Little Red Dots and Supermassive Black Hole Seed Formation in Ultralight Dark Matter Halos

TL;DR

The paper tackles how supermassive black hole seeds can form in the centers of ultralight dark matter halos without relying on external UV backgrounds. It introduces a mechanism in which ULDM solitons create deep central potentials that drive rapid, monolithic baryonic collapse, with fragmentation suppressed when the gas temperature exceeds about $3\times 10^4$ K; this yields SMBH seeds of order $M_{bh}\sim 10^5 M_\odot$, and an upper bound near $10^{10} M_\odot$, for a ULDM particle mass $m\simeq 10^{-22}$ eV. The work derives semi-analytic relations linking halo mass, soliton mass, and baryonic core properties via quantum Jeans scales and a core–halo relation, and shows that efficient seed formation is expected at $z\gtrsim 10$, consistent with observations of little red dots. It also connects the seed formation physics to galactic core scales and predicts testable implications for high-redshift SMBH demographics and ULDM parameter space.

Abstract

We investigate how supermassive black hole (SMBH) seeds form in the early Universe at the centers of ultralight dark matter (ULDM) halos. Focusing on the ULDM Jeans scale, we identify the critical conditions under which high-redshift baryonic gas, strongly confined by central solitonic cores of the halos, undergoes direct and monolithic collapse. The solitonic potential naturally drives rapid inflow and shock heating, allowing the gas to exceed the critical atomic-cooling and fragmentation-suppression threshold of $\sim 3 \times 10^4 {\rm K}$ without invoking an external UV background. We derive semi-analytic relations for the halo mass, soliton mass, baryonic core radius, and thermodynamic state of the gas, including the effects of baryonic contraction. These relations simultaneously determine the minimum and maximum SMBH seed masses as functions of redshift. In this framework, pristine gas clouds that satisfy the temperature threshold collapse without fragmentation, forming SMBH seeds with characteristic masses of order $\sim 10^5M_\odot$, while systems below the threshold are expected to form compact star clusters instead. Our model also implies an upper limit on the attainable SMBH mass, predicting a maximum mass scale of order $\sim10^{10}M_\odot$, consistent with the most massive quasars observed to date. The ULDM particle mass required to reproduce the inferred seed mass scale, $m \simeq 10^{-22}{\rm eV}$, coincides with the value favored by galactic-scale observations, providing a unified explanation for the characteristic masses of both galactic cores and early SMBH seeds. Our model predicts efficient SMBH seed formation at redshifts $z \gtrsim 10$ and offers a natural interpretation of recently observed little red dots as SMBHs embedded in compact, hot, ionized gas clouds.

Figures (3)

• Figure 1: Halo mass functions (HMFs) for CDM (solid lines) and ULDM (dashed lines, for $m_{22}=1$) at redshifts $z = 0\sim11$, computed within the Press–Schechter formalism. HMFs increase as $z$ decreases, with the highest curves corresponding to $z=0$. Relative to CDM, ULDM shows a pronounced suppression of low-mass halos arising from the small-scale cutoff in the matter power spectrum.
• Figure 2: The minimum mass $M_J$ (the thick lines) and the maximum mass $M_{upper}$ (the dashed line) of ULDM halos as functions of the redshift $z$ for $m_{22}=(0.1,1,10)$, respectively. The halo mass decides the core masses of ULDM and those of gas clouds using the core-halo relation. For $M_{upper}$, we used the CDM approximation. At a given $z$, only halos with masses between $M_J$ and $M_{ upper}$ can exist.
• Figure 3: The mass spectrum of SMBHs as a function of redshift. The black horizontal line denotes the masses of SMBH seeds corresponding to $\alpha_{th}$. The blue dashed line and the purple dashed line denote the possible SMBH seed mass in Eq. (\ref{['bound']}) for $\alpha=1$ and $\alpha=\alpha_{max}$, respectively. However, objects located between the black horizontal line and the blue line cannot be genuine black hole seeds because the gas temperature is too low and fragmentation is unavoidable; instead, these systems are expected to form star clusters. According to Eq. (\ref{['alphath']}) in our model, only gas clouds corresponding to the SMBH seeds in the gray region possess sufficient self-gravity and temperature to form a SMBH seed. The dashed horizontal red line denotes the maximum black hole mass $M_{bh}^{max}$ in Eq. (\ref{['Mbhmax']}) set by the stability of the soliton. Dots represent the observed masses of SMBHs from various observations Dewangan2008ApJVestergaard_2009Willott_2010Mortlock_2011Larson_2023natarajan2023detectionovermassiveblackhole. The red triangles denote XMM-Newton observations Dewangan2008ApJ, the green circles represent LBQS observations Vestergaard_2009, the black diamonds denote CFHQS observations Willott_2010. The red stars denote quasars with $z>7$Mortlock_2011Larson_2023natarajan2023detectionovermassiveblackhole, while the red star at $z=10.1$ is for the quasar in the galaxy UHZ1. The red disks denote the candidate SMBHs in LRDs Rusakov2026LittleRedDots. We choose $m=10^{-22}eV$ and $f_{bh}=0.1$ here.