Reionization-Limited HI Clouds (RELHIC)

Updated 29 August 2025

Reionization-Limited HI Clouds (RELHICs) are starless, compact neutral hydrogen reservoirs in low-mass halos governed by reionization and pressure equilibrium.
Simulations and observations reveal key characteristics such as HI masses around 10⁶ M_⊙, narrow line widths (12–20 km/s), and minimal or undetectable stellar components.
Studying RELHICs provides insights into reionization feedback, the critical halo mass for star formation, and the interplay between gas physics and dark matter.

A Reionization-Limited HI Cloud (RELHIC) is defined as a compact, starless neutral hydrogen (HI) cloud residing within a dark matter halo whose baryonic content and thermodynamic structure are determined by the photoheating and hydrodynamic effects of cosmic reionization. RELHICs are a robust prediction of the ΛCDM cosmological paradigm for low-mass halos (M_halo ≲ 10¹⁰ M_⊙) that have never formed stars and retain HI gas in hydrostatic and ionization equilibrium with the intergalactic ultraviolet (UV) background. They constitute observational and theoretical benchmarks for probing the low-mass end of the halo mass function, the nature of reionization feedback, and the limits of galaxy formation.

1. Theoretical Foundation and Formation Mechanism

The RELHIC scenario emerges naturally in high-resolution cosmological hydrodynamics simulations (e.g., APOSTLE) exploring the fate of low-mass halos after cosmic reionization (Benítez-Llambay et al., 2016). When reionization occurs, photoionization heats the intergalactic gas (to T ≳ 10⁴ K), dramatically increasing the Jeans mass and causing the baryonic content of shallow potential wells (halo masses M_200 ≲ 5 × 10⁹ M_⊙) to be depleted via evaporation and the suppression of further accretion. In such halos, the remaining baryons rapidly attain hydrostatic and thermal equilibrium with the photoionizing background, establishing characteristic gas and HI profiles.

RELHICs thus develop as “starless” minihalos that failed to reach the density and temperature requirements for sustained star formation, yet can retain a gaseous core due to the suppression of photoionization-driven winds in the densest regions. The boundary between “dark” RELHICs and luminous dwarfs is defined by a threshold halo mass (the critical mass for galaxy formation), empirically constrained by the presence or absence of any detectable stellar component (Anand et al., 27 Aug 2025).

A key analytic relation for the gas distribution, assuming spherical symmetry and hydrostatic equilibrium, is:

$\frac{1}{\rho} \frac{dP}{dr} = -\frac{GM(r)}{r^2}$

where P is the pressure, ρ the gas density, and M(r) the dark matter mass (typically modeled by the NFW profile) within radius r (Benítez-Llambay et al., 2016). The temperature-density relation for gas in thermal equilibrium with the UV background is:

$T(\rho) = T_0 \left( \frac{\rho}{\rho_0} \right)^{\gamma_0}$

with T₀ ≈ 10⁴ K and γ₀ ≃ 0.54 for low-density gas.

2. Observable Properties and Empirical Constraints

RELHICs are characterized observationally as compact, kinematically cold HI sources, with HI masses M_HI ∼ 10⁶ M_⊙, sub-kpc neutral cores, and narrow, thermally-broadened line widths (W₅₀ ≲ 20 km s⁻¹) (Benítez-Llambay et al., 2016, Zhou et al., 2023, Benitez-Llambay et al., 2023, Anand et al., 27 Aug 2025). The predicted HI column densities can reach up to 10²¹ cm⁻² in the most massive systems but fall steeply for lower-mass halos. The morphologies are typically round (axis ratio b/a > 0.8 for low column density contours), and significant non-thermal broadening or rotation is absent.

Key observational diagnostics:

HI Mass:

$M_{\mathrm{HI}} = 2.356 \times 10^5\,D^2\,S$

where D is the distance in Mpc and S the integrated flux in Jy·km s⁻¹.

Thermal Line Width:

$W_{50} \approx 2\sqrt{2 \ln 2}\,\sigma_v$

with σ_v the thermal velocity dispersion inferred from T ≈ 21.8 × (W₅₀ [km/s])².

HI-to-Stellar Mass Ratio: RELHICs are extreme outliers, with

$\frac{M_{\mathrm{HI}}}{M_\ast} \gtrsim 10^2$

in confirmed cases (Anand et al., 27 Aug 2025).

The recent identification of Cloud-9 near M94, supported by multi-telescope HI and deep HST ACS optical imaging, is the most compelling observational evidence for a RELHIC. Cloud-9 has M_HI ≈ 10⁶ M_⊙, W₅₀ ≈ 12 km s⁻¹, no detected stellar counterpart down to M_★ ≲ 10^{{3.5} M_⊙,} and a dynamical mass estimate (from hydrostatic equilibrium) of M_halo ≈ 5 × 10⁹ M_⊙ (Zhou et al., 2023, Benitez-Llambay et al., 2023, Karunakaran et al., 16 Jan 2024, Anand et al., 27 Aug 2025).

3. Physical Processes Governing RELHIC Properties

RELHICs result from the interaction of reionization feedback and halo structure:

Photoionization Heating: The UV background heats gas to ≳10⁴ K, enforcing a temperature–density relation and suppressing H₂ cooling in halos below the atomic cooling threshold.
Pressure Confinement: Gas in RELHICs is pressure-supported against the host halo's gravitational potential; at low densities, the external pressure provided by the IGM (itself photoheated) sets the outer boundary for HI cores (Suarez et al., 2020).
Self-Shielding and Neutral Core Formation: At sufficiently high density, inner gas regions in RELHICs become self-shielded, allowing a small neutral HI core to persist while the outer layers remain ionized (Benítez-Llambay et al., 2016, Garcia et al., 2017, Fan et al., 2022).
Limited Gas Accretion and Cooling: Below the critical mass (M_crit ≈ 10¹⁰ M_⊙), halos cannot accrete or retain enough cold gas to form stars post-reionization, ensuring starless, HI-dominated status (Anand et al., 27 Aug 2025).

4. Connection to Reionization Simulations and Feedback

Cosmological reionization simulations consistently predict the existence and properties of RELHICs:

Mass and Environmental Dependence: RELHICs occur primarily in low-mass halos (M_200 ≲ 5×10⁹ M_⊙) located in low-density, low-tidal environments, where ram-pressure stripping is negligible (Benítez-Llambay et al., 2016).
Photoionization and Recombination Regulation: Detailed ionization and radiative transfer modeling confirms that the balance of ionizing photon supply, inhomogeneous recombinations, and self-shielding determines HI core sizes and survival timescales (Sobacchi et al., 2014, Park et al., 2016).
Feedback and Clumping Factor: The clumping factor of ionized gas (C_HII ≈ 4 by end-reionization) boosts recombination rates in dense substructure, implying higher resilience of RELHICs in such regions (Sobacchi et al., 2014, Park et al., 2016).

Established analytic models solve for hydrostatic equilibrium within an NFW (Navarro-Frenk-White) halo with pressure and temperature relations set by the UV background and local density, yielding neutral core properties closely matching those of Cloud-9 (Benitez-Llambay et al., 2023).

5. RELHICs in the Context of the 21-cm Signal and HI Observations

RELHICs have direct implications for the cosmic 21-cm background and HI surveys:

21-cm Signature: RELHICs contribute a faint, compact 21-cm emission component, increasing the small-scale power and providing a source of residual HI in the nearly fully ionized IGM (0911.0244, Watkinson et al., 2015, Xu et al., 2019, Giri et al., 7 Mar 2024).
Power Spectrum Suppression and Variance: Residual HI inside HII regions and RELHICs suppresses the contrast in 21-cm brightness temperature maps, lowering variance and modifying the shape and amplitude of the power spectrum (Watkinson et al., 2015).
Detection Strategies: Next-generation blind HI surveys (e.g., with SKA, FAST, GBT, VLA) are predicted to detect the most massive RELHICs as resolved, kinematically cold, round, optically dark HI sources away from galaxies (Zhou et al., 2023, Karunakaran et al., 16 Jan 2024, Anand et al., 27 Aug 2025). The best RELHIC candidates exhibit no significant stellar counterpart even in deep CMD-based searches.

6. RELHICs as Cosmological and Galaxy Formation Probes

RELHICs occupy a critical position in constraining the physics of low-mass halos, feedback, and dark matter:

Galaxy Formation Threshold: The emerging consensus from simulations and the case of Cloud-9 is that the threshold halo mass for galaxy formation at z=0 is M_crit ≈ 10^{{9.7} M_⊙} (Anand et al., 27 Aug 2025). RELHICs with M_halo ≲ M_crit retain gas but form no stars.
Dark Matter and Halo Census: RELHIC discoveries empirically confirm the existence of low-mass, dark halos “missing” from the luminous galaxy census, thus bridging the theoretical halo mass function with observations.
Pure Tests of Halo Physics: RELHICs, being unaffected by stellar feedback processes, provide laboratories for testing the interplay of gas physics, dark matter potential structure, and external pressure in a minimally complex environment (Benitez-Llambay et al., 2023, Suarez et al., 2020).
Constraints on Feedback and Cosmology: The number, spatial distribution, and detectability of RELHICs inform models of reionization, small-scale structure, and dark matter properties.

7. Open Problems, Challenges, and Future Directions

Outstanding challenges in RELHIC studies include:

HI Spectral Structure: Observations such as GBT/FAST spectra of Cloud-9 sometimes reveal broader or asymmetric HI lines compared to classic RELHIC predictions, suggesting possible environmental perturbations or beam-smoothing effects (Karunakaran et al., 16 Jan 2024).
Core vs. Cusp Halo Profiles: Some candidate RELHICs appear more extended than standard NFW-based models predict, raising the possibility of inner halo mass deficits or cored dark matter distributions (Benitez-Llambay et al., 2023).
Numerical Resolution: Simulations require sub-kpc resolution, accurate radiative transfer (including beyond the “slab” approximation), and sub-grid models to resolve the HI features and abundance of RELHICs (Suarez et al., 2020, Sobacchi et al., 2014).
Stellar Counterpart Limits: The ultimate confirmation of a true RELHIC rests on robust non-detection of a stellar population to deep limits (e.g., M_★ ≲ 10^{{3.5} M_⊙} via HST/ACS CMDs) (Anand et al., 27 Aug 2025).
Blind HI Surveys: Continued deep, wide-field HI imaging is essential, and improved spatial/spectral resolution will enable identification of candidate RELHICs beyond the Local Group.

Ongoing and future high-resolution HI mapping, deep optical/infrared imaging (e.g., with HST, JWST), and advanced simulation campaigns are expected to refine the statistics and constraints on RELHICs, further anchoring their cosmological and astrophysical significance.

Selected Quantitative RELHIC Properties (from (Benítez-Llambay et al., 2016, Benitez-Llambay et al., 2023, Anand et al., 27 Aug 2025)):

Parameter	Value/Range	Context
Halo mass (M_halo)	10⁸–5×10⁹ M_⊙	ΛCDM predictions
HI mass (M_HI)	10⁵–10⁶ M_⊙	Sim./observed
Line width (W₅₀)	12–20 km s⁻¹	Cloud-9, others
HI core size (r_core)	0.5–1.4 kpc	Sim./observed
HI-to-stellar mass (M_HI/M_★)	≳400	Cloud-9
Critical mass (M_crit)	≈10^{{9.7} M_⊙}	SF threshold

RELHICs, exemplified by Cloud-9, thus constitute key astrophysical structures at the interface of cosmic reionization and the halo mass spectrum, illuminating the fate of baryons in low-mass halos, setting empirical thresholds for galaxy formation, and providing unique windows into dark matter and the IGM in the local and high-redshift Universe.