Galaxy clusters harbor the universe’s largest hot gaseous atmosphere, easily detectable through X-ray emission owing to their high temperatures. The intracluster Medium (ICM) contains most of the baryonic mass of a cluster and its overall structure is mainly governed by gravitational forces. The circumgalactic Medium (CGM) on the other hand is one of the least constrained components of the galactic ecosystem. The CGM is multiphase with large uncertainty in the amount of baryons distributed in different phases (hot CGM with T ⩾ 10⁶ K, warm CGM with T~10⁵-10⁶ K and cool CGM with T < 10⁵ K) that are driven by much more complex astrophysical processes[1][2][3]. Therefore, the CGM could be viewed as down-scaled ICM disrupted by feedback.

X-ray emission from the CGM

X-ray emission has been extensively used to characterize the ICM with successful analytical models and simulations capturing the observed trends dominated by gravity. Detecting X-rays from the CGM has been far more challenging. Additionally, the CGM relies on a more complex range of astrophysics compared to the ICM. The impact of non-gravitational processes such as radiative cooling and energy feedback from stars and black holes is much more significant at the masses of galactic halos.

Chadayammuri et al. 2022[4] obtained the first resolved X-ray emission profiles from the CGM. They showed that state-of-the-art hydrodynamic simulations with varied galaxy formation prescriptions are unable reproduce the observed X-ray profiles, highlighting the difficulty in simulating the observed properties of the CGM. The next big challenge lies in building state-of-the-art theoretical models grounded in modern day observations of galaxies.

Complementarity of analytical models and simulations

Analytical models are intuitive, useful for pinpointing the mechanisms responsible for a given observational trend and are computationally cost-effective. Continual improvements in the computational efficiency of numerical simulations are enabling them to produce a large number of realizations of the Universe and to include a variety of baryonic processes. It is therefore important to keep updating the analytical models for an accurate description of underlying physical processes over a wide range in halo mass and redshift. The combination of analytical models and state-of-the-art simulations will be necessary to explain upcoming high resolution observations of fainter halos as shown in Figure 1. Both kind of models are fundamental in forecasting the viability of future missions as well as motivating new observations .

The Baryon Pasting model is a simple analytical gas model including prescriptions for feedback, non-thermal pressure, and gas clumping [5][6][7][8]. It has been tuned and tested only for clusters thus far. Therefore, it must be tested and calibrated in the CGM regime to access its viability as an “Uber model” accurately describing gaseous halos over a wide range of halo masses. The Cosmology and Astrophysics in MachinE Learning Simulations (CAMELS) represent an avenue exploring precisely the CGM regime, in which the BP model can be updated to represent the vast number of feedback realizations.

CAMELS is a set of 4,233 simulations designed to serve as a training set for machine learning algorithms (see [9] and [10] for details of simulation setup). It will play a crucial role in propagating the uncertainty in our knowledge of subgrid modeling to the predicted properties of the CGM through its large set of multi-cosmology, multi-feedback realizations. A key step in that approach is to identify where and how different feedback parameters in the simulations map into analytical prescriptions for the CGM.

Impact of feedback on CGM profiles

The 1P CAMELS set (in which only one feedback parameter differs from its fiducial value) is ideal for disentangling the impact of various feedback processes. Figure 1 shows the impact of variation in each the four astrophysical or feedback parameters on the median soft X-ray (0.5-2 keV) brightness profiles (from [11]) for the halos in mass range $M_{200c} \sim10^{12}-10^{12.5} M_{\odot}$ (i.e., $L_*$ galaxies) and radial range 10-300 kpc. The differences between IllustrisTNG and SIMBA predictions highlight the differences in feedback implementation in the subgrid models of the simulations. For example, IllustrisTNG is more sensitive to SNe feedback, whereas SIMBA is more sensitive to the AGN feedback parameters. In all four panels, IllustrisTNG produces brighter X-ray halos compared to SIMBA, primarily driven by the higher density of the IllustrisTNG halo gas.

We also compare the simulated profiles with the predictions of Baryon Pasting [6] for model parameters fixed at their fiducial values except for feedback efficiency ($\epsilon_f$) which is set at $10^{-6}$ and $10^{-7}$ as shown by dashed-dotted and dotted black lines, respectively. The BP model predicts flatter X-ray cores compared to the simulated profiles, converging towards large scales. Note that, in this figure we do not show the fiducial Baryon Pasting model with $\epsilon_f=4\times10^{-6}$ since it produces very low density CGM profiles leading to negligible X-ray emission ($\propto n^2_e$), further highlighting that the Baryon Pasting models tuned at cluster scales predict extremely different CGM properties.

Though the 1P CAMELS set varies only one parameter at a time, it may not necessarily translate to varying only one mode of feedback. For example, increasing SNe feedback efficiency results in increased metal enrichment, thus increasing the rate at which the gas can cool. The cold gas can then condense and sink into the halo’s central parts, enhancing accretion onto the central supermassive black hole, and as a result increasing the AGN feedback. Therefore, it is important to understand how the feedback parameters are affecting the underlying physical quantities such as gas density, temperature, pressure, metallicity, entropy and black hole mass to understand how it translates to the trends seen in the observations.

Entropy is one of the main thermodynamic quantities bearing the history of feedback. In the absence of non-gravitational processes, the entropy profile follows a power law radial profile ($\propto r^{1.1}$) [12], and any deviations from such a form is known to carry the signature of feedback and cooling. In Figure 2, we show the median entropy profiles for the CAMELS-CGM normalized by the halo’s cosmological entropy scale ($K_{200}$) for halos in the same mass range and redshift as in Figure 1. For comparison, we also show the baseline entropy profile due to the cosmological structure formation [13] at median halo mass from the fiducial run. SNe feedback dominates the variation in the entropy profile for the IllustrisTNG and SIMBA, respectively, while other feedback parameters have negligible impact. SIMBA halos show higher entropy levels, especially at large radii compared to IllustrisTNG counterparts. Both subgrid models show higher CGM entropy levels compared to the baseline entropy profile out to large radii as opposed to groups and clusters where the entropy profiles converge to the baseline near halo outskirts[14].

The Baryon Pasting model produces a larger range in the entropy (and other thermodynamic quantities) compared to the simulated profiles. The lowest feedback efficiency ($\epsilon_f=10^{-7}$) investigated here is close to the baseline profile, whereas, the highest feedback efficiency ($\epsilon_f=4\times10^{-6}$) produces a flatter high entropy profile. The Baryon Pasting model has only one parameter, $\epsilon_f$, trying to capture both active galactic nuclei (AGN) and supernovae (SNe) assuming the feedback energy proportional to the total stellar mass. This assumption breaks at lower mass halos where a single feedback efficiency cannot capture both AGN and SNe driven winds. $L_*$ galaxies thus represent an ideal testbed where an updated Baryon Pasting model can be robustly validated for a wide variety of feedback realizations available from CAMELS.

Towards constraining CGM physics with multi-wavelength observations

Several ingredients of the analytical and simulation-based models are highly sensitive to still poorly constrained CGM physics, such as feedback and turbulent gas motions. Fortunately, a plethora of multi-wavelength astronomical surveys, such as Simons Observatory, CMB-S4, CMB-HD in microwave and eROSITA, Athena, and Lynx in X-rays, are underway to significantly constrain the CGM properties [15]. For example, ongoing Sunyaev-Zel’dovich (SZ) surveys have already improved our ability to probe gas pressure and density profiles in massive galaxies and groups [16][17][18], promising to provide stringent tests of CGM models.

In order to interpret these forthcoming multi-wavelength observations, we are developing a data-driven approach to modeling multi-wavelength CGM observations [19]. For example, we are developing an emulator (which can be thought of as an ‘interpolator’) that enables direct forecasts and statistical inferences on feedback parameters of the simulations for ongoing and upcoming X-ray and SZ surveys [20]. This emulator approach is complementary to the more physical analytic modeling, such as Baryon Pasting. These analytical and simulation-based CGM modeling tools, capable of transitioning from ICM to CGM scales while translating the multi-wavelength observations to the constraints on the CGM physics, are core to our understanding of how galaxies form from their galactic atmosphere cocoon.

Acknowledgements:  We gratefully acknowledge the CAMELS team for publicly releasing CAMELS simulation data [9][10]. This work is supported by NSF grant AST-2206055. PS also acknowledge support by the YCAA Prize Postdoctoral Fellowship.