A long standing problem in cosmology is that we do not have a full accounting of all the baryons that we believe to exist. Big Bang Nucleosynthesis (BBN) teaches us that the mass density in normal matter is Ω_b ≈ 5%. One can put a more precise number on it, but that’s close enough for our purposes here.

Ordinary matter fails to account for the closure density by over an order of magnitude. To make matters worse, if we attempt an accounting of where these baryons are, we again fall short. As well as the dynamical missing mass problem, we also have a missing baryon problem.

For a long time, this was also an order of magnitude problem. The stars and gas we could most readily see added up to < 1%, well short of even 5%. More recent work has shown that many, but not all, of the missing baryons are in the intergalactic medium (IGM).  The IGM is incredibly diffuse – a better vacuum than we can make in the laboratory by many orders of magnitude – but it is also very, very, very, well, very big. So all that nothing does add up to a bit of something.

A thorough accounting has been made by Shull et al. (2012). A little over half of detected baryons reside in the IGM, in either the Lyman alpha forest (Ly a in the pie chart above) or in the so-called warm-hot intergalactic medium (WHIM). There are also issues of double-counting, which Shull has taken care to avoid.

Gravitationally bound objects like galaxies and clusters of galaxies contain a minority of the baryons. Stars and cold (HI) gas in galaxies are small wedges of the pie, hence the large problem we initially had. Gas in the vicinity of galaxies (CGM) and in the intracluster medium of clusters of galaxies (ICM) also matter. Indeed, in the most massive clusters, the ICM outweighs all the stars in the galaxies there. This situation reverses as we look at lower mass groups. Rich clusters dominated by the ICM are rare; objects like our own Local Group are more typical. There’s no lack of circum-galactic gas (CGM), but it does not obviously outweigh the stars around L* galaxies.

There are of course uncertainties, so one can bicker and argue about the relative size of each slice of the pie. Even so, it remains hard to make their sum add up to 5% of the closure density. It appears that ~30% of the baryons that we believe to exist from BBN are still unaccounted for in the local universe.

The pie diagram only illustrates the integrated totals. For a long time I have been concerned about the baryon budget in individual objects. In essence, each dark matter halo should start with a cosmically equal share of baryons and dark matter. Yet in most objects, the ratio of baryons to total mass falls well short of the cosmic baryon fraction.

The value of the cosmic baryon fraction is well constrained by a variety of data, especially the cosmic microwave background. The number we persistently get is

f_b = Ω_b/Ω_m = 0.17

or maybe 0.16, depending on which CMB analysis you consult.  But it isn’t 0.14 nor 0.10 nor 0.01. For sticklers, note that this the fraction of the total gravitating mass in baryons, not the ratio of baryons to dark matter: Ω_m includes both. For numerologists, note that within the small formal uncertainties, 1/f_b = 2π.

This was known long before the CMB experiments provided constraints that mattered. Indeed, one of the key findings that led us to repudiate standard SCDM in favor of ΛCDM was the recognition that clusters of galaxies had too many baryons for their dynamical mass. We could measure the baryon fraction in clusters. If we believe that these are big enough chunks of the universe to be representative of the whole, and we also believe BBN, then we are forced to conclude that Ω_m ≈ 0.3.

Why stop with clusters? One can do this accounting in every gravitationally bound object. The null hypothesis is that every object should be composed of the universal composition, roughly 1 part baryons for every 5 parts dark matter. This almost works in rich clusters of galaxies. It fails in small clusters and groups of galaxies, and gets worse as you examine progressively smaller systems. So: not only are we missing baryons in the cosmic sum, there are some missing in each individual object.

The figure shows the ratio of detected baryons to those expected in individual systems. I show the data I compiled in McGaugh et al. (2010), omitting the tiniest dwarfs for which the baryon content becomes imperceptible on a linear scale. By detected baryons I mean all those seen to exist in the form of stars or gas in each system (M_b = M_*+M_g), such that

f_d = M_b/(f_bM_vir)

where M_vir is the total mass of each object. This `virial’ mass is a rather uncertain quantity, but in this plot it can only slide the data up and down a little bit. The take-away is that not a single, gravitationally bound object appears to contain its fair share of cosmic baryons. There is a missing baryon problem not just globally, but in each and every object.

This halo-by-halo missing baryon problem is least severe in the most massive systems, rich clusters. Indeed, the baryon fraction of clusters is a rising function of radius, so a case could be made that the observations simply don’t reach far enough out to encompass a fair total. This point has been debated at great length in the literature, and I have little to add to it, except to observe that rich clusters are perhaps like horseshoes – close enough.

Irrespective of whether we consider the most massive clusters to be close enough to the cosmic baryon fraction or not, no other system comes close to close enough. There is already a clear discrepancy among smaller clusters, and an apparent trend with mass. This trend continues smoothly and continuously over many decades in baryonic mass through groups, then individual L* galaxies, and on to the tiniest dwarfs.

A respectively massive galaxy like the Milky Way has many tens of billions of solar masses in form of stars, and another ten billion or so in the form of cold gas. Yet this huge mass represents only a 1/4 or so of the baryons that should reside in the halo of the Milky Way. As we look at progressively smaller galaxies, the detected baryon fraction decreases further. For a galaxy with a mere few hundred million stars, f_d ≈ 6%. It drops below 1% for M_* < 10⁷ solar masses.

That’s a lot of missing baryons. In the case of the Milky Way, all those stars and cold gas are within a radius of 20 kpc. The dark matter halo extends out to at least 150 kpc. So there is plenty of space in which the missing baryons might lurk in some tenuous form. But they have to remain pretty well hidden. Joel Bregman has spent a fair amount of his career searching for such baryonic reservoirs. While there is certainly some material out there, it does not appear to add up to be enough.

It is still harder to see this working in smaller galaxies. The discrepancy that is a factor of a few in the Milky Way grows to an order of magnitude and more in dwarfs. A common hypothesis is that these baryons do indeed lurk there, probably in a tenuous, hot gas. If so, direct searches have yet to see them. Another common idea is that the baryons get expelled entirely from the small potential wells of dwarf galaxy dark matter halos, driven by winds powered by supernovae. It that were the case, I’d expect to see a break at a critical mass where the potential well was or wasn’t deep enough to prevent this. If there is any indication of this, it is at still lower mass than shown above, and begs the question as to where those baryons are now.

So we don’t have a single missing mass problem in cosmology. We have at least two. One is the need for non-baryonic dark matter. The other is the need for unseen normal matter: dark baryons. This latter problem has at least two flavors. One is that the global sum of baryons comes up short. The other is that each and every individual gravitationally bound object comes up short in the number of baryons it should have.

An obvious question is whether accounting for the missing baryons in individual objects helps with the global problem. The wedges in the pie chart represent what is seen, not what goes unseen. Or do they? The CGM is the hot gas around galaxies, the favored hiding place for the object-by-object missing baryon problem.

Never mind the potential for double counting. Lets amp up the stars wedge by the unseen baryons indicated in red in the figure above. Just take for granted, for the moment, that these baryons are there in some form, associated in the proper ratio. We can then reevaluate the integrated sum and… still come up well short.

Low mass galaxies appear to have lots of missing baryons. But they are low mass. Even when we boost their mass in this way, they still contribute little to the integral.

This is a serious problem. Is it hopeless? No. Is it easily solved? No. At a minimum, it means we have at least two flavors of dark matter: non-baryonic [cosmic] dark matter, and dark baryons.

Does this confuse things immensely? Oh my yes.