Saturday, 19 July 2014

Resolving the mass--anisotropy degeneracy of the spherically symmetric Jeans equation

I am exhausted after a month of travel, but am now back in a sunny, but cool, Sydney. It's feels especially chilly as part of my trip included Death Valley, where the temperatures were pushing 50 degrees C.

I face a couple of weeks of catch-up, especially with regards to some blog posts on my recent papers. Here, I am going to cheat and present two papers at once. Both papers are by soon-to-be-newly-minted Doctor, Foivos Diakogiannis. I hope you won't mind, as these papers are Part I and II of the same piece of work.

The fact that this work is spread over two papers tells you that it's a long and winding saga, but it's cool stuff as it does something that can really advance science - take an idea from one area and use it somewhere else.

The question the paper looks at sounds, on the face of it, rather simple. Imagine you you have a ball of stars, something like this, a globular cluster:
You can see where the stars are. Imagine that you can also measure the speeds of the stars. So, the questions is - what is the distribution of mass in this ball of stars? It might sound obvious, because isn't the mass the stars? Well, you have to be careful as we are seeing the brightest stars, and the fainter stars, are harder to see. Also, there may be dark matter in there.

So, we are faced with a dynamics problem, which means we want to find the forces; the force acting here is, of course, gravity, and so mapping the forces gives you the mass. And forces produces accelerations, so all we need is to measure these and... oh.. hang on. The Doppler Shift gives us the velocity, not the acceleration, and so we have wait (a long time) to measure accelerations (i.e. see the change of velocity over time). As they say in the old country, "Bottom".

And this has dogged astronomy for more than one hundred years. But there are some equations (which I think a lovely, but if you are not a maths fan, they may give you a minor nightmare) called the Jeans Equations. I won't pop them here, as there are lots of bits to them and it would take a blog post to explain them in detail.

But there are problems (aren't there always) and that's the assumptions that are made, and the key problem is degeneracies.

Degeneracies are a serious pain in science. Imagine you have measured a value in an experiment, let's say it's the speed of a planet (there will be an error associated with that measurement). Now, you have your mathematical laws that makes a prediction for the speed of the planet, but you find that your maths do not give you a single answer, but multiple answers that equally well explain the measurements. What's the right answer? You need some new (or better) observations to "break the degeneracies".

And degeneracies dog dynamical work. There is a traditional approach to modelling the mass distribution through the Jeans equations, where certain assumptions are made, but you are often worried about how justified your assumptions are. While we cannot remove all the degeneracies, we can try and reduce their impact. How? By letting the data point the way.

By this point, you may look a little like this

OK. So, there are parts to the Jeans equations where people traditionally put in functions to describe what something is doing. As an example, we might choose a density that has a mathematical form like
that tells us how the density change with radius (those in the know will recognise this as the well-known Navarro-Frenk-White profile. Now, what if your density doesn't look like this? Then you are going to get the wrong answers because you assumed it.

So, what you want to do is let the data choose the function for you. But how is this possible? How do you get "data" to pick the mathematical form for something like density? This is where Foivos had incredible insight and called on a completely different topic all together, namely Computer-Aided Design.

For designing things on a computer, you need curves, curves that you can bend and stretch into a range of arbitrary shapes, and it would be painful to work out the mathematical form of all of the potential curves you need. So, you don't bother. You use extremely flexible curves known as splines. I've always loved splines. They are so simple, but so versatile. You specify some points, and you get a nice smooth curve. I urge you to have a look at them.

For this work, we use b-splines and construct the profiles we want from some basic curves. Here's an example from the paper:
We then plug this flexible curve into the mathematics of dynamics. For this work, we test the approach by creating fake data from a model, and then try and recover the model from the data. And it works!
Although it is not that simple. A lot of care and thought has to be taken on just how you you construct the spline (this is the focus of the second paper), but that's now been done. We now have the mathematics we need to really crack the dynamics of globular clusters, dwarf galaxies and even our Milky Way.

There's a lot more to write on this, but we'll wait for the results to start flowing. Watch this space!

Well done Foivos! - not only on the paper, but for finishing his PhD, getting a postdoctoral position at ICRAR, but also getting married :)

Resolving the mass--anisotropy degeneracy of the spherically symmetric Jeans equation I: theoretical foundation

A widely employed method for estimating the mass of stellar systems with apparent spherical symmetry is dynamical modelling using the spherically symmetric Jeans equation. Unfortunately this approach suffers from a degeneracy between the assumed mass density and the second order velocity moments. This degeneracy can lead to significantly different predictions for the mass content of the system under investigation, and thus poses a barrier for accurate estimates of the dark matter content of astrophysical systems. In a series of papers we describe an algorithm that removes this degeneracy and allows for unbiased mass estimates of systems of constant or variable mass-to-light ratio. The present contribution sets the theoretical foundation of the method that reconstructs a unique kinematic profile for some assumed free functional form of the mass density. The essence of our method lies in using flexible B-spline functions for the representation of the radial velocity dispersion in the spherically symmetric Jeans equation. We demonstrate our algorithm through an application to synthetic data for the case of an isotropic King model with fixed mass-to-light ratio, recovering excellent fits of theoretical functions to observables and a unique solution. The mass-anisotropy degeneracy is removed to the extent that, for an assumed functional form of the potential and mass density pair (\Phi,\rho), and a given set of line-of-sight velocity dispersion \sigma_{los}^2 observables, we recover a unique profile for \sigma_{rr}^2 and \sigma_{tt}^2. Our algorithm is simple, easy to apply and provides an efficient means to reconstruct the kinematic profile.

and


Resolving the mass--anisotropy degeneracy of the spherically symmetric Jeans equation II: optimum smoothing and model validation

The spherical Jeans equation is widely used to estimate the mass content of a stellar systems with apparent spherical symmetry. However, this method suffers from a degeneracy between the assumed mass density and the kinematic anisotropy profile, β(r). In a previous work, we laid the theoretical foundations for an algorithm that combines smoothing B-splines with equations from dynamics to remove this degeneracy. Specifically, our method reconstructs a unique kinematic profile of σ2rr and σ2tt for an assumed free functional form of the potential and mass density (Φ,ρ) and given a set of observed line-of-sight velocity dispersion measurements, σ2los. In Paper I (submitted to MNRAS: MN-14-0101-MJ) we demonstrated the efficiency of our algorithm with a very simple example and we commented on the need for optimum smoothing of the B-spline representation; this is in order to avoid unphysical variational behaviour when we have large uncertainty in our data. In the current contribution we present a process of finding the optimum smoothing for a given data set by using information of the behaviour from known ideal theoretical models. Markov Chain Monte Carlo methods are used to explore the degeneracy in the dynamical modelling process. We validate our model through applications to synthetic data for systems with constant or variable mass-to-light ratio Υ. In all cases we recover excellent fits of theoretical functions to observables and unique solutions. Our algorithm is a robust method for the removal of the mass-anisotropy degeneracy of the spherically symmetric Jeans equation for an assumed functional form of the mass density.

Tuesday, 8 July 2014

Should academia be like Logan's Run? All out at 40?

A quick post, as I am still on the road.

One of my favourite movies of all time is Logan's Run (partly because of the wonderful Jenny Agutter, who was also in another fav of mine, An American Werewolf in London). The premise of the movie is that in a futuristic society, to maintain populations, children are manufactured to order and when you get to thirty years of age, you go to carousel where you float up in to the air and explode.

 Should academia be like this? Not killing everyone at 30, but how about requiring everyone to leave at 40?

Now, before you start screaming about "academic freedom" and "tenure", hear me out. I quite like the idea. Let's start with what (I think) we can all agree on.

Basically, there are not enough academic jobs, and academic pipe leaks at all stages, with talented people having to leave due to the lack of positions at the next level.

Additionally, prising academics out of their jobs is notoriously hard, with many working until they drop. This is not helped by the push on retirement ages to older and older ages (by the time I retire, in Australia the retirement age will be 70, meaning I have quarter of a century until I can "retire" - although the meaning of that is complex). And, at some point, productivity declines as we get older. Now, my paper output is much larger than when I wore a younger man's clothes, but it is because I have a group of students and postdocs. My personal research time is squeezed by all of the "non-research" academic roles, including teaching and administration etc.

I think many would agree that they would like to be a postdoc for life if they could.

Now for another truth. Academics are expensive. Cards on the table, I am a Level-E professor and my salary is public information and is currently $177,887. The salary budget is a major part of a university's cost, and it is not getting easier as academics are getting more career driven and are climbing the academic scale a lot faster. Universities would save a lot of money if I was replaced with a junior academic, with a lecturer earning almost $95,000.

So, what's my proposal. We'll many sports stars retire quite young, when their bodies are worn, and they can no longer compete with younger incoming stars. This doesn't mean that these people sit around watching afternoon TV, but find new careers. Why don't academics do the same?

My proposal:

  • At 40, academics are given the option of retiring from academia. As we are unlikely to have the funds that sports stars into retirement, the academics are offered a lump sum (3-5 years of pay?) to smooth the transition into another career. This would be cheaper than paying you for the next 30 years.
  • Universities can fill your position with a junior academic with a job until they reach 40.
  • If you decide to stay with the university, your admin and teaching loads increase to ensure the junior academics get lots of research done (but they will still have a teaching and admin role at the university).
  • The "retiring" academics can still hold adjunct positions with the university, accessing resources, supervising students (with the junior staff) and effectively becoming hobby researchers. They could potentially be still be listed on grants and access some funds to attend conferences etc. Companies could view academic commitments as a social contribution and could offer some time (10% of the working week) to these duties.
As a lot of my personal research is done out of hours, I would probably get more done. 

Of course, there is the "fear" that you won't get a job at 40, but academics are supposed to be talented, smart people who know how to learn. I am not too stupid to say that academics can magically transform into leading hedge fund managers or brain surgeons, but I doubt we'd end up on the street begging for food. Many people make career stages at many stages of their life; academics are no different.

But what if we get less pay? Well, the payout will help smooth this (and will clear many a mortgage), and we didn't get into this game to get rich now did we?

And in reality, stepping aside doesn't mean that you are exiting the game, you will still contribute and be engaged. But the fact that junior academics will get longer in the game will be better for science and human knowledge. Isn't that a good thing?

Saturday, 28 June 2014

The Nature and Origin of Substructure in the Outskirts of M31 -- II. Detailed Star Formation Histories

I am still playing catch up on papers, and I've just woken up early here in San Francisco and have a small amount of time before I have to prepare for my talk today. So, this will be quick.

The topic again is our nearest largest companion, the Andromeda Galaxy, especially working out the history of how stars have formed in the (relatively) inner regions of the galaxy. It might seem a little strange that we can work that out, because all we can see is stars, but with the magic of science, it is possible. That's the topic of this new paper by postdoctoral researcher, Edouard Bernard.

This beautiful science is done with the Hubble Space Telescope. The first thing you need to do is decide where to look. So, here's the fields we looked at
One of the sad things is that the area Hubble can image (its field of view) is tiny compared to the extent of Andromeda, and so we are doing key-hole surgery in select areas on interesting bits of Andromeda, especially prominent bits of substructure scattered about.

We image each of the fields in two colour bands, a blue(ish) one and a red(ish) one, and once you have this you can construct a colour-magnitude diagram. But how do you work out the star formation history?

Well, every new star that is born lives initially on the main sequence, but massive stars live on there for a relatively short time, and little stars sit on there for a long time. So, if you create a bunch of stars at the same time, they are all on the main sequence, but as you wait, the massive ones move off first, and then the lesser massive ones etc. In fact, you can tell the age by looking at the mass of stars now moving off the main sequence, something called the main sequence turn-off (rather imaginatively). Here's a nice picture from the Lick Observatory


If you want to have a look at evolutionary tracks in details, have a look at the Padova isochrones.

So, every burst of stars gives you a new population on the main sequence, and then after time they start to move off, and if you imagine this happening over and over again, you get a complex mess in the colour-magnitude diagram. And, with hard work, you can invert this. Here's a picture from the paper
The colour magnitude diagram is in the upper right; if you are an amateur astronomer and understand the magnitude scale, check out the numbers on the side. This tells you about the power of Hubble!

The other panels give the star formation rate (SFR) in the upper left, and metallicity (chemical enhancement) in the bottom right.

So, what do we find? Fields were identified as being disk-like, being part of the main body of Andromeda, stream-like, so they look like they are associated with the giant tidal stream in Andromeda, and composite, which are, well, more complicated.

Here's the cumulative star formation history for the various fields, but it should be clear that stars in the disk-like fields (blue) formed more recently than those in the other fields. But why?
Here's the actual histories, which shows how much mass in stars is formed as a function of time.
Now, they look similar, but the disk-like distribution is skewed to lower times, again showing that more stars formed more recently. 

Argh! I'm running out of time, but could go on for ages, but we are scratching the surface. Essentially, but clearly we have on going star formation in the galaxy disk, making a lot recently, where as the stars in the giant stream (which was formed a while ago and then fell into Andromeda) are somewhat older.

But the star formation histories are not smooth, all with a broad peak in their earlier history, but rather curiously possessing a spike in star formation around two billion years ago. What caused this? Well, it looks like it occurred when M33 crashed the party, exciting a new burst of stars, and scattering others to large distance.

I'm out of time, but this is all cool stuff. Well done Eduoard!

The Nature and Origin of Substructure in the Outskirts of M31 -- II. Detailed Star Formation Histories

While wide-field surveys of M31 have revealed much substructure at large radii, understanding the nature and origin of this material is not straightforward from morphology alone. Using deep HST/ACS data, we have derived further constraints in the form of quantitative star formation histories (SFHs) for 14 fields which sample diverse substructures. In agreement with our previous analysis of colour-magnitude diagram morphologies, we find the resultant behaviours can be broadly separated into two categories. The SFHs of 'disc-like' fields indicate that most of their mass has formed since z~1, with one quarter of the mass formed in the last 5 Gyr. We find 'stream-like' fields to be on average 1.5 Gyr older, with <10 percent of their stellar mass formed within the last 5 Gyr. These fields are also characterised by an age--metallicity relation showing rapid chemical enrichment to solar metallicity by z=1, suggestive of an early-type progenitor. We confirm a significant burst of star formation 2 Gyr ago, discovered in our previous work, in all the fields studied here. The presence of these young stars in our most remote fields suggests that they have not formed in situ but have been kicked-out from through disc heating in the recent past.

Sunday, 22 June 2014

The outer halo globular cluster system of M31 - II. Kinematics

Well, I don't know where that month vanished, but I now find myself sitting in the very nice Swan's Hotel in Victoria, Canada, after doing some nice new work with Alan McConnachie at the Herzberg Institute of Astrophysics. The week has gone fast, and I've given two talks, and have four more to give in California next week.

But I realised that I have neglected the blog, and there has been quite a few papers of mine put on the arxiv I should talk about. I have quite a bit of catching up to do, so here's a first post, and I will try and post some more over the next couple of weeks.

A few weeks ago, I posted an article about the fact that we now have the final catalog of the globular clusters found in the PAndAS survey. This has been a major undertaking, seeing out these balls of a few million stars in the outer reaches of Andromeda. But it's been very successful, and we can now start to ask the question "what have we learnt?" This is the topic of this post, a new paper by recently- minded postdoc, Jovan Veljanoski.

Jovan went beyond what we can do with PAndAS data and used spectroscopy to measure the speeds of the globular clusters orbiting Andromeda. As globular clusters are significantly brighter than individual stars, we can use smaller telescopes, such as the William Herschel Telescope, to do this, it is still not a simple measurement.

But we can cut to the chase and see a nice graphical view of what we found:

So, here the globular clusters have been colour-coded by velocity, relative to Andromeda (which is moving at 300 km/s towards us). It doesn't take much staring to reveal a couple of very interesting things.

Firstly, on the South-West Cloud (the blob on the right side, just below the middle) there are three globulars with a very similar shade of blue, meaning they are moving at about the same speed. Are these associated with the globulars directly associated with the underlying stars, suggesting that they were brought in on a system now disrupting? More on that in the near future!

On the left, on the Eastern Cloud, there are two yellowy-orangey clusters, again moving at the same speed. Are these associated with the Eastern Cloud? That's something we'll have to come back to!

But there are more groups of globulars moving at similar velocity, and here we high-light a few of them.

This is cool as it's what you would expect from our models of galaxy formation and evolution, where galaxies grow over time through the accretion of smaller systems. We are really seeing galaxy evolution in action.

But there is more! It's also quite simple to see that the clusters on the left side of the picture are more orange and red, meaning they are moving away from us relative to Andromeda, whereas those on the right are blue, meaning they are coming towards us; the globular cluster population in Andromeda is rotating! Wow!

This is quite puzzling! If we are seeing a snapshot of galaxy evolution, where Andromeda has eaten lots of little dwarfs that fell in higgledy-piggledy, where does the coherent rotation come from? Well, we have a couple of options. Either what we are seeing is actually the result of one big accretion, which came in and deposited all of this material on one go, which strikes me as unlikely given the mess that we see, or the accretion wasn't random and dwarfs have been coming with a preferred direction.

Both options are head-scratchingly weird. But as we have said before, there are lots of weird motions in the halo of Andromeda, especially with the existence of the Vast Thin Plane of Dwarf Galaxies (and, I promise more on this interesting thing in the very near future), and, at least to me, all of this is pointing towards something we really don't understand. And I think that's fantastic!

Well done Jovan!

The outer halo globular cluster system of M31 - II. Kinematics

We present a detailed kinematic analysis of the outer halo globular cluster (GC) system of M31. Our basis for this is a set of new spectroscopic observations for 78 clusters lying at projected distances between Rproj ~20-140 kpc from the M31 centre. These are largely drawn from the recent PAndAS globular cluster catalogue; 63 of our targets have no previous velocity data. Via a Bayesian maximum likelihood analysis we find that GCs with Rproj > 30 kpc exhibit coherent rotation around the minor optical axis of M31, in the same direction as more centrally- located GCs, but with a smaller amplitude of 86+/-17 km s-1. There is also evidence that the velocity dispersion of the outer halo GC system decreases as a function of projected distance from the M31 centre, and that this relation can be well described by a power law of index ~ -0.5. The velocity dispersion profile of the outer halo GCs is quite similar to that of the halo stars, at least out to the radius up to which there is available information on the stellar kinematics. We detect and discuss various velocity correlations amongst subgroups of GCs that lie on stellar debris streams in the M31 halo. Many of these subgroups are dynamically cold, exhibiting internal velocity dispersions consistent with zero. Simple Monte Carlo experiments imply that such configurations are unlikely to form by chance, adding weight to the notion that a significant fraction of the outer halo GCs in M31 have been accreted alongside their parent dwarf galaxies. We also estimate the M31 mass within 200 kpc via the Tracer Mass Estimator, finding (1.2 - 1.6) +/- 0.2 10^{12}M_sun. This quantity is subject to additional systematic effects due to various limitations of the data, and assumptions built in into the TME. Finally, we discuss our results in the context of formation scenarios for the M31 halo.

Thursday, 29 May 2014

Misconceptions About the Universe

Over on youtube, Veritasium has a nice discussion of Misconceptions about the Universe. I  like it, especially as I was the consultant cosmologist :)

A little look down the comments tho, and we see several claims that what Derek says is not correct. Here's a little excerpt
Well, as a cosmologist, I was surprised to read that the Hubble Sphere is an "outdated concept" having seen it used in a professional meeting last week. But let's take a look at the other claims that are made by "fullyawakened" - I must admit they have the lead on me as I am partiallyjetlagged at the moment. As ever, I am going to steal Tamara Davis's standard cosmological picture in a few different sets of coordinates to do this. I've explained these before, but the top one has distance as we know it along the x-axis, and time as we experience it up the y-axis.

"Our observable Universe is getting smaller" is simply wrong. Let's look at the bottom figure, which is in conformal coordinates - basically the expansion has been taken out of the space direction, and the time has been modified so light rays travel at 45 degrees. Objects in the Universe, such as other galaxies, are vertical dotted lines. We are at "now" in the middle. The red lines are our past light cone, and so where the vertical dashed lines cross the red lines, those represent objects that we can see right now.

It doesn't take a lot of thought to see that as "now" moves up the page, the red lines will move up also move upwards, and so the points where they intercept the x-axis will move outwards. As time goes on we will see more and more universe. The cosmic microwave background we see today will be seen to cool and form galaxies into the future, while a more distant cosmic microwave background will take its place. For the eternity of the Universe, the observable Universe will continue to grow, albeit at a slower and slower rate.

As Derek pointed out, there is plenty of stuff outside the Hubble sphere (the yellow shaded area) which we can see; remember, this stuff is moving faster than light with respect to us. And we can see it.

Now, does the Hubble sphere grow or shrink as time goes on. Well, let's look at the top picture, which charts the Hubble sphere (in purple) in physical distance away from us. As you can see, the Hubble sphere is growing and, in our current cosmology, it continues to grow at, again, a slower and slower rate.

Things get more interesting as you look at this in the bottom panel, as if we remove the expansion and look in comoving coordinates, the Hubble sphere starts of growing and then shrinks into the future. But you should understand comoving coordinates before taking too much away from that.

What about the notion that things disappear as they are leaving the observable Universe faster than light? Well, this is not the case, as we've seen that the observable Universe will continue to grow. But things will vanish from sight into the distant future, as per
So, where do they go. I've written about the mapping between experienced time and conformal time in the Future, and one of the nice things about our Universe is that the infinite experienced time becomes a finite conformal time. It means there is one last light cone (the event horizon in the picture). When the dotted line of a galaxy crosses this, this must be the last view that we get of it. But what it means is that in the dim and distant future, the distant galaxies we see will appear to slow down, their rotation will look like it's stopping, exploding stars will take weeks, months, centuries to occur, and as they do, the light from the galaxies will become more and more redshifted, until finally they completely fade from view.

So, fulltawakened, yes, I do do this for a living, and I know what I'm talking about. Ain't the Universe fantastic!

Have cosmologists lost their minds in the multiverse?

Sorry, I've been traveling. I'll be posting soon, but please check out a recent article of mine over at the Conversation called Have Cosmologists Lost their Minds in the Multiverse?


Saturday, 10 May 2014

The outer halo globular cluster system of M31 - I. The final PAndAS catalogue

Back from an exhausting week in Canberra allocating grants for the Australian Research Council. Handing out a few tens of millions of dollars really takes it our of you. The sad part is not the excellent projects we funded, but the many excellent projects we could not as we ran out of cash. Anyway, the meetings are confidential, so I can't discuss them here.

But time to catch up on some of my own science. There is something super exciting coming, so here I'll focus on a merely excellent piece of work by globular cluster finder extraordinaire,  Avon Huxor (excuse his ever so happy face!).

I've written many times about the Pan-Andromeda Archaeological Survey, our superb survey of our nearest neighbour, the Andromeda Galaxy. As well as identifying lots of substructure, the shredded remains of small galaxies, we also see lots of globular clusters, balls of roughly a million stars living together. The Milky Way has about a hundred of these orbiting in the halo. Andromeda has even more.

We've already found a lot of really interesting things about this population of globulars in Andromeda, finding them out to extreme distances, finding them associated with substructure (which means many are immigrants which were born outside) and other excellent things. now it's time to give the data over to the public so they can start to use it. Hence this new paper which present the catalogue of the results.

Some think that science is all about whizz-bang results that "rewrite the textbooks", but science is much more than that. It's all about sharing knowledge, and through sharing it enabling more science to be done. In some areas, typically areas where you can make money (I'm looking at you pharmaceutical companies) data is protected and hidden, but in astronomy there is (generally) a good history of data sharing. We will, in the not too distant future, make our entire PAndAS data-set public. You two can use it if you want to :)

Avon's paper presents the new globular clusters we find. Here's what they look like:
 Cool eh! Importantly, a paper like this tells you a lot more than "these are what we found". It also presents the methods we used to find globular clusters, and how reliable our detections are. This means presenting the mis-detections, the things you initially thought were globulars and then, with more looking, realised they aren't.
And then there's the properties of each cluster, such as its size and brightness, to allow people to look at the properties of the population as a whole.
Then we can compare the properties of the globular around Andromeda to those around the Milky Way
And we find that they are kinda similar, but also not really. Andromeda has more, and they are more widely distributed, and several other things. The Milky Way and Andromeda are very similar, and so why their globular cluster populations differ is a bit of a mystery, is it due to the way they grew, or their current predicament, which is great because it means there's more work to do (keeping food on the table and a speedboat in the harbour [joking about the food!!])! Excellent!

Well done Avon!

The outer halo globular cluster system of M31 - I. The final PAndAS catalogue

We report the discovery of 59 globular clusters (GCs) and two candidate GCs in a search of the halo of M31, primarily via visual inspection of CHFT/MegaCam imagery from the Pan-Andromeda Archaeological Survey (PAndAS). The superior quality of these data also allow us to check the classification of remote objects in the Revised Bologna Catalogue (RBC), plus a subset of GC candidates drawn from SDSS imaging. We identify three additional new GCs from the RBC, and confirm the GC nature of 11 SDSS objects (8 of which appear independently in our remote halo catalogue); the remaining 188 candidates across both lists are either foreground stars or background galaxies. Our new catalogue represents the first uniform census of GCs across the M31 halo - we find clusters to the limit of the PAndAS survey area at projected radii of up to R_proj ~ 150 kpc. Tests using artificial clusters reveal that detection incompleteness cuts in at luminosities below M_V = -6.0; our 50% completeness limit is M_V ~ -4.1. We construct a uniform set of PAndAS photometric measurements for all known GCs outside R_proj = 25$ kpc, and any new GCs within this radius. With these data we update results from Huxor et al. (2011), investigating the luminosity function (LF), colours and effective radii of M31 GCs with a particular focus on the remote halo. We find that the GCLF is clearly bimodal in the outer halo (R_proj > 30 kpc), with the secondary peak at M_V ~ -5.5. We argue that the GCs in this peak have most likely been accreted along with their host dwarf galaxies. Notwithstanding, we also find, as in previous surveys, a substantial number of GCs with above-average luminosity in the outer M31 halo - a population with no clear counterpart in the Milky Way.