The selection effect at work with inclination is a little complicated, but it's worth being aware of. Suppose that we have a galaxy with a given mass of hydrogen. The signal to noise of the hydrogen signal will be given by the mass, rotation speed, and viewing angle. If the viewing angle is face-on, then the S/N will be highest because all the gas will be moving at the same velocity relative to us. If it's edge-on, then the S/N will be lowest because the galaxy is rotating, spreading out the hydrogen flux into multiple frequencies. So we will preferentially detect face-on galaxies if we look for them using hydrogen.
For optical wavelengths it should be the opposite. If they're face on, then their optical light is spread out over the largest possible area, minimising the S/N. If they're edge-on, then we're seeing all their stars compressed into the smallest area, maximising the S/N. So edge-on galaxies should be easy to detect in the optical but difficult using hydrogen. In reality it will be a bit more complicated than that : a large, faint thing may be easier (in some circumstances) to detect than a small faint thing, but as a general guideline it's reasonable.
The other complication is that surface brightness (i.e. no. stars per unit area on the sky) has to be corrected. You can't just measure it directly off the sky unless the galaxy is face-on. So correcting this when the galaxy is edge-on, and has all sorts of internal extinction effects (e.g. absorption by dust and gas), is tricky - but possible.
The first attempt to find UDGs in an HI catalogue looked at isolated objects and didn't particularly concern itself with viewing angles. These authors take the exact opposite approach, but still find that their galaxies are primarily in low density environments. That's not too surprising, since in a higher density environments there are effects which can trigger star formation that consumes the gas and/or directly remove the gas.
What I don't understand is their selection criteria. For the optical data they use SDSS DR7, but we're now on DR15. For the HI data they use the ALFALFA 40% complete catalogue, but the 100% complete has been out for months and the 70% one for ages and ages. Then - I think - they do surface brightness profile measurements to find objects with similar shapes to UDGs, although this isn't clear to me. Even the 40% catalogue has over 10,000 members so doing this in an automatic way is tough. So I don't understand how, but somehow they reduce this down to a catalogue off 11 candidate edge-on UDGs, after correcting the surface brightness for inclination. I found this section to be a bit odd and not at all clear as to what they did or how and why they did it.
Regardless, they find that their galaxies look relatively normal. They're very blue, edge-on discs, but nothing extraordinary. That suggests to me that there could be large numbers still undetected. They are, however, extremely gas rich, with HI mass-to-light ratios of between 5 and 30. So their mass really is dominated by gas, strongly suggestive of low star formation efficiency. Their most interesting plot shows that in color-magnitude space, UDGs found in isolation and those found in groups occupy distinctly different regions of parameter space, consistent with the idea that they could be formed by different mechanisms.
What about the all important dynamics ? Amazingly they say little about this - I don't know why people keep doing that. But their HI spectra look quite normal : broad velocity widths with double-horn shapes. Line widths are not extraordinarily high though, with a maximum of 150 km/s. That's in the upper range for dwarfs, but definitely not giants. I did a quick inspection of the Tully-Fisher relation, and their line widths and gas masses are, unlike some other UDGs, consistent with normal galaxies. That lends some credence to the idea that UDGs with unexpectedly low line widths are the result of a selection effect and their inclination angle hasn't been corrected properly. On the other hand, since they were here looking for edge-on galaxies, then they might have excluded those with low line widths by definition.
Overall, the general view that UDGs are mostly dwarves looks to be consolidating its position. It's still too early to say if this is true for all of them though, and the difference between UDGs in low and high density environments has yet to be explained.
Edge-on HI-bearing ultra diffuse galaxy candidates in the 40% ALFALFA catalog
Ultra-diffuse galaxies (UDGs) are objects which have very extended morphology and faint central surface brightness. Most UDGs are discovered in galaxy clusters and groups, but also some are found in low density environments. The diffuse morphology and faint surface brightness make them difficult to distinguish from the sky background.
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