The existence of supermassive black holes (SMBHs) with masses of 10⁸-10⁹ M⊙ in the early universe, evidenced by the observation of over 200 quasars at z>6, poses a significant theoretical challenge. The formation of such SMBHs within the short cosmic time since the Big Bang requires efficient mechanisms for rapid mass growth. Population (Pop) III stars, which collapse into black holes, are considered potential seeds for SMBHs, but achieving the Eddington accretion rate necessary for the observed SMBH masses is difficult due to feedback from star formation and BH accretion. The direct collapse (DC) scenario offers a more promising pathway, proposing that SMBHs originate from supermassive stars (SMSs; 10⁴⁻⁶ M⊙) forming in atomic cooling halos (ACHs) with halo masses of 10⁷⁻⁸ M⊙. In the DC scenario, suppressing H₂ cooling during cloud collapse is crucial. This can be achieved through photodissociation by far-ultraviolet (FUV) radiation from nearby stars or galaxies, or by collisional dissociation in high-density shocks. The cold accretion model is particularly interesting because it transports dense, cold gas into the halo center through cosmic filaments, potentially creating the necessary dense shocks. However, previous studies have yielded conflicting results regarding the prevalence of cold accretion in the early universe. Some studies have shown that cold flows penetrate into the virial radius of halos with halo masses of 10⁷⁻⁸ M⊙ at high redshifts, while others have found that accretion flows are virialized at the halo surface. This paper aims to determine the conditions for cold accretion in the early universe and to investigate whether it triggers SMS formation by collisional H₂ dissociation.

Existing literature presents conflicting views on cold accretion in early galaxy formation. Wise & Abel (2007) and Greif et al. (2008) observed cold flows penetrating halo virial radii in halos with masses of 10⁷⁻⁸ M⊙ at z>10, while Fernandez et al. (2014) found no such penetration, concluding that shock-heating via cold accretion is insufficient for SMS formation. The discrepancy highlights the need for further investigation into the conditions for cold accretion onset in the early universe, particularly considering the sharp decrease in cooling rates below 10⁴ K. Several models exist for SMS formation, including suppression of H₂ cooling via photodissociation by FUV radiation from nearby stars or galaxies (Chon et al. 2016), turbulent motion induced by halo mergers (Wise et al. 2019; Latif et al. 2022), or baryonic streaming motion (Schauer et al. 2017; Hirano et al. 2017). Birnboim & Dekel (2003) developed a semi-analytic model for cold accretion, predicting its occurrence in halos below a critical mass of ∼10¹¹⁻¹² M⊙ at low redshifts. This work aims to refine these models and investigate their applicability to the early universe.

This research employs a suite of cosmological simulations using the N-body + SPH code GADGET-3. Three different realizations of initial conditions were set up with MUSIC at redshift z=99, with a cosmological volume of (1 h⁻¹ cMpc)³. DM-only N-body simulations tracked halo assembly histories, identifying the most massive halos (∼10⁸ M⊙) at z∼10. Zoom-in simulations, incorporating baryonic physics, were then conducted within (0.4 h⁻¹ Mpc)³ regions centered on these target halos, using (1024)³ DM and gas particles. This resulted in mass resolutions of 68.1 h⁻¹ M⊙ for DM and 11.6 h⁻¹ M⊙ for gas, sufficient to resolve structures down to ∼10⁻¹⁻¹⁰² pc. Cosmological parameters were set to PLANCK13 values. A non-equilibrium chemistry network with 20 reactions among 5 species (e⁻, H, H⁺, H₂, and H⁻) was solved implicitly, including heating and cooling processes. A constant Lyman-Werner (LW) background radiation field (J₂₁ = 10) was assumed, sufficient to suppress Pop III star formation in mini-halos but not SMS formation. The sink particle method was employed to handle small-scale star formation, inserting sink particles when gas density exceeded 2×10⁶ cm⁻³. The equation of state was made adiabatic for slightly lower densities (≥10⁶ cm⁻³) to prevent artificial fragmentation. Each sink particle accreted gas particles within a radius 10 times the smoothing length (2-3 pc). Feedback effects from sink particles were ignored for simplicity. The researchers analyzed the gas distribution in phase space, focusing on the radial position-velocity plane, to quantify accretion flow penetration and shock positions.

The simulations revealed that the accretion flow penetrates deep into the halos after a certain epoch, with the shock position shifting inward from ∼0.1 vir to ∼0.01 vir. This transition consistently occurred when the halo mass exceeded a minimum mass of Mhalo,min ≈ 2.20 × 10⁷ M⊙ (1+z/15)⁻³/², corresponding to a virial temperature of Tvir ≈ 1.1 × 10⁴ K. This minimum mass is significantly higher than that predicted by previous studies of massive galaxy formation at low redshifts. The cold accretion emerged shortly after the first runaway collapse of a cloud in an ACH, with a time lag of Δt ≈ 10-30 Myr, suggesting that cold accretion follows the birth of normal Pop III stars in ACHs. A semi-analytic model, incorporating filamentary accretion, provided a more accurate estimation of the minimum halo mass, consistent with simulation results and previous studies. The supersonic accretion flow impacted the central gas discs (size ∼0.05 vir), generating dense accretion shocks. Despite most gas in ACHs having similar temperatures (∼10⁴ K) due to efficient Lyα cooling, the accretion flow was not exceptionally cold compared to the surrounding medium. Analysis of the central disc vicinity revealed a dense, hot (nH ∼10⁴ cm⁻³, T ∼8000 K) medium suitable for SMS formation, with a mass of ∼10⁴ M⊙. A maximal estimate of the ZoNR gas mass, derived using shock jump conditions, showed that after the emergence of cold accretion, gas consistently entered the ZoNR, primarily within the central disc. In some snapshots, this mass was comparable to the Jeans mass (∼10⁴⁻⁵ M⊙), indicating the potential for gravitational collapse and SMS formation.

The findings address the research question by establishing the conditions for cold accretion emergence in the early universe and demonstrating the potential for SMS formation via dense shocks generated by this process. The minimum halo mass for cold accretion is significantly higher than previously thought, and its emergence follows Pop III star formation in ACHs. The modified semi-analytic model that incorporates filamentary accretion accurately reflects the simulation results. The formation of dense, hot gas within the ZoNR, with mass comparable to the Jeans mass, supports the SMS formation mechanism proposed by Inayoshi & Omukai (2012). The study's findings are relevant to the field of early universe cosmology and galaxy formation by providing crucial insights into the formation of SMBHs and the role of cold accretion in this process. Further research is needed to address the limitations of neglecting stellar feedback, supernova feedback and metal enrichment.

This study established a minimum halo mass for the emergence of cold accretion in the early universe and demonstrated its potential role in SMS formation. The modified semi-analytic model successfully explained the simulation results. The simulations showed the formation of a dense, hot region with a mass potentially exceeding the Jeans mass, suggesting SMS formation. Future research should incorporate feedback processes to refine the model and investigate the actual occurrence rate of this scenario.

The study's main limitation is the omission of feedback processes, such as radiative feedback from stars, supernova feedback, and metal enrichment, due to computational constraints. These processes could significantly influence the gas dynamics and thermal evolution, potentially altering the minimum halo mass for cold accretion and the effectiveness of SMS formation. The sink particle method used for star formation introduces an artificial parameter (sink radius) whose impact on the results was assessed but not fully eliminated. Higher resolution simulations are necessary to explore the impact of these limitations.