This page gives a quick overview of some of the research I’ve worked on. If you want less detail, check out the “word cloud” visualization of my papers above; if you want more detail, you can browse my publications here.
Do Galaxy Clusters Boil?
Galaxy clusters are filled with a hot, magnetized plasma that’s surprisingly thermally conductive. This makes the gas susceptible to two recently-discovered instabilities known as the HBI and the MTI (pictured to the left). These instabilities are a lot like normal convection, but they depend on temperature instead of entropy. The gas in galaxy clusters is stable to the classical theory for convection, but unstable to these new instabilities.
Why’s this interesting? Clusters have long been assumed to be convectively stable, but it now seems that the intracluster plasma boils vigorously. This boiling represents a radical change in the dynamics of cluster gas, and could affect the way we interpret observations of galaxy clusters. Convection efficiently mixes the gas and would distribute metals more efficiently through the cluster. Boiling also drives turbulence, which influences the connection between gas pressure and gravity used to infer the masses of clusters.
I’ve worked on understanding the differences between the HBI and the MTI, and on understanding their non-linear saturation. Since the linear phases are so short-lived, understanding the non-linear behavior of the instabilities is essential for knowing their astrophysical implications.
The HBI: an instability seeking stability
The HBI, pictured below, turns out to be a fairly quiescent instability. As the instability grows, it reorients magnetic field lines to be preferentially horizontal. This stabilizes the gas against the HBI, so the instability effectively shuts itself off before it really develops. We end up with a stable atmosphere, without much turbulence, and with very horizontal magnetic field lines. This happens when the temperature increases with radius, as in the centers of cool-core galaxy clusters.
The MTI: boiling away
The MTI occurs in the outer parts of galaxy clusters, where the temperature declines with radius. In many ways, this instability is similar to the HBI: it creates buoyant plumes which rake out the magnetic field lines, reorienting an initially horizontal field to become predominantly vertical. This is where the similarity with the HBI stops, however: while vertical field lines are linearly stable to the MTI, they are non-linearly unstable (i.e., they become unstable if given a big enough push). So the MTI can’t shut itself off as efficiently as the HBI; it continues to grow and can eventually drive vigorous convection.
The simulations depicted above are idealized and are only intended highlight the basic physics of these new forms of convection. I’m currently working on a method to study the instabilities in a more realistic environment resembling a forming galaxy cluster. I’ve included a figure from a preliminary simulation below. This is a work in progress... stay tuned!
Gas Clouds in the Galactic Center
Disruption by shear instabilities
Using G2 to probe the galactic center accretion flow
A magnetically-enhanced drag force is very interesting, because there’s potentially a detection of a drag force on G2’s orbit! How to motivate the next project without going into too much detail?
The figure below shows a perspective rendering of the best model I found. I rotated the coordinate system so that G2 originates at apocenter along the x-axis and that the rotation axis of the accretion flow is in the x-z plane. This more clearly shows the rotation of the cloud’s orbital plane.
The gas cloud comes in from apocenter on a nearly radial orbit. The cloud’s orbital plane is misaligned with the rotation of the background flow; this results in a perpendicular component to the drag force. As the cloud approaches the black hole, the perpendicular drag force increases due to both the increasing background density and the increasing rotation velocity. The resulting torque rapidly re-orients the orbital plane. After about five pericenter passages, the orbital plane is aligned with the rotation axis of the accretion flow. No further rotation occurs, but the orbit circularizes and the cloud becomes approximately co-moving with the rotating gas. The drag force thus drops significantly; the cloud slowly sinks in toward the black hole. Of course, after many pericenter passages, the cloud may be tidally distorted to the point where it intersects itself; this process could lead to much more rapid circularization and inflow, but is not accounted for in our calculation.
I’ll admit that the orbit above looks slightly crazy, so I want to emphasize that it is in fact consistent with the observations. The plot below shows the trajectory of the cloud in the plane of the sky, along with the astrometric measurements for G1 and G2. I also show the line-of-sight velocities determined from spectroscopy of the Br-γ line. This model does just as well as fitting the G1 and G2 with two unrelated Keplerian orbits.
My long-term goal is to be able to do something useful with this type of analysis. Below I show probability distributions for six parameters in the model: the angular coordinates for the rotation axis of the accretion flow, the magnetic field strength and density profile for the gas in the galactic center, the shape of the cloud, and the rotation profile for the galactic center. Already, this constrains the rotation axis quite closely. The other parameters are strongly degenerate; the magnetic field strength and the density profile both control the magnitude of the drag force, and the cloud doesn’t really care where it came from. This does mean that measuring the magnetic field strength would yield a constraint on the density profile, however. Similarly, measuring the shape of the cloud would yield a constraint on the rotation profile for the galactic center accretion flow — both are very exciting prospects!
Cold Gas in Hot Halos
Remarkably, some galaxy clusters contain thin filaments of cold (104 K) gas embedded right within the hot (108 K) plasma. Below, the beautiful optical and x-ray images from Fabian et al. (2011) show the co-existence of these two phases of gas.
I’ve studied thermal instability in galaxy clusters and argued that it can produce filaments of cold gas like the ones observed. Whether or not the plasma in clusters is thermally unstable is a surprisingly tricky question --- it depends on the unknown “feedback” process heating the plasma, which is extremely difficult to model in detail and is still a very active field of research. My approach was to assume that the gas is thermally unstable, then to see what other testable implications that would have for the gas in galaxy clusters.
When do we get cold gas?
Even though I assumed that all of the plasma in every cluster is thermally unstable, it turns out that the instability only grows to large amplitudes at special locations in the cluster. We should only expect to see cold gas develop at locations where the cooling time drops below the free-fall (or dynamical) time. The plot below shows this result for various assumptions about the gas. In all cases, we only see clumps or filaments of cold gas when the cooling time is shorter than the free-fall time.
Though this result depends on the non-linear saturation of the thermal instability, we got lucky and it’s surprisingly simple to understand. The plot to the right tracks the growth of the instability in my simulations. Perturbations initially grow exponentially, which is not surprising since I put in an instability by hand. (The slower growth for the red curve happens because the instability switches to an overstability in that limit.) The exponential growth can’t continue forever, however; it stops when the damping rate due to internal gravity wave turbulence matches the driving rate due to thermal instability. This balance picks out a final amplitude δρ/ρ~(tcool/tff)-1. Multi-phase gas requires δρ/ρ>1, which explains why we only see it when tcool drops below tff.
What can thermal instability do for you?
The figure below plots the ratio tcool/tff as a function of radius in a handful of galaxy clusters. The ones shown in blue are clusters which are known to have filaments of cold gas, while the ones shown in red are known not to contain filaments. There does seem to be a threshold in tcool/tff separating the clusters with and without multiphase gas. Interestingly, the curves all reach a minimum at a few tens of kiloparsecs; this is exactly where we see cold gas seen in many clusters!
Why Aren’t Galaxy Clusters Isothermal?
Somehow, galaxy clusters maintain their large-scale temperature gradients in spite of thermal conduction and convection. Conduction and convection are enemies of temperature differences... they should only take a few billion years (less than the age of a typical cluster) to equilibrate and make the gas isothermal. But for some reason, clusters aren’t becoming isothermal. Since the convective stability of cluster gas depends on its temperature profile, I became very interested in this conundrum.
I put together a simple model for the formation of galaxy clusters in which the cluster assembles “shell-by-shell.” Each shell falls in a little faster than the last, and thus shocks to a higher entropy. Hydrostatic equilibrium then determines the temperature profile, which depends directly on the accretion rate of the cluster. The accretion rates typical for galaxy clusters turn out to yield declining temperature profiles, similar to what are observed. Measuring the properties of the gas in clusters may thus provide an interesting indirect measurement of the formation histories of clusters.
This model neatly reproduces the observed temperature profiles of galaxy clusters, but what about conduction and convection? Why don’t they wash out the temperature differences and make the gas isothermal? Conduction does indeed move thermal energy outwards in galaxy clusters. But, rather than heating the gas in the outskirts up to higher temperatures, the influx of thermal energy expands the gas — this pushes the shock further out and causes the temperature to actually go down!
This method provides an inexpensive way to model the temperature profile of a galaxy cluster given its accretion history. Since the scatter in accretion histories is well-known from cosmological simulations of structure formation, I outlined a method for using the (known) scatter in accretion histories to predict the (unknown) scatter in cluster observables at fixed mass. For example, the figure below shows that variation in accretion histories leads to about a 10% scatter in temperature at fixed mass. My collaborators and I are currently using this method to better understand potential biases in some cosmological measurements.
Spitting into the Wind
The filaments I mentioned above are a lot like star-forming clouds, but they don’t live in galaxies. Some friends and I submitted an observing proposal to study star formation in these filaments and compare it to star formation in molecular clouds in galaxies. While writing that proposal, we serendipitously discovered a bent radio jet in one of the galaxies in the Perseus cluster, pictured below.
The jet is a beam of energetic particles launched by the super-massive black hole in the center of the galaxy. In this galaxy, the jet is being bent backwards by the headwind the galaxy feels as it flies through the plasma filling the galaxy cluster in which it lives.
We weren’t the first to observe this phenomenon; in fact, it’s so well known that it’s been used to discover new galaxy clusters in radio surveys. However, our galaxy is the most extreme one known to date. This jet’s bending is so severe that its radius of curvature is much smaller than the size of the galaxy. This implies that the “wind” of intracluster plasma penetrates so deep into the center of the galaxy that it affects star formation in the galaxy and even the dynamics of its central black hole! The galaxy is totally changed due to the fact that it’s inside a galaxy cluster.
Because we know how strong a headwind this galaxy feels, we can model the dynamics of the jet in a little bit of detail. We found that the standard assumption of equipartition often used in interpreting other jets underestimates the pressure in this one by a factor of almost 30.
Mixing and the Kelvin-Helmholtz Instability
I actually haven’t worked on this at all, apart from using it to benchmark different codes. But I think it’s an interesting process, and it makes for some neat-looking plots!