A possible pathway to UHZ1-type systems at z~10 by heterogeneous mass primordial black holes as dark matter

TL;DR

Problem: explain the existence of UHZ1-like systems at redshift around 10 with a central massive BH and a substantial stellar component. Approach: propose that PBHs constitute part of DM with a broad mass function, which adds a granulation component to the small-scale matter power and drives earlier halo collapse. Mechanism: after halos virialize, dynamical friction moves the heaviest PBHs to the center, forming a central BH of order $10^{7}-10^{8}M_ullet$ by $z\sim 10$ in halos of $M_H\gtrsim 10^9 M_\ extodot$, while the baryonic gas collapses to form stars. Results: this PBH-DM pathway can reproduce UHZ1-like systems and may also account for other JWST-detected high-z objects such as the Little Red Dots. Significance: it provides a DM-driven channel for rapid SMBH assembly in the early universe, with testable predictions for the high-redshift halo and BH demographics.

Abstract

Recent space-based observations discovered several unusual objects, exhibiting similar properties, at redshifts $z\gtrsim 10$. Among them is the UHZ1 system at $z=10.1$, containing $\sim 10^8M_\odot$ in stars, with a similarly massive central black hole of $\sim 10^{7-8}M_\odot$. Here we propose a possible mechanism for forming such systems which hinges on the presence of primordial black holes (PBHs) covering a range of masses while contributing a significant fraction of the dark matter (DM). We evaluate the accurate expression for the small-scale power responsible for the collapse of the first halos in the presence of the PBH population. The extra power in the matter density field, produced by the granulation term, will cause an earlier collapse of DM halos, populated by PBHs of different masses. In these collapsed and virialized systems the PBHs will undergo 2-body relaxation, driving the more massive PBHs to the halo center under dynamical friction. We quantify this evolution for a distribution of PBH orbital parameters and halo properties. The analysis shows that PBHs can have appropriate mass functions capable of producing systems with parameters similar to what is observed for UHZ1. We suggest that the proposed mechanism could account for a subset of other systems newly discovered with the JWST at high redshifts, including the Little Red Dots.

Figures (4)

• Figure 1: High-redshift structure formation in PBH cosmology. Top: (a) Scaled power spectra for concordance (C)DM model at $z=700,100,20$, shown with red-dotted, blue-dashed and black-solid lines, respectively. (b) (C)DM power relevant for early small scale collapse, shown with black dotted line, compared to the fit according to Eq. \ref{['eq:power_small']} (blue solid line). Thickest, thick and thin solid horizontal lines correspond to $f_{\rm PBH}M_{\rm PBH}=20, 10, 2\, M_\odot$, respectively.
• Figure 2: Ratio of the ($1\sigma$) standard deviation of the density fluctuation amplitude to $\delta_{\rm col}=1.68$, shown in red at $z=700$, whereas the $3\sigma$ levels are shown in blue: dotted lines correspond to the power without PBH contribution, and thickest, thick and thin solid lines to PBH cosmologies with $f_{\rm PBH}M_{\rm PBH}=20, 10, 2\, M_\odot$, respectively. Horizontal dashed lines indicate the density amplitude required at that redshift to collapse at the marked values of $z$. Vertical dashed lines show the mass with $T_{\rm vir}>10^4$ K at the marked $z$, as required for the gas to cool, collapse and fragment into stars in the absence of H$_2$Oh2002. The estimated mass range of the UHZ1 BH is represented with the gray shading Bogdan:2024, whereas the estimated mass range of the stellar component is marked in green Goulding:2023. The vertical solid line marks the minimal halo mass implied by the stellar mass for UHZ1.
• Figure 3: Dynamical friction collapse time $t_{\rm df}$ from solving numerically eqs. \ref{['eq:motion']}, in units of the crossing/orbital time, $R_{\rm H}/V_0$ as a function of $\lambda$ and ${\cal C}$. These results correspond to $m_\bullet \ln \Lambda/M_{\rm H}=0.01$ and can be rescaled to other values since $t_{\rm df}\propto (m_\bullet \ln \Lambda/M_{\rm H})^{-1}$. Dashed horizontal lines mark $(1,2,3)\times t_{\rm cosm}(z)$, whereas the dotted line indicates the time for an individual halo to remain intact from $z=50$ to $z=10$. Left:$t_{\rm df}$ vs. $\lambda$; NFW halo profiles with ${\cal C}=10,20,30,40, 100$, are shown with blue, orange, green, red, and purple solid lines, and isothermal halo profiles with the same concentrations are shown with corresponding dash-dotted lines. The isothermal, non-truncated distribution ${\cal F}(E)$ was adopted. Right: Same vertical axis vs. the concentration parameter, ${\cal C}$. Solid lines represent NFW profiles with $\lambda=0.05,0.1,.0.15,0.2,0.3$ in blue, orange, green, red, and purple, respectively, and dash-dotted lines correspond to isothermal profiles.
• Figure 4: Impact of advection on the halo mass function. We compare the ratio of the number density of collapsed objects (per unit mass) for models with advection to models without it. Dashed (blue), dot-dashed (red), triple dot-dashed (green), long dashed (gold) and solid (black) lines correspond to $f_{\rm PBH}M_{\rm PBH}=(20,10,5,2,0)M_\odot$, respectively. The vertical gray lines correspond to the masses of halos that have reached a virial temperature $T_{\rm vir}=10^3$ K (left), which allows H$_2$ formation and cooling, and $T_{\rm vir}=10^4$ K (right), with atomic hydrogen cooling in the absence of H$_2$Jaacks2019. The different plots correspond to different $z$, as indicated.