From Feedback-Free Star Clusters to Little Red Dots via Compaction

TL;DR

The paper tackles the origin of JWST-detected Little Red Dots (LRDs) at cosmic morning by proposing a two-stage formation: first, feedback-free starbursts produce thousands of dense star clusters that form central black-hole seeds; second, these clusters migrate and merge dryly to build a compact central system, with wet compaction events further deepening the potential to retain black holes after mergers. Analytically, two-body relaxation and disk-driven dynamical friction enable inward migration on ~100 Myr timescales, yielding central clusters of order $M\sim10^9 M_\odot$ within $R\sim60$ pc, while BH seeds merge into central SMBHs only if the potential well is deepened. Cosmological simulations of VELA, FirstLight, and MAGE show compaction-driven growth can raise central densities and escape velocities by factors of $\sim0.5-1.5$ dex, enabling BH retention and producing LRD-like compact cores with post-compaction blue envelopes, consistent with the observed abundance $n\sim10^{-5}-10^{-4}\,\mathrm{Mpc^{-3}}$ and its redshift evolution from $z\sim8$ to $z\sim4$. Overall, the work links early cluster physics and gas-dynamics-driven compactions to the existence and later disappearance of LRDs, highlighting the role of dry cluster migration for BH seeding and the necessity of wet compaction to resolve GW recoil constraints in the early growth of SMBHs.

Abstract

We address the origin of the Little Red Dots (LRDs) seen by JWST at cosmic morning ($z \!=\! 4 \!-\! 8$) as compact stellar systems with over-massive black holes (BHs). We propose that LRDs form naturally after feedback-free starbursts (FFB) in thousands of star clusters and following wet compaction. Analytically, we show how the clusters enable efficient dry migration of stars and BHs to the galaxy center by two-body segregation and dynamical friction against the disk. The clusters merge to form compact central clusters as observed. Mutual tidal stripping does not qualitatively affect the analysis. The young, rotating clusters are natural sites for the formation of BH seeds via rapid core collapse. The migrating clusters carry the BH seeds, which merge into central super-massive BHs (SMBHs). Compactions are required to deepen the potential wells such that the SMBHs are retained after post-merger gravitational-wave recoils, locked to the galaxy centers. Using cosmological simulations at different epochs, with different codes and physical recipes, we evaluate the additional growth of LRD-matching compact central stellar systems by global compaction events. Adding to the dry growth by cluster mergers, the compactions can increase the escape velocities to retain the SMBHs. The LRDs appear at $z \!\sim\! 8$, after the formation of FFB clusters, and disappear after $z \!\sim\! 4$ when the stellar mass is above $10^9 M_\odot$ by growing post-compaction blue disks around the nuclear LRDs. The LRD abundance is expected to be $\sim\! 10^{-5} \!-\! 10^{-4}\,{\rm Mpc}^{-3}$, increasing from $z \!\sim\! 4$ to $z\!\sim\! 8$.

Figures (8)

• Figure 1: Migration timescales from the half-mass radius to the center as a function of cluster mass. The disk and cluster properties are the fiducial FFB values (§\ref{['sec:clusters']}). Shown are the timescales for two-body segregation (red, eq. (\ref{['eq:tseg']})), for dynamical friction by a hot disk (eq. (\ref{['eq:tdf_disk_1']})) for a smoothed component fraction $s\!=\! 0.1$ (solid blue) and $s\!=\! 0.5$ (dashed blue), and for dynamical friction by the halo (green, eq. (\ref{['eq:tdf_h1']})). For the segregation $M_{\rm c}$ stands for the maximum cluster mass, while for the dynamical friction it is the mass weighted average cluster mass.
• Figure 2: Evolution of central dry merger remnant. A sequence of mergers is followed using eq. (\ref{['eq:merger']}). Left: the incoming mergers are of mass $M_{\rm c} \!=\! 10^6M_\odot$. Right: the incoming mergers are of mass $M$ equal to the current central cluster. Shown are the half mass radius $R$, the corresponding 3D and surface mean densities within $R$, $\rho$ and $\Sigma$, and the escape velocity (multiplied by $\sqrt{2}$ to account for a dark-matter halo and gas component).
• Figure 3: Evolution of clusters in a sequence of mutual tidal encounters assuming the impulse approximation and the tidal limit. Left: Tidal mass loss, for clusters of initial mass $M_{\rm c} \!=\! M_{\rm p} \!=\! 10^6M_\odot$ and radius $R_{\rm c} \!=\! 7\,{\rm pc}$, for different values of relative velocities $V_{\rm p}$. The clusters largely remain in tact during the migration time of $\sim\!100\,{\rm Myr}$, while a non-negligible smooth component develops for $V_{\rm p} \!>\! 100\,\,{\rm s}^{-1} km$$s$^-1$$. Right: Evolution of cluster mass $M_{\rm c}$ (blue), radius $R_{\rm c}$ (red), and circular velocity $V_{\rm c}$ (green), compared to impact parameter $p$ (dashed red) and relative velocity $V_{\rm p}$ (dashed green, assumed here to be $50\,\,{\rm s}^{-1} km$$s$^-1$$). The validity of the impulse approximation and the tidal limit are indicated by $V_{\rm p} \!>\! V_{\rm c}$ and $p \!>\! R_{\rm c}$, respectively.
• Figure 4: The recoil bottleneck of SMBH growth by BH mergers based on Monte Carlo simulations dekel25_bh. The numbers (and colors) in each entry of the table represent the fraction of galaxies that allow SMBH growth exceeding $10^6M_\odot$, as a function of the escape velocity from the galaxy $V_{\rm esc}$. We consider the threshold escape velocity for retaining the SMBH to be given by a fraction of $\sim\!0.5$, namely near the entries colored yellow in the transition from red to blue colors. Shown are four cases of the BH mass-function slope $\beta$, with the fiducial case being $\beta \!=\! 1.5$. Also shown are cases of cold disk and hot disk, with spin-orbit misalignments $\theta \!=\! 0 \!-\! 10^\circ$ and $\theta \!=\! 0 \!-\! 30^\circ$, respectively. Within each of the eight sub-tables, shown are three cases of the initial primary BH mass, $m_0$, which was either selected to be $10^5M_\odot$ or $10^4M_\odot$, or was drawn at random from the seed BH mass function in the range $(10^2 \!-\! 10^4M_\odot)$. Focusing on the fiducial values adopted by dekel25_bh, of $\beta\!=\! 1.5$, a hot disk, and initial BH masses of $(10^2 \!-\! 10^4M_\odot)$, we read that the threshold escape velocity is $V_{\rm esc} \!\simeq\! 487\,\,{\rm s}^{-1} km$$s$^-1$$. In comparison, the fiducial escape velocity of an FFB galaxy is $V_{\rm esc} \!\sim\! 200\,\,{\rm s}^{-1} km$$s$^-1$$ when ignoring compaction (§\ref{['sec:clusters']}), but it could rise to several hundred $\,\,{\rm s}^{-1} km$$s$^-1$$ after compaction (§\ref{['sec:compaction']}).
• Figure 5: Wet compaction in a VELA simulation (V07). Shown is face-on density for gas (top) and stars (bottom). A merger causes gas compaction ($z\!=\! 3.4$), leading to a compact central star-bursting "blue nugget" ($z\!=\! 3.2$), which passively evolves to a long-lived "red nugget" (from $z\!=\! 2.6$ to $z\!=\! 1.2$ and on). The central mass allows the stabilization of an extended star-forming gas disk by incoming streams ($z\!=\! 2.6$), which evolves into an extended ring ($z \!=\! 1.2$). The red nugget resembles an LRD, while the emergence of an extended disk marks the end of the phase that is observationally identified as an LRD.