eROSITA X-ray Gas Fractions

• eROSITA X-ray gas fractions are precise measurements of hot, X-ray-emitting gas relative to total mass in galaxies, clusters, and filaments, highlighting key baryon cycle characteristics.
• The methodology employs spectral fitting and stacking techniques to distinguish diffuse hot gas from other X-ray sources, refining scaling relations across different mass scales.
• Results reveal mass-dependent gas fractions that inform cosmology by clarifying baryon distribution, feedback processes, and the role of the warm-hot intergalactic medium.

eROSITA X-ray gas fractions refer to the measurements and scaling relations quantifying the mass of hot, X-ray–emitting gas relative to the total or baryonic mass in galaxies, groups, clusters, and the cosmic web, as revealed by observations from the eROSITA X-ray telescope. These measurements are central to understanding the baryon cycle, cluster scaling relations, galaxy formation, and cosmological parameter inference. eROSITA has enabled the first statistically robust, all-sky quantification of hot gas fractions from galactic to cluster scales and in filaments, using physically motivated analysis pipelines and validated selection functions.

1. Measurement Methodologies and Scaling Relations

The determination of eROSITA-derived X-ray gas fractions relies on model-decomposition, spectral fitting, and stacking techniques, designed to isolate the hot, diffuse gas from other X-ray emitting components such as X-ray binaries (XRBs) or AGN.

Galaxy-scale Methods

For normal (non-AGN) galaxies, the total X-ray luminosity is modeled as the sum of XRB and hot gas components:

$$L_{\mathrm{X,gal}} = L_{\mathrm{X,XRB}} + L_{\mathrm{X,gas}}$$

The XRB component is further split into low-mass XRBs (scaling with stellar mass $M_\star$) and high-mass XRBs (scaling with SFR), following

$$L_{2-10,\mathrm{XRB}} = \alpha_0 (1+z)^\gamma M_\star + \beta_0 (1+z)^\delta \mathrm{SFR}$$

where the recommended constants are $\log\alpha_0 = 29.30$, $\log\beta_0 = 39.40$, $\gamma = 2.19$, $\delta = 1.02$ at $z=0$ (Basu-Zych et al., 2020).

Diffusive hot gas emission is parameterized differently for late- and early-type galaxies. In star-forming systems,

$$\frac{L_{0.5-2,\mathrm{gas}}}{\mathrm{SFR}} = (12.4 \pm 0.2) \times 10^{38}~\mathrm{erg~s}^{-1}$$

and for early types, the scaling with K-band luminosity (proxy for stellar mass) is:

$$\log\left(\frac{L_{0.3-8,\mathrm{gas}}}{10^{40}\ \mathrm{erg}~\mathrm{s}^{-1}}\right) = A\ \log\left(\frac{L_K}{10^{11} L_{K,\odot}}\right) + B$$

with $A=2.98$, $B=-0.25$.

Group and Cluster-scale Methods

For clusters, the fundamental approach is to model the X-ray surface brightness with azimuthally averaged profiles (e.g., $\beta$-model, Vikhlinin profile) convolved with the eROSITA PSF, fit for the 3D electron density $n_e(r)$, and integrate to obtain the gas mass:

$$M_{\mathrm{gas}} = 4\pi \mu_e m_p \int_0^{R} n_e(r) r^2 dr$$

where $\mu_e$ is the mean molecular weight per electron.

Cluster total mass $M_{500}$ is usually inferred from an $L_X-M_{500}$ scaling relation or using weak-lensing calibration. The gas fraction is then:

$$f_{\mathrm{gas}} = \frac{M_{\mathrm{gas}}(R_{500})}{M_{500}}$$

Stacking techniques (especially for optically selected, faint groups) enhance sensitivity and mitigate selection bias, allowing hot gas fractions to be probed down to Milky-Way-mass halos (Popesso et al., 25 Nov 2024).

In cosmic filaments, X-ray stacking is performed at the positions of filamentary structures extracted from large optical catalogs (e.g., SDSS), masking resolved clusters/groups and point sources. The spectral and spatial features are fit with thermal plasma models (APEC), and central gas density and baryon overdensity are extracted via modeling with a $\beta$-profile (Tanimura et al., 2022, Zhang et al., 31 May 2024).

2. Results: Hot Gas Fraction Scaling and Detection

Galaxies

eROSITA predicts (via bottom-up modeling) $\gtrsim 15,000$ normal galaxy detections at $50$–$200$ Mpc, with hot gas dominating X-ray emission in early-type galaxies. The applied scaling relations allow estimation of hot gas fractions and their dependence on galaxy mass, SFR, and K-band luminosity, facilitating comparison with hot gas content in clusters.

Clusters and Groups

For eROSITA-selected clusters and groups, gas mass and luminosity are robustly measured out to $R_{500}$. The empirical gas fraction–halo mass relation spans a wide mass range:

$$f_{\mathrm{gas},500} = (2.23 \pm 0.18) \times 10^{-7}\ \left( \frac{M_{500}}{M_\odot} \right)^{0.39 \pm 0.02}$$

and for $R_{200}$:

$$f_{\mathrm{gas},200} = (2.09 \pm 0.14) \times 10^{-6}\ \left( \frac{M_{200}}{M_\odot} \right)^{0.33 \pm 0.02}$$

In massive clusters, the hot gas fraction approaches the cosmic baryon fraction ($\Omega_b/\Omega_m \sim 0.15$) within $R_{200}$. In contrast, galaxy groups have $f_{\mathrm{gas}}$ at only $20$–$40\%$ of cosmic, indicating substantial baryon loss or redistribution (Popesso et al., 25 Nov 2024).

Cluster Outskirts and Filaments

Stacking reveals that the gas density profile in clusters persists to $3R_{500}$ with overdensity $\sim20$–$30$, and the gas fraction at large radii remains close to the universal value. In filaments, robust detections of warm-hot gas (WHIM) are achieved at $>5\sigma$, with best-fit values of:

• $kT \sim 0.6$–$1.0$ keV
• Central baryon overdensity $\Delta_b \sim 10^{1.88} \approx 76$ (log-scale; model-dependent)
• Metallicity $Z\lesssim 0.1~Z_\odot$

These measurements are consistent with state-of-the-art hydrodynamical simulation predictions for the high-density, high-temperature phase of the WHIM (Tanimura et al., 2022, Veronica et al., 2023, Zhang et al., 31 May 2024).

3. Selection Effects and Systematic Biases

eROSITA’s detection threshold and source classification favor high surface-brightness, gas-rich, centrally concentrated systems:

• At fixed mass, detected groups have systematically higher $f_{\mathrm{gas}}$ than undetected ones.
• Many low-mass groups remain undetected, and undetected optically selected halos show flatter gas profiles but similar total $f_{\mathrm{gas}}$ at large radii when stacked (Popesso et al., 2023, Marini et al., 19 Apr 2024).

Selection biases thus impact scaling relations and cosmological analyses, necessitating optically selected stacks and careful selection-function modeling to recover population-averaged $f_{\mathrm{gas}}$ (Popesso et al., 25 Nov 2024, Marini et al., 19 Apr 2024).

Spectroscopic systematics, especially temperature calibration, also introduce systematics in $f_{\mathrm{gas}}$ inference:

• eROSITA gas temperatures are systematically lower than those from Chandra or XMM-Newton by $20$–$38\%$ (increasing with $T$) in the $0.7$–$7$ keV band (Migkas et al., 30 Jan 2024).
• This leads to hydrostatic masses, and thus total mass estimates, being too low, which artificially boosts $f_{\mathrm{gas}}$.
• Published conversion relations between eROSITA and legacy instruments must be applied for accurate $f_{\mathrm{gas}}$ inference.

4. Physical Interpretation and Comparison with Simulations

The observed trend of increasing gas fraction with halo mass and the sub-cosmic $f_{\mathrm{gas}}$ in groups versus clusters directly reflect the impact of baryonic feedback:

• AGN feedback and supernova-driven winds can expel or redistribute gas to large radii in $M_{200} \lesssim 10^{14} M_\odot$ halos, depressing $f_{\mathrm{gas}}$ well below the cosmic baryon fraction.
• At cluster ($M_{200}\gtrsim10^{15}M_\odot$) scales, gravitational retention overcomes feedback, and the majority of baryons are found in the hot phase within the virial radius.

Comparison with leading hydrodynamical simulations (BAHAMAS, FLAMINGO, Illustris, IllustrisTNG, MillenniumTNG) shows these models generally overpredict $f_{\mathrm{gas}}$ in groups by up to a factor of three. Only Magneticum and SIMBA better match observed group-scale $f_{\mathrm{gas}}$, implying a need to calibrate feedback processes (energy input, frequency, coupling efficiency) to simultaneously reproduce the hot gas profile and stellar content (Popesso et al., 25 Nov 2024).

In filaments, eROSITA measurements of moderate temperature ($kT \sim 0.6$–$1.0$ keV) and baryon overdensity are consistent with the WHIM phase of cosmological simulations, though observed temperatures sometimes exceed the canonical WHIM ($T \lesssim 10^7$ K), likely due to gravitational heating and projection effects in dense environments (Veronica et al., 2023, Tanimura et al., 2022, Zhang et al., 31 May 2024).

5. Implications for Cosmology and Astrophysics

The systematic measurement of X-ray gas fractions with eROSITA has far-reaching implications:

• Cluster cosmology: $f_{\mathrm{gas}}$ measurements constrain the cosmic baryon fraction and are central to the use of clusters as standardizable mass proxies for cosmological tests.
• Scaling relation calibration: Hot gas fractions, together with cluster X-ray luminosity and temperature measurements, inform self-consistent calibration of scaling relations used for cluster mass estimation.
• Galaxy formation theory: Low $f_{\mathrm{gas}}$ in groups sets strong constraints on the efficiency and physics of baryonic feedback, with implications for galaxy quenching and circumgalactic matter cycling.
• Baryon census: WHIM detection closes the “missing baryon” budget, showing that a non-negligible fraction resides in hot, faint phases in filaments and the cosmic web, accessible only through stacking methods on wide-field eROSITA data.

6. Methodological Innovations and Future Prospects

Key methodological advances in eROSITA gas fraction science include:

• Non-parametric deprojection and PSF-corrected surface brightness fitting allow gas mass measurement at low S/N.
• Physically motivated stacking techniques, validated by realistic mocks using optical catalogs, extend $f_{\mathrm{gas}}$ studies to low-mass, X-ray–undetected groups.
• Multi-wavelength joint analysis (e.g., combining X-ray gas fractions with kinetic SZ, weak lensing) greatly improves constraints on gas expulsion, spatial gas distribution, and feedback physics (Popesso et al., 25 Nov 2024).

Future prospects include:

• Improved temperature calibration and deeper survey coverage will reduce systematic uncertainties in $f_{\mathrm{gas}}$.
• Cross-survey joint analyses will enable physical reconstruction of the full baryonic mass distribution and more stringent tests of feedback models.
• The upcoming next-generation X-ray missions (e.g., LEM) with higher spectral and spatial resolution will resolve multiphase gas components, testing projection and clumping systematics that eROSITA stacking cannot fully resolve.

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Summary Table: Key Scaling Relations for eROSITA Gas Fraction Studies

Scaling Relation	Formula / Parameterization	Applicability
Total galaxy X-ray luminosity	$$L_{\mathrm{X,gal}} = L_{\mathrm{X,XRB}} + L_{\mathrm{X,gas}}$$	Galaxies
XRB luminosity scaling	$$L_{2-10,\mathrm{XRB}} = \alpha_0 M_\star + \beta_0 \,\mathrm{SFR}$$	Galaxies
Diffuse hot gas, late/early types	$L_{0.5-2,\mathrm{gas}}/\mathrm{SFR}$ or $\log L_{0.3-8,\mathrm{gas}}$ vs $L_K$	Galaxies
Cluster/group gas mass	$$M_{\mathrm{gas}} = 4\pi \mu_e m_p \int n_e(r) r^2 dr$$	Groups, clusters
Gas fraction	$f_{\mathrm{gas}} = M_{\mathrm{gas}} / M_{500}$	Groups, clusters
$f_{\mathrm{gas}}$–$M_{500}$ relation (stacked)	$$f_{\mathrm{gas},500} = 2.23 \times 10^{-7} (M_{500}/M_\odot)^{0.39}$$	All masses (stacking)
Filament central baryon overdensity	$\log(\Delta_b) = 1.88 \pm 0.18$	Cosmic filaments (stacked)
$f_{\mathrm{gas}}$ normalization (clusters)	Approaches $\Omega_b/\Omega_m$	Massive clusters

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eROSITA X-ray gas fractions thus provide a physically grounded, multi-scale census of the hot baryon content in the universe—constraining feedback physics, informing cosmology, and mapping the thermodynamics of cosmic structure with a breadth and depth unparalleled in previous X-ray surveys.