Modeling the Structure of the Circumgalactic Bathtub

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Title: CloudFlex: A Flexible Parametric Model for the Small-Scale Structure of the Circumgalactic Medium
Authors: Cameron B. Hummels et al.
First Author’s Institution: California Institute of Technology
Status: Accepted to ApJ

If you or I spent a long time sitting in a bathtub, we’d probably shrivel up and quickly become indistinguishable from a raisin. Galaxies, on the other hand, spend their lives bathed in a reservoir of gas known as the circumgalactic medium. In fact, the presence of the circumgalactic medium is necessary for the long-term growth and survival of the galaxy. More precisely, the circumgalactic medium provides the gas that regulates a galaxy’s ability to form stars — for example, as star formation depletes gas from the interstellar medium, inflows from the circumgalactic medium replenish that supply.

Our understanding of this diffuse gas reservoir has largely been driven by observing its effect on background light (i.e., along so-called quasar sight lines) through absorption features. These measurements have indicated the presence of gas in both hot (T ~ 106 K) and cool (T < 104K) phases. However, the presence of such a stark temperature difference between the various components of this intergalactic gas would produce fluid instabilities that could quickly drive the cold component to fragment into a collection of small “cloudlets.” Self-consistently modeling these structures in large numerical simulations is challenging because they require significant dynamic range — one must be able to resolve clouds on scales smaller than a few light-years while also modeling the large scale motions of gas on galactic (thousands of light-years) scales.

Inspired by this challenge, today’s authors set out to construct a simple model to efficiently describe the distribution and properties of these cool gas cloudlets embedded in broader cloud complexes (larger clouds composed of many cloudlets) within the circumgalactic medium. Leveraging such a model to predict observed line shapes will allow us to begin to constrain the detailed substructure of this galactic bathtub.

Constructing the Model

To construct their model, today’s authors populate these so-called cloud “complexes” with a collection of randomly sampled cloudlets and observe the resulting configuration. In detail, they statistically sample cloudlet properties based on a series of predetermined distributions. For example, the total mass of their cloud is set to be a million times the mass of our Sun. Then, based on their chosen parameters for the minimum mass of an individual cloudlet and the shape of their mass probability distribution (i.e., the function that tells you how likely it is for a cloudlet with a given mass to exist), they randomly generate cloudlets until the total mass of these objects equals the pre-set total mass. They combine this with probability distributions for the distance of the cloudlets from the center of the complex and the turbulent velocity of the cloudlets to produce a mock cloud complex structure, such as the three examples shown in Figure 1.

examples of cloudlet distributions

Figure 1: Three examples of cloudlet distributions generated using the model with the minimum cloudlet mass varied from 10-3 solar masses at left to 105 solar masses at right. Because these are 3D distributions in reality, what is shown here is the cumulative distribution along one direction, with the colors representing the density of the gas along the line of sight at any given point. [Hummels et al. 2024]

Observing the Circumgalactic Medium

In this manner the structure of the cloud complexes is determined by a choice of 11 parameters that can be flexibly varied to explore the effects of cloud structure on the resulting observations. The key observational probe that has been historically used to study the circumgalactic medium is the shape of absorption features in the spectra of distant, luminous quasars. Because the shape of these features is a direct result of the interaction of background light with the circumgalactic medium gas and the circumgalactic medium is thought to be a highly disordered, turbulent medium, observed features will in principle be sensitive to where in the medium the light passes and how dense the absorbing objects are. For example, light passing through the center of the cloud in the left panel of Figure 1 will likely interact with more cloudlets than light passing near the edge and thus the observed spectra should reflect this.

simulated absorption lines for 17 cloudlets

Figure 2: Top: A predicted magnesium-II absorption profile (black) generated from the cumulative effect of absorption in the 17 cloudlets intersected along the chosen sight line. The absorption profiles are shifted left and right based on the velocity of the cloudlets. Bottom: A depiction of the chosen sight line along the z axis with the observer at the left. The velocity vectors of the intersected cloudlets are shown with colored arrows. [Hummels et al. 2024]

In Figure 2, today’s authors demonstrate how they can use this model to predict an observed line profile (read: shape) — in this case for a magnesium-II line. This chosen line intersects 17 cloudlets as it passes through the complex (i.e., travels along the z direction in the lower panel). Each of these cloudlets has a different velocity that will cause it to contribute to a slightly different absorption feature in the spectrum because of the Doppler effect (the motion of the cloudlet causes the wavelength of the light it receives to stretch or shrink so that a given absorption line — which should have a fixed wavelength location — appears at a longer or shorter wavelength in the rest frame of the quasar), yielding the left–right offsets of the dips in the upper panel of Figure 2. Each cloudlet’s contribution to the absorption is then modeled by a so-called Voigt profile, which describes how the width of a spectral line will be determined by its internal temperature and density. The cumulative contribution of these profiles then produces the observed spectral feature.

Turning the Knobs

To understand the utility of such a framework, the authors then demonstrate how observed profiles respond to variations in the chosen parameters, such as minimum cloudlet mass. To this end, they generate 10,000 random sight lines through a given cloud complex (i.e., they do the procedure shown in Figure 2 10,000 times) and analyze the properties of the absorption in aggregate (such as by counting the number of intersected absorbers). One key metric to quantify these effects is the observed equivalent width, which basically measures the strength/depth of an absorption feature — a sight line that passes through a high density of absorbers will have a larger equivalent width than one that intersects only a few. For example, from Figure 3, they show that decreasing the minimum cloudlet mass, which should increase the total number of cloudlets (as we saw in the leftmost panel of Figure 1), increases the number of intersected cloudlets, as you might expect. Because these cloudlets are much more common, there are more sight lines that will pass through a lower density column of gas, yielding a broader distribution of column densities. Despite these effects, the overall distribution of observed equivalent widths is roughly independent of minimum cloudlet mass, but the fraction of sight lines that yield a given equivalent width is significantly different between the different minimum masses.

Figure 3: Left three panels: The distribution of the number of intersected cloudlets, column density along the line of sight, and equivalent width for different choices of the minimum cloudlet mass (different colors). Rightmost panel: The fraction of sight lines yielding equivalent widths greater than the value on the horizontal axis. [Adapted from Hummels et al. 2024]

This cloud complex model can be applied in aggregate to “simulate” the distribution of clouds in the halo around the galaxy. That is, several of these complexes will populate the circumgalactic medium around a galaxy, so a given sight line will intersect a number of complexes, each of which is composed of a collection of cloudlets, as we’ve seen. Applying this procedure to such a distribution allows one to predict observed line profiles and thus equivalent width distributions, a key observable used to probe the circumgalactic medium.

Comparing the observed and predicted distributions and the sensitivity of these distributions to underlying parameters will shed light on the detailed structure of this complex medium.

Original astrobite edited by Jessie Thwaites

About the author, Sahil Hegde:

I am an astrophysics PhD student at UCLA working on using semi-analytic models to study the formation of the first stars and galaxies in the universe. I completed my undergraduate at Columbia University, and am originally from the San Francisco Bay Area. Outside of astronomy you’ll find me playing tennis, surfing (read: wiping out), and playing board games/TTRPGs!