The Case for Dark Matter

Unlike our normal articles, this one is not focused on a recent news item. We’re publishing it because it’s an excellent example of the power of graphs to show why something is without resorting to techno-jargon or a lengthy verbal explanation. – Ed.

There is so much evidence for dark matter that hardly any physicist doubts its existence. What dark matter is, is basegalacticrotationstill under some debate but that dark matter is, enjoys wide acceptance. Something unusual is happening in galaxies, something that we can’t explain with current physics. Something new is needed to explain it. The best evidence that something new was needed came from measurements of the Andromeda galaxy back in the late 1960s.

Background

Astronomers determine the relative masses of objects by observing how fast they move in relation to other objects. Most such systems of objects are like our solar system, with a big heavy object at the center (our sun) and smaller lighter objects orbiting it further out (plants, asteroids, comets, etc.) If gravity is the only thing holding these objects together then they must observe a certain speed limit. If they move faster than this speed limit gravity can’t hold them together and they fly apart. If they move slower than this speed limit they’ll crash into each other and become just one big object. Because gravity gets weaker with distance, the further an object is from the center the slower it will move. Pluto orbits the sun much more slowly than Mercury does, and it is not just because Pluto has further to travel, but because it is moving slower too. Currently Pluto takes about 250 years to orbit the sun once, but if Pluto were moving as fast as Mercury then it would only take about 25 years to orbit the sun.

The Study of Andromeda

Stars within galaxies behave similarly. In the 1960s no one had charted the speed that stars revolve around a galaxy before. This was the data the astronomers were collecting on Andromeda, the speed that various stars were moving around the galaxy. They sorted this data based on distance from the center of the galaxy and plotted a curve they call the galactic rotation curve. It is the shape of this curve that was the first most compelling evidence for the existence of dark matter.

The data revealed that objects far from the center of the Andromeda galaxy were moving faster than they should be. It is interesting to note that by the 1980s (some 15 years later) evidence was beginning to emerge that most galaxies and indeed the Andromeda galaxy harbored super massive black holes at their center. While, in the 1960s, this was a previously unknown source of mass, even this could not explain the surprising shape of the galactic rotation curve.

The Data

basegalacticrotationWhat astronomers had expected was a curve like the one shown at right. This curve shows that objects move slower the further away they are from the center of mass. This is how gravity works and represents graphically what was discussed above. Namely the further away an object is from the center the slower is must move. If it were moving faster, it would fly away from the center; if it were moving slower it would crash into the center.

bholegalacticrotationWhen a super massive black hole is added, the curve would look like this. The heavier object at the center allows objects to move just a little faster because the gravity is just a little stronger. This curve is the same as the previous curve, but with everything shifted up, everything moves just a little faster. Indeed, objects far from the center of the galaxy are moving faster in the presence of a super massive black hold than they would be without. However, like the graph above, everything also slows down the further it is from the center of the galaxy. The addition of a super massive black hole doesn’t change the shape of the curve, just how big it is.

actualgalacticrotationThe curve that emerged from the study of Andromeda looked like this. Not merely shifted a little, but a different shape entirely. Indeed, distance from the center didn’t appear to affect velocity at all.

Other astronomers were skeptical; this result was too unexpected to be correct. The simplest explanation would have been an error in the data. But eventually similar measurements were made on other galaxies and all of them had similar curves, all of them vastly different from the expected one.rotationcurves

Something different was needed to explain this, either a new theory of gravity or a new form of matter. Initially astronomers didn’t know what, but it was impossible to tweak the existing theories to obtain a result consistent with the data. A new theory was needed.

Conclusion

Nearly all media reports on dark matter state the evidence for it is that galaxies are rotating faster than can be explained by gravity alone. While this is true, it’s a gross simplification, so simplified as to be misleading. Now that you’ve seen these galactic rotation curves it should be easy to imagine hypothetical curves that simultaneously fit the criteria of a) stars moving faster than expected while b) fitting the profile of moving under the influence of gravity. Indeed the theoretical curve of a galaxy with a black hole shown above when viewed by someone ignorant of a black hole at the galactic core could be said to have stars orbiting it faster than expected yet still be explainable by gravity. Very few articles in the popular media push the experts to explain why they say that gravity alone can’t explain the rotation curves. The media seems to be content to report that “experts say” and not bother with any sort of follow-up as to why “experts say”. Yet as we’ve seen such an explanation is not that complicated, all it requires is a few pictures.

References

Vera Rubin and Kent Ford did the original work on galactic rotation curves. Their paper is: Rubin, Vera C.; Ford, W. Kent Jr., “Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions” Astrophysical Journal vol 159 p379 Feb 1970.

It is available online here:

http://adsabs.harvard.edu/abs/1970ApJ…159..379R

The image of rotation curves for multiple galaxies comes from page 4 of astronomy class notes from the University of Colorado. Available here:

http://rocinante.colorado.edu/~pja/astr3830/lecture17.pdf

Information about our solar system and relative masses of the planets is available here:

Pasachoff, Jay M. “Solar system” World Book Online Reference Center. 2004. World Book, Inc. http://www.worldbookonline.com/wb/Article?id=ar518960.

http://www.nasa.gov/worldbook/solarsystem_worldbook.html

http://solarsystem.nasa.gov/planets/index.cfm

The leading theory to explain these rotation curves is a sphere of dark matter encompassing most or all of the visible matter a galaxy, called dark matter halos. There are simulators online which allow you to tweak certain parameters of a galaxy and its halo. One of which is available here: http://burro.cwru.edu/JavaLab/RotcurveWeb/controls_MAIN.html and click on the “applet” button.

Finally, part of this website wants to be about compelling visual images. The rotation curves presented earlier are a little austere. The image below shows the Andromeda galaxy with the rotation curve superimposed on top of it. Hopefully this gives a better sense of what these curves mean.

rubin_galaxy

This image is available online here:

http://cosmicvariance.com/2005/08/30/painting-pictures-of-astronomical-objects/

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