Dark Matter

Spiral Galaxy M101, image from the Hubble Space Telescope

 Whenever I see a new article about dark matter appear online there seems to be a mandatory accompaniment of comments revolving around the feasibility of something we cannot see. Here is a basic run through of how we know dark matter is out there without the math, mostly.

The Theory:

It starts with assuming simple circular motion of stars in a spiral galaxy. Here gravity is holding the stars in the motion, so the gravitation acceleration is equal to the centripetal acceleration:

Where m is the mass of the star, M is the mass of everything within the stars orbit, v is the tangential velocity of the star, r is the distance from the center of the galaxy and G is the gravitational constant. Rearranging this we arrive at:

This may lead us to think that the velocity is constant the farther out we go in the spiral galaxy, except that M depends on the radial distance r. The dependency of mass on the radial distance is not an easy equation (meaning of course that I could not do it from first principles on the back of a notesheet). In the end the theoretical plot of galactic velocity versus radius is shown towards the end of this post as line A.

The Evidence:

Alright so now we have this sweet theory of how the galactic velocities should look. I mean we know it is a good thing since we also have a graph, and graphs are never a bad thing. With theory in hand we trot off to our nearest observatory to do some spectral line analysis of a spiral galaxy to determine the red shift along the radial axis. Ah good times.

So what does that mean? Well stuff that moves away from us lengthens the wavelength of light emitted so it appears red. Stuff moving towards us is slightly bluer. Kind of like the Doppler effect when a siren zooms by, the pitch goes up (shorter wavelength) as it approaches and depends when it moves away (longer wavelength). Sort of like that, except not really. We look at a spiral galaxy (let us say edge on) and find the red shift all along the diameter, from there we get the velocity (v = c*z, with v as the velocity, c the speed of light and z the redshift). After we account for the part where the entire galaxy is moving away from us we get a nice profile of the galactic velocity as a function of radius. This is curve B in this graph:

Rotational velocity versus radius in a spiral galaxy. Image from wikimedia.

See our nice A line from the theory? See this new B line from what we actually see? See the big gap between them? That is where dark matter comes in. The circular velocity is determined by the mass of stuff within the orbit and so there must be more mass then our original theory predicts. Something is there that is massive and dark (since we cannot see it). This dark stuff. With an Astrophysicists naming ability it is dubbed Dark Matter.

One question that seems to come up a lot: what if the theory of gravity is wrong? Well it is actually wrong, that is why Einstein came up with general relativity. If we altered the theory to explain away dark matter then a lot of other things the theories predict, that are right, would now be wrong. We just use Newtons theory of gravity since it is accurate enough is most cases but it is not perfect. The best way I have heard it said, “It is good for ‘stuff falls down'”.

With dark matter we do not know what it is. We do know where it is and roughly how much there is. Now we just need to find out what it is made of.

My guess: clouds of Higgs Bosons floating around in space. I am sure that is it.

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Astrophysics

 

Edinburgh Observatory

Up until last year my only exposure to astrophysics has been through books like The Universe in a Nutshell and Hyperspace. After starting to take a upper division course in astrophysics I have found that it is harder then other subjects in physics and much more interesting. I took these classes at the Edinburgh Observatory while studying there last year (one problem of the class was the great views of Edinburgh it offered), because of them I am planning on continuing in astrophysics or maybe space physics.

To get into graduate school for physics I need research experience, except they say that they don’t require it. But they do. Over the past two months I have been procrastinating contacting professors about a research position in the fall. Finally I realized I need to do it sooner or later. I crafted e-mails for four different professors in the UCSB Astrophysics group asking if they would possibly perhaps know of anything about an opening in the fall for an undergraduate. It would have been easier but I was someone they never met asking out of the blue. Two said no outright, I am thankful that were honest and in such a timely fashion. Another might have a position but I would need to learn python before the fall. The fourth was interested. I called the next week and I now will have a place in his lab come the fall. I get to pick out what looks interesting in the lab once I get there, I also get units for it!

Knowing that I will have some research experience by the time I apply for graduate school I looked at the schools I had placed in my top schools category. This time I looked at non-academic aspects: namely location and archery teams. My list had four schools: Stanford Applied Physics, University of British Columbia, University of New Hampshire and Montana State University. For location the first three have good locations, Stanford is nearby, UBC is near Seattle and my Uncle and from what I can gather there is an entire branch of my family in the northeast I have never met. Then someone asked me where Montana State was located, I knew that, it is in Bozeman. Where was Bozeman? In Montana, somewhere. So I google mapped it and discovered something. Montana was not where I thought Montana was. I expected it to be sort of south of Utah, don’t know why, it could be because I have not really been to many states aside from California, Hawaii and Alaska. Now that I know that Montana State is near North Dakota I have moved it down to my secondary school list which leaves only three as the forerunners for schools I really want to go too.

The next aspect I considered was archery. At Edinburgh I was in the Archery Club and participated in several competitions including the British Universities Sports Association indoor archery competition. I really liked archery, sadly there was no place for me to shoot at home or at Santa Barbara. The closest I could get were outdoor ranges geared toward hunters with compound bows (that would be my brother). So I was happy to find that the three schools left on my list had recurve archery teams or at least places to shoot recurve bows. So whichever I get into I can look forward to starting up archery again, maybe since I am in another country and another league I can pass as a novice for another year.

Hopefully this time I will be able to buy my own bow.

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