On the baryon budget in the X-ray-emitting circumgalactic medium of Milky Way-mass galaxies

Technical Summary: On the baryon budget in the X-ray-emitting circumgalactic medium of Milky Way-mass galaxies

Problem Statement
In the standard cosmological model, baryonic matter constitutes approximately 15.7% of the total matter content of the Universe. While this fraction is recovered within the virial radii ($R_{500c}$) of massive galaxy clusters, a significant "missing baryon" problem persists for lower-mass galaxy systems, particularly those with Milky Way (MW) masses ($M_{vir} \approx 10^{12} M_\odot$). A large fraction of baryons in these systems remains unaccounted for within $R_{500c}$. Recent observations by SRG/eROSITA have provided the average X-ray surface brightness ($S_X$) profile of the X-ray-emitting circumgalactic medium (CGM) around MW-mass galaxies. However, converting this observed surface brightness into a baryon mass estimate is highly degenerate, relying on critical assumptions regarding gas density profiles, temperature, metallicity, and the underlying dark matter halo mass distribution. The paper aims to quantify how variations in these assumptions affect the inferred baryon mass of the X-ray-emitting CGM.

Methodology
The authors utilize the stacked $S_X$ profile of MW-mass central galaxies (CEN) from Zhang et al. (2024) as a benchmark. They adopt a fiducial model assuming an NFW-shaped dark matter halo with $M_{vir} = 1.3 \times 10^{12} M_\odot$ and $R_{vir} = 285$ kpc. The analysis involves fitting various physical models to the observed $S_X$ profile to derive the X-ray-emitting gas mass ($M_{X-ray-emitting, <R_{vir}}$) and the corresponding baryon fraction ($f_{X-ray-emitting, <R_{vir}}$).

The study systematically varies the following parameters relative to the fiducial case (isothermal $T=0.12$ keV, metallicity $Z=0.3 Z_\odot$, and a beta density profile with $\beta=0.4$):

1. Gas Density Profile ($n_H$): Testing steeper beta models ($\beta=0.5$) and a modified Vikhlinin profile to account for potential steepening at large radii.
2. Temperature ($T$):
   • Isothermal: Testing values consistent with MW measurements (0.17 keV), virial temperatures at $R_{500c}$ (0.08 keV), and extrapolations from the $T-M_{500c}$ scaling relation.
   • Non-isothermal: Modeling temperature fluctuations using log-normal distributions and physically motivated frameworks like ExpCGM (which assumes hydrostatic equilibrium with a generalized pressure shape).
   • Simulations: Comparing results with forward-modeled lightcones from the TNG300 cosmological simulation (LC-TNG).
3. Metallicity ($Z$): Testing constant low ($0.1 Z_\odot$) and high ($Z_\odot$) metallicities, as well as radially varying profiles inspired by intracluster medium (ICM) measurements.
4. Halo Mass Uncertainty: Assessing the impact of $\pm 0.1$ and $\pm 0.2$ dex uncertainties in the halo mass, both directly on the mass fraction calculation and indirectly through the temperature-mass scaling relation.

Key Results
The analysis reveals that the inferred baryon mass is extremely sensitive to the assumed physical parameters, leading to a variation in the estimated X-ray-emitting baryon mass by nearly a factor of four ($0.8 - 3.5 \times 10^{11} M_\odot$).

• Temperature Dependence: This is the dominant source of uncertainty. Variations in the assumed isothermal temperature cause the baryon fraction to fluctuate between 6% and 27%. The cooling function ($\Lambda_{0.5-2 \text{ keV}}$) is highly sensitive to temperature around 0.1 keV; for instance, a log-normal temperature distribution with a median of 0.08 keV yields a baryon fraction (~17%) that is ~160% higher than the isothermal assumption at the same median temperature.
• Halo Mass Uncertainty: Uncertainties in the halo mass introduce significant scatter. An overestimation of the halo mass by 0.1 dex can lead to an underestimation of the baryon fraction by ~30%, while a 0.2 dex uncertainty can cause a ~60% deviation.
• Density Profile: Modifying the density slope (e.g., using $\beta=0.5$ or a modified Vikhlinin profile) reduces the inferred baryon fraction by approximately 20–30% compared to the fiducial beta model.
• Metallicity: Assumptions about metallicity contribute an additional uncertainty of approximately 50%. Varying $Z$ from $0.1 Z_\odot$ to $Z_\odot$ changes the inferred baryon fraction by up to a factor of three.
• Model Comparisons:
  • The fiducial model yields $f_{X-ray-emitting, <R_{vir}} \approx 0.097$.
  • The ExpCGM framework yields $f_{X-ray-emitting, <R_{vir}} \approx 0.11$.
  • The LC-TNG simulation suggests a lower value of $f_{X-ray-emitting, <R_{vir}} \approx 0.047$.

Significance and Claims
The paper asserts that the 0.5–2 keV X-ray surface brightness profile alone is insufficient to robustly constrain the baryon mass of the CGM in MW-mass galaxies due to the strong degeneracies between temperature, density, metallicity, and halo mass. The authors emphasize that:

1. Dominant Uncertainties: Variations in temperature profiles and uncertainties in halo mass are the primary drivers of the large scatter in baryon mass estimates.
2. Need for Spectral Constraints: Accurate determination of gas temperature and metallicity via X-ray spectral analysis is essential. The current CCD spectral resolution (e.g., eROSITA) provides limited constraints, particularly for the low-temperature plasma ($\sim 0.1$ keV) characteristic of MW-mass halos.
3. Future Requirements: The authors conclude that future X-ray microcalorimeter missions (e.g., NewAthena, HUBS, Arcus, LEM) with high spectral resolution ($\sim 2$ eV) are crucial. These instruments will be necessary to separate emission lines (such as O VII and O VIII), constrain multi-temperature components, and ultimately close the baryon census at the MW-mass scale.
4. Methodological Shift: A differentiable forward-modeling approach that synthesizes data from X-rays, the Sunyaev–Zel'dovich (SZ) effect, and Fast Radio Bursts (FRBs), while accounting for intrinsic scatter and systematics, is required to break these degeneracies.