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Friday, 23 September 2022

The best best fit

Do you know what my ever-so-lovely girlfriend said to me the other day ? 

She said I'd make a terrible detective.

Well !

"Scientists are like detectives" is practically outreach 101. It's standard practise for explaining science to children. So such a claim is so outlandish as to require a weeks' answer or none, so I settled on an intended look of blank bafflement which I'm afraid probably ended up as more of a scowl. 

But it gets worse. Apparently I was failing to only adjust one variable at once.

I mean, really ! There's several tens of thousands of lines of meticulously debugged Python code that will attest otherwise.

But describing the process of debugging code is about as exciting as watching the George Clooney version of Solaris in slow motion. Let me instead give a much more fun example of science-as-detectoring with a figure in my latest paper. This is a not a brand new plot, but a very famous discovery to which I've added my own meagre data. I'll cover the science of my own work in a the next post - in this one I want to look more at the background and the major aspects of what it shows.

This infamous Tully-Fisher relation is deceptively simple : a nice straight line plotting how one variable affects one other. At it simplest, it says that bigger galaxies spin faster, which is just about one of the most boring things you can say about them. Hundreds of billions of stars, uncounted planets, supernovae, great hulking black holes at their heart, the not-quite-infinite majesty of the darkened cosmos... nope, today, "big ones are more spinny".

Really, this is what we're going with ? Oh. Okay.

Start to look a little closer though, and the Tully-Fisher relation blossoms into a bewildering array of complexity and ugly truths. This is a good opportunity to examine just how messy the coalface of research can really be, and a reminder that while science certainly does depend very strongly on rigorous, objective facts, it has no small component of subjective choice behind it too. It's also a good example of how much frickin' work goes into a single bloody plot.

Surely the term "data mining" must have originated in Wales.

This is for once an intentionally long post. If, though, you're already familiar with the Tully-Fisher relation, or don't really care about it very much, feel free to scroll ahead to section four.

1) The Tully-Fisher Relation And How To Measure It

Here's the plot. For an astronomy post I'm afraid this one is going to need quite a lot of graphs and precious few pretty pictures of galaxies.

Simplified by a just a smidgen.

This is the original version from a famous 1977 paper by Brent Tully and James Fisher. What it shows is how bright a galaxy is (vertical axis) as a function of how fast it's rotating (horizontal axis). Regular readers will know I've shown versions of it before because although the basics are simple, the devil is in the details - and the devil is a jolly interesting chap if nothing else.

Let's look at the basics first though. We'll get to exorcising demons examining the details later. First, here's how we get the data.

Measuring the brightness

In this original plot the vertical axis is how bright the galaxies are at ordinary optical wavelengths. Astronomers use a horrible thing called the magnitude system, which expresses brightness in some convenient but monstrously unintuitive and literally arse-backwards way*. The simplest version is apparent magnitude, which just means how bright things appear in the raw observations from the sky. 

* The brighter something is, the more negative its magnitude. I mean, come on.

A nice chart I found here. The Andromeda Galaxy is about +3.4.

Problem is, this tells you little or nothing about the physics of what you're looking at. For that, as in the Tully-Fisher plot, you have to convert to absolute magnitude. This is what the apparent magnitude would be if you were a fixed distance (10 parsecs, about 33 light years) from the source. Keeping everything at the same distance means you can make fair comparisons. For the enthusiasts, absolute magnitudes for galaxies typically range from about -20 (very bright) to -10 (very faint), but these aren't strict limits at all.

The conversion from apparent to absolute magnitude is easy as long as you know the distance. Admittedly, getting this can be extremely difficult, depending on how accurate you need to be. But let's tackle the other variable in the plot first.

Measuring the rotation

Finding out how fast galaxies are spinning is a bit more complicated because there are several different ways to measure this. The most obvious is to simply sit back and watch the stars move across the sky (their "proper motions"*). But that's only really possible in our own and the very nearest galaxies. And to determine their full 3D motion, we need to measure their speed towards or away from us - that is, along our line of sight.

* I have no idea where this term comes from. A Google search for "improper motion" returns results about everything from flawed legal practises to unpleasant bowel movements.

That turns out to be much easier : we can measure the redshift of stars surprisingly easily, even at very large distances indeed. And this has some key advantages. Here's a simple model of a galaxy showing how things rotate relative to an observer. If we're viewing it face-on :

With a reasonably realistic rotation pattern but a very simplistic distribution of stars.

All this movement is in the plane of the screen sky, which means in this case we've no option but to sit and wait long enough to see something move - redshifts won't help here. This gets a trifle dull after a millennium or two, so face-on galaxies aren't much use. Whereas if we're edge-on :

In the middle, all of the movement is across the screen, with nothing moving towards or away from us. But at the sides, all the motion is towards or away from us. Here, measuring motion across the sky would be very tough, but redshifts become easy, and then give us the rotation velocity directly. For galaxies to have stable rotation and not be tearing themselves to bits, the rotation speed at their edges must be the same as everywhere else.

Well... it's not quite that simple, unfortunately. If we happen to see a galaxy which is exactly edge-on, then the stars right at the edges will indeed tell us exactly how fast they're rotating, directly - with no need for any further corrections at all.

Like NGC 891, for example.

Of course most galaxies don't happen to line up with us like that otherwise we'd have to seriously consider Intelligent Design as a legitimate theory, assuming that the whole point of the Universe was so that human beings could do really good extragalactic astronomy*. Most galaxies are somewhere in between face-on and edge-on. But, provided they're not too close to the former**, and we assume they're basically circular in shape, it's easy enough to correct for this.

* Not that we need Intelligent Design to assume that, of course. It goes without saying the astronomers are obviously the highest form of life.
** The errors in this are pretty large : a galaxy has to be more than around 30 degrees or so inclined away from us for this correction to work, otherwise the correction becomes so great that small measurement errors lead to big problems. 

A second problem is that actually, using starlight is not a good idea. Stars are usually embedded in much larger gaseous discs, which we observe with radio telescopes. Using those measurements, we find that the stars don't probe the full extent of this rotation curve : that is, they'll underestimate how fast the galaxy is truly rotating.

This is one of the main pieces of evidence for dark matter. Without extra, unseen mass to hold it all together, most galaxies are rotating so fast they ought to quickly fly apart

Now to get a nice rotation curve like that one isn't easy. You need to have observations of the gas of very high resolution, so you can see exactly which bit is moving at which velocity, and that's technically difficult to do. What's much easier, however, is to get an observation which integrates all the gas in the galaxy at once. What you see in such data is a bunch of blobs : you can't see any structure to them at all, all your spatial information is blurred out - but you can still see the velocity range over which they're detected. You can plot this very easily as a spectrum, which shows how bright the gas is (or rather, how much there is) as a function of velocity :

By measuring where the real emission begins and ends, we get a line width. Where exactly you choose to make the measurement is a bit tricky, but the usual convention is to measure it at either 50% or 20% of the peak brightness (flux) level : the W50 or W20 parameters. Generally these are similar, though not always. In combination with the inclination which we estimate from the optical data, we can correct it to get a estimate of the true rotation speed.

So this is pretty complicated already. Brightness is okay, but rotation is quite tricky. 

BUT, we do have some cases where we can get those nice rotation curves, so we can compare the line width measurements with these... and it works well. It's certainly not ideal, but it does work.

Measuring the distance

But wait ! Remember, we can't estimate the intrinsic brightness without knowing how far away the galaxies are. Now Tully & Fisher had a sample of galaxies for which they did have decent distance measurements (there are various ways to estimate this). What they found was that this relation between rotation speed and brightness is so good, you can use it as another way to estimate distance.

That is, you can very easily measure the apparent magnitude of a galaxy, and quite easily determine its line width. With these two measurements, assuming the Tully-Fisher relation holds, it's then easy enough to work out the galaxy's distance for its absolute magnitude to match the prediction.

I'll spare you the details of measuring distances except to note Hubble's famous law : the faster a galaxy is moving away from us (which is another thing that's easy to measure), the further away it is. This law isn't perfect, galaxies can have "peculiar motions" which deviate from the large-scale flow. But it's pretty darn good. So on very large scales, in most cases we can get a reliable distance estimate very easily. And that lets use use the TFR in a completely different and much more interesting way than as a glorified tape measure. 

2) The Baryonic Tully-Fisher Relation

It might help to take stock of how complicated this relation has already become. To measure rotation speed we need to get the line width and also inclination, which means combining data from very different wavelengths. We can't do this viewing-angle correction at all unless galaxies are more inclined than about 30 degrees, otherwise the errors are too large. And using the line width is never quite as good as measuring a proper rotation curve.

In contrast, measuring the brightness is quite a lot easier. Or at least, it was, until Stacy McGaugh came along and made everything more complicated.

They're darned ugly plots, I know, but don't blame me !

McGaugh found a sample of galaxies that stubbornly refused to obey the standard TFR (green points on the left). There didn't seem to be anything wrong with the measurements, they just rebelliously failed to follow the trend. But when he changed the vertical axis from brightness to mass, everything changed. On the right, the green points now happily agreed with all the others : a nice neat line reappeared !

McGaugh called this the baryonic Tully-Fisher Relation. "Baryonic" being just a fancy word for "normal matter", the stars and gas we're all familiar with - as opposed to the more exotic "dark matter", which remains mysterious.

Why does this work ? In bright galaxies, their baryonic mass is dominated by stars. So using either stellar mass or brightness will give the same result, and adding in the gas doesn't do anything. But in faint galaxies it's the opposite. Their baryonic mass is dominated by gas, so you have to use the gas mass for those and you can ignore the horrible stars.

What's interesting is this reveals the original Tully-Fisher relation was just one particular form of a more fundamental relation. Replacing brightness with mass puts it on a much more physical footing : brightness depends on what wavelength you're using, but mass is mass. And notice how vast the mass range here is, from ten million to a hundred billion times the mass of the Sun. This relationship holds across four orders of magnitude - a factor of ten thousand. Clearly something important is going on.

In practical terms, measuring the mass of the gas turns out to be relatively easy. While converting the optical brightness to stellar mass is not at all trivial, it does seem to work. But before we get to the glorious nitty-gritty of all this, let's take a step back, assume the relation is basically right, and think about what it actually means.

3 Why Does It Do This ?

Sorry Homer, but worse is to come.

At a naïve, hand-waving level, this relation makes sense. A more massive galaxy has to spin faster to be stable against gravitational collapse. And though galaxies are mass-dominated by their dark matter, the more dark matter they have, the more gas they can accumulate and the more stars they can form. So it's not at all surprising to find that the faster-spinning galaxies (that is, the most massive objects) have the most gas and stars.

As I said at the start, big things spin faster. Whoop-dee-bloody-doo, another marvellous scientific breakthrough. Your tax dollars* at work.

* Actually, Czech crowns. But you get the idea.

But... what should the exact relation be ? Should it be the same for all galaxies ? What about those that don't have any gas at all ? What about those which are interacting with other galaxies ?

This is where it gets complicated, and sometimes extremely puzzling. First, in clusters galaxies are prone to losing large amounts of gas through a process that doesn't much affect their stars. When enough of their gas is removed, what remains is the most tightly-held stuff in the very centre, which doesn't probe the full rotation curve. So these highly gas-deficient galaxies don't follow the BTFR, but this is most likely just because we're not able to measure their rotation correctly : intrinsically, they probably do follow the usual relation.

Some galaxies not only lack gas completely but have likely done so for many billions of years. These "elliptical" and "lenticular" galaxies tend not to have rotating discs, so plotting these on the BTRF wouldn't really make any sense. However, they have their own version : the Faber-Jackson relation . Rather than rotation, velocity dispersion - the speed of random motions - correlates very well with their total brightness. The principle is exactly the same as the BTFR, in that the stars have to be moving faster to maintain stable orbits (and even the quantitative gradient of the relations is the same), it's just that they don't do so in coherent rotating discs as in spiral galaxies.

So those points are probably only minor caveats. But optically faint galaxies are another story. Yes, it's nice that if you plot their total mass they agree with the main relation... but this is not at all what was expected.

This comes about from a clever mathematical trick. It's actually possible to predict the Tully-Fisher relation using some simple equations :

You don't have to go through all this. I just like making myself look clever.

The equation predicts that the baryonic mass (Mbar) should scale in proportion to velocity (v) to the fourth power. Which is exactly what it does. Hooray ! But it also shows that it should scale according to two other parameters : the mass-to-light ratio of the whole galaxy and its average surface mass density. And it doesn't do that. It appears that these exactly cancel each other out, and no-one has any idea why. 

In other words, there should be a lot of scatter in this relation. The more spread out the stars in a galaxy of a given mass, the lower its surface brightness and the more it should deviate. But in fact the scatter is very low, with some claiming that it's so low as to be consistent with pure observational errors. All galaxies appear to obey this relation perfectly. 

And that's just damned odd. It raises the suspicion that we're examining not just the processes governing galaxy formation and evolution, but something altogether more fundamental, not galaxy-specific but relating to physics itself : in a word, gravity.

How much scatter is there, exactly ? Given the possible importance of this, in the last few years this has become controversial. There are now a host of challengers to this apparently universal relation, above and beyond the gas-deficient objects which are generally considered to be a bit dull. That's why I cheekily called it a "non-relation" in the last picture, though this is a bit facetious.

Because I'm just so damned edgy.

Chief among these are the Ultra Diffuse Galaxies, which have very low surface brightnesses indeed, as well as some other much brighter (but still small) objects. But there are also so-called "super spirals", the biggest and brightest spiral galaxies of all. And of course there are my own favourites, the optically dark gas clouds which seem to be rotating like galaxies.

What this all means depends on what really gives rise to the BTFR. If it's some detailed aspect of galaxy formation, then there's probably nothing very interesting going on. But if it's something really fundamental like gravity, then things get much more complicated. The most radical interpretation would be that the perfection of the BTFR actually constitutes evidence for a different theory of gravity that replaces dark matter (though as far as I can tell, this doesn't really stand up, and it can probably be accommodated just find in the conventional paradigm*).

* In principle, if it's gravity at work, then all stable systems in equilibrium should follow this relation. But establishing whether a system really is in stable equilibrium is not always easy, so outliers don't automatically constitute proof that we've disproven any alternative theories of gravity.

All of these challengers to the neatness of the BTFR have their own issues. Measuring the inclination angle for UDGs is extremely difficult and it's by no means clear that estimates are correct - while they appear to be rotating unexpectedly slowly, it's possible that they're just closer to face-on than we think. The same can't be said for the gas clouds, which rotate too quickly even without correcting for viewing angle*, but that they deviate in the opposite way to UDGs makes any connection between the very faint and truly dark objects hard to sustain. And super spirals do appear to be explicable by standard galaxy formation theory.

* This correction can only make the rotation larger than the observed line width. Some other corrections can reduce it, however, which we'll get to later.

So what's going on ? We don't know. If the BTFR really is as nice as it appears, this might be evidence that the theory of gravity is wrong, though it probably wouldn't be very good evidence by itself. On other other hand, if there's actually a strong scatter in the BTFR, we still need to explain how this happens and why it wasn't seen before. Basically, it's confusing but interesting every which way you look at it.

4) Mine Own Fit

One of the coolest things I've been unfortunate enough to discover is that some gas clouds in the Virgo cluster don't obey the standard BTFR. I've plotted this in different papers for years. Now it's not really surprising that some floofy gas clouds don't have the same dynamics as stable rotating galaxies, but simulations show that making clouds with line widths as high as these is damn near impossible. In contrast, if they were to be galaxies, but having a much larger dark matter content than most optically bright objects, this would explain everything pretty nicely.

Now along comes some new Arecibo Galaxy Environment Survey (AGES) data of the Leo Group. Here we found some more gas clouds, and the picture is quite different : some follow the BTFR, but some don't.

I have to say that the initial referee report was the nicest I've ever received, which frankly I think is only bloody fair as I've had far more unduly critical reports than I deserve for making entirely uncontroversial claims. But I digress. Anyway, this super-lovely referee asked if I could demonstrate more robustly whether these clouds really do sit on the BTFR or not. It was an entirely reasonable request, but it led me down a much deeper, more complicated rabbit hole than I ever would have guessed. In fact the whole sorry process ended up being exactly like this :

Here are the basic plots I started with :

All points use my own measurements except for the green ones, which use other people's reported measurements. The red points are the ones I was interested in.

The two plots are the same except in that the one of the left uses the "W50" measurement to estimate the rotation speed whereas the one on the right uses the "W20" parameter. You can see some of the black points - nice bright normal galaxies - have baryonic masses well above the best-fit dashed line using W50, but not using W20. That's because the spectral profiles can be asymmetrical. Sadly this has nothing to do with wonky ghosts : it just means that the emission is a lot brighter on one side than the other. So occasionally, the W50 value is much lower than it really should be, and the W20 value is generally the more accurate - though it too has its own problems, especially since it's measured at a level much closer to the noise. 

In short, W50 can sometimes give you erroneously slow rotation speeds, while W20 has the opposite problem - you have to pay close attention to the spectral profile.

Cheer up ghost, you're not that wonky.

The fit for the two different estimates for the line widths does change the interpretation somewhat. But most of them, eyeballing it, look to be consistent with the general scatter using the W50 version - most have higher velocities than the best-fit line, but only slightly. Using W20, there might be more of a deviation, though some clearly follow the general trend.

But in the course of addressing the reviewer's points, I found something else : I could not reproduce the best-fit lines ! All the data points themselves were fine, but how the hell I'd fitted the original lines I know not. Only through much toil did I eventually get a reproducible version that doesn't look too awful. The original W50 fit still looks better to me, but since I've no idea how I originally did it, this has to be discarded. Here are the replacement versions which appear in the published paper.

The best-fit is obtained only through the black points : bright, normal galaxies, with all the other points being dark gas clouds. The clouds themselves can't be used for the fit, since the goal was to see if they follow the usual relation for galaxies or not. While we can't change the values of the data, the fit matters in that this tells us if and how much the clouds deviate. In this version, the basic result still stands, but the clouds now agree better using the W20 than the W50 relation.

This at last is where we get to the title of this post : which best fit is the best best fit ? And that's tricky to answer. It might help if there were error bars, or if we compared the results to previous findings rather than relying on our own fit.

To that end, the referee quite rightly suggested to compare with the results of a later McGaugh paper. This is a good one to use because there McGaugh used a sample of gas-rich galaxies which were of similar masses to the Leo clouds, with proper rotation curves for all objects. Using a gas-rich sample means minimal problems with calculating the stellar mass, which, as we'll see very soon, can be a right bugger, and as we've already seen, rotation curves are much superior to using line widths.

A First Guess

So I set about to apply the corrections McGaugh describes for a fair comparison to his fit for the BTFR. My first quick attempt was very promising. Sure, the result isn't perfect for the more massive galaxies, but it's not too bad. There's more scatter than with McGaugh's data but that's to be expected since we have to use line widths, which aren't as accurate. 

The solid line show's McGaugh's relation, with the dashed and dotted lines showing the scatter at one and two sigma.

Those deviating black points probably wouldn't have bothered me except that they're all to the right - they all have higher velocity widths than expected. What could have gone wrong ? Could I have systematically overestimated the widths ? I went back and checked the spectra (this being data from ten years ago and more !) and found nothing much wrong. And then I realised there was a bug in my plotting code.

In the original plots I'd used my own measurements with the absolute minimum of corrections. So those, having at last found a reproducible best fit, are solid. To compare with McGaugh requires more sophisticated corrections, and there's a lot more to go wrong. For this one I'd started with a correction he prescribes to adjust the line widths, since these don't always give the same results as rotation curves (they tend to overestimate things a little). But I'd accidentally applied this correction to the logarithmic values used for the final plot, whereas it should have been done in linear units... !

A quick correction

Well, I couldn't leave well enough alone. I must admit I thought about pulling a fast one, but I just couldn't. Given how much it took to get the final result I almost wish I had... here's what happened when I corrected my mistake :

Booo ! It was just pure dumb luck coincidence that my original incorrect correction gave a better best fit than the correct correction. Doing things properly gave an unhappily worse result, with more of the galaxies deviating than before !

A new (mis)fit

Things went from bad to worse. I decided that if I was going to do this, I'd better do all the corrections McGaugh used, and not just pick-and-choose the factors which seemed likely to be dominant. So I tried plotting a sample from another paper (an ALFALFA paper - another Arecibo survey, not as sensitive as AGES but much larger) which did all this, and their results sat very nicely around McGaugh's trend. Even for galaxies matched with those in my own sample, their values were in good agreement, but mine weren't.

This led to a paper chase to find exactly what corrections were supposed to be applied. After combining absolutely everything, using my own data the result was... disappointing.

The normal galaxies barely follow McGaugh's relation at all ! At this point I began to seriously consider not showing them. And this would have been an entirely valid thing to do. The full set of corrections needed for optically bright galaxies (which I'll go through at the end) is a lot larger than what you need to do for the gas clouds, and it's those I was interested in. So the comparison between the gas clouds and McGaugh's relation is valid regardless of the terrible "fit" from the normal galaxies. Still, there are some corrections which apply to both samples, and if there was any systematic difference between our data and previous results, I'd rather know what the heck it was.

I can't say it was particularly fun, mind you.

The "correct" correction

At this stage I knew :

  • Using other people's data for the same galaxies gave a result in excellent agreement with McGaugh's relation
  • Using my own data but applying all the corrections described gave a wonky result that would shame an asymmetrical ghost
So there simply must be something wrong with my original measurements (and/or further bugs in my plotting code). But where ? I went right back to the raw, uncorrected values : the apparent magnitudes and line widths. The AGES and ALFALFA measurements were in good agreement on both counts, though not as much for the line widths. I picked out random galaxies and went through the entire correction process to see if I could spot what was going on.

Some dozens of plots later (that's only a slight an exaggeration), I found the solution.

It turns out there was nothing much wrong with either my magnitudes or line widths. ALFALFA have a much more sophisticated but hard-to-reproduce method for estimating the width, but that wasn't the problem. The problem was with my inclination angles*. In defiance of advice I'd been given years back, it was better by far to use the automatic values obtained through the optical survey catalogues**. So when I used these, together with all the corrections needed (which also involved finding more bugs in my code, but also typos and the wrong citations in other people's papers, as well as finding out that they were using a slightly but crucially different calibration parameter for stellar mass to the one I'd always used), I got...

* And also distances. Again, AGES generally uses a simple estimate for this, whereas ALFALFA have something more sophisticated.
** The SDSS is (or was) notorious for giving unreliable values, making it necessary to re-analyse the data by hand. At some point, it appears that this was dramatically improved.

(drumroll, please)

(continue waiting)


Err. Umm. Oh.

I mean, it's certainly a heck of an improvement. But it's hardly perfect - there's still a lot of scatter, especially galaxies with higher velocities than expected, and the slope of the galaxies still looks off - even if by only just a tad. And according to this, there are some galaxies which deviate just as much as those Virgo clouds (blue circles), which would rather undermine how interesting they are.

Well, bugger.

Correctly correcting the correct correction

The final step turned out to be much less onerous. I'd already tried plotting the AGES-ALFALFA matched sample and found a much better agreement than in that last plot, so that gave me an idea : what if I tried limiting it to the brightest detections ? ALFALFA, being less sensitive than AGES, was only able to find the brightest galaxies. So when I did that :

The open circles are McGaugh's own super-accurate data.

And here at last is a plot I'm satisfied with. Only a handful of points lie significantly outside the general scatter, which is about as good as we can expect given that we have line width data and not proper rotation curves. But now the significance of the clouds is again clear, and the brightness cut I used is such that the galaxies and clouds are being compared fairly : it's only the fainter detections which have that stronger scatter.

A few final points remain. Of those normal galaxies which deviate even in this plot, two have surprisingly low velocity widths - both of which are very faint and very slowly rotating. This means a small error in the width measurement, combined with a small error in the inclination angle, could easily be enough to reconcile them with the standard relation. Two have higher widths than expected, but these are genuine errors which disappear if we used more modern routines to do the measurements, as were used for the Leo clouds. So at some point we'll probably need to redo everything (maybe when we release the final AGES catalogue), but this is overkill for the result we presented here.

It's also interesting that the matched sample gave good results using the ALFALFA velocity widths despite that survey having less sensitivity. While I instinctively dislike how complex their method is for measuring the line widths, I have to concede that it does work. So that might also be something to look into for a future AGES data release as well, as it could potentially increase our sample size by allowing us to use fainter galaxies.

And finally, choosing to show only the brightest objects is a perfectly valid selection criteria. The fainter the galaxies, the more affected the width measurements by noise : especially the W20 parameter required for the McGaugh relation. There are other potential selection criteria we could use instead, but this one is much the easiest. The clouds we're interested in are bright enough to make the cut, so the comparison is fair.

5) Conclusions

The baryonic Tully-Fisher relation is deceptively simple. It's just a relation between how fast a galaxy spins and how much gas and stars it has, but to get from the raw observational data to those physical parameters requires a whole series of extremely annoying steps.

Rotation speed is obtained by doing all this bloomin' stuff :

  • Choosing whether to use the width at 50 or 20% of the peak value
  • Halving the width to account for the galaxy rotating both towards and away from us
  • Correcting for inclination, obtained from optical data
  • Reducing the width by an additional small factor for using line widths instead of rotation curves, which varies depending on whether they're dominated by gas or stars
  • Reducing by an extra amount due to limitations of the spectral resolution, depending on their brightness and velocity resolution
  • Reduced to account for the effects of cosmological expansion, which depends on their redshift
Then we have to get the stellar mass, which is actually way more complicated than this list makes it look because each one of these is a multi-step process involving many parameters :
  • Measuring the brightness in at least two optical wavelengths 
  • Correcting this for the dust clouds in our own galaxy, which make everything look fainter and redder
  • Correcting this for the dust in the external galaxies, which depends on their inclination angle
  • Converting this final corrected brightness to stellar mass, using some recipe or other 
And the atomic mass :
  • Measure the brightness from the radio observations, multiplying by some factor to account for stuff we don't detect directly (hydrogen -> hydrogen + helium)
  • ... summing the gas and stellar mass gives us the final total baryonic mass
But don't forget about distances - all of the above depend on these !
  • Measure the redshift of the galaxy, using either the radio or optical data
  • Converting this to the correct reference frame, and then choosing a value of Hubble's constant to convert to distance
  • Where other redshift-independent distances are known, replacing the above values with these
Finally, you need to choose which galaxies to actually plot :
  • Galaxies which are strongly gas-deficient probably don't have accurate rotation velocities, so you need to reject these
  • Galaxies where the gas was detected but only faintly also probably don't have accurate rotation velocities, so you need to reject these too
  • Objects where the inclination is too low will have wrong rotation velocities as well, so chuck these out
It's not much of an exaggeration to say that I probably made mistakes in every single one of those steps before I got the final graph.

So no, this is not a simple plot. And all this is still a simplification ! For example, the stellar mass calculation depends on the absolute magnitude value you use for the Sun (used as calibration), and there are a number of different choices available for that. Even the peak flux value can be measured differently, with ALFALFA choosing to subtract the background noise first whereas in AGES we don't do this.

In his 2005 paper, McGaugh considered many different variations on some of these parameters. He showed that you can get a substantially different slope to the one shown here : while this one goes as rotation to the fourth power, you can get it to go as low as the third power. But he argues that this particular version has the lowest scatter, so this is more likely to be the "correct" relation.

This make a certain degree of intuitive sense. If there really is a tight relation between these two parameters, then one should choose the form that minimises the scatter. That seems fair enough. But for my part, given not only that there are so many subjective choices to be made here, but also the spate of recent objects found which don't seem to sit on the standard BTFR, I find it very difficult to believe we can really say with any confidence at all that the scatter is consistent with zero. It might be, but I doubt it.

Not everything here is subjective. You can't just make up a recipe for stellar mass or decide that you'll correct for dust based on how loudly the birds are singing. But there's plenty which is. Can we really be sure that gas-deficient galaxies must be rejected ? What's the best method to use for measuring line width ? Choosing these deliberately to get the BTFR with the lowest scatter would be, of course, dangerously circular reasoning.

As to the scientific conclusions behind my own plot, I'll leave that for next time. For now I'll just say that there's an ironic puzzle here. Some of these clouds we've found in Leo at least are almost certainly just plain-old tidal debris. But if that's the case, it's a bit weird that some of them seem to follow the standard BTFR established for much larger galaxies : there's no particular reason why unstable bits of debris should have dynamics in common with stable, rotation-dominated galaxies. Only one of the clouds shows a clear deviation - but a deviation it doth show. 

So whether any of these clouds are galaxies or if all are tidal debris, and whether they tell use anything fundamental about the nature of gravity... on that, I make no claim. I just happy to have got the damn plot to work. Time to kick back and fight international crime.

Wednesday, 27 July 2022

Attack Of The Multitudinous Space Blobs

Space blobs ! They're like regular blobs, except... they're from space...

I continue my long-standing policy of blogging every paper I'm involved with, but this latest one poses more of a challenge than most. In general, we try and write papers that focus on the science. Of course, you can't do science unless you've got something to do science on. In my case, this usually means finding the atomic hydrogen gas* component of galaxies. This is a subject about which I've gone on rants ad nauseum, albeit usually with lots and lots of pretty pictures.

* Most gifs in that post are broken, because Google FRICKIN SUCK at maintaining gifs for some reason. They're uploaded files, for heaven's sake, they shouldn't just stop working.

This post has to be a bit different. In this new paper, the balance is more towards, "look at all this lovely data" and away from" "here's what we learned from it". Let me explain why.

The main survey I get to play with is the Arecibo Galaxy Environment Survey, which looks at 16 different fields on the sky, each looking at different galaxy environments. In the field described in the latest paper, we found... rather a lot of detections, over 450 in fact. Only one other field so far contains more, and we haven't done much with that one because it was far too scary. 

Yes, exactly like sorting a big pile of clothes, except the clothes are galaxies, and if you put them in the wrong piles, a referee will shout at you. This analogy definitely works.

This large number means that doing an in-depth examination of such a complex field is just a right pain in the backside. And there's another, more pragmatic reason : it's not quite "publish or perish" for grant reporting purposes, but number of publications is a factor. So we could wait five years and get a bunch of papers all at once, or do one now and go from there. And lead author Boris Deshev was funded by a grant which was expiring. So we chose/were forced into the latter approach.

But actually this might be the better option. Science is not just a process of hypothesis-testing but of open-ended exploration and discovery. In fact that's one of the big advantages of AGES, that it has these regions we deliberately target but also a huge amount of foreground and background where we have no idea at all what we might find. That's where the excitement is. The downside, of course is that it's much harder to formulate a specific goal when you have no expectations. Sometimes you'll be lucky and a clear result will jump out at you, but often it's not easy to know what questions to ask. So it can be better to just say to the community, "look, here's the data, see what you can make of this."

Now you might be wondering if 450 sources is really such a large number. When you see the data, you'll probably understand why : even extracting those signals is a challenge, then we have to measure them, compare them with existing measurements, cross-correlate them with other catalogues, and then try and work out sensible ways to arrange the data so that we can squeeze valid result from it. It's not really 450, it's many thousands of different measurements and comparisons. Creating a sensible framework to organise everything isn't easy.

And samples of this size have their own challenges : they're small enough that every value matters, as even a few weird outliers can skew the trends (whereas with big data they'd get washed out) but large enough that taking minute care with every galaxy becomes burdensome.

Wait, what about the space blobs ?

Oh, sorry, I got a bit ahead of myself. Perhaps I should give some background overview of the science and the survey. If you're already familiar, skip ahead for the latest results.


What's all this about hydrogen then ?

A good place to start, as atomic hydrogen is just about the simplest substance there is. One electron orbits one proton. We usually call it "HI" (H one) by convention. You can also have molecular hydrogen (H2, H two), which is two hydrogen atoms stuck together, or ionised hydrogen (HII, confusingly also pronounced as H two) which is just one proton. Or even maybe hydride (H-), but that one need not concern us further today because it's useless.

Hydrogen in general is the most common stuff in the Universe. All stars are ultimately made from hydrogen, but the steps to get there are complicated and involve some or all of its different versions.

HI is the most common variant of hydrogen. We think of it as the reservoir of fuel for star formation : this is where it all comes from initially. But it's pretty toasty, typically hanging out at around 10,000 K*. It cools very slowly, and this high temperature means it has extreme difficulty getting dense enough to collapse into stars : the temperature keeps pushing back. Once it does get sufficiently dense, however, it can cool to form much denser H2 (typically ~100 K), which doesn't have the temperature to resist a runaway gravitational collapse, leading ultimately to star formation. Stars in turn inject energy into the surviving gas, ionising it to produce hot HII, which can slowly cool to HI, and so on.

* No intuitive feeling for how hot this is ? No matter. Just wait a few years and let global warming sort it all out.

Sometimes we say that HI is like a galaxy's fuel tank, and it's an interesting question how far this analogy can be pushed. With a car, you can still do 70 mph even if your tank is one-quarter full, but you'll stop pretty quickly when you reach empty. Likewise with a galaxy, perhaps. If the HI is in the tank, it's the molecular gas which is in the engine. So losing even a considerable fraction of HI doesn't necessarily mean you directly affect the star formation rate. The relationship status for HI and star formation is very much set to "it's complicated."

In terms of hydrogen, a typical galaxy looks like this : a big halo of very low density gas, within which lies the main disc of HI. The density of the HI rises towards the inner regions, where it flattens and you get a mixture of HI, HII, and stars.

Physically, the dense disc has the same thickness ratio as a CD. The larger HI disc is only a little bit thicker, while the halo is spherical.

So how do you find all this gas then ?

It depends what you're looking for. The hottest gas (~1,000,000 K) emits at X-rays*, which needs space telescopes, while HII can be seen using ordinary optical telescopes. H2 is hard to see directly but there are ways of tracing it using other elements, often at mm wavelengths. HI is comparatively simple. Very helpfully, it spontaneously sends out radio waves of 21cm wavelength, so all you need is a radio telescope. You can detect it directly and it's super simple to convert between measured brightness and physical mass. 

* This is ionised, but not usually referred to as HII. As I understand it, HII is used somewhat interchangeably with the recombination lines that are used to detect it. For this to happen the gas has to be only just above the temperature where ionisation happens. Too hot, as in X-ray emitting gas, and no recombination happens so you can't detect it at optical wavelengths.

The good thing is that the required radio telescopes are not too difficult to make. They don't need especially complex electronics or other equipment, they just need to be - and this is the downside - friggin' massive.

"It's what you do with it that counts !" said no astronomer ever. Well, not really, but sometimes bigger really is better.

Once you've got the data, you go through it by eye looking for the signals, something I've covered before. And in our data the galaxies aren't well resolved, so they all look like blobs. In this case, lots of blobs.

Ahh, I see. And galaxy environments ?

Nothing to do with saving the rainforest or tying oneself to trains. Rather, galaxies don't all live in the same places. Some live in very sparse voids where there's not much of anything. Others live in little groups of a few other galaxies orbiting each other, while others live in massive, rich clusters thousands strong. And on the largest of scales, groups and clusters alike are mostly found in giant filaments.  

Most galaxies live in small groups, with probably only ~1-2% in rich clusters. This means we have to be very careful with drawing general conclusions about galaxy evolution from such extreme locations, but they do let us sample huge numbers of galaxies with only a small amount of observing time.

Does gas vary with environment ?

Indeed. Remember that the HI is generally more extended than the stellar disc of a galaxy. This means it's less tightly bound, so any process which disturbs the galaxy (like other galaxies passing by, cruelty to animals, people who wear socks with sandals... that sort of thing) has more of an effect of the gas than the stars. So by looking at the gas, we can get a better idea of what the different environments really do.

AGES was designed to cover the whole range of galaxy environments, from voids to isolated galaxies to small groups and giant clusters. But each of our target regions also covers what's in front and behind of its target as well, so we get an awful lot of bonus data. This "AGES volume" is actually where most of our detections are found. And that, more than the target cluster, is what we started with in this paper.

AGES XI : The Franchise Continues

We're not going to let a little thing like the collapse of the telescope stop us, are we ? Of course not. In this paper we look at the Abell 1367 cluster. It's not a sexy, famous cluster like Virgo or Coma, but like all clusters, there's plenty of interesting stuff going on here. In fact it contains one of my favourite objects of all, the appalling-named "blue infalling group" :

The brightest blobs are galaxies, with the faint trails between them being ionised gas. Image from this paper.

It always makes me think of the smoke trail from a bumblebee with its bum on fire. What's actually going on, we think, is that a group of galaxies are orbiting each other while also falling into the cluster proper. As they enter, ram pressure stripping removes their gas, which traces out these nice helical patterns. Try turning on a hosepipe and waving it around and you'll see what I mean, and possibly soak the neighbours too. Don't worry, it's very hot, so they'll definitely thank you.

Or, the internet bizarrely lacking adequate hosepipe gifs, you can use ropes, but that's not as much fun.

Add in this particularly weird hot gas cloud and some very long HI tails and the cluster begins to seem like a place worth studying. Actually, the very first paper I was on (my role was pretty much 100% doing observations) was looking at the earlier AGES data of this region, which covered the central 5x1 degree strip. This covered the main part of the cluster but not much else. Interestingly, we saw that the galaxies detected in HI didn't follow the general pattern of galaxies detected through more familiar visible-light surveys. In 3D space they're distributed like so :

Galaxies detected with gas are in black, while those without are in red.

What's going on here ? All the optically detected galaxies are in a neat line ! This is the finger-of-god effect. But look at the axes : we have velocity, not distance. Now as a proxy for distance, velocity (which is much easier to measure) works pretty well in general. This is Hubble's famous law, that there's a neat, linear relation between the two. But though this works just fine in most places, this isn't true in massive clusters*. Here the great mass of the cluster means that galaxies are moving much faster than in the general field, even though they're all actually at the same distance.

* In fact, as early as 1932, Fritz Zwicky found that cluster galaxies don't follow Hubble's Law - which constitutes some of the earliest evidence for dark matter.

Okay, so the optical galaxies look like a "finger" because we've measured their velocity and not true distance. If we could measure distance, we'd probably find they were all much more bunched-up here.

From another, much larger, survey. On the left, velocity is used for distance, hence all the fingery "streaks". On the right "true" distance is used, or at least a better approximation of it. No streaks !

But the HI detections don't show this behaviour. They seem to be found all over place, as though the cluster hadn't made any difference. Why not ? Are gas-rich galaxies like honey badgers and just don't care ? Nothing so exciting I'm afraid; it's just a selection effect.

Galaxies in the centres of clusters can easily lose all their gas as the clusters' own hot gas pushes it out and ionises it. At this distance (92 Mpc, 300 million light years) even a slight loss of the HI would make it undetectable. So we can only detect galaxies which haven't been much affected by the cluster - our detections are likely either just on the outskirts and entering it for the very first time, or not quite at the same distance after all.

Does this mean there's no point in our survey ? Is even the mighty Arecibo inadequate to the task of detecting gassy cluster galaxies ? This is too pessimistic. Rather, we can still detect galaxies just entering the cluster, and that's important. Understanding whether galaxy evolution is dominated by clusters or if they can have equally thrilling adventures elsewhere is controversial. The Blue Infalling Group is a nice example, but doesn't by itself prove that this so-called "pre-processing" is very important in the grand scheme of things.

What did we find this time ?

Space blobs

Well, now the survey is complete we have the full 5x4 degrees of coverage, so we can look in much more detail at those galaxies on the cluster outskirts. But first, here's what all those blobs actually look like in the original data.

Not my prettiest picture, to be sure... but you can play with this interactively online, which is quite fun. Might take a minute or two to load.

I told you going from the data to a catalogue wasn't easy ! We use a combination of manually looking at the data and automatic source-finding algorithms to turn a bunch of blobs into a list of carefully-measured galaxies. In this case, because the galaxies are preferentially found over narrow velocity ranges, a lot of detections are confused with each other and hard to disentangle. Cataloguing involves a great deal of careful work to differentiate between galaxies as best we can, and flagging those where it's just an ugly unsalvageable mess. And large swathes of the data are dominated by whacking great big blobs, which are not alien megastructures but the effect of interference (yes, sometimes the hunt for aliens really does turn into a hunt for washing machines and other annoying electronic equipment).

This picture of the blobs is in the raw pixel coordinates of the data. When we convert everything to proper physical units, we see our our detections have quite a different distribution to the first paper :

Left : original, as above. Centre : only the HI detections in the original survey area (a few more are present now thanks to improved cataloguing). Right : the HI detections from the complete survey, over the region corresponding to the cluster (the full velocity range of the data is -2,000 -> +20,000 km/s).

It seems that there's a large group close to the main cluster which is rather gas rich, compared to the cluster itself which you'd never guess was there from the HI data alone. You can play with a 3D version of this here.

Silent but deadly : galaxies have gas we can't detect

So the environment of the cluster itself is different to what we thought. Boris has a thing against treating clusters as spherical systems, because they generally aren't. Often we see them still assembling, sometimes along filaments. Alas, the techniques used previously didn't really show much in this case - there's no evidence that galaxies experiencing anything particularly location-specific here. We were hoping that maybe we'd some clear signs that the environment varied : maybe the ones in that group would be especially gas rich, maybe the ones nearest the cluster would be gas poor, but actually no, not really.

Which is not to say that the cluster doesn't do anything. On the contrary, it's annoyingly effective at gas removal. For comparison, in the much closer Virgo cluster, we could detect galaxies with only 10% or even 1% of the gas content of similar galaxies found elsewhere. But here, as soon as galaxies lose even quite a small fraction (say 50%) of their gas, they become undetectable. And this means we can't properly comment on exactly where or which structures galaxies in the cluster are losing gas, because we just can't find the gas-poor galaxies. 

But it does enable a neat trick. In Virgo, we tried to "stack" the non-detected galaxies (adding their signals together) to increase our sensitivity. Which it did, by a factor 10... but no detection resulted. At the closer distance of Virgo, AGES is sensitive enough that it can detect the faintest whiff of gas*, so if it's not detected straight away, chances are it doesn't have any gas at all. Not so in A1367. Here, stacking results in a lovely clear detection :

* Do your own joke.

Stacking three different parts of the data set. As a sanity check, the blue curves show what happens when we stack galaxies we already detected - we always get a nice clear signal. The red curves show the stacked non-detections : we get a signal (a big bump) in the cluster and background, but not the foreground. The grey is a control stack where no galaxies are expected to be present.

Does this point to a difference between the clusters ? Probably not. More likely, our stacked sample does include some galaxies which are totally gasless, but it also includes plenty which are only slightly gas-deficient : the sort we could detect directly in Virgo, but can't here because of the greater distance. The two clusters may or may not be more effective in gas removal, but we honestly just can't tell. 

In short, in Virgo we'd already detected all the galaxies with even small amounts of gas. Stacking the rest didn't help because they'd lost the whole lot. Here, we can't tell which ones still have most of their gas, so we're stacking some which have no gas at all along with others which actually still have quite a lot left. Likewise in the foreground region here : at lower distances we're back to the same situation as Virgo... if we don't directly detect a galaxy here, it probably has no gas at all, so stacking doesn't do anything.

Is there a best way to measure gas loss ?

Getting this paper through the reviewing process was unfortunately another unnecessarily tiring exercise. Some of the comments were extremely valuable, but some smacked of the referee trying to write the paper for us, and other comments were honestly just wrong (somewhat amusingly, citing papers which actually claimed the exact opposite of what they said they did). And we made mistakes too, which made the experience about as much fun as wrestling a blindfolded bear while blindfolded ourselves.

What we did show, I think (though this one had to be heavily toned-down to make it palatable to the referee), was that we can use a simple statistical parameter to understand the effects of gas loss. Traditionally, we quantify how much gas a galaxy in a group or cluster has lost by comparing it with a control sample of similar galaxies in isolation. This "HI deficiency" can be computed for individual galaxies. It isn't at all exact though, because there's a lot of intrinsic variation in this parameter. Realistically, it can only tell you if a galaxy has :

  • A lot more gas than expected (very rare !)
  • A bit more gas than expected
  • About as much gas as expected
  • A bit less gas than expected
  • A lot less gas than expected

And that's it. You can measure it as precisely as you like, but you if pretend this precision is actually meaningful, you're fooling yourself. Still, it can be done on a galaxy-by-galaxy basis, which is very useful.

But with a sample like this it doesn't really tell us very much. As we've seen, even a slight gas loss makes the galaxies undetectable. We can compute a lower limit on the deficiency, but this is misleading, as the galaxies could easily have lost a lot more than that.

A better approach might be to just calculate the fraction of galaxies detected in HI. This can only be done on a whole population, so we lose all the individual information. And the choice of which population to select is arbitrary. But, for example, we can say that the detected fraction varies radially, being lowest in the centre (the main cluster) and highest in the outskirts (the first infallers). And because it's just a fraction, it doesn't give any impression of the gas loss being any particular amount, just that some has happened. Which is sometimes all you really need.

Now the referee got a bit over-zealous here. We did not say, at any point, that the detection fraction was a better parameter than deficiency, nor did we even ever give that impression (a better approach is not the same thing at all !). It's better in some ways, in some circumstances, but the converse is equally true. In fact the deficiency is always preferable whenever you can use it, but the detected fraction is simpler and always available (though it becomes meaningless if your sample is small). 

Brief intermission in which I rant against referees

I don't know why this happens, but it seems common for referees to think even weak, throwaway assertions in a paper must be held as inviolable Gold Standard claims that will survive any assault short of a tactical nuclear weapon. In my view, that's not what papers are for, never has been and never should be. All claims in papers are still subject to the broader peer review of the entire community. Papers are not textbooks but part of the discussion themselves; yes, they should be more rigorous than, say, blog posts (ahem), but there's no value in making them utterly unassailable. First, it can't be done (no referee is perfect), and second, because of that, it artificially shuts down discussion and so means that neither author nor community ever learn anything. Even papers are, ultimately, a step in the road - you want to make sure that potholes are minimised, but if you never put down any tarmac at all because the mixture isn't perfect, you'll never have a damn road at all

And now back to our feature presentation

Fortunately, what did survive the referee's onslaught (and I have to say was improved by it) was a comparison between deficiency and fraction as a function of local and global density :

Wait ! Don't run away ! It looks a bit scary, and it is a complex plot. So let's break it down into manageable chunks. First, the data is divided into two samples which we refer to as the global density : those in the velocity range of the cluster, and those elsewhere. The latter are largely in low-density regions, mainly groups in filaments. The former include galaxies in the cluster outskirts as well as deep in the interior. In the upper section we plot trends using deficiency while on the lower panel we use the non-detected fraction.

Let's forget about that nasty plot for a moment and just look at the first two panels. These are the most important anyway.

What we're plotting here is how the deficiency and non-detected fraction vary as a function of local density : that is, how many galaxies are present in different spatial bins. In an earlier version of the paper, we made a mistake and found that local density made absolutely no difference and that it was due entirely to global density (cluster or non-cluster). But when we corrected that, we found the opposite : there's a nice trend with local density, and clusters are only different because the local density is generally higher there. This fits with our other recent findings too.

(That we were able to spin some quite elaborate but plausible-sounding justifications for the first (wrong) interpretation I take as an important lesson in the dangers of rationalising. Again, no one paper should be held as anything more than evidence, never as proof.)

We can see from the plot that this result is much clearer with the non-detected fraction than with deficiency. The referee was concerned that this might be a statistical effect rather than representing real physics : yes, there's a clear trend, but maybe this is only because galaxies vary in some other way with local density. So to exactly reverse my previous rant, we wouldn't have looked at this without the referee's diligent nit-picking. Thank you, kindly pedantic stranger !

This is where the other panels come in : plotting deficiency/fraction as functions of stellar mass and star formation rate. We also took great pains to ensure that, unlike previous claims, we used a properly complete sample for this area, meaning that we're comparing like-for-like, something the referee seemed not to really believe for some reason.

What do we find ? Something like this :

  1. Overall, for all parameters, both deficiency and non-detected fraction are higher for cluster galaxies than for non-cluster galaxies. That's a good sanity check : there's definitely gas loss in the cluster, as we'd expect.
  2. There's little or no variation with gas loss (by either parameter) as a function of stellar mass. So our trends in gas loss aren't being driven by selectively detecting smaller or larger galaxies. This is important, because we'd only be able to detect high deficiencies for the biggest galaxies; likewise, we wouldn't expect to detect small galaxies unless they were actually gas rich.
  3. There's not much trend in deficiency with star formation rate. This might be a bit more surprising, but remember the fuel tank analogy : the relation between HI and star formation is indirect. But it could also be something simpler, since the error bars here are very large.
  4. In contrast, there's a clear trend between fraction and star formation rate. Here the error bars are much smaller. So tentatively, it looks like the large errors on deficiency are masking the trend : less gas, less stars. The detected fraction might be offering us more information in this case, at the cost of knowing which particular galaxies have lost gas.

Conclusions and where we go next

There are three main outcomes from this paper. First is the catalogue itself, together with an "atlas" : a set of visual charts for each galaxy, including the HI spectra and maps and the corresponding optical images, all labelled with the known galaxies present. Hopefully we can use this retroactively on our other data, looking towards the time when we release the full AGES data set for the whole survey.

Second, stacking galaxies works in this field. Having spent feckin' ages trying this during my PhD (there's a subheading in one chapter, "Four hundred million non-detections"), I was despondent that it would ever work at all. But it very clearly does, opening up scope for utilising this elsewhere. Boris has some intriguing ideas about what we might do with this.

Third, detected fraction can offer a viable alternative to HI deficiency. Despite the referee's protestations I think this could indeed be more useful at larger distances (where it seems galaxies were considerably more gas rich). Note that you don't get something for nothing - you get significantly reduced errors, but only because this has to be applied to galaxies en masse; individual information is lost. Fully understanding this parameter is more subtle than it may first appear, and needs a lot of work to ensure it is indeed telling us what we think it's telling us. It is absolutely legitimate that one can still have reservations about this. We think it's at the point where it deserves wider attention, but no more than this.

And scientifically, the view that it's local density which drives gas loss is an interesting one. It's not what one would naively expect. In massive clusters, gas loss is mainly due to ram pressure stripping, whereas in small groups it's from tidal encounters. These two processes scale completely differently, but we're seeing a smooth change in gas loss as a function of density. And in our previous study, we found that there's a smooth change with ram pressure as well, extending down even to very low pressures indeed.

This is a bit strange. It's a bit like saying that the fastest horse is always the biggest one : surely, you wouldn't expect a shire horse to come top of the league. You expect a broad correlation (Shetland ponies can't compete with a thoroughbred), but not a nice, simple, continuous trend.

It's hard to say what might be going on. My guess is the data isn't precise enough, that we're smoothing out any more sudden changes because the error bars are quite large : the change isn't really as continuous as it looks. I am not sure if this is a matter of getting better data or analysing the data in different ways to reveal if there really is any qualitative difference between small groups of massive clusters... then again, maybe the counteracting effects cancel out and the smooth change is correct after all. It's possible.

What next ? Well, some of our galaxies have no optical counterparts, for which we have follow-up observations using the Chinese FAST telescope. If any of these are detected that's an automatically interesting result. And of course, we can dig down deeper into the data to study the cluster itself in much more detail, as well as other individual objects with HI streams, galaxies with low star formation rates but high gas contents and other weird oddballs.... a veritable host of things ! As I said, defining the problem is likely to be the hardest part. But now we have a basic catalogue to start from, making comparisons and looking for trends gets a whole lot easier.

And all this from a bunch of blobs.