Monday, 26 December 2011

Ah Bottomium!

When I was an undergraduate student, I had thought about becoming a particle physicist, but a summer school first at the Rutherford Labs (working on proton-anti-proton scattering) and then CERN (search for charged Higgs particles) beat that out of me :)

There is a lot of chatter about the Higgs out there at the moment, but unfortunately I think that a lot of it illustrated the poor understanding of statistics by journalists (and even scientists). p-values make me weep.

But I thought I would talk about something else, the the discovery of bottomium at the LHC. Funnily enough, it's not actually a new particle, and that's something I thought I would try and explain.

Let's start with a picture - what's this?

Of course, it's an atom. Well, except we know this is just a schematic picture of an atom, a nucleus with some electrons whizzing around. A real atom is more complex than this, being described by the laws of quantum mechanics. Electrons are not little particles on defined orbits, but are quantum wave functions that (if you want to try and visualize them) look something like this -
Chemists call these things orbitals.

One of the other things you remember from high school science is that each of these orbitals has a different energy level (some have the same, but let's not worry about this at the moment), and that when atoms absorb energy, the it changes energy levels, and this energy can lost through the emission of photons. For lithium, the energy levels look like this
These discrete transitions give us discrete lines in the spectrum of the elements.
 Of course, spectroscopy is vital in many fields - in astronomy it allows us to calculate the chemical composition of distant stars and galaxies.

Now, it might seem we are going a little off topic, but let's keep going. What about the nucleus of an atom? We know that the nucleus is made of protons and neutrons, and that protons carry positive charge, while neutrons are, well, neutral. This leads to a bit of a conundrum, as that positively charged protons will repel each other - how does the nucleus hold itself together?

This is where the strong force comes in. It provides an attraction which overcome the repulsion of the electromagnetic force between the protons. But the nucleus, like the atom, is governed by the rules of quantum mechanics, and so has quantized energy levels. So we get a picture like this

Because the forces are larger, the differences between the energy levels are larger than those you see in atoms, but the nucleus can undergo transitions in the same way that an atom can. Here's an example
We start with Cobalt-60, which is radioactive, and emits an electron from it's nucleus. In doing this, it changes a neutron to a proton, and so becomes Nickel instead. On the right, we can see that it can emit an electron at either one of two energies, 0.31 MeV or 1.48 MeV, and this leaves the Nickel in one of two energy states. These states decay down into the ground state through the emission of γ-ray photons. So, γ radiation is nothing but nuclei undergoing transitions in the same way as atoms!

Now, one thing that some people don't know is that if we have a Nickel atom in its ground state, and one in a higher energy level, the one at the higher energy level is more massive than the one in its ground state. This, of course, makes sense. We know from special relativity that mass and energy are interchangeable, and so the excited nucleus has more energy and so more mass.

OK - finally, let's get back to the announcement of bottomium. Bottomium is a meson, meaning that it is make of a quark and an anti-quark, held together by the strong force. Looks something like this -
Now, there are only 6 different quark (up, down, top, bottom, charm and strange) and so there are only a finite number of combinations you can have to make mesons; the one above is a pion Bottomium is a quarkonium state, made of a bottom quark and an anti-bottom quark.

So, did the LHC discover bottomium in the previous week? Well, no. The ground-state bottomium particle was the ηb was discovered by the BaBar experiment in 2008. So what is the bally-hoo coming from the LHC.

Well, mesons (and they close companions, the baryons) obey the rules of quantum mechanics, and like atoms and nuclei, they have quantized states. They can be in their ground state, but if you give them energy, they can move into a higher energetic state. Just like nuclei, the more energy means more mass, and so the new particle, the χb(3P) is just the same old bottom-anti-bottom, but just in a higher energy state (in fact, the 3P gives it away, as those chemically minded would remember the P from SPDF). So, it's not really a new particle in the sense that it is made of something new, but is the same old particle but now with added energy. I guess that would not have been such an amazing press release :)

One last thing. As we've noted above, nuclei and mesons (and baryons) have more mass when they absorb energy and move to higher level. But the same must be true of atoms, and an excited hydrogen atom has more mass than an atom in its ground state. But the amount of energy held in an excited electron system is quite small compared to the overall atomic mass. Cool eh!

Note added in proof: Due to a convoluted history, the first excited bottomium state was discovered in 1977, with the ground state discovered in 2008. Here's the energy level diagram from the 2008 article above.
and while the press has been going on about bottomium, the correct name is bottomonium :)

Tuesday, 20 December 2011

What shape is the ocean on a cubical planet?

Clearly, they are circular!
The question is, however, how do you calculate this?

The first step is to realise that the surface of a liquid is an equipotential surface. This means nothing more than the value of the potential energy over the surface is the same. This is easy to think about if you remember your classical mechanics as if there were differences in the potential energies in the water, so one bit of water was higher than the other, then that potential can be converted to kinetic as the water flows downwards. When could all this be static? When the surface of the water is at the same potential, so no one bit is "higher" (in terms of potential energy) than another.

So, to work out the shape of the ocean, we just need to calculate surfaces of the same potential energy. But how do we do that for our cubical world?

In the following, I've made a few simplifying assumptions. I assume my planet is not rotating (that adds a further set of energy terms) and that I can ignore the mass of the water (so ignore its potential energy). All I need to do is work out the potential energy of the cubical planet!

Many will remember from school that the potential energy of a point-like mass is given by
where M is the mass, G is Newton's gravitational constant and r is the distance away from the mass.

One thing that often confuddles students is that this expression diverges as r goes to zero. But what's the potential of an extended mass distribution? Well, then we need to add up all the little mass bits to give the total potential which, when we have a continuous mass distribution, we can represent as an integral. So the potential now looks like this
Let's not worry about the details, but those in the know will know that such an integral can be done quite efficiently as a convolution using Fourier transforms. If you are not in the know, just put it down to mathemagic.

Once we know the potential, we just plot up up the surface of the planet and the surface of the water (and equipotential) and voila. I choose to use povray for this.

Let's add a little more water. What do we get?

Notice that the water bulges out significantly. So what would life be like on the cubical planet? Well, it should be clear that the corner of the cubes would be like mountains, and so if you lived in the centre of a cube face, you would be able to stand upright, but as you walks towards the edge you would feel the orientation of the gravitational field changing. As you move away from the centre, it would feel that the climb was getting steeper and steeper, event though you are on an apparently flat plane!

But remember that the surfaces of the water are equipotentials, so you can happily sail over the ocean with little effort. In fact with a little more water, we can sail right around the planet. The view would be cool!

But what about other planets? What would the ocean be like on a dumbell planet? Easy
An uneven dumbell
Slab planet

The possibilities are endless :) I'll play some more with this in the future.

In closing, I just want to note that I didn't design the planetary textures in povray, but I have lost the reference to where I got it from (although it is called Cheap World). Thanks to the original author!

Sunday, 18 December 2011

The Sydney-AAO Multi-object Integral field spectrograph (SAMI)

When I say modern astronomy, what do you think of? Large telescopes peering into the sky, looking to unlock the secrets of the Universe? Of course, telescopes drive astronomical research, but what is often forgotten is the business end of the telescope, the instruments that collect the light, are the things that really define the science we can do. And such instruments can be extremely complex, and extremely expensive.

Here at Sydney we have a group working on astronomical instrumentation and a new instrument, The Sydney-AAO Multi-object Integral field spectrograph (SAMI), has recently be commissioned and the first paper has been accepted.

So, what does this new instrument do? Well, spectroscopy is an essential part of astronomy. Basically, it just means collecting light and dispersing it into a rainbow. Over to Pink Floyd
We don't use prisms any more (we use volume phase holographic gratings, which sounds much more science fiction). Looking at the light tells us lots and lots about the object we are looking at; the velocity, the chemistry, the star-formation history etc.

The problem has been that spectroscopy is that often you can only collect light from a single object at a time (long-slit spectroscopy). However, more recently we have been able to multi-object spectroscopy, using instruments like 2dF
Each little red dot here is little prism connected to a fibre, and so when pointed at the sky we can collect the light from lots of objects (and in this case, around 400 at a time).

 The problem is that the prism is just a single `hole' and so if plopped onto a complex object with lots of structure, like a galaxy, will not see any of the complexity, it will just collect all the light in a smush.

But what if we want to get spatially resolved spectroscopy, to measure the chemistry and velocity from little bits of a galaxy? Enter SAMI!
What is it? Well, put simply, instead of single fibres, each fibre is made of a bunch of tightly packed fibres, and each collects light over a small patch of sky. You get a picture like this

This field is 1.6 arcseconds across and has been plonked on a galaxy. What we are seeing is the velocity field of the galaxy, measured from the Doppler shift (the numbers on the side are km/s, so we can see a clear rotation curve for the galaxy. 
I've been working with a student on measuring cosmology by looking at the correlations between galaxy spins and where the galaxies live. So with SAMI (which is on the Anglo-Australian Telescope), which can collect the light from 13 objects at a time, we have the prospect of surveying a large number of galaxies and actually undertaking the measures we propose. Exciting stuff!

But as I said at the start, the first SAMI paper is accepted for publication, with the SAMI team as authors and Scott Croom as head author. Well done Scott!

Scott M. Croom (1 and 2), Jon S. Lawrence (3 and 4), Joss Bland-Hawthorn (1), Julia J. Bryant (1), Lisa Fogarty (1), Samuel Richards (1), Michael Goodwin (3), Tony Farrell (3), Stan Miziarski (3), Ron Heald (3), D. Heath Jones (5), Steve Lee (3), Matthew Colless (3 and 2), Sarah Brough (3), Andrew M. Hopkins (3 and 2), Amanda E. Bauer (3), Michael N. Birchall (3), Simon Ellis (3), Anthony Horton (3), Sergio Leon-Saval (1), Geraint Lewis (1), A. R. Lopez-Sanchez (3,4), Seong-Sik Min (1), Christopher Trinh (1), Holly Trowland (1) ((1) University of Sydney, (2) ARC Centre of Excellence for All-sky Astrophysics, (3) Australian Astronomical Observatory, (4) Macquarie University, (5) Monash University)
We demonstrate a novel technology that combines the power of the multi-object spectrograph with the spatial multiplex advantage of an integral field spectrograph (IFS). The Sydney-AAO Multi-object IFS (SAMI) is a prototype wide-field system at the Anglo-Australian Telescope (AAT) that allows 13 imaging fibre bundles ("hexabundles") to be deployed over a 1-degree diameter field of view. Each hexabundle comprises 61 lightly-fused multimode fibres with reduced cladding and yields a 75 percent filling factor. Each fibre core diameter subtends 1.6 arcseconds on the sky and each hexabundle has a field of view of 15 arcseconds diameter. The fibres are fed to the flexible AAOmega double-beam spectrograph, which can be used at a range of spectral resolutions (R=lambda/delta(lambda) ~ 1700-13000) over the optical spectrum (3700-9500A). We present the first spectroscopic results obtained with SAMI for a sample of galaxies at z~0.05. We discuss the prospects of implementing hexabundles at a much higher multiplex over wider fields of view in order to carry out spatially--resolved spectroscopic surveys of 10^4 to 10^5 galaxies.

Friday, 16 December 2011

Gravitational Waves and the Wild Wild West

I started this post at Perth airport, but the wireless was too slow to complete it. So here goes (again).

I'm back in Sydney after a few days in Perth. I gave a talk at ICRAR and the The Australian International Gravitational Research Centre at the University of Western Australia. Perth clearly is a boom town, with plenty of money flowing from the mining (a bottle of house white cost $58!), and it still has a slight feel of the wild-wild western - the police were touring the lounge where I was sitting at the airport as, as you can imagine, several hundred miners were heading out on a Friday afternoon and, apparently, there has been trouble in the past.

I had several really interesting meetings in Perth, especially with regards to writing grants in the next ARC round (which has come round really quickly again). I'll write about those at a later date. On Thursday I was heading up to Gingin, north of Perth, for a BBQ at the Gravitational Wave Centre, and I was invited to take a look inside the research part of the centre. So, here's some piccies.

This is the view from the top of the 13 storey leaning tower (and it's quite an exciting climb!). The big building off in the distance is the research centre, and the smaller buildings are the ends of the arms of the interferometer (the length is about 80 m).

The tower leans do you can recreate Galileo's mythical dropping of canon balls from the leaning tower of Pisa. No canon balls here tho, only water filled balloons.

So, what does gravitational research, at the experimental end look like. Here's some examples.
There's a lot of plastic sheeting, clean rooms, optical benches, vacuum chambers etc. The optical benches are amazing as they look chaotic, but each optical element has a purpose, and the laser light makes its way through all of them.

The thing about research labs (in physics at least) is that they often look  like a nightmarish mish-mash of cables and equipment, dewers, liquid nitrogen, helium tanks, random computers, etc, and there will often be people squirreling about in various corners apparently oblivious to what is going on in the rest of the lab. But amazingly, it is in this environment that great advances and discoveries are made. Neatness gets you nowhere (at least that is the excuse I use to explain my office).

They have a pretty cool visitors centre at Gingin, with lots of hands on things for kids to crazy with. But one thing caught my eye.
On the wall is the Einstein equation. To me, it is barse-ackwards as I would want to calculate the gravitational field (G) from the mass and energy distribution (T), but being gravitational wave research, where they want to detect G, they then want to calculate T (the source of the gravitational waves). Cool eh!

Saturday, 10 December 2011

Scary monsters (and supermassive black holes)

A quick post this morning as I have spent a few hours plumbing in a new dishwasher (the previous one decided it would like to be like the Nile, and so flooded every so often), and have a children's party this afternoon. But, I've had a new article published on The Conversation titled Scary monsters (and supermassive black holes).

It's a review of the discovery of the most massive supermassive black holes yet. As I note in the article, the discovery itself is not such a surprise as we know that there is a well known relation, the M-sigma relation which shows that larger galaxies have larger black holes (the astronomers in the article weren't just blindly looking for black holes - they knew where to look).

Also, in the article, I touch on another article in The Conversation called Black holes might exist, but let’s stay sceptical, which was in response to a previous article I published on black holes. This article seemed to suggest that astronomers believe black holes are real, and so think that there is little point to supporting experiments to test general relativity, especially the search for gravitational waves. Here's a quote from the article;
"And, hence, you’re less likely to support gravitational wave astronomy. General relativity predicts unique patterns of the gravitational waves produced in collisions between event horizons."
As I noted in the comments, this is completely wrong.  Any perceived lack of support is purely financial, not scientific. In fact, I wrote
"There is a finite pot of money, and astronomy is big science. If you ask an optical astronomer which should I fund, the Square Kilometre Array, LIGO or the next generation of optical telescope, then the response will be "in a perfect world, with an infinite amount of cash, funding all would be excellent, but given that you have asked me to choose, I will support the one that has the direct impact on my research, the optical telescope", and I am sure you will get different answers from the radio astronomers, and, of course, the gravitational wave astronomers."
In fact, astronomers are searching for the signal of gravitational waves using pulsar timing, wanting to attempt to snatch a potential Nobel from the LIGO teams.

Finite pots of money are the source of many problems, but, after mentioning Nobel prize winners, I just want note that Brian Schmidt of the ANU, one of this years winners of the physics Nobel prizes, is donating some of his prize winnings for a primary school science program the federal government has stopped funding. What an exceedingly noble thing for a Nobel to do. Well done Brian!

Wednesday, 7 December 2011

More dark matter shenanigans

The internet is alive again with another cry that dark matter is dead (again) and the slashdot-eratti are getting themselves into the usual lather and "DM is BS" claims.

I've written my views on slashdot commenting previously, and will not reiterate them here, but will comment on the paper and the "meaning" of dark matter to astronomers.

OK. The paper can be read here and here's the press image that goes with it.
The picture is correct. If we just considered the gravitational attraction of stars, then their rotation speed should follow the red curve, but when we measure it (and we can measure it far outside the stellar disk by looking at the rotational velocities of HI gas) it actually follows the white curve.

So, the big question is why? The prevailing hypothesis is that there is more mass there than we can see, i.e. dark matter. But others suggest that dark matter is not there, and there is some other influence, usually by modifying the laws of physics (i.e. MOND) which accounts for the extra acceleration which is needed to give the larger speeds.

The current paper suggests that the extra acceleration comes from the attraction of mass in the local universe *outside* of the galaxy. Those that remember their classes on Newtonian physics will remember that if you sit inside a spherical shell of mass, you do not feel any gravitational pull from the mass. But this paper says "well matter is not smooth but is lumpy" and the author, Carati, tries to calculate the influence of this lumpiness.

This is all quite legit, but it turns out the calculations are very difficult, so instead of directly calculating the influence, he calculates some average effect. What happens is the "average" effect modifies the gravitational attraction in galaxies and so looks like this
It's the second term that modifies the gravitational attraction due to this average effect. Take a couple of rotation curves of galaxies, and viola
The left-hand panel has the data (the dots and error bars) and the effect of two components; the disks is due to the mass we see, and the halo is the influence of dark matter. The right-hand panel is the result of this new model, which only has the disk we see and then the correction due to the cosmological mass. Excellent. Let's have a press release!

But, hold your horses. Is everything as excellent as it seems? Well, no. Firstly, we knew we could get this model to work in some galaxies as it basically looks extremely similar to the mathematical form of MOND, and we know that works in some galaxies (and so, in some sense, we knew the answer beforehand). And remember that we have taken some sort of averaging effect, rather than calculating the actual effect, and, as it is stochastic should be stochastic and I can't imagine that it will give a smooth influence on the galaxy.

Are the religious, dark matter zealots up in arms, calling for Carati's head for daring to suggest that the god of dark matter may not exist? Well, no. While the majority of scientists will be nowhere near convinced by this one paper, Carati is free to do whatever research they want to, and I am sure they know that if they want to convince us that their model is viable, the maths needs to be worked out, and then they must show that their model explains everything that dark matter does; from gravitational lensing, big-bang nucleosynthesis, hot gas in clusters etc etc.

Again, scientists don't believe in dark matter. Currently all the evidence points to a material substance explaining what we see out there in the Universe, and so people are heavily weighted into using this particular model. But if we woke up tomorrow and some one has convincing proved that dark matter as a substance can be conclusively ruled out, there will be no wailing and gnashing of teeth, and most scientists will say "oh, that's interesting! what more does that tell us about the Universe". Science will move on. And I am sure the Slashdotters will tell us "we told you so!".

Saturday, 3 December 2011

How many tanks?

The German tank problem is a fav of mine. The wikipedia page on it is a little long winded, but I think it can be looked at a lot faster with a little numerical mucking about.

The problem is quite simple. The enemy are producing tanks, and each has a sequential serial number (for simplicity, let's assume that the numbers are reset every month). You encounter this scene on the battle field;
and we see that this is tank number, say, 15 of a particular months production. How many tanks were produced in that month? Can we even answer the question?

This is the problem that faced the Allies in WWII; you really wanted to know how many panzers are out there. Intelligence officers were reporting productions of more than a 1000 tanks per month, but based on statistics, the predicted number was significantly fewer than that, in the hundreds. After the war, the numbers were checked against records and the statistical answer was amazingly correct (read the wikipedia page for more details).

But let's see the how we can calculate this. We'll adopt the Bayesian approach (because that's the correct thing to do it :). So, let's assume that the number of tanks actually made is a number N, and let's assume that we guess that the maximum number of tanks that could be possibly be made is M (we'll insert some real number in here soon).

On the battle field, we find a tank with a serial number, A. What is your estimate of the number of tanks made in that months (let's call this X)? We want to make a probability distribution, and where this peaks, this is our best estimate for the number of tanks build.

Clearly, the minimum number of tanks is A (because you have the serial number you have). What about the rest of the probability distribution? If you think about it, if the total number of tanks is X, then the probability of randomly selecting tank A is simply 1/X. So the probability distribution look like this

This is the case where the actual number of tanks produced was 274, and the maximum we think they could produce is 1000, and the serial number of the one tank found was 217. So the most likely number of tanks is 217, but there is still a lot of probability that there could be 900 or 1000.

Now for the cool part. You hear a report that another tank has been knocked out, this time serial number 91. You might think that tells you nothing new, as you know the minimum number is 217, but 91 has a similar probability distribution to 217, and to get the resultant distribution for the total number of tanks you multiply these together.

I've brushed over some of the key Bayesian words and concepts here, but this is basically what it boils down to; we get more evidence and we update our beliefs. So, what's the result of now finding tank 91? The result is the red curve below.
Notice that the most likely number of tanks is still 217, but knowing 91 as well has really started to suppress the numbers up near 1000.

Reports come in that three more tanks have been knocked out, 256, 248 and 61. What's the resultant distribution look like?
Again, each of the blue curves is the probability distribution for each tank, whereas the red is the total. Notice that the peak is now at 256, and the chances of more that 600 tanks being produced per month is pretty small, and 1000 is negligible.

Report come in of 5 more tanks, number 250, 172, 189, 29 and 170. What's the distribution now?
For clarity, I've left out the blue curves, but you can see that with just 10 tanks, we know the number produced is more than 256, but quite probably less than 400.

We can continue to play this game, and with 25 tanks knocked out, we get
Notice that I've changed the scale on the x-axis. We can be quite confident that less than 300 were made.

Now I think that is cool. And that's how information should be used.

Friday, 2 December 2011

The Beast with Four Tails

The Sagittarius Dwarf galaxy is a pretty cool object. It was discovered by a very close collaborator of mine, Rodrigo Ibata of the Strasbourg Observatory, way back in the ancient past (well, 1993), and it is clearly a little galaxy in trouble. It's orbit brings it dangerously close to the Milky Way, where its tidal gravitational pull is ripping it apart.

During its destruction, stars have been continuously pulled from the dwarf and are now wrapped around the Milky Way. These tidal streams are really interesting, and can be used to work out how the dwarf has been pulled apart. More importantly, if we can work out the orbit of the streams, then we can measure the amount of dark matter surrounding the Milky Way, a very important thing to do.

But look at this
This is a map of the sky in coordinates where the tidal stream of Sagittarius wraps around the equator.  You can clearly see the Milky Way galaxy. The colour are fields from the Sloan Digital Sky Survey where stars in the halo of the Milky Way have been isolated.

A couple of years ago, when there was less Sloan data, the right-half of the image was called the field of streams. Here's the patch
and it was clear that the stream of Sagittarius seemed to split into two. This is exceedingly weird, we really didn't expect it to do this, and none of the models we had predicted this. What the new data does is double the trouble as we now see that the forked stream continues into the South.

So, we have an object like this
a real Beast with Four Tails. Honestly, this is very bizarre, and as of yet we have no real explanation on why it looks like this.  I remember when Sagittarius was discovered, and it was going to tell us what the dark matter halo of the Milky Way looked like, and it would all be wonderful, but what has happened is that every observation seems to make thinks more and more complex. But it keeps us in a job :)

A new paper on this, written by Sergey Koposov and Vasily Belokurov, and me, has been submitted for publication. Well done Sergey and Vasily!

The Sagittarius Streams in the Southern Galactic Hemisphere

Sergey E. Koposov (1,2), V. Belokurov (1), N. W. Evans (1), G. Gilmore (1), M. Gieles (1), M. J. Irwin (1), G. F. Lewis, M. Niederste-Ostholt (1), J. Peñarrubia, M. C. Smith, D. Bizyaev, E. Malanushenko, V. Malanushenko, D. P. Schneider, R. F. G. Wyse ((1) Institute of Astronomy, Cambridge, UK, (2) Sternberg Astronomical Institute, Moscow, Russia)
The structure of the Sagittarius stream in the Southern Galactic hemisphere is analysed with the Sloan Digital Sky Survey Data Release 8. Parallel to the Sagittarius tidal track, but ~ 10deg away, there is another fainter and more metal-poor stream. We provide evidence that the two streams follow similar distance gradients but have distinct morphological properties and stellar populations. The brighter stream is broader, contains more metal-rich stars and has a richer colour-magnitude diagram with multiple turn-offs and a prominent red clump as compared to the fainter stream. Based on the structural properties and the stellar population mix, the stream configuration is similar to the Northern "bifurcation". In the region of the South Galactic Cap, there is overlapping tidal debris from the Cetus Stream, which crosses the Sagittarius stream. Using both photometric and spectroscopic data, we show that the blue straggler population belongs mainly to Sagittarius and the blue horizontal branch stars belong mainly to the Cetus stream in this confused location in the halo.

Thursday, 1 December 2011

Probing planetary mass dark matter in galaxies: gravitational nanolensing of multiply imaged quasars

One of the big questions of modern astrophysics is "what is dark matter?" Of course, we all know that there is a possibility that it is not a material substance at all, and the extra gravitational influence we need to explain observations may be due to a modification in the laws of physics, but it being matter is the simplest of hypotheses and it seems to work very well (but, of course, to the media and rabid slashdotters/internet trollers, we are nothing but religious fanatics pushing our wheelbarrow of dark matter, blinkered to the geniuses out there!).

If it is a material substance, then we have ruled out a number of candidates (in terms of stellar mass black holes etc), and the weight of evidence is pointing towards a subatomic particle. As the Universe evolves, dark matter clumps together to make dark matter halos within which galaxies like our own Milky Way form.

How small do dark matter halos get? Well, some think it continues down to planetary mass scale. If it does, out galaxies dark matter halo is made of a myriad of small mass halos whizzing about. How do we test if they are actually out there?

One method is to search for their gravitational lensing effect. The problem is that studying the effect is very difficult, as the number of little masses along the line of sight to a distant source is huge, and computing their influence is very hard.

Luckily, one of my PhD students (who recently submitted his thesis), Hugh Garsden, is a computing expert and he developed a brand new supercomputer code to address such a problem, and, with postdoc, Nick Bate, we just had a paper accepted for publication in the Monthly Notices of the Royal Astronomical Society.

The paper look at nanolensing, the effect of small masses in galactic halos on our view of distant quasars. To do that, we need to calculate a magnification map, tracing the paths of billions of rays through hundreds of millions to billions of lensing masses. Here's an example of the maps we produce
The little wibbles and wobbles in the map are due to the effect of the small masses. We can use these to work out how the brightness of a source will fluctuate as these masses move in front of it. You end up with the follow
As you can see, the presence of the small masses cause quite rapid, small time-scale fluctuations which, if you try hard enough you can actually observe. Of course, if we don't see them, then we can rule out this kind of dark matter clumping, and science can move on.

Well done Hugh and Nick.

Probing planetary mass dark matter in galaxies: gravitational nanolensing of multiply imaged quasars

H. Garsden, N. F. Bate, G. F. Lewis
Gravitational microlensing of planetary-mass objects (or "nanolensing", as it has been termed) can be used to probe the distribution of mass in a galaxy that is acting as a gravitational lens. Microlensing and nanolensing light curve fluctuations are indicative of the mass of the compact objects within the lens, but the size of the source is important, as large sources will smooth out a light curve. Numerical studies have been made in the past that investigate a range of sources sizes and masses in the lens. We extend that work in two ways - by generating high quality maps with over a billion small objects down to a mass of 2.5\times10-5M\odot, and by investigating the temporal properties and observability of the nanolensing events. The system studied is a mock quasar system similar to MG 0414+0534. We find that if variability of 0.1 mag in amplitude can be observed, a source size of ~ 0.1 Einstein Radius (ER) would be needed to see the effect of 2.5\times10-5M\odot masses, and larger, in the microlensing light curve. Our investigation into the temporal properties of nanolensing events finds that there are two scales of nanolensing that can be observed - one due to the crossing of nanolensing caustic bands, the other due to the crossing of nanolensing caustics themselves. The latter are very small, having crossing times of a few days, and requiring sources of size ~ 0.0001 ER to resolve. For sources of the size of an accretion disk, the nanolensing caustics are slightly smoothed-out, but can be observed on time scales of a few days. The crossing of caustic bands can be observed on times scales of about 3 months.