In the Milky Way, dispersion measures to pulsars have been used to map distribution of ionized gas.  Dispersion measure is the frequency-dependent time lag relative to the speed of light it takes radiation to propagate through a plasma.  This lag is proportional to the total column of electrons along the sightline and, hence,  constrains the distribution of baryons to the source.  Measuring dispersion measures to extragalactic sources would be at least as interesting as these measurements have been in the Milky Way, constraining the cosmic distribution of baryons, but this would require a very bright transient source.

In 2013, a population of bursts that appears to be extragalactic was  (re)discovered, fast radio bursts (FRBs).  Motivated by this development, I wrote a paper on how extragalactic dispersion measure estimates could be used to constrain the distribution of matter in the low-redshift intergalactic medium.  The top-left plot shows the probability distribution of dispersions (electron columns) along different sightlines to z=1 for different toy models for how the cosmic barons are distributed (as well as a cosmological simulation).  Most of the variance in dispersion measures comes from striking the dense CGM around galaxies.  Indeed, to z=1, a sightline on average goes within the virial radius of one >10^13 Msun halo and several 10^12, making the variance a potentially interesting probe of the extent of the CGM.  (It is also a source of noise for the many papers trying to constrain cosmology from using FRB DM.)  Unlike other probes, which typically are the columns in various ions, it is sensitive to electron column and so would be very interesting.  A stacking analysis would also not be biased by the electron column in the host system and  galaxy.  There are observational efforts trying to do just this as we are entering the era of mass FRBs.

Jumping to 2020, I was involved in the first study that could really constrain models.  The plot in the right middle shows a now-famous plot of the Macquart relation, named after the study's first author and a leader in the field of FRBs (who passed away soon after this study was published).  The scatter in this relation constrains CGM models.  The different points are the sample of localized FRBs, most with the ASKAP telescope.

Now in 2022, graduate student Xiaohan Wu led a stacking analysis using the 500 published CHIME FRBs to constrain the CGM density profile of halos.  While the constraints are not yet amazing, these are really the only way to constrain these Galactic halo mass scales (shown is 10^11-10^12, but we present a similar measurement at 10^12-10^13 Msun).  With better localizations than CHIME, such a stack would yield much tighter constraints.  The future of this is exciting and should ultimately provide a precise measurement of the CGM profile at these halo masses!

There have been few detections of emission from the low-z CGM far from galaxies.  This is going to change.  CGM line emission is one of the frontiers in this field, with both satellites being designed and with sensitive IFUs on large optical telescopes coming online.   Starting in 2021, I have been involved in an effort led by University of Washington Prof. Sarah Tuttle to launch a CubeSat targeting diffuse line emission from the CGM.  In the process of helping to design the specs for this satellite, I became unsatisfied with the scientific literature on this topic.  Even a basic understanding for what intensity might be expected in various lines was largely missing.  In a study led by two undergrads in my group, Daniel Piacetelli and Erik Solhaug, we filled in some of these important details.  Our study provides a physical understanding of sets the amount of CGM emission in all important lines and, hence, what emission at a certain level would indicate about the CGM.  

HST/COS observations of the circumgalactic medium (CGM) around Milky Way size galaxies are extremely interesting.  They show large OVI columns out to ~150 kpc and broad line widths.  In addition, each sightline intersects approximately one cloud with velocity offsets with respect to the host galaxy of a couple hundred km/s. The figure below highlights some of the most important (baffling) observational results from the `COS-Halos’ collaboration.  

Collaborating with Prof. Jess Werk, we tried to explain this phenomenology.   First, we argued that the bulk of the OVI has to be diffuse collisionally ionized gas that occupies the bulk of the halo -- it is not a boundary layer, a shock, or photoionized gas as some had surmised.  Then, we showed that a substantial fraction of the galactic feedback energetics, >10%, must be going into supporting the gas cooling through the OVI phase. Arguing the OVI arises from cooling gas, we showed that the amount of gas that must be participating in cooling is large, of order the closure baryon fraction.   We further argued that to explain the broad lines and their velocity offsets requires turbulently entrained hot gas and coherent ~100 km/s sloshing motions on the scale of the halo.

The part of our paper that I think may be most interesting (but that has also been the most ignored) is the last part where we tried to estimate the density of the colder photoionized halo clouds seen in absorption from lower ionization state metals.  Previous analyses found the density of these colder clouds to be exceedingly low, 10-100 times smaller than the expected density if in pressure equilibrium with the hot halo gas (adopting standard models for this component).  For these constraints, people constructed slab photoionization models that assumed ionization and thermal equilibrium (using some uniform ionizing background model to model photoionization).  These models can then be used to infer the density and metallicity by matching to observations of the ionic columns for each CGM absorption system.  This modeling makes a fair number of assumptions, which perhaps is the reason for the extreme densities found.  

We were able to derive an essentially model-independent upper limit on the density for CGM absorption systems using the HI columns as well as the columns in twice ionized nitrogen silicon or carbon.  It turns out that COS detects quite large columns in each of these ions (and, for many systems, these large columns are driving the low densities inferred).  If one assumes all the carbon is in the twice ionized phase, to place an upper bound, then the metal column scales with density (and metallicity).  Meanwhile the HI column scales as density squared, and the scaling constant -- the HI photoionization rate -- is well constrained from Lyman-alpha forest studies.  This allows one to solve for an upper bound on density as shown in the figure on the left.  The error bars and upper bounds (the latter of which represent the case where the metal column had only a lower bound) are the measurements.  The y-axis is proportional to density.  The yellow region is the range for the bounds on the hot phase pressure in our paper plus pressure equilibrium.   The conclusion is that the density of the cold (photoionized) CGM clouds is quite low for many systems.  The inferred low densities may suggest that some clouds are out of thermal pressure equilibrium with the hot phase.  We showed that this conclusion was robust to the assumed temperature and to density inhomogeneities.  Weird!