Probably not. As previously suggested, it could all be due to the way the data was processed. Over such a large area as Virgo, few are brave enough to attempt a search by eye, and automatic algorithms are very sensitive to their input parameters. Typically they return initial catalogues of the order of millions of objects, which have to be carefully culled down to a few hundred or thousand objects that can be examined the old-fashioned way. And even slight differences in the way the data was processed, which might not make any difference at all to the brighter galaxies, can cause big changes in how many UDG candidates pop out.
This paper searches the previously UDG-free data from the Next Generation Virgo Survey (the most sensitive large-scale optical survey of the cluster to date) and produces a catalogue of up to 70 objects. Oddly, they don't mention any special data processing, so why previous searches of this same data set have come up empty (if I recall correctly, only three UDGs were hitherto known in Virgo) is anyone's guess.
The broad definition of a UDG, which became widely accepted very quickly, is that it's large and faint. These two parameters are relatively easy to measure (but see this) but the authors decide they need a better definition since there isn't a good physical motivation for the conventional criteria. So, annoyingly, they come up with a more physical but far more complex selection criterion that a UDG is anything which deviates by more than two sigma from no less than three non-linear scaling relations. Yikes.
This isn't as mad as it sounds. As clear from their plot, the conventional definition would miss quite a lot of really interesting objects - specifically the largest ones. But it's awkward, and it doesn't help that their plot has an extremely strange vertical stretch. I don't see this catching on, and for smaller objects it doesn't appear to make much difference anyway.
One point that's probably worth mentioning, though, is that choosing objects which are in the tail-end of a distribution does not necessarily mean that those objects are simply more extreme versions of the general population : that would be a statistical bias. It's possible to populate parameter space with objects that form by very different mechanisms, so that the distribution is continuous isn't evidence in itself that the objects are all part of the same population.
Most of the rest of the paper is a tedious slog-through all the possible analysis using rather small number statistics. Great for the enthusiast, no doubt, but not exactly thrilling bedtime reading. Also their thumbnail images (figure 6), while very nice, look extremely red, which seems just a bit odd.
They find two quite interesting things. First, the core of the cluster has more UDGs than elsewhere, in contradiction to other surveys which find that UDGs are not clustered. How this compares with the overall galaxy density they don't say, so I wonder how big a deal this really is. And is it telling us something about the nature of the UDGs or their environment ? The statistics are just too small to say anything. Second, all the globular clusters of the UDGs are redder than globular clusters around non-UDGs of the same stellar mass. Why that should be is anyone's guess.
Overall, they conclude as others have that UDGs likely form by a variety of mechanisms. They seem to occupy the tails of various distributions, suggesting they're normal but extremely faint galaxies. There really doesn't seem to be anything much at all to distinguish them from other galaxies except that they're faint for their size. Potentially this is extremely interesting, but without proper dynamical measurements the key feature - how much dark matter they have - will have to wait. Some of them are definitely tidally interacting, so it's possible that this is part of their formation mechanism in at least some cases, but it seems they don't think this is likely to explain the majority.
In short, Virgo does have UDGs after all, but how they form remains pretty much as mysterious as ever.
The Next Generation Virgo Cluster Survey (NGVS). XXX. Ultra-Diffuse Galaxies and their Globular Cluster Systems
We present a study of ultra-diffuse galaxies (UDGs) in the Virgo Cluster based on deep imaging from the Next Generation Virgo Cluster Survey (NGVS). Applying a new definition for the UDG class based on galaxy scaling relations, we define samples of 44 and 26 UDGs using expansive and restrictive selection criteria, respectively.
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