wouldn't find it, because it's been swept away by the condensed masses. But the rings of Saturn (and the asteroid belt) are suggestive of a large amount of such sweeping. Anyway, a smooth region of gas would be consistent with the smoothness of the Cosmic Background. Consider that all the galaxies could be just condensations in a universe with an almost crystalline pattern of hydrogen gas, held apart by an almost perfectly symmetrical initial big bang. Galaxies could be whirlpools in a sea of hydrogen instead of a vacuum, as is usually assumed.

While nonbaryonic dark matter seems to exist, it seems to appear mainly in the course of violent explosions, with a very short half-life, and in insufficient quantities to create the Galaxy Rotation Curve result.

Corrections welcome. JDoolin 00:45, 22 August 2006 (UTC)

## Reverted contributions

[1]

I reverted this contribution because it represents a rather extreme minority theory for an explanation of dark matter. If and when this idea receives more notice within the community we can begin to include it, but it will probably find itself at dark matter rather than here.

ScienceApologist (talk) 18:22, 11 January 2008 (UTC)

## BEC or Scalar field dark matter model (SFDM) of halos is not an extrem minority theory

Dear ScienceApologist

—Preceding unsigned comment added by Scikid (talkcontribs) 07:12, 12 January 2008

Just to chime in with my view: it may not be an extreme minority theory but it is, at the moment, not well established as a serious alternative to CDM (despite your exaggerated account of it's successes). In any case, as ScienceApologist says, the article on dark matter is the correct place for outlining different theories on the nature of dark matter. From the point of view of galaxy rotation curves, the main debate is over whether dark matter is neccessary at all, although a single sentence pointing out that different kinds of dark matter predict slightly different rotation curves may be appropriate here. Cosmo0 (talk) 13:06, 12 January 2008 (UTC)

## Direction of acceleration

It may be an over-simplification to assume a radial accelaration towards the centre of mass. From the viewpoint of a star near the rim of the galaxy, the concentration of mass in the spiral arms will act as a significant gravitational attractor, in comparison with the more distant central bulge.
Envisaging the space as a deformed stretched membrane, the outer reaches of the galaxy will look like a corrugation of valleys and ridges corresponding to the arms and voids respectively. A test mass would roll forwards down one of these valleys and spiral in towards the centre of mass. The acceleration would therefore have a forward as well as an inward component, speeding up the rotation of the outer parts and helping to preserve the structure of the spiral arms.
This would explain at least part of the observed phenomenon without modifying Newton or positing dark matter.Brian O'Donnell (talk) 15:47, 29 July 2008 (UTC)

I've just discovered an explanation of the above with some arithmetic at [2].Brian O'Donnell (talk) 07:22, 30 July 2008 (UTC)
What you say is perfectly true, but I don't quite see what your point is. This is a well known fact, even if we often neglect it in practice when considering the average motions of stars in a galaxy. It has no bearing on the need for dark matter - if that's what you're implying - since it doesn't contribute anything to the average rotation curve. Cosmo0 (talk) 14:23, 30 July 2008 (UTC)
The problem here seems to be getting enough mass at the outer reaches of the galaxy. But what if the spaces between the arms were actually empty voids and all the mass was concentrated in the spirals? I.e. just as it appears in a telescope. The arms would have to be semi-stable structures, e.g. vortices, and gravity would act in a line of thrust along the axis of each arm. A test mass released at the end of an arm would curve along it into the centre instead of a direct straight line. A body in orbit would be accelerated forwards as well as inwards and would keep up with the arm to a greater extent than in a uniform disc. The need for dark matter would therefore be reduced or even eliminated for spiral galaxies.Brian O'Donnell (talk) 13:15, 5 August 2008 (UTC)
If it is assumed that the mass distribution in the galaxy is uniform then a Newtonian solution is not possible. More subtly, if the idea of a centre of mass is assumed to be accurate enough within the galaxy, the same effect ensues. Between galaxies, the centre of mass approach is a good approximation but it is less accurate for less uniform mass distributions and for distances closer to the centre.
If it is proposed that the arms are real, local effects have to be considered if they are to be stable. They would collapse into themselves along their axes unless the component stars were orbitting around each axis. At[3]a reciprocal simple harmonic motion is proposed but isn't this a kind of flattened ellipse? The website goes on to explain gravitational attraction to the arms as well as to the centre.
I am not trying to rubbish the general idea of new physics, merely to point out that a solution using the old physics is plausible in this case.Brian O'Donnell (talk) 20:26, 16 August 2008 (UTC)

## Galactic Jets

How much of the anomalous rotation curve can be ascribed to gravitational attraction between stars and the long relativistic jets that the central supermassive black hole has been emitting for billions of years? It seems likely that some of the flattening of the rotation curve should be due to the long axial jets, which should extend far beyond the halo and beyond the radius ascribed to a spherical distribution of cold dark matter. I don't know how much mass is ejected into jets for either an active galactic nucleus or an old galaxy but their mass should affect stars at large enough distance from the galactic center. Perhaps the radius of the galactic bulge is a clue to the mass of the jets?

WalterU (talk) 11:17, 25 June 2009 (UTC)

## Work of Cooperstock and Tieu

This should be added to the alternatives theory. Cooperstock is a decades-long researcher in GR with a long and fine publication record, and his contributions to this subject, insofar as they are a direct attack on this problem, should be pointed out. Antimatter33 (talk) 14:23, 5 September 2009 (UTC)

## Radial Velocity Profiles in Globular Clusters

Analysis of globular clusters shows similar anomalous behavior in the radial velocity distribution of cluster members. Since dark matter cannot account for these, while the work of Cooperstock, in principle, can (effect of non-linearity in GR, cluster members not test particles), this should also be pointed out in the "alternatives" section. Antimatter33 (talk) 14:23, 5 September 2009 (UTC)

If that is true the article is wrong! From the article: "It [dark matter] has been uniquely successful in ... explaining the dynamics of groups and clusters of galaxies". Aarghdvaark (talk) 06:19, 31 January 2012 (UTC)

## The relevance of gravitational lensing needs to be explained

Someone significantly smarter than myself needs to explain how gravitational lens measurements can distinguish between a) alternative gravity theories, and b) dark matter. The statement is made that it does, but it feels like the article is truncated.

Though the fact doesn't surprise me, I can't see why gravitational lens predictions would differ between the two kinds of rotation anomaly]y explanations. --TechnoFaye Kane 12:00, 13 December 2009 (UTC)

## Newtonian gravitation is wrong

IMHO, the graph is embarrassing; Newtonion gravitation is known to be wrong, so why base ANYTHING on it? The argument that relativistic effects don't matter is IMHO BS, because there is a supermassive black hole in the center of the galaxy, and orbital speed of stars observed in outer reaches of other galaxies show that there is a fixed relation between the mass of the galactic supermassive hole and orbital speed of stars. That is, THE HOLE CONTROLS THE ENTIRE CURVE. So this is NOT evidence for dark matter, it is epicycles. —Preceding unsigned comment added by 128.231.213.25 (talkcontribs)

Well, there are a couple of things you can do here. If you have a reliable source that backs up your assertion that the galaxy rotation curve can be explained by relativistic corrections and "epicycles" then you can include it in the article. If, on the other hand, you believe you have a unique explanation for the galaxy rotation curve that has not yet been discovered by mainsteam science then write a paper, get it published in a peer-reviewed journal and then include it in the article. Gandalf61 (talk) 10:04, 25 March 2010 (UTC)

## Rubin's inclusion in the main article text

Vera Rubin is present as a "See also" link and the first two entries in the bibliography. Should she be moved into the text itself? Her own article seems to suggest she most certainly should be. —Preceding unsigned comment added by 67.161.160.57 (talk) 10:55, 14 November 2010 (UTC)

done Aarghdvaark (talk) 01:53, 1 February 2012 (UTC)

## Just wondering if anyone had thought to take in account that space has could have mass and repulsive forces.

all this talk of dark matter and trying to explain abnormalities in the way the universe rotates and the way light is seen is retarded. Stop trying to find out what is wrong with the equations u all ready have and make up some new ones. Creating a fictional material to explain that u fucked up is childish. (dark matter my ass).

Signed, Keaton McMahon, 92234

## Velocity: Angular or Linear?

Just one question: The diagram in the article does not have units for velocity, so it is unclear to me if this is angular (revolutions per time) or linear (distance per time) speed. And the text offers no clues for me… A physics buff probably takes one look and knows, but I have no idea. 217.237.90.57 (talk) 16:27, 30 December 2011 (UTC)

The Y axis of the graph shows linear velocity, measured in km/s; in fact, it's true that in this case it should be called Speed, instead of Velocity, as velocity is a vector, and therefore, a sign (positive or negative) should be used in order to express the whole measurement: notice that we are working with absolute values of velocity, that is, the magnitude component of the vector, as we just want to see how it changes deppending on the absolute value of the distance (which initially was a vector -displacement-, but now we just use its magnitude component, so it's scalar -distance-). If we plotted an angular speed Vs distance graph, we would see that the line would remain constant in the part that previously was a 'growing' line (where linear speed increased at a constant ratio), and it would tend to decrease in the part in which linear speed remains constant (horizontal line in the original graph). Hope it's helpful. Pichiniqui (talk) 00:55, 8 January 2012 (UTC)

hopefully clarified with edit "represented by a graph that plots the orbital speed (in km/s) of the stars". Aarghdvaark (talk) 02:02, 1 February 2012 (UTC)

## "needs attention from an expert on the subject" heading

I'm removing this tag. I went over the article a few months ago and there have been only minor changes since then. So, although I'm not an expert, it seems no expert is coming along to the rescue and the article is good enough not to cause problems. Also there was no section added here in talk explaining why the tag was needed in the first place. If you put the "needs attention from an expert on the subject" tag back, please also discuss here why you think it needs attention. Aarghdvaark (talk) 03:04, 16 April 2012 (UTC)

## Further investigation

The original wording in this section and my first change are given here [4]. The original is clearly wrong since there has been no observation of the distribution of dark matter. A small edit war then ensued about whether the wording should be "the simulations assume" (me) or "the simulations show" (User:Junjunone [5], with finally an article cited by Junjunone, presumably in support of his view. I have skimmed the article and I don't understand why Junjunone cited it? The last sentences in the conclusion are "The hypothesis that the inclusion of baryons would resolve the discrepancy between theory and observation have been shown to be wrong. Worse, the disagreement actually grows larger if one utilises strong feedback physics schemes that can reproduce the observed stellar fractions in these systems". There is more of course, but I think I'm justified on the basis of this cited paper on stating that "State-of-the-art cosmological and galaxy formation simulations of dark matter with normal baryonic matter included do not resolve the discrepancy between theory and observation". Aarghdvaark (talk) 14:42, 14 September 2012 (UTC)

It appears that Aarghdvaark is not capable of understanding the papers beings cited. A standard treatment in simulations is to add baryons to dark matter. In these scenarios, the baryons follow the dark matter because gravity works that way. The cited paper shows that this happens and then asks the question whether feedback from baryonic processes can affect the dark matter and they get a negative as the answer. The simple fact is that this is just an example of one of the hundreds of papers written that show that baryons follow the dark matter. There are no assumptions and it is a bit strange that one would change the wording of the sentence to refer to a completely separate issue. Junjunone (talk) 16:00, 15 September 2012 (UTC)
Don't be so patronizing. It is obvious that normal matter will follow dark matter since the assumption is that dark matter is subject to gravity and that there is approximately five times as much exotic dark matter as normal matter. Have you really just used the paper by Duffy et al to try and justify the seemingly simple and innocuous looking sentence that "state-of-the-art ... simulations ... show that baryonic matter traces dark matter structures" [6]? But this sentence is wrong:
• the presumed distribution of dark matter is in a Dark matter halo around a galaxy, and obviously this is not how baryonic matter is distributed - so baryonic matter clearly does not trace dark matter structures.
• the sentence is too emphatic as it could easily be read as implying dark matter structures had been observed, when no one has seen any dark matter structure outside of a simulation.
• the point under discussion is not that baryonic matter "traces" or follows dark matter, but why the baryonic matter tail wags the dark matter dog - why is the amount of dark matter the right amount to make the galaxy rotation curve appear to depend on the baryonic matter, as per the well-established Tully-Fisher relation?
I took it that rather than trying to support the facile truism that baryonic matter and dark matter are both affected by gravity, you had cited Duffy et al's paper to support a statement something like "state-of-the-art ... simulations ... show that the amount of dark matter is dependent on the amount of baryonic matter" or the other way round - either of which which would go some way to explaining the Tully-Fisher relation. The paper is well written and is a summary of a large number of simulations. They investigate the back-reaction of baryons on the dark matter halo density profile - i.e. is the amount of dark matter dependent on the amount of baryonic matter, or can the tail wag the dog. Their conclusions were:
• "in the inner ten per cent of the virial radius the models are only successful if we allow their parameters to vary with baryonic physics, halo mass and redshift, thereby removing all predictive power" (my emphasis). What they mean is the models only show the correct result if the input parameters are adjusted to give the correct result. Or to put it another way, there is no theory to show any direct relation between the amount of dark matter and the amount of baryonic matter up to 10% of the virial radius.
• "On larger scales the profiles from dark matter only profiles consistently provide better fits", and "The most significant effects occur in galaxies at high redshift, where there is a strong anti-correlation between the baryon fraction in the halo centre and the inner slope of both the total and the dark matter density profiles" (my emphasis). i.e. there was a hypothesis which sought to explain how the amount of dark matter could depend on the amount of baryonic matter - only that hypothesis has been shown to be utterly wrong because it actually made things worse.
As I said the paper is well written and the conclusions are clear - state of the art simulations demonstrate there is no dark matter theory which can currently explain the Tully-Fisher relation. Aarghdvaark (talk) 04:41, 17 September 2012 (UTC)
There is something seriously wrong with your reading comprehension. I will ask to find out what the procedure is for disciplining someone who either misrepresents sources or cannot understand very simple points of clarification. Junjunone (talk) 17:22, 17 September 2012 (UTC)
Junjunone, Please avoid personal attacks against other editors. Comment on content, not personality. Thanks. Ebikeguy (talk) 01:30, 18 September 2012 (UTC)

Junjunone has taken this further. This is the timeline of his actions on 17 Sep 2012:

Those are the pages I'm aware of. Suggest to keep everything in one place that further discussion on content only be at Wikipedia talk:WikiProject Astronomy#Need a dark matter.2Fbaryonic matter simulations expert? Aarghdvaark (talk) 03:35, 18 September 2012 (UTC)

That doesn't make sense, why would we move the discussion about the article off this page? The ANI thread and Jimbo thread have nothing directly to do with this discussion. IRWolfie- (talk) 00:01, 19 September 2012 (UTC)
OK keep it here. Aarghdvaark (talk) 22:42, 19 September 2012 (UTC)
You said "There has been no observation of the distribution of dark matter": [7]: "Direct measurement of a dark-matter ‘filament’ confirms its existence in a galaxy supercluster." It sounds like the basis of much of your reasoning above, and for the removal is original research. IRWolfie- (talk) 23:16, 18 September 2012 (UTC)
I'm not sure I see the relevance of your reference here. The article is about galactic rotation curves, and hence is concerned with the dark matter distribution within galaxies. I read Aarghdvaark's statement as saying that there has been no observation of the dark matter distribution on these scales (i.e. on scales of tens of kiloparsecs). The Nature news article you link to is concerned with an observation of dark matter on the scale of a supercluster of galaxies, and tells us something about how dark matter is distributed between galaxy clusters, on a scale of greater than a megaparsec, but not about how it's distributed on smaller scales. Scog (talk) 13:19, 19 September 2012 (UTC)
Hi IRWolfie. Did you actually read this reference you cite above or just go on the headline: "Direct measurement of a dark-matter ‘filament’ confirms its existence in a galaxy supercluster"[8]? Because it says there "Mark Bautz ... notes that astrophysicists do not know precisely how visible matter follows the paths laid out by dark matter", which is exactly the point I was making. Incidentally, I would also disagree with the claim of direct measurement of dark matter, because what they actually did was "the team calculated that no more than 9% of the filament's mass could be made up of hot gas. The team's computer simulations suggest that roughly another 10% of the mass could be due to visible stars and galaxies. The bulk, therefore, must be dark matter, says Dietrich". That's not direct observation, that's using simulations to predict what is happening in some observations. Sloppy writing in Nature - sigh Aarghdvaark (talk) 00:27, 20 September 2012 (UTC)

After reading the rather confused commentary here, I am of the opinion that the problem is one of WP:DUE. In particular, Stacy McGaugh's reasonable pointing out that MOND works well for galaxy rotation curves should be discussed in this article, but we currently devote a bit too much to it in relation to what the literature shows. The Tully-Fisher relation has no scatter and MOND reproduces some interesting bumps and wiggles that are not as easily accounted for in the halo fitting picture, but that's, for better or worse, only a small part of the galaxy rotation curve story. We have little discussion here on how these plots are actually made, how the data is gathered, and what the standard way of fitting dark matter profiles is. I think that if this was added to the article with some paring back of the WP:BALL issues associated with McGaugh's work, we could resolve much of this. I am willing to begin writing this revision soon. Junjunone (talk) 03:13, 24 September 2012 (UTC)

Junjunone. The statement you have put back in:[9] "though state-of-the-art cosmological and galaxy formation simulations of dark matter with normal baryonic matter included show that baryonic matter traces dark matter structures" is at the very least misleading, e.g. see above for the cite from IRWolfie- that "astrophysicists do not know precisely how visible matter follows the paths laid out by dark matter". As I said before, since ordinary matter and dark matter are both affected by gravity they will tend to clump in the same place - that's a no-brainer. So either your sentence is trivial if you meant that, or wrong if you meant that dark matter determines precisely where ordinary matter ends up. Instead of asking for me to be banned for not understanding you, try and argue your case and explain what you meant to say. Aarghdvaark (talk) 03:56, 29 September 2012 (UTC)
There is something you're missing, but I'm not sure what it is. Either your opinion of what is trivial is not trivial to me, or your view of what "precisely" means is beyond what any source we have or what any statement being made is trying to say. In any case, I do not see this as being meaningful once this page is rewritten since the discussion of McGaugh's points will be diminished to the level that they are considered in reference to this subject. Junjunone (talk) 01:52, 30 September 2012 (UTC)
When challenged about what you have written, you are supposed to explain in more detail what you mean by what you write. Not just say it is the readers fault if they cannot understand you. You have actually done nothing apart from repeat your original sentence all through this and avoided any attempt to explain yourself, see above for a typical example - that is not constructive argument. Aarghdvaark (talk) 14:08, 1 October 2012 (UTC)
I don't understand what your challenge means and I welcome your clarification. I believe it is based primarily on something you are not understanding properly, but I am not sure exactly where your misconception lies from what you are writing as there are two distinct possibilities I outlined. I agree that this argument is not constructive, which is why I think you should not continue here as your comments are mostly distractions from the job of retooling the article. Junjunone (talk) 14:30, 1 October 2012 (UTC)
A good start would be to write what you are trying to say in a different way, here, on the talk page. Aarghdvaark (talk) 22:33, 1 October 2012 (UTC)
I think that's what I'm doing. Junjunone (talk) 11:59, 2 October 2012 (UTC)

## Images

It would be a good idea to have actual data and modeling for this article like this image. We need to find one that is free for use. I could create new images, but it would be good if I didn't have to spend my time on that. Junjunone (talk) 14:30, 1 October 2012 (UTC)

Regarding the below image used at the top of the article:
The embedded comment in the wikitext at the top of the article asks where the image came from. Visually, it appears that the creator of the .svg may have based it on the image here: http://astrodidyouknow.blogspot.com/2011/07/proof-that-dark-matter-exists.html. As for additional images, you can find some at the Harvard citation under the image, or by a search for "spiral galaxy rotation curves" on Arxiv.org. I'll be referencing a couple of those papers in an upcoming article. Cheers, Al'Beroya (talk) 09:46, 11 July 2014 (UTC)

## Citation needed

The article that is missing here may be this one: http://adsabs.harvard.edu/full/1978ApJ...225L.107R

Extended rotation curves of high-luminosity spiral galaxies. IV - Systematic dynamical properties, SA through SC by Rubin, V. C.; Thonnard, N.; Ford, W. K., Jr. 78.42.234.105 (talk) 10:13, 26 February 2014 (UTC) buonshi