Gravothermal Collapse: Robust Against Baryonic Feedback

Using N-body simulations and a semi-analytical model, this study demonstrates that gravothermal collapse in self-interacting dark matter halos remains robust against baryonic feedback, with high-concentration halos collapsing despite strong feedback and median-concentration halos resuming collapse after feedback ceases, thereby supporting the identification of dense compact perturbers in strong-lensing observations as core-collapsed SIDM halos.

The Gist

Imagine the universe is filled with invisible "ghost" matter called Dark Matter. For a long time, scientists thought these ghosts were shy and never bumped into each other (this is the standard "Cold Dark Matter" model). But new ideas suggest these ghosts might actually be a bit more social, occasionally bumping into one another. This is called Self-Interacting Dark Matter (SIDM).

When these social ghosts bump into each other, they exchange heat. This process, called gravothermal collapse, is like a slow-motion dance where the center of a dark matter cloud can either puff up (become a fluffy core) or shrink down into a super-dense ball.

The big question this paper asks is: What happens if you shake the table while the ghosts are dancing?

In the real universe, normal matter (stars and gas) explodes and pushes back on dark matter. This is called baryonic feedback. It's like a rowdy crowd at a party throwing energy around, potentially messing up the dark matter's dance. The authors wanted to know: Does this rowdy crowd stop the dark matter from collapsing into a dense ball, or does the dance continue anyway?

Here is what they found, using a mix of math and computer simulations:

1. The Two Types of Dancers

The researchers tested two different types of dark matter clouds:

• The "Tight-Knit" Group (High Concentration): These clouds are already very dense and packed together. Because they are so close, the ghosts bump into each other constantly and very quickly.
• The "Loose" Group (Median Concentration): These clouds are more spread out. The ghosts bump into each other much less frequently.

2. The "Shaking" Experiment

The scientists simulated a scenario where they shook the system violently (strong feedback) to see if it would stop the collapse. They used a model where the "shaking" happened in cycles, like a rhythmic pulsing of energy.

3. The Results: Who Stopped Dancing?

The Tight-Knit Group (High Concentration): Unstoppable
For the dense clouds, the shaking barely made a dent. Because these ghosts bump into each other so fast (their "thermalization timescale" is very short), they can ignore the rowdy crowd.

• The Analogy: Imagine a group of people in a tiny, crowded elevator. If someone starts jumping around, the people in the elevator might sway a little, but they can't stop moving because they are already so packed together. The collapse happens almost on schedule, just slightly delayed.
• The Claim: Even with extremely strong shaking, these dense clouds never stopped collapsing. They just took a tiny bit longer to finish.

The Loose Group (Median Concentration): Delayed, but Not Defeated
For the spread-out clouds, the shaking was much more effective. It pushed the ghosts apart, creating a large, empty "core" in the middle and pausing the collapse.

• The Analogy: Imagine a loose circle of people holding hands in a park. If a storm starts blowing (the feedback), they get pushed apart and the circle breaks. The collapse stops.
• The Twist: However, once the storm stopped, the people didn't stay scattered. They slowly drifted back together and resumed the collapse.
• The Result: The final shape of these clouds depended entirely on when and how long the storm blew. Some ended up very dense, some less so. This creates a huge variety of shapes, which is actually a good thing because real galaxies look very different from one another.

4. Why This Matters

The paper concludes that gravothermal collapse is a "smoking gun" for self-interacting dark matter.

• It's Robust: Even if the universe is chaotic and full of exploding stars (feedback), the dense dark matter clouds will still collapse. This helps explain why we see some extremely dense, compact objects in the universe (like those found by gravitational lensing) that standard "shy" dark matter models can't explain.
• It Explains Diversity: The fact that the "loose" clouds can be delayed and then resume collapse explains why we see such a wide variety of galaxy shapes. Some have shallow cores, some have dense centers, and it all depends on their specific history of being "shaken" by normal matter.

In short: The universe might be a chaotic place with exploding stars and gas, but the self-interacting dark matter is tough. It might get pushed around for a while, but if it starts dense enough, it will inevitably collapse into a tight ball. If it starts loose, it might get delayed, but it will eventually find its way back to the dance floor, creating a diverse universe of galaxy shapes.

Technical Summary

Technical Summary: Gravothermal Collapse in SIDM Halos Under Baryonic Feedback

Problem Statement
The standard Cold Dark Matter (CDM) model predicts steep central density cusps in dark matter halos, which often conflicts with the shallow cores observed in dwarf galaxies. While baryonic feedback mechanisms (e.g., supernova-driven outflows) can inject energy to transform cusps into cores, recent observations reveal a broad diversity in dark matter distributions—ranging from shallow cores to extremely dense cusps—that CDM struggles to reproduce. Furthermore, strong gravitational lensing and stellar stream observations have identified compact perturbers with densities significantly higher than typical CDM predictions. In the Self-Interacting Dark Matter (SIDM) framework, dark matter self-interactions drive gravothermal evolution, naturally producing both low-density cores and high-density collapsed states. However, previous studies largely relied on SIDM-only simulations or static baryonic potentials. Since realistic baryonic potentials shaped by feedback are dynamic and non-adiabatic, it remains unclear whether the defining prediction of SIDM—gravothermal collapse—remains robust against the energy injection and potential fluctuations caused by strong baryonic feedback.

Methodology
The authors perform controlled $N$-body simulations using the code GADGET-2 with an SIDM module to stress-test gravothermal collapse under strong baryonic feedback.

• Initial Conditions: Two dark matter halos with mass $M_{200} = 2 \times 10^9 M_\odot$ are simulated: a high-concentration halo ($c_{200} = 42$, representing a $3\sigma$ fluctuation) and a median-concentration halo ($c_{200} = 15$, the cosmological median). Both follow Navarro–Frenk–White (NFW) profiles.
• SIDM Parameters: The self-interaction cross-section per unit mass is fixed at $\sigma/m = 50 \text{ cm}^2/\text{g}$, consistent with models explaining high-density strong-lensing perturbers and the diffuse dwarf galaxy Crater II.
• Feedback Model: A semi-analytical oscillating potential is implemented to mimic baryonic feedback. A central Plummer potential with a time-dependent mass $M_{ext}(t)$ is added to the force calculation. The model includes "Strong Feedback" (where $M_{ext}$ oscillates between positive and negative values, creating repulsive acceleration) and "Weak Feedback" (oscillating between zero and positive). The oscillation period is set to $P = 0.2$ Gyr, with a maximum mass amplitude $M_{max} = 10^7 M_\odot$ and scale radius $a = 0.1$ kpc.
• Scenarios: The study compares SIDM-only evolution against cases with continuous strong/weak feedback, and episodic feedback (active for specific intervals, e.g., 0–4 Gyr or 8–10 Gyr) followed by either removal or replacement with a static potential.

Key Results
The simulations reveal that the resilience of gravothermal collapse depends critically on the competition between the SIDM thermalization timescale ($t_{th}$) and the feedback oscillation period ($P$).

1. High-Concentration Halos ($c_{200} = 42$):

   • The thermalization timescale is short ($t_{th} \sim 0.01\text{--}0.04$ Gyr), significantly shorter than the feedback period ($P = 0.2$ Gyr).
   • Consequently, SIDM dynamics dominate over baryonic feedback.
   • Under strong feedback, the collapse is only mildly delayed (by $\sim 1$ Gyr) and never stalled. The central density eventually reaches levels consistent with SIDM-only simulations and observational constraints for dense perturbers (e.g., JVAS B1938+666).
   • Weak feedback has a negligible effect or slightly accelerates collapse due to contraction during inflow phases.

2. Median-Concentration Halos ($c_{200} = 15$):

   • The thermalization timescale is longer ($t_{th} > P$ for most of the evolution), making the halo susceptible to feedback-driven heating.
   • Strong Feedback: During the core-expansion phase, strong feedback can rapidly generate large cores (up to $\sim 0.8$ kpc) and reduce central density to $\sim 25\%$ of the initial value. However, once feedback ceases, gravothermal collapse resumes, albeit at a slower rate.
   • Episodic Feedback: The final density profile is highly sensitive to the feedback history.
     • If feedback occurs early (0–4 Gyr) and is removed, the halo collapses later than the SIDM-only case.
     • If the oscillating potential is replaced by a static potential after feedback, collapse is accelerated.
     • If feedback occurs late (8–10 Gyr) during the collapse phase, it temporarily halts but does not reverse the process.
   • This sensitivity produces a broad diversity in final central densities, ranging from shallow cores to dense cusps, depending on the specific feedback timeline.

Significance and Claims
The paper establishes that gravothermal collapse is a robust prediction of SIDM, resilient even to extremely strong, oscillating baryonic feedback.

• For High-Concentration Halos: The short thermalization timescale ensures that collapse proceeds regardless of feedback intensity. This strengthens the interpretation of dense strong-lensing perturbers and compact objects as core-collapsed SIDM halos. It also supports SIDM-based scenarios for seeding supermassive black holes in the early Universe, even in environments with bursty star formation.
• For Median-Concentration Halos: The interplay between feedback and self-interactions can explain the observed diversity in dark matter distributions (from shallow cores to dense cusps) within halos of similar mass. The final state is not determined solely by the halo mass or initial concentration but is modulated by the episodic history of baryonic feedback.
• Conclusion: The results suggest that gravothermal collapse remains a "smoking-gun" signature of SIDM. The predicted diversity in density profiles, driven by the combination of self-interactions and feedback history, offers a testable framework for future observations of galaxy rotation curves and the nature of dark matter.