The clusters that went RAR !

Not much has been said about the radial acceleration lately. It seems to be a problem which is thoroughly licked, but these authors decide that the dead horse is worth flogging a bit more.

The RAR is the relation between the acceleration due to baryons and the acceleration due to dark matter. This has been measured in galaxies and it's found that there's a very tight relation between the two. This is surprising, since the mass of dark matter is heavily dominant over the baryons - you might expect that there should be a lot more scatter. But then people realised that this happened in their simulations anyway, pretty much exactly in agreement with observation.

What seems to be going on is that there's a characteristic regime in which galaxies form. You don't get galaxies above or below certain mass thresholds, thus avoiding extremely high and low accelerations, and the density profiles of dark matter halos tends to be similar. So as you move radially outwards in any galaxy, the acceleration experienced changes in the same characteristic way. Furthermore, although the baryons don't interact with dark matter except through gravity, that interaction can be strong enough to cause selection effects as to where stars form. The RAR, then, is just the result of several quite subtle but powerful and entirely expected selection effects.

The RAR was initially very interesting to modified gravity supporters, who'd predicted it ahead of time. At best, it now looks as though there's no way to distinguish between the predictions of standard dark matter theories and those of modified gravity - both give identical results. But what if we looked at totally different systems ?

This paper extends the results to galaxy clusters. If RAR is the result of modified gravity theories that predict a characteristic acceleration, the same sort of relation ought to be visible in any system, on any scale, bound by gravity. Hence the effort here to test it in galaxy clusters.

The procedure needs some adaptations. In individual galaxies, you can measure how fast the gas and stars are actually moving and directly measure their densities. So you can calculate their acceleration due to their observed baryonic mass and compare this with their actual acceleration (knowing their velocity, distance from the centre of the galaxy, and assuming stable circular orbits), which is dominated by the dark matter.

In clusters things aren't so elegant. Galaxy orbits can be trick to compute, and it's not safe to assume they're moving in neat circles. Instead, the authors use measurements of the hot intracluster gas. Unlike galaxies, the gas motion is heavily influenced by its own thermal pressure keeping it from collapsing into a dense lump in the centre, so its actual acceleration is not dominated by the dark matter. It seems the authors are able to account for this and estimate the acceleration due to dark matter without the pressure from the baryons, as well as the acceleration from the baryonic mass alone. So this should be a fair comparison with the galaxy-based RAR, which is based on only gravitational effects.

They find that the cluster-based RAR is strongly deviant from the galaxy-based relation. It seems that it does not behave in a universal, acceleration-dependent way : there is no evidence for a universal acceleration scale. Which is very odd if this is due to gravity, as MOND predicts.

Case closed for alternative theories of gravity ? They say their result does impact certain theories, but not necessarily MOND itself. Here it gets highly confused. I applaud the authors sterling efforts to remain impartial, but I think they may be going too far, exploring too many ifs and buts in too short a space, sacrificing clarity for brevity. For instance they say the calculated characteristic acceleration is almost ten times larger than the expected standard MOND value, but then immediately say that this is also somehow consistent with MOND. In support of this they cite two enormously long papers, and I'm just not interested enough to read either of them. They mention all sorts of possible modifications to MOND, like relativistic versions or even including some dark matter, which just makes the whole message hard to discern. Does the damn thing work or not ?

I know MOND behaves in a radically different way to Newtonian gravity, but I'm having an increasingly hard time buying it as a sensible theory. Gravity that works differently on different scales and still requires dark matter ? Were the issue just about galaxy rotation curves, there would be no philosophical advantage to either MOND or dark matter. But the more complex things get, the more contrived the alterations to MOND seem to become. MOND feels ever more like a bizarre and unnecessary solution, offering not a single advantage over dark matter - it now seems so complex that it's little better than magic. I'd rather postulate an unknown type of matter than accept a theory that breaks basic physics like this. I could be wrong, of course, but basic intuition is hard to surrender.

EDIT : Barely days later, here's another paper trying much the same thing. It's somewhat easier to follow in its conclusions but more difficult for its method. They use lensing for the total mass and the hot gas for the baryons, but I cannot see anywhere where they describe how they calculate the accelerations. They seem to find a broadly similar RAR as the first paper and conclude that there is no universal RAR. Their acceleration constant is much closer to the ordinary MOND value - the slope of their RAR is similar to previous calculations but the intercept is different. They say their results are consistent with CDM, but they completely avoid any discussion on MOND (probably wisely).

The radial acceleration relation in galaxy clusters

Recently, the discovery of the radial acceleration relation (RAR) in galaxies has been regarded as an indirect support of alternative theories of gravity such as Modified Newtonian Dynamics (MOND) and modified gravity. This relation indicates a tight correlation between dynamical mass and baryonic mass in galaxies with different sizes and morphology.

The Joy Of Stacks

Sensitivity is somewhat of a recurring topic, and I don't mean the kind where people whinge about offensive statements about Nazi-themed beards on twitter. I mean the sort where you look at your data and try and work out what the hell it is you've managed to detect, if anything.

I've already covered that sensitivity can't really be given as a single number when you're dealing with real data. You have to account for how complete your catalogue is (how many sources present you've detected) and how reliable it is (what fraction of sources you identify correctly). I've also examined in some length how quantifying this can be arguably impossible, which is philosophically interesting even if practically there's bugger all you can do about it.

But I've glossed over sensitivity itself : the capacity to detect things in the first place, even if you don't actually detect anything at all. This is generally easier to grapple with than the statistical problems of completeness and reliability, but there are still subtleties that need to be dealt with. One particular aspect had me tearing my hair out during my PhD, and recent developments have made me realise that this wasn't just me who was thoroughly perplexed. It's one of those features which will seem, I hope, quite obvious when it's stated, but can be completely non-intuitive if no-one tells you what's going on... to some people at least.


Stacking Made Simple

Suppose you target a well-studied region of space with a nice shiny new HI survey. You've already got a lovely optical catalogue, and notwithstanding the problem of completeness, there are plenty of galaxies there you already know the positions and redshifts and all that other gubbins for. You spend ages and ages doing your radio survey, and behold ! Nothing. Nada. Not a single bloody detection. What's an astronomer to do ?

Well, the most obvious answer is to panic and run around the room tearing other people's hair out extract the radio data at the positions of all the known galaxies, add them together and divide the result by the number of objects. This process of averaging the data is called stacking. The idea is that by combining all the different signals, you're essentially doing the equivalent to taking a longer exposure. You're increasing your sensitivity and should be able to detect fainter emission than you could otherwise. Depending on the qualities of your data and the number of galaxies you detect, you might well be able to increase your sensitivity by, oh, say, a factor ten, which is pretty awesome since you don't need to do any new observations. Woohoo, free sensitivity !

Formally, the noise level of your stacked data scales by a factor n^-0.5, where n is the number of galaxies you stack (at least that's the theoretical best expectation; it will usually be a bit worse). In the ideal case, if you have a signal present that's too weak to detect in any individual sections, then averaging those weak values will give you the average value of the signal. In contrast, if you average noise values together, they should be purely random and the more noise you combine the closer you get to zero. So your signal to noise increases, as long as your noise really is purely random or nearly so.

It's well-known that the penalty you pay for stacking is that, in the event you manage to detect something, you don't know which objects actually contain the gas you've detected. Some individual objects might have a bit more gas than your final detection, while others might have less. The crucial thing is that the stacked data tells you about the average amount of stuff present, and absolutely nothing about individual galaxies. After all, the process of adding up and dividing by the total number is the very definition of averaging.


Stacking Made Unnecessarily Complicated

What's all too easy to forget is that this means you do not improve your sensitivity to the total amount of gas present. In fact, your sensitivity to the total gets worse : it's only your capability to detect the average mass per object which improves. You have, after all, averaged your signal, so your new measurement must be an average measurement by definition. I'm going to keep repeating that.

Perhaps the simplest way to understand this is to imagine you had two galaxies with clear detections. If you wanted their total mass, you'd simply add their signals together. If you wanted their average mass, you'd add them and divide by two. Exactly the same principle applies when stacking non-detections : the sum gives you the total mass, the stack gives you the average. And the total mass cannot possibly be less than either of the individual components.

When you put it like this it might seem so buggeringly obvious that you'd laugh in the face of anyone who doesn't understand it, which is very mean* considering the massive confusion I got myself in when trying to work it out from first principles (see chapter 7). The thing is, when you do a stack and you calculate how much stuff you're sensitive too, it's awfully tempting to assume this means your sensitivity to the total, because that's how things normally work. Thinking in terms of averages isn't natural.

* Pun NOT intended.

Or we can look at this mathematically. In any survey, the mass sensitivity is governed by the noise of the data :
M ≡ σ_rms
Where  σ_rms is the noise level. Note the equivalent sign rather than an equals sign : the precise equation will depend on the exact nature of the data. It doesn't even have to be mass - it can be whatever quantity we're studying - but I'll use this as it's probably the easiest thing to understand.

Let's alter this slightly and let σ₁ be the rms noise level for an single observation. We know that if we stack n galaxies, the new noise level becomes σ₁n^-0.5, so our new average mass becomes :
M_av ≡ σ₁n^-0.5
Which is clearly an improvement over what we started with - we can detect smaller masses than we could before, which is good. But remember, this is our average mass. The total mass is simply n*M_av, so :
M_tot ≡ σ₁n^+0.5
Keeping in the plus sign so it's easier to see the difference compared to the average. But look - this is worse than what we had originally ! The more galaxies we add, the better our average mass sensitivity, but the worse things get for total mass.

Averaged noise level as a function of the number of objects stacked.

Equivalent noise level for the total number of objects stacked.

A final way to think about it is to consider information. To get better sensitivity to the total mass, we'd need more information per individual object, and obviously we can't do that just by adding in data from other objects.

It's high time we had a visual example. In the data below, I injected a faint source into 100 images. The left panel shows the raw individual images with no further processing. The middle panel shows the cumulative sum of the images, while the right panel shows the averaged result. Exactly the same colour scale is used for all images.

You can see the source is never detected in any of the raw images, but it's quickly visible in the summed and averaged images. But you can also see that the values are much more extreme in the simple summed panel compared to the averaged image. The averaged value is simply the sum divided by the total number of images, so, essentially, the averaged image is simply a scaled version of the summed image. This means that despite appearances, it's really the summation that improves detectability, not the averaging. We can see this if we use an adaptive colour scale that sets the colour range based on the minimum and maximum value in each image :

Then we see that the summed and averaged images are visually identical. The actual values shown are of course different, but how we display them matters a great deal. The noise averages to zero, but it doesn't necessarily sum to zero; the source sums to ever-greater values for each image it's present in, but averages to its true value.


Stacking Made Subtle

To re-iterate : stacking is the same as averaging, so while it improves your sensitivity to the average, it makes things worse for the total. Summing improves your signal strength and thus detectability, but only for data points in which a source is present.

Of course, once we get beyond that, things get more complicated. Normally you wouldn't necessarily do such a simple averaging, because the noise isn't usually the same everywhere. So you'd weight each source by its local rms value and then divide by the sum of the weights rather than the numerical total. This decreases the contribution of the noisiest regions and maximises the benefit from the ones with the lowest noise.

Another issue is whether you go for sheer noise level or actual physical mass. For the former, you want as many objects as possible. But for the latter, you want to account for the distance of your targets - the further away, the less sensitive to mass you'll be, so you might not want to combine them with closer objects. Remember, the equations had an equivalent sign, not an equals sign. Mass sensitivity does not directly equate with simple rms value, though it may be directly proportional to it.

Finally, it's important to realise that this is a general case and a fundamental property of stacking. If you smooth your data spatially you're doing much the same thing : your sensitivity to the average mass per pixel improves, but at the cost of not knowing quite so well where that mass is precisely located, and your total mass sensitivity gets worse. This is why spatially smoothing isn't guaranteed to detect anything if you go nuts with it and smooth it to hell : sure, your surface brightness sensitivity can be phenomenally good, but yer total mass sensitivity is crappy. You're hoping not only that there's some big diffuse material lurking around, but that material is also very substantial : sure it can be thin, but it also has to be present over a larger area.

The same goes for stacking in velocity space in radio data, which is what prompted this post. Integrated flux maps actually have worse mass sensitivity than individual channel maps, despite containing information from more channels. Of course if you were to average them by the number of channels you'd see an improvement : again, you increase your sensitivity to the average column density of the gas but at the expense of your sensitivity to total mass. In essence, your average mass sensitivity represents the mass you could detect if it was present in every stacked location.


So that's it. Stacking is a useful addition in the arsenal of Tools For Detecting Stuff, but like everything else, it's got limits.

The Incredible Shrinking Galaxies

Ultra Diffuse Galaxies are a dead sexy topic in extragalactic astronomy, and took the community by storm as soon as they were found. The one-line description of why they're so cool is that they're the same size as the Milky Way but a thousand times fainter.

But are they really the same size as the Milky Way ? Maybe not, say the authors of this paper. I was fortunate enough to have a sneak preview of the results at a conference last year in Tenerife, but the authors asked everyone very nicely to keep things under wraps. And quite properly so, as this is the kind of "I wish I'd thought of that !" result that could be extremely important for the lead author as a PhD student (or early postdoc, I forget which).

It's often awkward to define the size of a galaxy. Their shapes vary tremendously, as do their brightnesses, and while some do seem to have distinct edges, others fade more gradually. The two main ways around this are to use the effective radius (R_e - the radius enclosing half the total light) or the Holmberg radius (R_H - the radius measured at a fixed brightness level). Both have their uses, but both are pretty arbitrary definitions and don't really have any physical motivation.

That's where this first paper comes in. The authors clearly had a flash of enviable inspiration, because their new proposed definition is simple, intuitive, and just makes absolutely everything better. They noted that there seems to be a well-known threshold for star formation in terms of gas density, about 1 M_⨀ pc^-2. This is hardly exact, mind you, and there's a lot of complicated physics at work. But it's pretty good, and all things considered, the threshold is remarkably robust. Above 10 M_⨀ pc^-2 the atomic gas seems to saturate and become molecular, which inevitably leads to star formation, but star formation really only seems to be actively suppressed below the lower value.

Somebody in the team realised that if this quite neat threshold applied so well to the gas, it might be important for the stars to. So they define their new proposed radius R₁ as corresponding to the distance at which the stellar density drops to 1 M_⨀ pc^-2. Very simple, and very effective. Using this new definition, the scatter in the size-brightness relation drops substantially. Visually, R₁ looks much closer to the true edge of both dwarf and giant galaxies - R_e tends to be far too small, since it can be dominated by small, bright knots of intense star formation. And at very high masses, where galaxies transition from rotation-dominated discs to dispersion-dominated spheroidal systems, the scatter in the size-brightness doesn't change but the slope does*, clearly showing that the galaxies are dynamically different. Hooray !

* This reminded me of a similar-ish recent finding on the most massive spiral galaxies, though I'm not sure the results are really comparable.

Of course, galaxies are messy things, so there are a few caveats. Interacting galaxies can show very complex outer morphologies indeed; dwarf irregulars can have highly complex internal structures; a few galaxies have averaged stellar densities below this new threshold everywhere, so R₁ would not give a good value in those cases. But for the most part it should be helpful, clearly demarking where the galaxy disc ends and any extensions begin. It's not perfect, but it does better than existing parameters.

A more practical matter is that R₁ is harder to measure. Other values can be measured using a single wavelength, but R₁ needs at least two independent wavebands in order to properly calculate the stellar mass. And that means making multiple surface brightness profiles per galaxy. On the other hand, R_H looks like a reasonable approximation in most cases, so perhaps a prescription can be developed to convert between the two.

A few small caveats on the paper itself. First, they keep saying that they measure R₁ with an isophotal contour, but all their figures show ellipses, not contours. So some averaging has obviously been done. It would be interesting to see a true contour, especially for interacting galaxies. Second, it's not clear to me how many slope changes their are in their size-brightness relation plots - sometimes it looks like there's just the one, in others like there might be two. And on a related point, they say that the slope change using R_e is not monotonic, but I can't see any evidence of that.

To summarise the different measurement parameters :

• R_e is the radius enclosing half the light, often much smaller than the "true" size of the galaxy.
• R_H is the radius at a fixed brightness value, which usually seems a much better estimate of the true size but lacks a physical motivation.
• R₁ is the new parameter, measured at the point the stellar density drops to the equivalent of 10 M_⨀ pc^-2 (the threshold gas density for star formation).

What does all this mean for the Ultra Diffuse Galaxies ? In their second, companion paper (linked below), they essentially say this means they're just ordinary dwarfs.  Their R₁ sizes are perfectly typical for dwarf galaxies and not at all unusual. Using the new R₁ parameter, they follow exactly the same size-brightness relation as for previously known dwarfs. Even their R_e values, though on the high size, aren't that extraordinary compared to other dwarf galaxies.

But of course these new galaxies are not totally identical to the old. UDGs clearly have much lower R₁/R_e ratios. They allude to this many times, noting that the reason R_e is so small in many dwarfs is because of bright central knots of high star formation activity. But they never quantify it explicitly (and unfortunately we'll have to wait for the final published paper for the full table). So we might not want to chuck out the whole UDG bandwagon just yet - these guys clearly are different from typical dwarfs, but it's a bit more subtle than the standard take-home message. Something must be going on to suppress star formation in the central regions of these guys that doesn't happen in regular dwarf galaxies.

While the innermost regions of UDGs are clearly different, their outer regions look to be identical to other dwarfs. They plot the surface brightness profiles of normal dwarfs and UDGs, and the slope of the outer regions looks the same. So any suggestion that UDGs are giant galaxies looks highly unlikely. Should we even still call them ultra diffuse galaxies, or use ultra flat instead ? I think we can probably stick with UDGs, not need to go around confusing everyone... and since their stars are less concentrated, it's still okay to call them diffuse.

There are two major caveats to all this. First, there are UDGs with gas, sometimes a great deal of gas. It remains to be seen if the overall star formation activity in UDGs is abnormally low compared to other dwarfs, but I'd be very surprised if it isn't. Second, on a related point, those peculiar rotation velocities of the gas aren't going away - at least some UDGs look to be rotating so slowly that they don't have dark matter at all. That marks them out as spectacularly different from ordinary galaxies.

So the day of the UDGs is by no means over yet. This paper is also a very small sample of UDGs, so who knows, some of the others may turn out to be different again (the first claim for a giant UDG seems to have been completely forgotten, perhaps unfairly*). Even though it's now getting on for five years since UDGs first hit the headlines, we still don't have enough data to really say what the hell is going on. Is their gas density unusually high or low ? No idea, we have just six objects with well-resolved gas measurements. Are their kinematics truly weird or have we got their inclination angles wrong ? Again, dunno. The research continues.

* If Dragonfly 44 really is representative of a new class of "failed giants", then while it may be superficially similar to UDGs, most other UDGs are clearly different beasts.

Are ultra-diffuse galaxies Milky Way-sized?

Now almost 70 years since its introduction, the effective or half-light radius has become a very popular choice for characterising galaxy size. However, the effective radius measures the concentration of light within galaxies and thus does not capture the intuitive definition of size which is related to the edge or boundary of objects.

It'a always in the last place you look

Just before Christmas last year, I had a paper accepted after more than a year of review. You can read about the horrors of the refereeing process here, or the extended public outreach post here. This post is the shorter description for the enthusiasts.


The Virgo Cluster is chock full of galaxies which are clearly deficient in HI (atomic hydrogen) compared to field objects. Hundreds of galaxies appear to have lost a lot of gas, yet there are only about a dozen with known hydrogen streams. Now, many of the galaxies could have lost their gas so long ago that it's dispersed and become undetectable, especially since the cluster contains its own (much hotter) gas that the streams could dissolve into. Most people, I expect, would be happy enough with that explanation. After all, the conventional explanation of how galaxies lose gas in the cluster - through the effects of ram pressure stripping, as the galaxies move at high speeds through the cluster gas - seems to do an excellent job of explaining everything else.

But there are a few of notable oddities that don't seem to fit. A small number of galaxies with streams don't seem to have lost much gas at all, being otherwise undisturbed. Galaxies with normal gas content and those which are deficient are found in close proximity to each other, suggesting that we should be seeing at least some which are currently in the process of actively losing gas. And of the streams which do exist, most are very short, faint little things, but a few are enormous, spectacular features containing literally tonnes and tonnes* of gas. If the stripped gas usually evaporates or disperses, why doesn't this happen in every case ? Is there something special about the largest surviving streams ?

* Okay, billions of solar masses.

We need to quantify what's going on. There are three aspects to the problem, all of which we tackle in this paper to various degrees :

1. How many galaxies are actually losing as right now ? If stripped gas is rapidly rendered undetectable, then we only expect to see streams from those which are actively stripping.
2. How many of the streams which exist should be detectable ? That is, what happens to the stripped gas once it's removed from its parent galaxy - how quickly does it disperse and reach such a low density (and/or change to a different phase) that we can't detect it ? 
3. Have we really found all the potentially detectable streams ? This has bugged me from the days of my PhD, ever since when I'd been adamantly declaring that there were no streams in our data sets - much to the surprise and annoyance of my PhD supervisor. Perhaps we were just not looking hard enough, although that seemed extremely unlikely to me.

For item 1, we already have a very nice analytic model of ram pressure stripping which can predict which galaxies are currently stripping. Unfortunately, the data we need to feed the model is only available for a limited fraction of the galaxies in our data, so we couldn't use this to make a prediction of the number of streams. We could still use it to say which galaxies should or should not be stripping, but not to give us the more important grand total. And, assuming we found a stream, we could also use it to estimate how long the stripping had occurred and thus how fast the gas was dispersing.

For item 2, we made a simple model of how streams should appear in our data. These weren't designed to be physically realistic, but to probe parameter space to see what we could detect. For a stream of any given mass and length, its detectability depends on viewing angle. If we're looking at its longest axis, so that its length on the sky is exactly equivalent to its true length, then its flux will be spread out to the maximum extent across the sky. This means the flux per spatial pixel is reduced. But if we're looking down the stream, such that it appears to have a much smaller length, its flux is distributed over more velocity channels. So the signal to noise is greatest within a range of viewing angles, depending on its exact characteristics. The lower the mass in the stream, the smaller the range of viewing angles over which it's visible.

Using this, and given the fraction of galaxies previously known to have streams, we estimated how many streams we ought to see in the archival data (assuming the previous cases were representative). The answer was 11, for the same data cubes I'd looked at for my PhD. And for the much larger ALFALFA survey (we don't have access to that data and it would take too long to search anyway), the number was 46. During our first analysis, we'd only reported 2 and ALFALFA only 5, so clearly there was a big discrepancy here.

The answer to item 3 turned out to be, "nope". For those first data cubes I'd looked at and so insistently proclaimed that there were no streams present, I was expecting any streams to be big, obvious features. You wouldn't need any special viewing technique, you'd just see them straight away. But actually, the method used does matter, a lot, - at least if you're looking for short, faint features. And lo and behold. contour plots and isosurfaces revealed that many of the galaxies showed distinct (if short) extensions that we'd never have seen otherwise.

Admittedly many of these are faint, and consequently we spent a lot of time proving their validity. The way we did this was to find empty regions in our data and inject them with fake galaxies with extensions. We took 100 blank, adorable little cubelets from our data and added galaxies into all of them, randomly varying the existence and characteristics (length, brightness, orientation) of the stream. Then we searched these, not knowing any of the properties, or even if a stream was present at all, until after we'd finished. This meant we could quantify how many false positives we'd expect due to the noise in the data. The answer ? None of the false positives we found were as strong or as extended as the features we'd found around real galaxies.

At least, that holds for the ten strongest streams we'd detected. We found 16 other streams we're much less confident about, and a significant fraction of those may well turn out to be spurious. But we largely ignored these in our analysis, so they don't really matter very much.

Taken all together, it now seems that we can explain the "missing stream" problem pretty well. Plugging the new numbers back into our model, we could calculate how fast the streams we see are evaporating. It's quite a narrow range (between 1 and 10 solar masses per year), but enough to explain why we see lots of short, faint streams but also a few long, massive ones. Think of a very tall waterfall. If just a trickle flows over the edge, the water will disperse and evaporate before it even hits the ground. But if there's a raging torrent, then plenty of water will make it all the way, even though some gets lost in the process - sheer mass plays an important role.

(More speculatively, I'd also suggest that the longest streams are probably more the result of tidal encounters than ram pressure stripping. Close interactions can remove gas extremely rapidly, whereas this should only be possible for ram pressure near the very centre of the cluster.)

Interestingly, one referee seemed to think we were making an astonishing, even outlandish claim. Ten streams ?!? Surely not - there are only a dozen known in the cluster. Another seemed to view it as mediocre. Only ten streams ? It's not worth this much effort, chaps.

The truth is somewhere in the middle. Ten streams in an area of about 10% of the cluster means we can expect of order 100 streams in total. When we eventually have that data, we might be able to say something really interesting about how galaxies in the cluster evolve. For now, having ten streams is very nice, but they're pretty much exactly what we expect to find, so it shouldn't come as a revelation. We can also say that the isolated dark clouds (that look like galaxies and are usually claimed to be tidal debris) probably don't originate from any of the streams we've detected, which is interesting. Mainly we've solved a problem that hardly anyone else was bothered by but I personally found quite annoying, so I for one am satisfied for a while. Happy Rhysy FTW !

Faint and fading tails : the fate of stripped HI gas in Virgo cluster galaxies

Although many galaxies in the Virgo cluster are known to have lost significant amounts of HI gas, only about a dozen features are known where the HI extends significantly outside its parent galaxy. Previous numerical simulations have predicted that HI removed by ram pressure stripping should have column densities far in excess of the sensitivity limits of observational surveys.

Goldilocks And The Three Ghosts

On the 23rd December 2019 I received a particularly nice early Christmas present : confirmation that my paper had, at long last, been accepted. We submitted it on 18th October 2018 and it went through three(!) reviewers before it was finally accepted, so this was much, much more of a saga than I was expecting. Whether it's more like Goldilocks And The Three Reviewers, or of a visitation of the three ghosts of Christmas, I'm not sure. It's probably best told as a mash-up of the two.

Challenge accepted. Here goes.


Once upon a time, there was a nice little blonde astronomer named Goldilocks who noticed some interesting things in his data that he hadn't noticed before. He decided to write a paper about it.

"Ho hum !", he said to himself. "This should be an easy little write-up, and then I can do something else."

But then he found that there was a weird pattern in his data that didn't make much sense. He decided to run a public poll to make sure he hadn't gone mad. He got about a hundred responses on the so-called "ghost town" that was Google Plus, and everyone agreed that the findings were correct. So he thought about it very carefully and realised that it was probably just an interesting but not terribly unlikely coincidence. He wrote up his paper and sent it to his co-authors for comments. As no-one had much to add, he submitted it to a journal and slept soundly, thinking it should not be a terribly controversial discovery.

That night he awoke with a start. A chill air filled the room and there was a most terrible wailing. Suddenly a ghastly phantom rose from the floorboards and cried,
"Rhyyyyy.... I mean, Gooolldddiiiiiloooooocks ! You shall be visited by three ghostly reviewers to inspect your paaaapppeeerrrr !"
"But why ?", cried Goldilocks. "It's nothing special. I mean, it's nice enough, but it's just some galaxies with stripped tails of gas that are pretty much exactly what we expected to find. Come on, galaxies in the Virgo cluster, losing gas exactly as predicted ? Fun, but hardly a revelation. The only real oddity is the way the streams are pointing, but we've explained that well enough. Why should it need three reviewers ?"
"I doooon't knoooooooow !" wailed the phantom. "They just woooooon't belieeeeeeeve yoooooou ! Expect the first ghost quite soooooon !".

A few weeks later Goldilocks again awoke to the clanking of chains and a mysterious wailing. Creeping downstairs, he found a middle-aged man lounging on his sofa and throwing popcorn at his TV in a carefree fashion.

"Yo," said the man, "Someone's been sleeping in MY bed... ! I'm the Daddy Ghost of Utter Pointlessness. Here's yer report." And with that he vanished.

Goldilocks picked up the report and read it carefully. It was quite long, but it didn't seem too bad at first. It was pretty darn clear that the Ghost really just wanted extra citations to their own papers and didn't understand some very basic concepts from radio astronomy. That was a bit worrying, but easy enough to address. It also came with the dreaded task of "shorten the text", which was, as usual, quite meaningless as it came with no further instructions. "Too many notes", tutted Goldilocks to himself. "But everyone says that, so it's not much to worry about".

More reassuringly, the Ghost didn't ask for anything drastic or express any major scientific skepticism, and the requests to make things "more convincing" seemed quite reasonable : clarifying the improved sensitivity from the new analysis, more labels on figures, that kind of thing. It made sense that one might be a bit skeptical about detecting this many new gas streams, even knowing that the cluster was exactly the environment where one should expect such features, since they were somewhat on the faint side.

Goldilocks did as the seemingly sensible (if rather ignorant and uninformed), Ghost suggested and duly returned the paper. Before long, the Ghost came back with a new report and vanished once more, feeling even less inclined to discourse than the last time.

Goldilocks eagerly read the report and immediately fell into despondency. This wasn't so much pointless as it was downright rude. He'd carefully addressed all the points from the first report and explained things at length in the accompanying letter. Yet the Ghost's report was barely a single paragraph and, worst of all, insisted that Goldilocks hadn't done what was asked. Even on those points that were really simple, like asking for a number which was now very clearly highlighted in bold. And the Ghost had asked for more explanation on the improved sensitivity, while Goldilocks had explained several times that sensitivity wasn't the issue, it was about visualisation. Of course he'd explained the procedure in more detail as well, just to make sure, but the Ghost either just didn't get it or was being deliberately obtuse.

"What on Earth am I to do," said Goldilocks to the co-authors, "when someone asks me what the number is, I tell them 'it's six, six is the number, and the number shall be six' and they insist that I haven't told them what the number is ?"

Goldilocks was both cross and confused. The Ghost's response was hopelessly inconsistent. Whereas before the Ghost seemed a bit concerned if the admittedly quite faint tails were real, now they were wondering if they could have been produced by something other than ram pressure stripping. That was something they easily could have pointed out at the first stage, and adding it now really felt like being strung along. And the Ghost made a bizarre claim that one source, already firmly established in the literature through several other independent observations, was only "probably" real. This was a bit like saying it bricks would only "probably" hurt if you dropped them on your toe. It was pointless.

Goldilocks couldn't see the point of answering a referee report knowing that they might just ignore everything and shift the goalposts again. Especially since they insisted the paper was now longer when it was objectively shorter.

"FFS", said Goldilocks to himself.

After consulting the co-authors, Goldilocks decided to ask the editor what to do. He was a bit disappointed that the editor hadn't already intervened, because the problems with the Ghost's response weren't subtle. They were, in fact, glaringly obvious, and he'd seen editors intervene by themselves in the past with things less blatant than this. Goldilocks complained that addressing this new response wouldn't work, since the referee was so inconsistent and asked for things which were already done and stated very clearly indeed in the main text. Trying to address things raised by someone who would simply ignore you no matter how clearly you stated things was indeed Utterly Pointless.

The editor thought for a while and declared, "Hum ! So, this porridge is a bit hot, is it ? We'll see if we can find some that's a bit cooler". And with that Goldilocks waited for a brand new Ghost.

Some time later Goldilocks again awoke to hear a low moaning. This time there was a slightly older matronly figure sitting in a more dignified position and wearing a monocle. "WoooOOooo !", said she. "Behold, I am the Mummy Ghost of Undue Skepticism. Read my report, mortal, if you dare !". She shook her fist in a dramatic fashion and disappeared.

Goldilocks read the report with some trepidation, but was soon confident he knew what to do. The report wasn't without problems. This Ghost was asking for a figure to be both improved and removed, which was very confusing. However, they were very explicit about their main concerns, which made them a lot easier to address. First, they were worried that some of the streams might not be due to ram pressure stripping. Goldilocks was fine with that, he'd never thought that the situation would be otherwise. Making this clearer was no problem. Second, the Ghost wasn't sure all the streams were even real. That wasn't too big of a deal either, as it was quite straightforward to give their statistical significance and predict how many false streams should be expected in a data set this large (the answer, it turned out, was a healthy zero).

The other referees' comments being minor, Goldilocks soon found a way to measure the statistical significance objectively and clarify that the streams might have multiple formation mechanisms. He didn't really understand why anyone would be hung up on these points though, as it was hardly a breakthrough discovery and plenty of other much stupider papers were floating around in the literature. Surely, he thought, the results are at least solid enough that the rest of the community deserved a look at them. "And anyway," he said to himself, "it's well-known that if you provide enough details to recreate your results, which I bugger well have, it isn't necessary that the referee actually has to agree with your conclusions. They shouldn't reject it unless they can actually find a flaw in the analysis, or better yet they should correct it."

So Goldilocks sent off the report feeling cautiously optimistic that this time he'd succeed. The referee certainly seemed more familiar with radio astronomy, which seemed like a good sign.

Alas ! Some considerable time later, the Ghost re-appeared. "Woe !" she cried with a banshee wail, "I remain unduly skeptical ! This porridge is too cold. Thou hast not addressed my concerns, and I reject thine paper ! May it be cast into the pits of hell !"

Goldilocks was astonished and dismayed. He read the report with contempt. The Ghost had blathered about a few points that made little or no sense, but worst of all he hadn't responded to the correction on the main point - at least, not sensibly. Instead of addressing the whole new section dedicated to assessing statistical significance, which was objective and quantitative, she'd simply said she "understood" it, but thought that "the evidence should be in the images".

This didn't sit well with Goldilocks at all. "Fair enough," he thought to himself, "an objective analysis can absolutely be wrong if the wrong procedure is used or whatnot. But surely in this case someone needs to tell me what the blazes actually is wrong with it, rather than just saying they understand it. If they really understand it, they bloomin' well ought to be able to explain why it's wrong." And he was also more than a little annoyed that they wanted "evidence in the images". All this amounted to the Ghost wanting subjective proof in place of an objective one, without saying what was wrong with the method. Goldilocks was Not Happy.

(He thought about complaining to the editor but decided it would do little good. He also noted that the Ghost claimed to remain skeptical of the "majority" of the streams, but when you added up the number of individual streams they said they were happy with, found that they came to 60% of the total.)

What to do ? Goldilocks was not as despondent as you might think. He'd been working on the analysis for well over a year already, and every time someone had come up with a reason to doubt their existence, the tests had only strengthened the case for the streams. True, two ghastly shades hadn't been convinced, but both appeared to be quite bizarre. The other co-authors were all happy with the result, all of whom were more senior and more experienced than him.

"Right," said Goldilocks. "None of the objections raised by the referees make any sense. Therefore, strange as it is, the only reasonable conclusion is that I'm right and they're wrong. I'm not going to dump more than a year of work on the scrapheap because some spectral nit doesn't understand it. I'm going to submit it to a whole new journal."

Goldilocks did, however, accept that images can often be more persuasive than numbers. So he did a whole new analysis in which he injected fake sources into real data, not only measuring the very few false positives that appeared but also making the same contour plots of them as were presented for the real streams. It was pretty effin' clear that you just didn't get false positives that looked anything like the real streams, exactly as the earlier analysis had shown. And so Goldilocks submitted the paper and once again waited.

And waited.

And waited some more.

Well, actually not really, because this time the Ghost was very prompt.

"Ahhhwoooooo !" cried the spectre. "Behold, I am the Baby Ghost of Precise Instruction ! Read my report with the utmost care and all will be well !"

"Oh spirit," said Goldilocks, "I fear you more than any ghost I have yet witnessed. Can it really be true that you are indeed the Ghost of Precise Instruction ?"

But the miniscule phantom only pointed a spectral finger at the report and disappeared.

Now you must understand that Goldilocks was in a pretty strange mental state but this point. He'd been haunted by three strange spectres all questioning his spectra, and was both quite cross and trepidatious. He didn't doubt himself, but he was highly suspicious that the Ghost would actually do their dang job properly. He read the report quite nervously, and decided to avoid reaching any conclusions, knowing that you can't judge someone until you see how they respond a second time.

Still, it looked promising. There were no clear indications that this doubt thought the porridge was too hot or too cold, only that the height of the chair was a bit off and the window needed oiling. That is, the Ghost didn't seem concerned about whether the streams were real, only that the paper was too long and didn't have a good comparison sample.

"Well, fair enough really," thought Goldilocks. "A comparison sample is a great idea, but unfortunately just not practical. Hopefully the ghost will understand this if I explain in sufficient detail."

The Ghost had, however, provided very Precise Instruction indeed when it came to shortening the manuscript. Goldilocks didn't particularly want to do this, but instructions this clear were difficult to get wrong. Best of all, by the very simple direction to "concentrate on the new results", this made it trivial to extrapolate as to which other parts could be cut. Those few words transformed a task ordinarily fraught with problems into the work of a couple of a days. Soon the paper was five pages shorter and, Goldilocks had to admit, considerably more focused.

"I'm still in two minds about it," said he, "but overall this is probably better. I liked the more detailed original version, but more people are likely to actually read this shorter document."

So Goldilocks made the remaining changes and carefully explained why they couldn't provide a comparison sample, substituting this for a literature search of similar features instead. He poked and prodded his co-authors until they finally gave the go-ahead, and then he submitted the revised paper. And very soon the Ghost returned and said "this porridge is just right !", all was well, and there was dancing in the streets.

"Hooray !" said Goldilocks. "But we've learned some valuable lessons here. First, the rules of refereeing ought to be clearly spelled out and not just left to the referee to make them up however they see fit. You can't just go around saying, 'I don't agree' without providing any justification. Second, editors ought to actively check if both sides follow the rules, and not just act as postmen. Pretty much a year of valuable research time has been wasted dealing with this crap and that needn't have happened. I'm going home."

And with that he stomped off and had a lovely Christmas. The end.

Get Off My Fundamental Plane

Or at least off my Tully-Fisher relation, which is almost the same thing. Yes, it's another case of galaxies rotating more slowly than expected given their mass, and which might not even have any dark matter at all.

The worryingly astute reader may remember that I briefly mentioned this paper back in this post last year. I didn't give it its own post then because of various problems : confusing language, poor figure labels, lack of any statement about which journal it was in, and lack of citation of a similar analysis from the same data set. Much of that is now cleared up - it's accepted in Nature Astronomy and had a press release late last year. Some figures still aren't labelled as clearly as they should and "inclination angels" wins the Typo Of The Day award, but mostly it seems in much better shape than it was. I still think they should have cited the earlier analysis, even though this is admittedly a different sample.

Previously we've seen a slew of claims that some Ultra Diffuse Galaxies (large, fluffy galaxies that are very spread out and usually quite faint) have weird dynamics. Whereas most galaxies are rotating so quickly that they should fly apart without dark matter, some UDGs are rotating exactly as their baryonic mass (that is, ordinary gas and stars) predicts. It seems that they don't need any dark matter at all, or at least, much less than other galaxies of comparable baryonic mass. One early worry was that there might be a problem correcting the inclination angles (not angels), meaning that the rotation speeds could have been underestimated, but recent data seems to make that less likely.

The galaxies in this sample are quite different. The deviant UDGs are extremely gas-rich, optically faint objects, whereas the ones in this sample are neither*. There gas content looks entirely normal compared to typical galaxies, so their star formation is - presumably - ticking over just fine. Nor are they especially faint. Indeed, their self-imposed brightness cutoff stands out quite clearly in their data, tentatively suggesting that there could be eve more massive galaxies hidden in the sample. So in essence these appear to be relatively normal galaxies chock-full of gas that's forming stars at a normal rate, but don't have nearly as much dark matter as normal galaxies (if they have any at all). And most of them aren't in groups or clusters, so interactions are probably not responsible.

* Strictly speaking we can't say if these galaxies are UDGs or not without more precise measurements of the radial stellar profile, but looking at some of the images, it's clear that they're pretty normal-looking objects.

This is getting very strange indeed. If you don't have much dark matter, feedback from stars and supernovae should make it much easier to blast apart any luckless galaxies that happened to form like that. But this hasn't happened in these cases. Why not ? The two options they suggest are either that there is an inclination angle estimation error here (if not in the other cases), so their true velocity width is actually much higher and they have dark matter after all, or that the feedback helps "flatten out" the dark matter potential during formation. So they'd still have dark matter, it would just be distributed in an unusual way.

The second option may or may not work but it would take detailed numerical studies to properly investigate (so far as I know, no such objects have shown up in existing simulations). The first option doesn't look likely either. Although they'd like to have resolved gas observations to measure the gas disc angle directly, looking at the optical images it seems very unlikely that there could be a big error in the estimated angle. They say that perhaps the presence of strong bars may have screwed things up, but again, inspecting the optical images, that doesn't seem likely either. Look, here's a few :

Those are as normal a set of galaxies that you could ever hope to meet. Except, apparently, they're just very slow.

Unfortunately they only plot the optical Tully-Fisher relation (optical brightness as a function of rotation speed). Baryonic mass would have been better, but since they're brighter than expected, there's no way including the gas mass can solve the problem.

Finally, they note that if you plot the distribution of the ratio between dynamic and baryonic matter, you get a nice Gaussian but with a tail at the low end where these galaxies live. They say this indicates they're a truly separate population rather than outliers. I'm not sure I'm convinced by that - maybe the normal population just has a non-Gaussian distribution. And in terms of their deviation from the Tully-Fisher, they look like a continuation of the general scatter, not outliers. But it's an interesting thing to plot even so.

So what's going on here ? Damned if I know. Apparently some otherwise normal galaxies just don't have any dark matter. How many more objects like this could there be ? Well, their main sample was 324 objects, of which 19 are weirdos, so 6%. That used the now-obsolete 40% ALFALFA catalogue. From the 100% catalogue size, that's about 1,850 objects - possibly more due to their brightness limit. As for such deviants affect MOND, which predicts a low scatter in the TFR, I've no idea, though I assume it wouldn't be good news given that most of these objects are quite isolated.

Spare a thought for poor van Dokkum, who had to face a barrage of skepticism over the claimed distance to his "original" galaxy without dark matter. That may be a concern for some of the objects here, but not all of them - they're just too far away for there distance to be drastically over-estimated. So regardless of whether van Dokkum's original claim stands up, it really does seem as though there's a population of very strange objects out there. Fun times !

EDIT : A very short rebuttal paper claims that it is all due to inclination angle after all, essentially saying that the galaxies could simply be not circular - i.e. they might be close to face-on, just not-disc shaped (as is quite usual for dwarf galaxies). I'm not convinced by this. No dwarf I ever plotted in the TFR showed any deviation like this, and I didn't correct for their shape either. Nor are these particularly low-mass dwarfs, and again, there seems to be cut-off in mass that's purely an arbitrary choice, hinting at more massive objects. And looking at the images, it just doesn't feel right - if this was the explanation, we ought to have heard previous similar claims, and to my knowledge we never have. Finally, the claim that the sample is biased because of their large axial ratios doesn't make any sense to me, since the authors specify they deliberately chose the sample in this way (since this is a necessary criteria for edge-on galaxies). Still, I could be persuaded with a longer paper : show me some comparable objects and simulations showing that such objects would be stable.

EDIT 2 : And because these are big, bright objects, whether they are rotating or not would be relatively easy to test. High resolution HI observations or spectroscopy with an IFU ought to give a definitive answer with little or no wriggle room.

Further evidence for a population of dark-matter-deficient dwarf galaxies

In the standard cosmological model, dark matter drives the structure formation of galaxies and constructs potential wells within which galaxies may form. The baryon fraction in dark halos can reach the Universal value (15.7%) in massive clusters and decreases rapidly as the mass of the system decreases 1,2 .

Things are getting CHILE

The COSMOS HI Large Extragalactic Survey is an ambitious, 1000-hour VLA project to map the HI content in a bunch of galaxies at relatively high redshift (~0.4). Here they present some preliminary results from 178 hours of observing ten galaxies at a more modest redshift of 0.1 (a distance of about 430 Mpc, or a travel time of 1.2 Gyr at the speed of light). That's still impressive for HI studies, only a few of which have ever probed distances this large.

Although the abstract makes something of a song and dance about how the HI is aligned with filaments in the cosmic web, and even the title of the paper mentions this, in fact there's very little about this in the paper at all. And since they only have ten galaxies, I'm going to entirely discard their "main" result here.

In fairness, the authors say themselves, "any of the relations shown should be considered only a hint of a trend at most". This is very much a preliminary paper, but it does show some interesting possibilities for the future. Although they only have ten galaxies, they've also (don't ask me how) determined the large-scale structure of many other galaxies, i.e. the 3D geometry of the cosmic web. That means they can plot the properties of their sample as a function of true filamentary distance. Normally everyone uses projected distance, which assumes that any two objects are at the same distance from us and then just measures their distance across the sky as a proxy for their separation. Using true distance is obviously better, although just how accurate this I'm not at all sure.

But let's assume that it's fine. What do they find ?

Quite a few things. But not as much as they might, because they select their sample not only by HI detection but also Halpha (which traces star formation activity). So although they potentially had 33 galaxies to study, they limit themselves to 10. It would have been nice to use the rest for the HI-only trends, but oh well.

Anyway, even though they're only sensitive to dense gas, most galaxies in their sample show lopsidedness. They also have weird-looking spectra, including one with a triple peak instead of the usual double-horn (Batman-shaped) profile. They don't comment too much on this, though they may be signatures of interactions.

More interesting are the possible large-scale trends. There doesn't appear to be any relation at all between stellar mass and gas loss, but it looks to me that galaxies closer to the filament have lost less gas and may even be gas-rich. The authors disagree though, saying there's no trend, and admittedly this appearance is dominated by a single, weirdly gas-rich galaxy. It's still odd if you ask me.

On the other hand, HI mass quite clearly decreases with distance to the filament. Absolute mass is a tricky quantity, mind, and it probably would have been a good idea to also plot stellar mass. There seems to be hint that specific star formation rate (that's s.f.r. per unit mass, useful to correct for the fact that bigger galaxies tend to have more gas to form stars simply just because big things are bigger) increases closer to the filaments. Gas fraction shows no evidence of any trends at all.

This is a nice way to illustrate how difficult it is to interpret the results. Other studies have variously found evidence of gas depletion or enhancement within filaments. It may also depend on whether you look at the gas fraction of individual galaxies as opposed to the fraction of galaxies which have gas detections at all. If instead you plot distance not from filament but from nearest neighbour, things get different again, with the trends changing considerably (they say they are no obvious relations at all - I'm not sure about that, but with ten galaxies... well...).

Finally, they note that galaxies tend to have a constant gas density, which agrees well with previous claims. There's no obvious trend in any deviation from the Tully-Fisher relation either, although one interesting object does look at though it might be rotating too slowly.

This is all very inconclusive. It does demonstrate the potential of the full survey quite well, but I would have liked it more if they'd used their full HI sample where possible. It's a nice enough analysis, but the final result is very definitely "watch this space".

CHILES VI: HI and H${\alpha}$ Observations for z < 0.1 Galaxies; Probing HI Spin Alignment with Filaments in the Cosmic Web

We present neutral hydrogen (HI) and ionized hydrogen (H${\alpha}$) observations of ten galaxies out to a redshift of 0.1. The HI observations are from the first epoch (178 hours) of the COSMOS HI Large Extragalactic Survey (CHILES). Our sample is HI biased and consists of ten late-type galaxies with HI masses that range from $1.8\times10^{7}$ M$_{\odot}$ to $1.1\times10^{10}$ M$_{\odot}$.