Thursday, December 14, 2006

Sagittarius

The constellation Sagittarius, 8000 light-years away, imaged by the Hubble Space Telescope. Until recently it was thought that just one star lies in the centre of this maelstrom. Now it is theorised there are three, each with 100 times the mass of our Sun. The matter that we see is just 4.507034% of mass. The hidden mass is responsible for sculpting those immense pillars. There is far more to our Universe than meets the eye.

Anonymous said...

... The matter that we see is just 4.507034% of mass. ...

Quoting this prediction (presumably a parametric best fit) to seven significant figures is very impressive. What are the error limits (systematic + statistical) on this best fit parameter as a result of the uncertainties in the underlying data and the applied numerical fit? Are the total uncertainties limited to the sixth decimal place?

9:26 AM
CarlBrannen said...

Is the belief in unseen things universal in academia?

11:21 AM
Kea said...

Er ... anon

Plug (pi - 3) / pi into your calculator.

11:39 AM
Anonymous said...

Plug (pi - 3) / pi into your calculator.

It seems that this wonderful algebraic result should be telling us something very profound about the structure of the Universe. Is there a theory that helps us understand the underlying physics at work here?

12:45 PM
Kea said...

We're working on it. At what point it manages to qualify for the name Theory is a matter of semantics.

4:42 PM
Anonymous said...

Is the ratio constant over cosmological time scales?

5:03 PM
Kea said...

Anon

Check out some of Louise's top few Links on this blog.

5:31 PM
L. Riofrio said...

Nice to hear from you all. Carlb, the majority of researchers agree that most mass is unseen. The best value I've found from WMAP is 4.4 +/- 0.3% for baryonic matter. Kea is again divinely insightful in figuring out the ratio.

This does tell us about the structure. If it is approximately spherical, then the volume V = [2*pi^2*(ct)^3]^{-1}. Initial density rho_i for a mass M before matter formation is just M/V, where M = tc^3/G. We then have rho_i = (2*pi^2*G*t^2)^{-1}.

Stable density rho_0 after matter formation is (6*pi*G*t^2)^{-1}. Difference between those is 4.507034% taken to as many decimals as you like. If the Universe were a different shape, or R were some other multiple of ct, density would be very different.

The Planck spacecraft promises to measure rho_0 to an accuracy of +/- 0.1%, which will allow us to check the first two significant figures. At our late cosmological time the figure 4.507034% is nearly constant, since nearly all the matter has formed.

11:07 PM
Gebar said...

Hi Louise

Recently I found a way that could add math support to Blogger. I remember this is something you were looking for, so if you have not seen the posts in Bee's and Clifford's blogs here it is.

Have a look here. Peter Jipsen of Chapman University has written ASCIIMathML, a great javascript program that converts ASCII notation (more or less the one used in math and physics newsgroups, and of course in blogs) to MathML. It also recognizes latex notation. Firefox rendering is great, although you may need to download some fonts. IE needs a plugin and rendering is not so good, but still readable. You are supposed to upload the javascript file to your server, but I suspect that it will work also if you put the content of the file in the head of your Blogger template. (Be warned though that the file is 42K, and that I have not tried this, I just assume it will work.)

If you do not want to risk this, there are two more solutions mentioned in the page given above. The first one are the ASCIIMath Image Fallback Scripts which use a public mimetex server (meaning you do not have to have mimetex in your server).

The second is LaTeXMathML, which as you may have guessed translates latex notation to mathml using again a public server if you cannot upload the file in your own. To use this, you just need to add one line in your template head, so that the javascript file can be read from a public server.

12:50 AM
L. Riofrio said...

Thanks gebar! Best wishes on your endeavours too.

6:41 AM
Kea said...

Gee, thanks, gebar!

11:36 AM
Gebar said...

Hi Louise and Kea. It's my pleasure.

My site approaches completion. It's a theory development portal with a wiki (Mediawiki), forums and blog(s). The framework is in place and I am the process of adding content to the wiki. When I launch it, I hope both of you, and Carl of course, will be visiting to contribute.

12:46 PM