Cold clouds for missing mass?

I like to go to the Cosmology Journal Club when I can. They discuss papers (mostly the profs talking, I notice) that are in the news. Somebody reads it and presents a summary and attempts to field questions about it (but since he’s not the author, "I don’t know" is a legitimate answer). (I sit quietly at the side and listen and try to figure out what they're talking about.)

This week they finally discussed Do the Herschel cold clouds in the Galactic halo embody its dark matter?. I read the article and sensed some plausibility, but I couldn’t tell if the methods the authors were using were appropriate.

The idea is simple: there are clouds of something emitting light at about 250microns wavelength, which implies (very) cold temperatures, in the view when the Herschel-SPIRE system tried to look at the Magellanic Clouds. Careful analysis shows that they're actually in our galaxy, and a study of their angular sizes suggests a simple distribution radius from the center of the galaxy. We haven't seen things like this before because we haven’t had the instruments to look for such cold clouds.

If they are in fact distributed spherically about the galaxy and if the clouds have about 15,000 times the mass of the Sun then the amount of cold matter is enough to account for the previously unseen mass in our galaxy. An astrophysicist almost a hundred years ago predicted that gas clouds would spontaneously tend to break up into clumps of about 40,000 solar masses, which is comparable to what would be needed here. So maybe the missing matter is solved: Do we need dark matter theories?

Well, the devil is in the details. (I thank the Journal Club for the details; I didn't know any of this except that he was guessing about the mass.)

For starters, the Herschel-SPIRE system looked in a few other directions, and at several other wavelengths—and none of that appears here. Maybe it is too early, since it takes time to do the studies, or maybe he wants that study to be an independent analysis

The astute reader will have noticed that the mass is a guess. The equations in the paper have the proper scale factor in there, but that scale factor can be pretty much anything less than 1—there is no proof that the clouds are anything like that massive.

UPDATE from comments:

He figured out what average mass the clouds needed to completely account for missing mass, and called it M (actually with a bar over the top but I can't do that easily in html). Then in the equations describing galactic gravitation he wrote c*M. "c" is the scale factor here. He doesn't know the real mass of the clouds, which I'll call "m". You can always find "c" so that m=cM (c=m/M). That's the scale factor here; instead of using "m" (the real-but-unknown mass) he uses "c*M" (an unknown fraction of his favorite guess for the mass).

We know the clouds aren't going to be more massive than M--by construction that would make the galaxy too massive. So c<=1. And they aren't empty, so c>0. But whether they mass fifteen thousand suns or a sand-box worth isn't obvious. It is legitimate to do such mathematical maneuvering if you're trying to illustrate some important connections. Unfortunately his important connection is purely hypothetical.

Another question that arose was what the clouds are supposed to be made of: cold gas isn’t going to radiate; you need dust.

UPDATE from comments:
One of the profs reminded us that cold gas won't be ionized, and neutral atoms only absorb and radiate in particular characteristic wavelengths. Only much more complicated (dust-sized) particles can radiate in a spectrum when they're that cold.

Another question is when such clouds form. If after the transition from which we get the cosmic microwave background (when the universe cooled enough to turn transparent to light(*)), then there are some technical questions about how uniform the gas can be, since structures are already starting to coalesce.

In the main author's pet theory the Jeans clouds should further condense into clouds with embedded "micro brown dwarfs" of about Earth's mass, consisting of about 14 degree blobs of hydrogen at nearly the triple point (solid, liquid, and gas happily coexisting). (They’d be too small to search for with "microlensing", since the radius at which their gravity would cause interesting curvature of distant stars would actually be inside the liquid blob. So you’d not see any strange "jumps" when a star passed near one.)

The upshot: interesting observation, but the model proposed has problems and isn’t near explaining the missing matter problem.

(*) When you have a dense plasma, light doesn’t go very far. Only when things cool down enough so that nuclei get their full complement of electrons, and neutral atoms form, does light get a chance to shine.