The Missing Baryon Problem & the WHIM
Big Bang Nucleosynthesis and the Cosmic Microwave Background independently fix the cosmic baryon density at Ω_b = 0.0493 ± 0.0006 (4.93% of critical density), and Lyman-alpha forest observations at z > 2 directly detect nearly all of these baryons. In the low-redshift universe (z < 1), however, stars, cold gas in galaxies, and hot intracluster X-ray gas account for only ~60–70% of Ω_b. The remaining ~30–40% of normal matter was located in the Warm-Hot Intergalactic Medium (WHIM)—diffuse cosmic-web filament gas shock-heated to 10⁵–10⁷ K—confirmed via X-ray O VII/O VIII absorption, stacked Sunyaev-Zel'dovich maps, and Fast Radio Burst (FRB) dispersion measures.
Physical Mechanism & Dynamics
As cosmic-web filaments collapse gravitationally and receive energetic feedback from active galactic nuclei and supernova winds over the past 10 billion years, intergalactic hydrogen and helium are shock-heated to temperatures of T ≈ 10⁵–10⁷ K at low overdensities (δ_b ≈ 5–100, n_e ≈ 10⁻⁶–10⁻⁴ cm⁻³). At these temperatures, hydrogen is completely ionized (so it produces no optical Lyman-alpha absorption), yet the gas is too diffuse to emit bright thermal Bremsstrahlung X-rays (since j_ff ∝ n_e²).
Three complementary techniques closed the low-redshift baryon budget: (1) high-resolution X-ray grating spectroscopy (XMM-Newton and Chandra) of highly ionized oxygen lines (O VII at 21.60 Å and O VIII at 18.97 Å) toward bright blazars; (2) stacking Planck/ACT thermal and kinetic Sunyaev-Zel'dovich signals along intercluster bridges; and (3) Macquart's (2020) relation using the plasma dispersion measure DM = ∫ n_e dl / (1 + z) of localized extragalactic Fast Radio Bursts.
Quantitatively, this mechanism is governed by Macquart FRB Intergalactic Dispersion Measure Relation (⟨DM_IGM(z)⟩ = (3 c H_0 Ω_b f_IGM / 8π G m_p) ∫_0^z [(1 + z') χ_e(z') / E(z')] dz' ≈ 930 z pc cm^-3 (low z)). Counts every free electron along the sightline regardless of gas temperature, directly measuring Ω_b = 0.049 ± 0.004 in the late universe (Macquart et al. 2020).
Macquart FRB Intergalactic Dispersion Measure Relation
⟨DM_IGM(z)⟩ = (3 c H_0 Ω_b f_IGM / 8π G m_p) ∫_0^z [(1 + z') χ_e(z') / E(z')] dz' ≈ 930 z pc cm^-3 (low z)Counts every free electron along the sightline regardless of gas temperature, directly measuring Ω_b = 0.049 ± 0.004 in the late universe (Macquart et al. 2020).
Quantitative Benchmarks & Parameters
| Parameter / Observable | Measured Value / Scale | Method & Context |
|---|---|---|
| Primordial baryon fraction Ω_b | 0.0493 ± 0.0006 (ω_b = 0.02237) | Planck CMB acoustic peaks + BBN D/H |
| Baryons in stars & cold galactic gas | ~9–10% of total baryons | Optical/NIR stellar mass functions + 21-cm H I + CO |
| Photoionized Lyα forest + circumgalactic gas | ~40–45% of total baryons | HST COS UV absorption at z < 0.5 (Shull et al. 2012) |
| Warm-Hot Intergalactic Medium (WHIM) | ~35–40% of total baryons (T = 10⁵–10⁷ K) | XMM-Newton O VII absorbers (Nicastro et al. 2018) + FRB DMs |
Observational Evidence & How Scientists Know
Nicastro et al. (2018) detected two intervening O VII WHIM absorption systems at z = 0.355 and z = 0.434 in a deep XMM-Newton RGS spectrum of the blazar 1ES 1553+113, while Macquart et al. (2020) and subsequent ASKAP/DSA-110/CHIME localized FRB samples measured the cosmic electron column density out to z > 1, matching the Planck Ω_b value to within 1σ.
Across reference datasets (Planck 2018 Cosmological Parameters (PR3)), quantitative benchmarks for the missing baryon problem & the whim are anchored by: Primordial baryon fraction Ω_b (0.0493 ± 0.0006 (ω_b = 0.02237), via Planck CMB acoustic peaks + BBN D/H); Baryons in stars & cold galactic gas (~9–10% of total baryons, via Optical/NIR stellar mass functions + 21-cm H I + CO); Photoionized Lyα forest + circumgalactic gas (~40–45% of total baryons, via HST COS UV absorption at z < 0.5 (Shull et al. 2012)); Warm-Hot Intergalactic Medium (WHIM) (~35–40% of total baryons (T = 10⁵–10⁷ K), via XMM-Newton O VII absorbers (Nicastro et al. 2018) + FRB DMs).
Uncertainties, Systematics & Open Questions
Determining what fraction of ionized baryons resides inside extended galactic halos (the circumgalactic medium out to 2–3 R_vir, expelled by AGN feedback) versus unbound intergalactic filaments is a major target of FRB cross-correlations and kinetic SZ mapping.
Real Astronomical Benchmarks & Cross-Domain Links
Fast Radio Bursts (FRBs)
Millisecond radio transients whose frequency-dependent dispersion measures weigh ionized cosmic-web electrons
Baryonic & Dark Inventory
Full breakdown of cosmic energy density across radiation, baryons, dark matter, and dark energy
XMM-Newton Space Observatory
High-throughput X-ray mission whose reflection grating spectrometers detected O VII WHIM absorbers
Guided Learning Path
Related Concepts, Methods & Explorers
Scientific Sources & Provenance
- Planck 2018 Cosmological Parameters (PR3) (PR3 (2020 A&A 641, A6)) — Planck Collaboration, Aghanim, N., et al. 2020, A&A, 641, A6. Archive / Reference ↗
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