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Enhanced density fluctuations: consequences for stellar dynamics and dark matter substructure

This paper investigates how enhanced primordial density fluctuations facilitate the early formation of stars and black holes at high redshifts, leading to a significantly increased abundance and density of dark matter subhalos and stellar clusters in the Milky Way that vary sensitively with the specific shape of the power spectrum enhancement.

Original authors: Wenzer Qin, David E. Kaplan, Neal Weiner

Published 2026-09-30

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CC BY 4.0

Original authors: Wenzer Qin, David E. Kaplan, Neal Weiner

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast, cold expanse of the early universe, gravity acts as the great sculptor, pulling invisible clumps of dark matter together to form the first gravitational wells. These wells are the nurseries where normal matter, mostly hydrogen and helium gas, can eventually settle, cool, and ignite into the first stars and galaxies. For decades, the standard model of cosmology has suggested that this process follows a predictable path: small clumps form first, but they are often too warm and too diffuse to let gas cool down enough to make stars. Only much larger, heavier clumps could get hot enough to trigger the formation of the first celestial bodies. However, this view assumes that the distribution of matter in the early universe was relatively smooth and uniform on small scales. If the universe was actually "bumpy" with much larger density variations than expected, the rules of the game would change entirely.

A new study by researchers at New York University and Johns Hopkins University explores exactly what would happen if the early universe was indeed bumpier than we thought. They investigated a scenario where the density of dark matter fluctuates more wildly than standard theories predict. In this environment, tiny clumps of dark matter would collapse much earlier and become much denser than usual. Because these clumps are so dense, they would be incredibly hot, far hotter than the standard models allow for objects of their size. This intense heat changes the way gas behaves inside them, potentially allowing stars to form in places where they were previously thought impossible, and creating a unique kind of stellar system that has never been seen before.

The researchers used analytical toy models and specialized codes to trace the fate of these early, dense clumps. They found that the extreme density of the dark matter creates a powerful gravitational environment that traps gas and heats it up. In the standard model, small clumps are too cool to form stars, or if they do form stars, the resulting explosions from dying stars blow the remaining gas away, leaving the clump dark and empty. But in this "bumpy" universe, the clumps are so dense that the gas can cool and condense even in these tiny, early structures. The gas doesn't just form a few scattered stars; the density is so high that the stars interact with each other constantly.

This constant interaction leads to a fascinating phenomenon called dynamical friction. Imagine a crowd of people walking through a room; if a heavy person walks through, the lighter people around them will naturally drift toward the heavy person's path, slowing them down. In these dense early clumps, the stars act like the heavy people, and the invisible dark matter acts like the lighter crowd. As the stars move through the dark matter, they lose energy and sink toward the very center of the clump. This process happens so quickly that the stars pile up into a tight, dense ball, forming a star cluster rather than a sprawling, diffuse galaxy. The researchers calculated that if the density fluctuations were just right, the early universe could have been filled with these compact, ancient star clusters, with initial stellar masses ranging from roughly 200 to 500 solar masses, forming when the universe was less than 1% of its current age.

The study also looked at how many of these objects might still be around today, specifically within our own Milky Way galaxy. The answer depends heavily on the shape of the initial density fluctuations. If the fluctuations were very sharp and narrow, the simulations suggest the Milky Way might have captured about 50 of these ancient clusters. If the fluctuations were broader and stepped, the number could be as high as 410,000. While many of these clusters would have been destroyed over billions of years by tidal forces and other cosmic events, the sheer number of survivors in the broader scenario could explain the roughly 150 globular clusters we see in the Milky Way today. This offers a potential new explanation for how these mysterious, ancient star clusters formed, linking them directly to the hidden structure of dark matter.

Beyond the stars themselves, the study reveals that these dense early clumps leave a lasting mark on the dark matter that surrounds them. Because the clumps formed so early and so densely, the dark matter substructures they became are much more compact and concentrated than those predicted by standard models. This increased density makes them more likely to be detected by future astronomical surveys. When stars in the Milky Way move in long, thin streams, they can be disturbed by passing dark matter clumps, leaving gaps or ripples in the stream. The denser, more compact clumps predicted by this study would create much stronger disturbances, making them easier to spot. This means that upcoming surveys, which will map the movements of stars with extreme precision, could potentially find evidence of these enhanced density fluctuations, effectively seeing the invisible dark matter by watching how it shakes the visible stars.

The researchers emphasize that while their findings are robust within the limits of their simulations, there are still many uncertainties. The exact number of stars that form, how efficiently they cluster, and how many survive to the present day depend on complex astrophysical processes that are difficult to model perfectly. However, the core idea remains clear: if the early universe was denser in small patches than we thought, it would have created a rich, hidden population of ancient star clusters and compact dark matter structures. These objects would not only change our understanding of how the first stars formed but also provide a new way to test the fundamental nature of the universe's smallest scales. The study does not claim to have solved the mystery of globular clusters or dark matter, but it opens a new door, suggesting that the key to understanding these ancient objects might lie in the subtle, bumpy texture of the early cosmos.

Technical Summary: Enhanced Density Fluctuations: Consequences for Stellar Dynamics and Dark Matter Substructure

Problem Statement
The small-scale matter power spectrum ( $k \gtrsim 10$ Mpc $^{-1}$ , corresponding to halo masses $M < 10^9 M_\odot$ ) remains poorly constrained. Within the standard $\Lambda$ CDM cosmology, halos below this mass scale are generally considered incapable of forming stars due to low virial temperatures (insufficient for atomic cooling, $T_{vir} \sim 10^4$ K) or are rendered dark by supernova feedback. However, various exotic particle physics models (e.g., ultra-slow-roll inflation, early matter domination, axion misalignment) predict enhanced density fluctuations at small scales. These enhancements lead to the formation of early, high-density dark matter halos with elevated virial temperatures. While the formation of primordial black holes (PBHs) and "not-quite-primordial" black holes (NQPBHs) in such environments has been explored, the baryonic consequences—specifically the formation of stars, star clusters, and the resulting stellar dynamics—remain underexplored. This paper addresses the conditions under which these enhanced overdensities form dark halos, early galaxies, or star clusters, and quantifies the resulting astrophysical observables.

Methodology
The authors employ a semi-analytic framework combining cosmological perturbation theory with astrophysical modeling to determine the fate of baryons in early-forming halos.

Halo Formation and Thermodynamics: The virial density ( $\rho_{vir}$ ) and virial temperature ( $T_{vir}$ ) of halos are calculated as functions of the initial density fluctuation amplitude ( $\delta_{c,0}$ ) and wavenumber ( $k$ ). The authors establish thresholds for atomic cooling ( $T_{vir} \sim 10^4$ K) and molecular cooling ( $T_{vir} \sim 10^2-10^3$ K) to determine if baryons can condense.
Feedback and Unbinding: The stability of formed stellar systems against supernova feedback is evaluated by comparing the gravitational binding energy ( $E_{grav}$ ) of the halo to the effective energy injected by supernovae ( $E_{SN,eff}$ ). This calculation incorporates star formation efficiency ( $f_*$ ), the fraction of stars undergoing core-collapse ( $f_{SN}$ ), coupling efficiency ( $f_{coup}$ ), and radiative cooling losses ( $\Lambda$ ).
Stellar Dynamics and Clustering: The paper investigates whether stars in these dense halos undergo efficient dynamical friction. Using the Chandrasekhar dynamical friction formula, the authors calculate the relaxation timescale ( $t_{relax}$ ) and the timescale for stars to contract and dominate the gravitational potential ( $t_{cluster}$ ). If $t_{cluster} < t_{lifetime}$ , the system evolves into a compact star cluster rather than a diffuse galaxy.
Mass Function Estimation: To predict the abundance of these systems, the authors adapt the Press-Schechter formalism. They utilize an excursion set approach with a non-trivial, $k$ -dependent collapse threshold derived from their dynamical criteria (specifically the intersection of formation redshift with cooling and clustering thresholds). They apply this to two toy-model power spectrum enhancements: a narrow Gaussian peak (approximating a $\delta$ -function) and a step-function enhancement, both calibrated to explain the abundance of "little red dots" (LRDs).
Substructure Analysis: Using the Galacticus semi-analytic code, the authors simulate the subhalo mass function and density profiles (characterized by $r_{max}$ ) for a Milky Way-mass halo ( $10^{12} M_\odot$ ) under these enhanced power spectra.

Key Contributions and Results

Categorization of Astrophysical Systems: The authors delineate three distinct regimes based on initial fluctuation parameters:
- Dark Halos: Regions where $T_{vir}$ is below the molecular cooling threshold or where supernova feedback unbinds the gas/stars ( $E_{SN,eff} > E_{grav}$ ). These objects remain starless.
- Old Galaxies: Regions where stars form and remain bound ( $E_{SN,eff} < E_{grav}$ ) but dynamical friction is inefficient ( $t_{cluster} > t_{lifetime}$ ). These resemble high-redshift galaxies.
- Star Clusters: Regions where stars form, remain bound, and dynamical friction is efficient ( $t_{cluster} < t_{lifetime}$ ). In these systems, stars sink to the center, dominating the potential and forming compact clusters.
Cluster Abundance Sensitivity: The initial abundance of star clusters captured by the Milky Way is highly sensitive to the shape of the power spectrum enhancement.
- A narrowly peaked enhancement (at $k \sim 100$ Mpc $^{-1}$ ) yields an initial capture of $\sim 50$ clusters with stellar masses of $\mathcal{O}(100) M_\odot$ .
- A step-function enhancement (for $k > 80$ Mpc $^{-1}$ ) yields an initial capture of $\sim 4.1 \times 10^5$ clusters, also with stellar masses of $\mathcal{O}(100) M_\odot$ .
- The authors note that while the step-function case produces a number far exceeding the observed $\sim 150$ globular clusters in the Milky Way, subsequent destruction mechanisms (evaporation, tidal shocks) could reduce this population.
Dark Matter Substructure: Enhanced power spectra lead to a significant alteration of dark matter substructure.
- For the narrow-peak model, subhalos with masses $M < 10^7 M_\odot$ are suppressed (due to early merging/accresion), while those with $M > 10^7 M_\odot$ are enhanced by up to a factor of $\sim 6.5$ compared to $\Lambda$ CDM.
- The step-function model enhances subhalo abundance across the entire mass range considered.
- Crucially, subhalos in these enhanced scenarios are more compact (smaller $r_{max}$ ) due to their high formation redshifts. This increased density enhances their gravitational "kick" on stellar streams, potentially increasing their detectability in future surveys like the Via Project.

Significance and Claims
The paper claims to provide a general framework for understanding the baryonic consequences of enhanced small-scale density fluctuations. It argues that the threshold for forming astrophysical objects (stars and black holes) can be lower than standard $\Lambda$ CDM expectations if the initial density is sufficiently high.

The authors emphasize that the formation of star clusters via dynamical friction in these early, dense halos offers a potential pathway to explain the origin of globular clusters and their "multiple populations" (via the retention of enriched ejecta from a first generation of massive stars). Furthermore, the paper posits that the enhanced abundance and compactness of dark matter subhalos in these scenarios provide a new, testable signature for small-scale structure. Specifically, the increased density of subhalos makes them more detectable via gaps and spurs in stellar streams, offering a probe of the matter power spectrum at scales previously unconstrained.

The work remains modest regarding specific predictions, acknowledging large astrophysical uncertainties in parameters such as star formation efficiency ( $f_*$ ), supernova coupling, and the initial mass function of high-redshift stars. The authors explicitly state that detailed studies of cluster mass evolution, chemical abundances, and the precise impact on reionization are left for future work.

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