A systematic study of AGN feedback in a disk galaxy II: MACER prediction of X-ray surface brightness profile and comparison with eROSITA observations

As the second paper in a series on AGN feedback in disk galaxies, this study demonstrates that MACER simulation predictions for X-ray surface brightness profiles, derived without adjusting model parameters, show strong agreement with stacked eROSITA observations of circumgalactic medium emission, thereby supporting the thermal origin of the detected X-ray signal.

The Gist

The Big Picture: The Galaxy's "Weather Report"

Imagine a galaxy like our Milky Way not just as a collection of stars, but as a giant, swirling city. Surrounding this city is a massive, invisible atmosphere called the Circumgalactic Medium (CGM). This isn't air like we breathe; it's a super-hot, thin soup of gas that glows in X-rays.

For a long time, astronomers have been arguing about what keeps this "atmosphere" hot and puffy. Is it just the gravity of the galaxy holding it together? Or is there a giant, cosmic heater blowing hot air into it?

This paper is the second part of a study by a team of scientists (led by Yuxuan Zou and Feng Yuan) who built a virtual simulation of a galaxy to answer this question. They wanted to see if their computer model could predict exactly how bright this hot gas glows, and then check if their prediction matched real photos taken by a space telescope called eROSITA.

The "Virtual Galaxy" and the "Cosmic Thermostat"

The scientists used a sophisticated computer program called MACER. Think of MACER as a high-end flight simulator, but instead of flying a plane, it simulates the life of an entire galaxy over billions of years.

In their simulation, they included:

• The Stars: The visible city lights.
• The Black Hole: A supermassive monster sitting in the center of the galaxy.
• The Feedback: This is the key. When the black hole eats gas, it doesn't just swallow it; it burps out massive jets of energy and wind. This is AGN Feedback.

The Analogy: Imagine the galaxy is a house. The black hole is a furnace in the basement.

• Without Feedback: The furnace is off. The house gets cold, the air settles, and everything becomes dense and quiet.
• With Feedback: The furnace is blasting. It blows hot air into the attic (the CGM), keeping the air puffy, hot, and spread out.

The team ran their simulation and asked: "If we turn the furnace on (AGN feedback), does the 'attic' look like the real thing?"

The "Stacking" Trick: Blurring the Lines

Here's a tricky part of the science: The simulation only followed one galaxy over time. But the real telescope (eROSITA) looked at thousands of galaxies at once.

To compare the two, the scientists used a clever trick. They treated time like space.

• The Analogy: Imagine you have one person taking a photo of a busy street every second for an hour. You have 3,600 photos of the same street, but the people are in different spots. If you stack all those photos on top of each other, you get a blurry image that looks like a crowd of people moving at once.
• The scientists did this with their galaxy. They took snapshots of their single simulated galaxy at different times, stacked them up, and created a "virtual crowd" to compare with the real telescope's "crowd."

The Results: The Simulation Got It Right!

The team compared their "virtual stack" with two sets of real data from the eROSITA telescope:

1. Distant Galaxies: A huge stack of far-away galaxies (from a study by Zhang et al.).
2. Nearby Galaxies: A stack of galaxies right in our cosmic neighborhood (from a study by He & Li).

The Verdict:
When they turned the "furnace" (AGN feedback) ON, their simulation matched the real telescope data almost perfectly. The brightness of the X-ray glow in their computer model lined up with the brightness seen in the sky.

The "No-Furnace" Test:
To prove the furnace was necessary, they ran the simulation again with the AGN feedback OFF.

• Result: The X-ray glow was much dimmer than what we actually see in the sky.
• Why? Without the black hole's wind, the gas cooled down too much and sank inward. It became too dense but too cold to glow brightly in X-rays. The simulation showed that without the black hole's feedback, the galaxy's atmosphere would look completely different than what we observe.

The Metal Mystery

There was one small variable they had to guess: Metallicity. In astronomy, "metals" are any elements heavier than hydrogen and helium (like oxygen, iron, carbon). These metals act like "glow-in-the-dark paint" for the gas.

The scientists tested different amounts of "paint" (from very little to a lot). They found that no matter how much paint they used, the simulation only matched the real world if the black hole was actively blowing wind. This confirmed that the X-rays we see are coming from hot gas, not from some other weird, non-thermal source (like cosmic rays).

The Takeaway

This paper is a victory for our understanding of how galaxies work. It tells us:

1. Black Holes are the Thermostats: The supermassive black holes in the centers of galaxies aren't just destructive; they are essential for keeping the galaxy's atmosphere hot and puffy.
2. The Models Work: Our computer simulations are getting good enough to predict the real universe without needing to "tweak" the numbers to make them fit.
3. The Telescope is Right: The eROSITA telescope is seeing exactly what we expected: a hot, glowing halo of gas that is being kept warm by the galaxy's central engine.

In short: The universe is a bit like a house with a very active furnace in the basement. If you turn the furnace off, the house gets cold and the air settles. But because the furnace (the black hole) is running, the house stays warm, puffy, and glowing in X-rays, just as we see it in the sky.

Technical Summary

1. Problem Statement

The origin and thermodynamic state of the hot circumgalactic medium (CGM) in Milky Way-mass galaxies remain a subject of debate. While galaxy formation models predict extended hot gas heated by gravitational accretion shocks, the relative contributions of gravitational heating versus feedback mechanisms (Active Galactic Nuclei [AGN] and stellar feedback) are difficult to distinguish. Recent X-ray observations by eROSITA have detected faint, extended emission out to the virial radius ($\gtrsim 100$ kpc), revealing that the hot CGM is more extended than previously thought. However, existing cosmological simulations (e.g., IllustrisTNG, SIMBA) often struggle to simultaneously reproduce observed CGM X-ray properties and stellar mass-halo mass relations without fine-tuning. This paper aims to test a specific, high-resolution AGN feedback model against new eROSITA data to determine if AGN feedback is the dominant driver of the observed CGM X-ray emission.

2. Methodology

The authors utilize the MACER framework (Model for Accretion and Cosmological Evolution of a single galaxy), a 2D numerical simulation designed to resolve the Bondi radius and self-consistently model black hole accretion and feedback.

• Simulation Setup: The study uses a single isolated, Milky Way-mass disk galaxy simulation from a previous paper (Paper I). The system includes a supermassive black hole (SMBH), dark matter halo, stellar bulge/disk, and a hot CGM.
  • Physics: The model self-consistently calculates black hole accretion rates based on mass flux at the inner boundary (below the Bondi radius). AGN outputs (radiation, wind, jet) are prescribed based on accretion theory (cold vs. hot modes), with jet properties derived from GRMHD simulations.
  • Time Ensemble: To mimic the observational stacking of many galaxies, the authors treat the time evolution of a single galaxy as an ensemble. They average X-ray surface brightness profiles over multiple evolutionary epochs, excluding rare, extreme quasar-mode phases inconsistent with the observational samples.
• Observational Comparison: The simulated X-ray surface brightness profiles are compared against two independent eROSITA stacking studies:
  1. Zhang et al. (2024) [Z24]: 85,222 central galaxies ($\log(M_*/M_\odot) = 10.5-11.0$) at $z \approx 0.02-0.10$.
  2. He & Li (2026): Nearby $L^*$ galaxies within 50 Mpc ($\log(M_*/M_\odot) > 10.38$).
• Synthetic Observations: The 3D simulation data is projected to 2D, convolved with the eROSITA Point Spread Function (PSF), and rescaled to the physical distances of the observational samples.
• Metallicity Handling: Since the simulation does not track metal enrichment, the authors test four representative metallicities ($Z = 0.02, 0.3, 0.5, 1.0 Z_\odot$). They use sub-solar metallicities for Z24 (event-level stacking) and solar metallicity for He & Li (image stacking with count-rate conversion).

3. Key Contributions

• Direct Model-Data Comparison: This is the first study to directly compare MACER simulation predictions with eROSITA CGM X-ray surface brightness profiles without adjusting model parameters.
• Validation of Thermal Origin: The study provides strong evidence that the diffuse X-ray emission detected by eROSITA is predominantly thermal in origin, rather than non-thermal (e.g., cosmic-ray dominated).
• Quantifying AGN Feedback Impact: By running a "noAGN" control model, the authors isolate the specific thermodynamic impact of AGN feedback on the CGM, demonstrating its necessity in reproducing observations.
• Constraining CGM Mass: The study uses the X-ray surface brightness to constrain the total mass of the hot CGM, ruling out models with excessively high initial gas masses.

4. Key Results

• Agreement with Observations:
  • The Fiducial Model (with standard initial conditions) shows excellent agreement with the Z24 stacked profile over a broad radial range (out to $\sim 100$ kpc) and with the He & Li (2026) profile from $\sim 20$ kpc to $120$ kpc.
  • The agreement holds across different metallicity assumptions ($0.02 - 0.5 Z_\odot$ for Z24; $1.0 Z_\odot$ for He & Li).
• Role of Initial Conditions (CGM Mass):
  • A "Fiducial 3" model (initial CGM mass increased by a factor of 3) predicts X-ray surface brightness values 5 times higher than observations in the 20–100 kpc range.
  • This result strongly constrains the typical total CGM mass of Milky Way-mass galaxies to be $\sim 5 \times 10^{10} M_\odot$, ruling out models with masses approaching $10^{11} M_\odot$.
• Critical Role of AGN Feedback:
  • The "noAGN" model significantly underpredicts the X-ray surface brightness (by nearly an order of magnitude compared to Z24).
  • Physical Mechanism: While the noAGN model has higher gas density, it lacks the AGN-driven heating. Consequently, the gas temperature is lower ($\sim 10^6$ K vs. $10^6-10^7$ K in the Fiducial model) and entropy is lower by two orders of magnitude.
  • Emissivity Physics: The lower temperature in the noAGN model shifts the cooling function to a regime where metal-line emission dominates. However, because the Fiducial model has higher temperatures and entropies, it maintains a higher emissivity via free-free continuum and line emission at higher temperatures, matching the observed brightness. The noAGN model fails to reproduce the observed high-entropy, hot CGM state.
• Thermal vs. Non-thermal: The consistency between the thermal-only MACER predictions and eROSITA data supports the conclusion that the CGM emission is thermal. Non-thermal contributions (e.g., inverse-Compton scattering) are not required to explain the data.

5. Significance

This paper validates the MACER framework as a robust tool for studying galaxy evolution and AGN feedback. By successfully reproducing eROSITA observations without free parameters, the study confirms that:

1. AGN feedback is essential for regulating the thermodynamic state (temperature and entropy) of the hot CGM in Milky Way-mass galaxies.
2. The thermal nature of the CGM is confirmed, challenging interpretations that rely heavily on non-thermal processes to explain extended X-ray halos.
3. The total mass of the hot CGM is tightly constrained, providing a critical benchmark for future cosmological simulations and feedback models.

The work bridges the gap between high-resolution, physics-rich single-galaxy simulations and large-scale observational surveys, offering a new pathway to constrain galaxy formation physics using X-ray surface brightness profiles.