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Role of prompt cusps in driving the core collapse of SIDM halos

Using high-resolution N-body simulations, this paper demonstrates that prompt cusps embedded at the centers of self-interacting dark matter halos delay the onset of core formation by a factor of two and induce a late-stage core-collapse deviation of approximately 5% due to a complex interplay between increased halo concentration and outer halo temperature.

Original authors: Vinh Tran, Daniel Gilman, M. Sten Delos, Xuejian Shen, Oliver Zier, Mark Vogelsberger, David Xu

Published 2026-03-30

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CC BY 4.0

Original authors: Vinh Tran, Daniel Gilman, M. Sten Delos, Xuejian Shen, Oliver Zier, Mark Vogelsberger, David Xu

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: A Cosmic Dance of Invisible Particles

Imagine the universe is filled with a giant, invisible fog called Dark Matter. This fog isn't just sitting still; it's swirling into giant balls called halos, which act as the scaffolding for galaxies.

For a long time, scientists thought these halos were like smooth, fluffy clouds. But a new theory, Self-Interacting Dark Matter (SIDM), suggests these particles bump into each other like bumper cars. When they bump, they swap energy (heat). This causes the center of the halo to behave strangely: first, it puffs up into a soft, round "core," and later, it can suddenly collapse inward like a deflating balloon.

This paper asks a specific question: What happens if we put a tiny, super-dense "seed" right in the very center of this halo before the dance begins?

The Characters in Our Story

The Halo (The Ballroom): A massive cloud of dark matter particles.
The Prompt Cusp (The Heavy Anchor): In the very early universe, some tiny clumps of matter collapsed so fast they formed incredibly dense, sharp spikes at the center of halos. Think of this as a heavy, dense anchor dropped right into the middle of our ballroom.
The Heat Transfer (The Bumper Cars): Because the dark matter particles bump into each other, heat flows from the hot center to the cooler edges. This flow of heat is what drives the halo to change shape.

The Experiment: Dropping an Anchor in a Pool

The researchers ran computer simulations (like a high-tech video game) to see how these halos evolve. They set up four scenarios:

The Control Group: A standard halo with a smooth center (no anchor).
The Test Groups: Three halos with "Prompt Cusps" of increasing weight (a small anchor, a medium anchor, and a giant anchor) dropped right in the center.

They watched to see how the "core formation" (puffing up) and "core collapse" (crunching down) happened.

The Findings: What Happened?

1. The "Heavy Anchor" Slows Down the Start

In the beginning, the halos with the heavy anchors (Prompt Cusps) were surprisingly sluggish.

The Analogy: Imagine trying to stir a pot of soup. If you drop a giant, heavy rock into the middle, it's harder to get the soup swirling around it. The heavy anchor creates a steep "temperature hill." Heat doesn't want to flow down that steep hill easily.
The Result: The halos with the biggest anchors took about twice as long to start forming their soft cores compared to the smooth halos. The dense center acted like a traffic jam, delaying the heat transfer.

2. The "Reset Button"

Once the core finally formed and the system started to collapse, something magical happened.

The Analogy: Imagine the heavy anchor was so dense that it eventually got "swallowed" by the swirling soup. The particles mixed so thoroughly that the memory of the anchor disappeared.
The Result: After the initial delay, all the halos (even the ones with giant anchors) started evolving in a very similar way. If you adjusted the scale (like zooming in or out on a map), the halos looked almost identical. The specific shape of the initial "anchor" was erased by the chaotic mixing of particles.

3. The Late-Stage Twist: The Outer Shell Matters

Here is where it gets tricky. Even though the centers looked similar, the timing of the final collapse was slightly different for each halo.

The Analogy: Think of the halo as a house. The Prompt Cusp changed the foundation (the center), but it also changed the roof and walls (the outer edges) slightly.
- Some halos had "loose" outer walls that let heat escape easily, causing the house to collapse faster.
- The "Extreme" halo had a heavy anchor that made the outer walls "tighter" and hotter. This trapped the heat, acting like a thermal blanket, which actually slowed down the final collapse.
The Result: The final collapse time wasn't just about how heavy the center was; it was a tug-of-war between the heavy center (which wants to collapse fast) and the temperature of the outer edges (which can speed up or slow down the process).

Why Does This Matter?

This paper is important because it tells us that the history of a galaxy matters.

If we look at a dwarf galaxy today and see its core collapsing, we can't just look at its current shape. We have to ask: Did it start with a heavy, dense seed (a Prompt Cusp)?

If it did, it might have taken longer to start the process, but it might collapse at a different time than a galaxy that started smooth.
This helps astronomers figure out the "particle physics" of dark matter. By measuring how fast these cores collapse in the real universe, we might be able to tell if dark matter has these "Prompt Cusp" seeds or not.

The Takeaway

Think of a Self-Interacting Dark Matter halo like a kitchen mixer.

The Prompt Cusp is a heavy lump of dough you drop in the middle.
The Bumper Cars are the mixer blades.
The Result: The heavy lump slows down the mixer at first (delaying the core formation). But once the mixer gets going, it blends everything so well that the lump disappears. However, the exact speed at which the mixture finishes depends on how the rest of the dough (the outer halo) was affected by that initial lump.

The paper concludes that while the universe tends to "smooth out" these early irregularities, the initial conditions leave a subtle, complex fingerprint on the timing of the galaxy's evolution.

1. Problem Statement

The internal structure of dark matter (DM) halos provides critical constraints on the particle nature of dark matter. Self-Interacting Dark Matter (SIDM) models predict that DM self-interactions conduct heat, leading to the formation of constant-density cores in dwarf galaxies, followed by a "gravothermal core collapse" (runaway contraction).

However, recent theoretical work suggests that in the early Universe, primordial density fluctuations do not immediately collapse into standard Navarro-Frenk-White (NFW) profiles. Instead, they form Prompt Cusps (PCs)—structures with density profiles steeper than $r^{-1.5}$ (compared to the NFW $r^{-1}$ cusp).

The Gap: While cosmological simulations with suppressed matter power spectra (which predict PCs) exist, they lack the resolution to resolve these inner cusps. Consequently, it remains unknown how the presence of a massive, dense PC at the center of a halo affects the subsequent thermal evolution, core formation, and the timing of the core collapse in SIDM models.
The Question: Does the presence of a PC accelerate or delay the onset of core collapse, and how does it alter the structural evolution of the halo?

2. Methodology

The authors conducted a suite of ultra-high-resolution, isolated N-body simulations using the AREPO code to investigate the evolution of SIDM halos with embedded Prompt Cusps.

Halo Initialization:
- They modeled isolated halos with a virial mass of $M_{200} = 10^7 M_\odot$ .
- Instead of standard NFW profiles, they initialized halos with a composite PC+NFW density profile based on the cusp-halo relation from Delos (2025).
- Four Configurations:
  1. SIDM-control: Standard NFW profile ( $y=0$ ).
  2. SIDM-low: PC with amplitude 30% below the median (cusp mass $\sim 3.6\%$ of total).
  3. SIDM-high: PC with amplitude 30% above the median (cusp mass $\sim 4.7\%$ ).
  4. SIDM-extreme: PC with amplitude 47% above the median (cusp mass $\sim 5.0\%$ ).
- Initial conditions were generated using Eddington's inversion formula, modified to account for softened gravity (Plummer-equivalent softening length $\epsilon = 3.1$ pc) to ensure dynamical stability.
Dark Matter Physics:
- The simulations employed a velocity-dependent cross-section (VDCS) typical of SIDM models with light mediators: $\sigma(v) = \sigma_0 (1 + v^2/w^2)^{-2}$ .
- Parameters were chosen to match a model with a kinematic decoupling temperature $T_{kd} = 1.46$ keV, which suppresses small-scale power.
- For comparison, runs were also performed with an effective velocity-independent cross-section (VICS) of $\sigma/m = 83.86$ cm $^2$ g $^{-1}$ .
Resolution:
- Each halo contained $\sim 4 \times 10^6$ particles, with $\sim 10^4$ particles resolving the inner region ( $r \le 0.1 r_{-2}$ ), ensuring convergence for gravothermal collapse studies.

3. Key Contributions

First High-Resolution Study of PCs in SIDM: This work is the first to explicitly resolve Prompt Cusps within SIDM halos to study their impact on late-time evolution, bridging the gap between early-Universe structure formation and late-time halo dynamics.
Quantification of Delay Mechanisms: The study identifies that the presence of a PC creates a specific thermal gradient that delays the core-formation phase by a factor of $\sim 2$ compared to NFW halos.
Discovery of Self-Similarity with Rescaling: The authors demonstrate that despite different initial cusp masses, the evolutionary tracks of SIDM halos with PCs become self-similar to NFW halos when rescaled by effective density, radius, and velocity dispersion parameters, provided the physical time is used rather than a simple collapse timescale.
Complex Interplay of Factors: The paper elucidates the competing factors governing collapse time: the increased central density (accelerating collapse) vs. the elevated temperature in the outer halo regions (potentially inhibiting heat transfer and delaying collapse).

4. Key Results

A. The Core-Formation Phase (Delay)

Slower Evolution: Halos with more prominent PCs evolve significantly slower during the initial core-formation phase (up to $\sim 3$ Gyr).
Mechanism: The PC creates a steeper density profile but a smaller velocity dispersion gradient in the inner region. Since heat transport in SIDM depends on this gradient, the inward heat flow is delayed.
Erasure: By $T \approx 1$ Gyr ( $\sim 2.5\%$ of the collapse timescale), the distinct signatures of the PC in the density profile are erased as the halo thermalizes into an isothermal core.

B. The Core-Collapse Phase (Divergence)

Rescaling: Once the core forms, the evolution of PC halos aligns with the NFW reference when densities, radii, and velocities are rescaled by effective parameters ( $\bar{\rho}_s, \bar{r}_s, \bar{\sigma}_s$ ).
Concentration Increase: The presence of a PC effectively increases the halo's concentration. The effective NFW equivalent of a PC halo has a higher concentration than the original NFW halo but preserves the virial mass.
Late-Time Deviations:
- Low/High Cusp: These halos collapse slightly faster than the NFW control.
- Extreme Cusp: This halo collapses slower (delayed by $\sim 5\%$ relative to the reference track).
- Cause: The delay in the extreme case is attributed to the "outer halo effect." The PC configuration leads to an excess of mass in the outer regions ( $r > r_{200}$ ), which increases the temperature of the outer halo. This reduces the temperature gradient between the core and the outskirts, suppressing heat transport and slowing the collapse.

C. Timescale Predictions

The standard effective collapse timescale ( $\tau \propto 1/\bar{\rho}\bar{\sigma}$ ) fails to accurately predict the collapse time for PC halos.
The collapse time depends non-trivially on both the inner concentration (driven by the PC) and the thermal state of the outer halo.

5. Significance and Implications

Observational Constraints: Small-scale probes of dark matter (dwarf galaxies, stellar streams, strong gravitational lenses) are sensitive to the timing of core collapse. If PCs are present, the predicted density profiles and collapse timescales for SIDM models must be adjusted.
Early Universe Connection: The results link the initial conditions of structure formation (Prompt Cusps) directly to the observable properties of dark matter halos today.
Model Validation: The findings suggest that SIDM models predicting small-scale suppression of the power spectrum (and thus massive PCs) will exhibit delayed core formation and potentially altered collapse timescales compared to standard SIDM models.
Future Directions: The authors note that whether PCs survive the initial collapse in a fully interacting SIDM scenario remains an open question, motivating future full cosmological simulations with high resolution.

In summary, the paper establishes that while Prompt Cusps are eventually erased by thermalization, their initial presence significantly delays the onset of core formation and introduces complex dependencies in the late-time collapse dynamics driven by the thermal coupling between the halo core and its outer envelope.