Saturday, 23 February 2013

The Three-Dimensional Structure of the M31 Satellite System; Strong Evidence for an Inhomogeneous Distribution of Satellites

Back in Sydney after a busy couple of days in Brisbane at the Seventh ANITA (Australian National Institute for Theoretical Astrophysics) Workshop. It was a good two days listening to talks on the cutting edge theory (a lot by very smart PhD students and postdocs). A quick look at the program shows the incredibly diverse range of cool science being done in Australia.

But a quick post (as I am still playing astro-ph catch-up), but it's time to post an excellent paper from proto-doctor Anthony Conn (proto- as his PhD has been submitted and is being examined). But the paper provides a key input to our recent Nature paper, namely nailing the distance to the dwarf galaxies orbiting Andromeda.

I've written before about Anthony's sterling work using Bayesian techniques to provide the most accurate and robust distances, using the tip of the Red Giant Branch. It's not easy work and has consumed more than three years of work. But results, as you know, have been excellent.

What is essential to know is that while Nature is considered one of the top journals to publish in for astronomers, their papers are often very concise and condensed. This paper presents the nitty-gritty of measuring the distances.

There are a lot of technical things which are important in such a scientific paper, the stuff you don't see in the press-releases, but are needed to convince other academics. These include selection functions, and errors distributions, and many others. I'll summarize these with one of the pictures from the paper :)
The paper then took the three dimensional distribution of dwarf galaxies and started looking for significant planes, planes where there more galaxies aligned than you would expect from random. As you can guess from the Nature paper, we found one very significant plane, which has the properties that have been described before.
Again, it would bad to underestimate just how much effort this took, with computers chugging away for weeks at end, with us sitting there waiting for it to spit out the answers. Lots and lots of waiting, and then checking, and waiting, and checking. And then making pretty pictures.
So to close, it's important to remember that behind every press-release, there's a story, a story of hard work and effort (well, there should be at least). If you are writing a press release about your cool scientific result, then add a link to you paper. And if you are reading a press release, and get a chance to check out the paper, then you should. You may not understand every work or figure in the paper, but you might get a chance to appreciate the effort that has gone into the work. And that's not a bad thing.

Well done Anthony!

The Three-Dimensional Structure of the M31 Satellite System; Strong Evidence for an Inhomogeneous Distribution of Satellites

Anthony R. Conn, Geraint F. Lewis, Rodrigo A. Ibata, Quentin A. Parker, Daniel B. Zucker, Alan W. McConnachie, Nicolas F. Martin, David Valls-Gabaud, Nial Tanvir, Michael J. Irwin, Annette M. N. Ferguson, Scott C. Chapman
We undertake an investigation into the spatial structure of the M31 satellite system utilizing the distance distributions presented in a previous publication. These distances make use of the unique combination of depth and spatial coverage of the Pan-Andromeda Archaeological Survey (PAndAS) to provide a large, homogeneous sample consisting of 27 of M31's satellites, as well as M31 itself. We find that the satellite distribution, when viewed as a whole, is no more planar than one would expect from a random distribution of equal size. A disk consisting of 15 of the satellites is however found to be highly significant, and strikingly thin, with a root-mean-square thickness of just $12.34^{+0.75}_{-0.43}$ kpc. This disk is oriented approximately edge on with respect to the Milky Way and almost perpendicular to the Milky Way disk. It is also roughly orthogonal to the disk like structure regularly reported for the Milky Way satellite system and in close alignment with M31's Giant Stellar Stream. A similar analysis of the asymmetry of the M31 satellite distribution finds that it is also significantly larger than one would expect from a random distribution. In particular, it is remarkable that 20 of the 27 satellites most likely lie on the Milky Way side of the galaxy, with the asymmetry being most pronounced within the satellite subset forming the aforementioned disk. This lopsidedness is all the more intriguing in light of the apparent orthogonality observed between the satellite disk structures of the Milky Way and M31.

Tuesday, 19 February 2013

Pale Blue Dot....

... but how blue?

I'm a fan of learning things through problems. Specifically, in this example, I wanted to shuffle off my dinosaur image with regards to programming, and learn more python, which is the language of choice of the younger generation (although why people think that an interpretative language is better than a "deeper" programming language, I don't know - grumble, grumble, grumble....).

Right, to the problem in hand. The Pale Blue Dot is our planet Earth, our home. We know that it is a Water-World, but luckily not the Waterworld, but a planet whose surface area is 70% water. We're plodding along on a minority of the planet.

So, I woke up on Sunday and thought - "What is the view of the Earth that shows the maximum amount of ocean?" and conversely "What is the view of the Earth that shows the most land?". Yeah, I know, but my head chugs through things like this on a Sunday morning.

So, the question I have, to be answered with python, where do I stand on the Earth, such that, if I fly vertically upwards and look back, I get a particular view, either the most ocean or the most land in our view.

I gave this a minutes thought before I started, and I came to the conclusions which I am sure you did. To see the most ocean, surely we should start somewhere over the Pacific, probably the Southern Pacific. For a view of land, then Russia is your target. Starting somewhere in Russia and heading upwards will give you a view of lots of land.

But can we confirm this?
That's the pale blue dot by the way. Can you see it?

In fact, it turns out to be more interesting than you might think. To start with, we need a map of where is the land and where is the ocean. Luckily, these exist, and you can download them, for free, from NASA, and do this yourself.
The above picture is my version of the Earth from this data. How did I make this? Well, I had to deal with a tricky thing, namely, how to you draw equal-sized patches on a sphere? If you don't think this is an issue, look at a soccer ball - you can't cover a sphere with equal, regular shaped pieces.

But wait, there is a very neat solution, called healpix, which covers a sphere with little shapes. The cool point is that, while the little patches have slightly different shapes, they have the same area, making calculations of the density easy.
There is a port of healpix into python, so it is easy to load the land map above and place it onto a sphere, with zeros for the ocean, and one for land.

Each of the dots in the picture represents the centre of the pixels, and so if I've got enough of those, I've got a pretty good coverage of the surface of the Earth.

What I do then is take a look above each of the pixel centres, and see how much land and how much sea I see. But firstly, there is something I have to take account of, namely this:
Huh? Well, it's something familiar to fans of rugby. Basically, the posts are a fixed distance apart, but the angle they present depends upon the orientation of the posts relative to the kicker, something known as projected area, and we need to multiply by a cos(φ) term. We'll also assume that we are far enough away that we see one-half of the Earth around our point of interest.

OK, with all of this, we can ask what the distribution of views gives us. Remember, roughly 71% of the Earth's surface is covered in water. This is the distribution we get
This is very cool! This is the proportion of our view which is land (taking into account the geometrical effects I noted above). It ranges between ~0.1 and 0.5, so clearly, there is no view of the Earth which is 100% water, and the best we can do is roughly 50% of an image containing land.


So, where are the most and least watery views. The minimum, with 8.3% of the image being land is, as you thought, above the South Pacific, at a (lat,long) = (-15.1,-165.4). Here's the view from Google Earth; pretty watery!
And the opposite, the most land based image? It is still 49% water, but here it is, above (lat,long) = (52.8,42.3), and as you quite smartly guessed, it's in Russia :)
Excellent!

But another question hit me. Remember, what we are looking at here is what fraction of the image is water and what fraction is blue and which is green (roughly). But the question I had was "In which views do you seem the most land area, and in which the least?" This means taking out the projection effect, so land and water near the edge will contribute strongly to the total amount of actual proportions of each in our image.

Cutting to the chase, here's the most water, from a (lat,long) = (-40.2,-177.9);
 
 As expected, lots of water around the edge, and, in fact, we are only seeing 15% of the land of the Earth, making up 10% of the surface we can see! And the opposite, with the minimal amount of water?
This is above (lat,long) = (40.2,2.1), above the Balearic Sea, although it is nice to see Blighty so prominently placed. As expected, a lot of land is visible around the edge, and we can see all of the continents except for Australia and Antarctica, and land makes up 45% of the surface of the Earth we can see.

Finally, a little home work. I was initially surprised when I looked at the distribution of views we get in this case. It looks like this;
Clearly, it is symmetric, and I thought that this must be wrong. But a little thought and a few tests, it was clear that it is correct. But why? I'll give you a clue, it is symmetric about ~0.29.

Answers on a postcard....

Saturday, 16 February 2013

The Milky Way is on a diet

Watching the Russian meteor explosion sent a shiver down my spine. When I was young, I avidly devoured a magazine called The Unexplained, about the paranormal and mysterious events (although, as a good friend of mine said, the only unexplained thing is why I paid for the rag) and so was familiar with the Tunguska Event in 1908. The rock that exploded in 1908 was roughly 10x larger than yesterday's explosion, but seeing the effect of the shock-wave gives us a feeling of what Tunguska must have been like!

I wrote a little about a result by my student, Prajwal, on measuring the mass of the Milky Way, but we just wrote up a short media story on it. I've popped the entire story below. We're not expecting the story to be travel to far and wide, but it has appeared on the roof of the world, at Nepal News.

The Milky Way is on a diet

A team of University of Sydney astronomers, led by international PhD student, Prajwal Kafle, and his collaborators, Joss Bland-Hawthorn, Geraint Lewis and Sanjib Sharma have shown that the Milky Way is a lot slimmer than we previously thought.

Like all galaxies, the mass of The Milky Way Galaxy is dominated by an immense "dark halo" that can only be studied through detecting its gravitational pull, and our location, deep in the disk of the Milky Way, makes detecting this large scale pull very difficult.
Artists impression of the Milky Way Galaxy. The blue halo of material surrounding the galaxy indicates the expected distribution of the mysterious dark matter.(Credit: ESO/Calcada)
Artists impression of the Milky Way Galaxy. The blue halo of material surrounding the galaxy indicates the expected distribution of the mysterious dark matter.(Credit: ESO/Calcada)
The dark halo is comprised of dark matter, the dominant form of matter in the Universe, and in the early 1970s, Australian researcher, Professor Ken Freeman of the Mount Stromlo Observatory realised it actually dominates motion of individual stars, including our Sun. This work was recently rewarded with Professor Freeman receiving the Prime Minister's Prize for Science.
"Living inside the Milky Way provides some unique opportunities to estimate how much dark matter there is in the dark halo of a typical large spiral", said Professor Freeman.
The amount of dark matter that surrounds our Galaxy and how is it distributed became the target of Kafle's research.
"We still struggle to answer these questions," said Kafle
He called on a technique derived by British astronomer, James Jeans, in 1915, to attempt to weigh the amount of dark matter. While the approach is mathematically robust, it requires the detection of very distant stars in the halo.
"There were so many assumptions going into those calculations, I would take almost all the previous estimates that use this technique with a pinch of salt," said Kafle.
"I turned to a massive survey of the sky, the Sloan Digital Sky Survey, delivering an unprecedented view of our Milky Way. This magnificent survey means we can do away with many of the previous assumptions," said Kafle.
Professor Freeman adds "Kafle's new analysis uses robust techniques, and the sample of tracer stars is much larger than anyone has used before. His new estimate is a big step forward from previous work."
To make the calculation more accurate, Kafle used the speeds of the stars, as measured by the Doppler effect, to see how fast they are moving in the halo. With this, the Jeans's technique revealed that the mass of dark matter within 0.8 million light years radius of our Galaxy, is almost half the amount reported previously, weighing 1.2 trillion times that of the mass of the Sun.
While this represents one of the most accurate measurement, Kafle admits that "The uncertainties in the quoted number is still around 30%. But this is an indication of how well we understand the amount of mass in the Milky Way".
"This is challenging work", said Kafle's supervisor, Professor Geraint Lewis, "but it is great to uncover how much dark matter is there in the Milky Way one of the great astronomical mysteries."
Now, Kafle is looking forward to settle the controversy about the rotating stellar components in the Halo, where it appears that there are two populations of stars moving in opposite directions and its direct implication on the formation history of our Galaxy.
After 3 years of devoted work far far away from his home and family in Nepal, Kafle said, "It was worth traveling all the way from the roof of the world, Nepal, to the country with beaches, BBQs and snags. With icons of the Dark Force, Professor Freeman and Nobel Laureate Professor Brian Schmidt around, I am more motivated as I push our understanding one step further."
Kafle's candidature is supported by the University of Sydney International Scholarship.
Read the paper in The Astrophysical Journal at: http://iopscience.iop.org/0004-637X/761/2/98/ orastro-ph at: http://arxiv.org/abs/1210.7527

Report by Tom Gordon

Friday, 15 February 2013

The only thing that isn't moving at the speed of light is light itself!

Time to give you some brain food. The title of this post is correct, and I will go further.
"and the speed that light travels is not the speed of light, it is zero"
I hope that this has opened your eyes and got the cog-wheels turning. You might be even thinking that I have gone slightly mad. But stick with me, and you'll see that this is true, and you can use these facts to wow your mates down the pub.

The key issue is the difference of traveling through space, and traveling through space-time. I think the latter is more fundamental, and so my statement is more truerer than the usual comments you hear. But to understand this, we need to remember what speed actually is!

Remember from school that speed is simply the distance travelled divided by the time that it took to travel the distance. If we moving at uniform speed, then our speed at all points in the journey would be the distance covered divided by the time.

Maths time!
Where the triangle (the greek letter delta) means change in - so it is change in x (distance) over change in t (time).

But we know speeds are not uniform, and we want to know the instantaneous speed. This means that we want to find out just how much distance we're covering in a little bit of time right now. This means that we need to take the delta up there to be as small as possible, and, you know this was coming, use the differential form, invented by Newton and some german bloke*.

This means that the speed is just the slope of the plot of distance verses time, something like this:

and we write the speed as:

Excellent, now we have speed in one direction. But what if we are moving in two directions, x and y. What's our speed then? Remembering your high-school physics, we could talk about the vector components of the velocity, and the speed would be the magnitude of the vector, so we would have

Clearly, if I am not moving, then the velocity components are zero, and so is my speed, so what the flip was I talking about at the beginning of this post?

OK, we need to move from the concept of motion through space to movement though space-time. This is now motion through 4-D, three spatial dimensions and one time dimension. We have a picture that looks like this
Just as above, we can define a velocity through space-time defining the tangent to the "world-line", the path we trace out. But we have a little bit of a problem; looking back, the derivative is with respect to time (i.e. the change of distance over time), but time is now one of the dimensions.

This is where it gets cool. There is another time involved, and that's the time that ticks off on watch as I trundle along my world-line. This is called the proper time and is denoted by the greek symbol τ, and, of course, runs at a different rate when compared to a clock at rest in the coordinate system.

If we take our derivatives with respect to this proper-time, and then ask the question "What is the speed through space-time?" we get

While this looks similar the equation above for the speed, there are some important differences. The first are the minus signs in there. For those interested in the technical reason, it's because space-time is pseudo-Riemannian, and a simple application of Pythagorous's theorem does not apply. If you are not interested in the technical, just take it that space-time is weird.

However, these minus signs have an interesting effect (well, truth be told, all of the interesting effects in relativity are due to these minus signs). Firstly, it means that the right-hand side of the equation is one - we'll come back to this in a moment. But as the velocity in through space changes, the velocity through time changes accordingly, so that we always get one on the right-hand side. But this you knew; special relativity says that the relative rate that clocks tick depends upon the velocity.

Back to what the right-hand side means. Well, it's the speed through space-time, and it's a constant. And in the units I've adopted here, this one is the speed of light. Your motion through space-time is the speed of light. It is always the speed of light, even when you are standing still.

How cool is that!!

Now, this works for any massive object. If someone tells you what you a lazing away, sleeping on the couch, point out that you are moving at the speed of light and tell them to leave you alone. Although, I am not sure you can use this information to beat a speeding ticket!

Right, time to get ready for work, but what about non-massive objects, namely light. Well, things are trickier, as light does not have a proper time we can take the derivatives with respect to, but there is another thing (which, if you must know, is called an affine parameter) with which we can calculate the speed through space-time. This now looks like this;

As you can see, the derivatives look very similar, but the right-hand side is now zero! The speed that light travels through space-time is zero!

Welcome to the wonderfully whacky world of special relativity.

* Apologies to my German colleagues - I know perfectly well how much Leibniz contributed to the development of differential calculus, and I know how much Newton's ego influenced the history of the discovery.