Saturday, 22 June 2013

Observing time on the Hubble Space Telescope

Reviewing grants and postdoctoral researchers have completely absorbed the last week, and will similarly consume the week to come, so a quick post today, just posting a news article from our School of Physics webpage.

Sydney University astronomers granted observing time on the Hubble Space Telescope

17 June 2013

Two astronomers, Professors Geraint Lewis and Joss Bland-Hawthorn, from the Sydney Institute for Astronomy, located in the School of Physics, have been awarded observing time on one of the world's premier observing facilities, the Hubble Space Telescope. Obtaining observations with this unparalleled telescope is extremely competitive, and this award has demonstrated that their research is world-leading.

As part of an international team, Professor Lewis has secured 28 Primary Spacecraft Orbits and 28 parallel spacecraft orbits in Cycle 21 of the Hubble Space Telescope (HST) program due to begin in October this year. In addition, Professor Bland-Hawthorn has been awarded 50 Primary Spacecraft Orbits in the same cycle.

Globular ClustersProfessor Lewis' team will use the allotted time on the telescope to observe globular clusters in the halo of galaxy M31. Globular Clusters are fossil relics from which we can obtain critical insights into events that underlie galaxy assembly.



Image of the PAndAS survey. The colour is the number of stars at each point, with black being the main Andromeda and Triangulum galaxies. The yellow at the edge of Andromeda and the faint blue spread around are the tidal debris of smaller galaxies ripped apart by the strong tidal forces. Credit: Mike Irwin

As part of the major Pan-Andromeda Archaeological Survey (PAndAS) the team have discovered two groups of Globular Clusters that closely trace narrow stellar debris streams in the halo of galaxy M31. With the time on the HST, the team will image 14 Globular Clusters spanning these two accreted families, allowing measurements of the stellar populations, distance, and structural parameters of each object."

This imaging provides a unique opportunity for the study within a single galactic halo of two different Globular Cluster sub-groups that we know to be accreted. This novel approach opens a new angle of attack on long-standing questions in the field," Said Professor Lewis.

The team will, for the first time, quantify the typical properties of accreted Globular Clusters in the M31 halo as well as the degree of variation amongst them, and how closely they correspond to the suspected accreted Globular Clusters population in the Milky Way."Observing these globulars is like delving into the past, a true cosmological archaeologist" said Professor Lewis.

Combined with new radial velocity measurements for the Globular Clusters, the observations will allow the team to trace the orbits of the two streams within the M31 halo, and thus break the main degeneracies that plague numerical models designed to probe the gravitational potential and distribution of dark mass.



Illustration of the Fermi gamma-ray bubbles extending ~10 kpc or ~50 degrees above and below the GC, as viewed from outside the Galaxy (courtesy NASA/GSFC). Superimposed (in yellow) are four of our AGN sight lines, which bracket the vertical extent of the Fermi bubbles, and (in red) two of the halo-star sightlines.
Galactic wind Professor Bland-Hawthorn's proposal is to follow up his discovery in 2003 of a huge wind blowing out from the centre of the Galaxy. The Hubble observations are to make comprehensive, high resolution spectral observations of six distant halo stars in the Milky Way. The light from these stars is used as a background source to "see through" the Galactic wind."Like other spiral galaxies, the Milky Way has highly concentrated galactic wind extending out to the top and bottom from the centre of the Galaxy, the nuclear wind is thought to be powered by either the central black hole or active star formation in the galaxy," said Professor Bland-Hawthorn.

Professor Bland-Hawthorn's Hubble time will reveal the relationship between the different components of the wind, which will aid the understanding of outflows from other galaxies and our own Galaxy nucleus.

Contact: Tom Gordon
Phone: 02 93513201
Email: t.gordon@physics.usyd.edu.au

Wednesday, 19 June 2013

The Arbitrarily Large Monty Hall Problem

I've just fallen off a plane from the UK, and am a little tired, but here's some interesting mathematics that kept me busy `on the road'.

I've loved the Monty Hall problem since I first heard about it. It is not a difficult problem, but the outcome can seem quite counter intuitive. Before I look at the problem in more detail (more detail than I should?) you should have a look at this little video as a refresher.


So, let's try and represent all we've seen in the movie in this as a picture. 


At the top is the initial situation, with the car, C, and two goats, G, behind the doors. The next level down is what we end up with, either with you choosing the car and one goat door open (with a probability of 1/3), or choosing a goat and a goat door revealed (with a probability of 2/3).

Looking at this , it's clear that if you choose to stick with your original choice of doors, you will win the car with a probability of 1/3 and will win the goat with a probability of 2/3.

However, if you swap doors, the probability of getting a goat is now 1/3 and winning the car is 2/3; the chances of winning a car has increased by a factor of two by simply switching doors.

How cool is that!

But I started thinking, if we change the problem, change the number of doors, cars and goats, but always reveal one door with a goat, will it always boost your chances to swap?

OK, here we go. Now we have 4 doors to start with, but one car and now three goats. So, similar to the picture above, we get to the final state, with you either choosing the car with the first guess, with the probability of 1/4, or a goat with the probability 3/4.



So, looking at this, then of you stick with the original choice, the chance of winning the car is 1/4 and winning a goat is 3/4. But what if you choose to swap?

Clearly, if you chose the car to start with, then when you swap you will get a goat. 

If, however, you chose the goat to start with, then if you swap then you could swap to the car or you could swap to a goat. At this stage, if you swap you have a 50-50 chance of getting the goat or car. What the chance of winning the car now? 


So, the chance of winning the car if you don't swap is 1/4 (or 2/8), but if you swap it is 3/8, so there is an improved chance of 1.5 times in winning the car if swapping doors than keeping your original choice. 

OK, let's spice things up a little. Let's now have two cars and two goats. Same picture as before, but now the initial chance of choosing a car or a goat is 1/2. 


So, if you stick with your original choices, you have a 50-50 chance of winning a car. But what if you swap?

If you originally picked a car, then there is a 50-50 chance that you will swap to a car or a goat, so you can win or lose. If you originally chose a goat, then when swapping you have a 100% chance of getting a car.

So, what's the chance of winning when swapping now?


So, again, the chances of you winning are boosted by a factor of 1.5 times by swapping rather than keeping your original choice.

So, what if you have originally n cars and m goats, hidden behind (n+m) doors. What's the ratio winning when swapping compared to keeping your original choice? I will leave the algebra to the reader, but you can show this ratio is


Woooooh! This result does not depend upon the actual number of cars and goats, only the number of doors (I should point out, there has to be at least one car and two goats for this to work).

Let's just check this works. In the original problem, there are three doors, so ndoor=3, and this ratio is 2. Excellent. What about four doors, with ndoor=4? The ratio becomes 1.5, just as we saw before.

I don't know if this has been derived before, but I think it is a cool result. 

It tells you a few things. Firstly, as we increase the number of doors, the ratio between swapping and sticking approaches unity, irrespective of the number of cars and goats. But more importantly, the limit is approached from above; the numerator of the fraction is always bigger than the denominator, and so the ratio is always greater than one. It might be only a little bit bigger than one, but it always is.


The moral of the story is to always swap, no matter how many doors are presented to you. Good luck!

(note - badly formed maths fixed since original post - kids, don't blog while jet-lagged!)

Sunday, 9 June 2013

At the Edge of the Empire

I'm traveling (hence the lack of recent posts) and am in Blighty for two weeks. I'm a distinguished visitor at the Jeremiah Horrocks Institute at the University of Central Lancashire in the much prettier than I expected city of Preston. I'll write more about that in a little while (it's been a busy trip, with a few talks etc, and more to come).

However, I find myself in South Wales for the weekend visiting family, sitting at the bottom of the Brecon Beacons National Park in the little village of Coelbren. It's gloriously sunny at the moment, but in winter, this is a reasonably harsh place to be.

Anyway, I went for a run this morning and took this photo.
In many ways, it looks relatively unremarkable, but this view almost 2000 years ago would be very interesting. Why? Here's the view from googlemaps, with my location marked with the circles.
I was looking towards the bottom centre of the map, but notice how square the field is next to the circle is; it's edge is the fence in the right-hand side of the image. Shapes like that are suspicious, clearly being man-made, but by who?

A look at the Ordnance Survey map, it's clear;
The square is a roman fort and there was a larger camp just across the road. As well as a permanent form, this region is a marching camp, with a place for troops marching from the roman settlement in Neath (where I was born, but not in roman times) to Brecon. The roman road they marched along still exists (and is called the Roman Road) and when you look at the original photo, the soldiers marched down off the hill top, through the village and over to the fort; the romans marched on the hill tops, rather than in the wooded valleys, as it aided their fighting tactics.

And the village, that's Banwen, which happens to be where my mother was born, and it is known that it  was a village in Roman times. In fact, it is often touted that as a birth place of Saint Patrick and the locals have put up a sign to promote this;
I know that people think of the Roman soldiers standing on Hadrian's Wall facing the Picts (yes, the picts, not the Scots who only arrived from Ireland in the 5th century), but here, South Wales, is a long way from Rome and must have felt like the end of the world, especially in winter.

I must admit, growing up here, I didn't really notice the local history, but standing there this morning, thinking about roman soldiers wandering about, collecting water at the local stream, and fighting the locals hiding in the woods, really brought it home. Now I think it's pretty cool.