⚛️ phenomenology

Prompt cusps in hierarchical dark matter halos: Implications for annihilation boost

This study incorporates long-lived "prompt cusps" into a hierarchical substructure framework to demonstrate that these compact remnants can significantly enhance the dark matter annihilation boost factor in Milky-Way-sized halos to approximately 50, while revealing that unifying peak-based formation with merger-tree evolution yields lower abundance estimates than universal-average models.

Original authors: Shin'ichiro Ando, Martin Moro, Youyou Li

Published 2026-02-06

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CC BY 4.0

Original authors: Shin'ichiro Ando, Martin Moro, Youyou Li

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

The Big Picture: Dark Matter's "Hidden Sparklers"

Imagine the universe is filled with invisible "dark matter." We know it's there because it holds galaxies together, but we can't see it. Scientists think dark matter might be made of tiny particles that occasionally crash into each other and disappear, releasing a flash of light (gamma rays). This is called annihilation.

The brighter the flash, the more dark matter particles are packed tightly together. The denser the crowd, the more collisions happen.

For a long time, scientists thought dark matter was spread out somewhat evenly in giant clouds (called halos) around galaxies, like a smooth fog. They knew there were smaller clumps inside these clouds (subhalos), which made the light brighter, but they thought the "fog" was the main event.

This paper introduces a new idea: Inside those small clumps, there might be tiny, incredibly dense "sparklers" called prompt cusps. These are remnants from the very first moments of the universe. They are so dense that they might make the dark matter glow much, much brighter than we previously thought.

The Analogy: The Cosmic Matryoshka Doll

To understand how the authors calculated this, imagine a set of Russian nesting dolls (Matryoshka dolls).

The Big Doll (The Host Halo): This is the giant galaxy, like our Milky Way.
The Middle Dolls (Subhalos): Inside the big doll, there are many smaller dolls (subhalos) that got swallowed up as the big one formed.
The Tiny Dolls (Sub-subhalos): Inside those smaller dolls, there are even tinier ones.
The Sparkler (The Prompt Cusp): The authors propose that inside the very first tiny dolls that ever formed, there is a super-dense "sparkler" at the center.

The Problem: As the big galaxy forms, it eats up the smaller dolls. Usually, when a big doll eats a small one, the small one gets squashed and torn apart (tidal stripping). Scientists wondered: Do these tiny sparklers survive the eating process, or do they get crushed?

What the Authors Did

The authors used a computer model called SASHIMI (which sounds like a sushi knife, but is actually a tool for simulating how galaxies grow).

The Old Way: Previous studies assumed that if you took a snapshot of the whole universe, you could count the sparklers and just divide them by the total mass. It was like saying, "There are 100 sparklers in the universe, so every galaxy gets a fair share."
The New Way: The authors built a "family tree" for the Milky Way. They simulated the history of how the galaxy grew, doll-by-doll, over billions of years. They tracked every single subhalo and asked: "Did this specific subhalo survive? Did it keep its sparkler? Did the sparkler get stripped away?"

They treated the sparklers as long-lived survivors. Even if the "doll" holding the sparkler gets torn apart by the galaxy's gravity, the sparkler itself is tough and might survive as a free-floating, dense object.

The Results: A Brighter Galaxy

When they ran their simulation with these "surviving sparklers," they found a surprising result:

The Boost: In the old models, the extra light from subhalos was a small bonus (a "boost" factor of about 2 or 3).
The New Boost: With the prompt cusps included, the total light from the Milky Way could be 50 times brighter than the smooth fog alone.

Think of it like this: If the smooth fog is a single candle, the subhalos add a few more candles. But the prompt cusps add a whole stadium of fireworks.

Why Their Number is Different from Others

Another team of scientists (Delos and White) previously estimated that the boost could be as high as 200. The authors of this paper found a boost of 50.

Why the difference?
The previous team used a "universal average." They assumed that sparklers are distributed perfectly evenly everywhere, like sprinkles on a cake.
The authors of this paper used a "hierarchical" approach. They realized that in the messy, chaotic history of how a galaxy like the Milky Way forms, not every potential sparkler gets to survive. Some get crushed, some get lost.

It's like baking a cake:

Universal Average: Assumes you can sprinkle exactly 100 sprinkles on every cake, no matter how big or small.
This Paper: Simulates the actual baking process. It realizes that when you mix the batter (galaxy formation), some sprinkles get crushed, some stick to the bowl, and only about 25 make it into the final cake.

So, while the sparklers definitely make the galaxy brighter, there are fewer of them in a specific galaxy like the Milky Way than the "universal average" predicted.

The Bottom Line

Prompt cusps exist: Tiny, super-dense cores formed at the beginning of the universe likely survived to today.
They matter: They significantly increase the amount of light we should expect to see from dark matter annihilation in our galaxy.
Context is key: You can't just count them globally; you have to simulate how they survive the specific history of a galaxy.
The Result: For a galaxy like ours, the signal is boosted by a factor of about 50, which is huge, but slightly lower than the most optimistic global estimates.

This work helps astronomers know exactly how bright to look for when searching for dark matter signals, ensuring they don't miss the signal or get confused by the noise.

Technical Summary: Prompt cusps in hierarchical dark matter halos: Implications for annihilation boost

Problem Statement
The standard Cold Dark Matter (CDM) paradigm predicts a hierarchical structure formation where small bound objects collapse first and merge into larger halos. While numerical simulations have long established that dark matter halos generally follow a Navarro-Frenk-White (NFW) density profile ( $\rho \propto r^{-1}$ in the inner regions), recent high-resolution simulations indicate that the earliest-forming halos (primordial microhalos) undergo rapid, nearly self-similar collapse. This process generates "prompt cusps" with significantly steeper inner density profiles ( $\rho \propto r^{-1.5}$ ). Because the dark matter annihilation rate scales with the square of the density ( $\rho^2$ ), these steep profiles could substantially enhance the gamma-ray luminosity from dark matter annihilation.

However, existing analyses of this enhancement typically rely on a "universal-average" approach, assuming that cusp properties and survival statistics are identical across all cosmic environments. This methodology fails to capture the dependence of annihilation enhancement on host-halo mass, redshift, merger history, and the complex hierarchical structure of subhalos and their internal evolution. Furthermore, previous estimates often treat cusp abundance as a fixed universal quantity, potentially overlooking environmental conditioning and tidal disruption effects specific to the assembly history of a host halo.

Methodology
To address these limitations, the authors integrate prompt cusp physics directly into SASHIMI (Semi-Analytical SubHalo Inference ModelIng), a framework that constructs a weighted catalog of subhalos based on the extended Press-Schechter (EPS) formalism and tidal evolution models. The key methodological steps include:

Prompt Cusp Characterization: The authors adopt the theoretical framework where primordial density peaks collapse to form cusps if their ellipticity and prolateness satisfy specific conditions. They define the cusp properties (amplitude $A$ , core radius $r_{\text{core}}$ , and outer radius $r_{\text{cusp}}$ ) based on peak statistics (height $\nu$ , curvature $x$ ) and the primordial phase-space density limit.
Hierarchical Embedding: Instead of applying a universal average, the authors embed one prompt cusp into every first-generation microhalo generated within the SASHIMI merger tree. They track the survival of these cusps through the full hierarchy of substructures, including sub-subhalos and higher-order progenitors.
Tidal Stripping and Survival: The model explicitly treats the tidal evolution of hierarchical substructure. Subhalos (and their associated cusps) located outside the truncation radius of their immediate parent are classified as "stripped." The authors introduce two key parameters to model survival:
- $f_{\text{cusp}}$ : The fraction of collapsed halos that host a cusp contributing effectively to the annihilation signal (fiducial value $f_{\text{cusp}} = 1$ ).
- $f_{\text{surv, stripped}}$ : The fraction of cusps associated with stripped subhalos that remain identifiable and contribute independently to the annihilation signal (fiducial value $f_{\text{surv, stripped}} = 1$ ).
Boost Factor Calculation: The total annihilation luminosity is calculated as the sum of the smooth host halo, the hierarchical subhalo population (up to $n=4$ levels of substructure), and the prompt cusp population. The annihilation boost factor $B$ is defined as the ratio of the total substructure/cusp luminosity to that of a smooth host halo.

Key Results

Convergence of Hierarchy: The authors find that the substructure hierarchy converges rapidly. Including substructure levels up to $n=3$ or $n=4$ (sub-subhalos and beyond) is sufficient to obtain a stable prediction for the boost factor, with diminishing returns beyond this depth.
Enhancement of Annihilation Boost: For a Milky-Way-sized host halo ( $M \sim 10^{12} M_\odot$ ) at $z=0$ , the inclusion of prompt cusps raises the total annihilation boost to $B \sim 50$ under fiducial assumptions ( $f_{\text{cusp}} = 1, f_{\text{surv, stripped}} = 1$ ). This is a significant increase compared to the subhalo-only baseline, which yields $B_{\text{sh}} \sim \text{few}$ .
Mass and Redshift Dependence: Across a wide range of host masses and redshifts, prompt cusps increase the normalization of the boost factor $B(M_{\text{host}}, z)$ while largely preserving the mass and redshift trends of the baseline subhalo-only prediction.
Comparison with Universal-Average Estimates: The authors' fiducial boost ( $B \sim 50$ ) is approximately a factor of four lower than the $\sim 200$ predicted by Delos and White [27] using a universal-average approach. This discrepancy is attributed primarily to a lower inferred abundance of surviving cusps in the hierarchical SASHIMI framework ( $N_{\text{cusp}} \sim 10^{16}$ vs. $2 \times 10^{16}$ in the universal estimate). The authors suggest this difference arises because the EPS-based merger tree used in SASHIMI may extrapolate differently to the microhalo regime compared to the universal peak-statistics mapping, and because environmental conditioning (e.g., anti-bias in voids vs. clusters) is not captured in universal averages.

Significance and Claims
The paper claims to provide the first fully hierarchical, environment-dependent calculation of the dark matter annihilation boost that consistently tracks prompt cusps through the merger history of a host halo. By moving beyond the "universal-average" assumption, the work highlights the importance of unifying peak-based cusp formation statistics with merger-tree evolution.

The authors emphasize that their results are physically grounded in the specific assembly history of the host, offering a more self-consistent framework than previous estimates. They acknowledge that the absolute normalization of the boost depends on the mapping between the cutoff scale and halo mass in the EPS formalism (parameterized by $\alpha$ ), noting that variations in this parameter can significantly alter the predicted cusp abundance. Consequently, the paper positions its implementation as a flexible platform for future work, specifically calling for dedicated calibrations of microhalo abundance using ultra-high-resolution simulations to resolve the remaining uncertainties in cusp counts and survival probabilities. The authors do not claim to have definitively resolved the tension with universal-average predictions but rather demonstrate that a hierarchical treatment yields a systematically lower, yet still significant, enhancement.