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

Recent simulations have identified long-lived ``prompt cusps’’ – compact remnants of early density peaks with inner profiles $ρ\propto r^{-3/2}$. They can survive hierarchical assembly and potentially enhance signals of dark matter annihilation. In this work, we incorporate prompt cusps into the semi-analytic substructure framework SASHIMI, enabling a fully hierarchical, environment-dependent calculation of the annihilation luminosity that consistently tracks subhalos, sub-subhalos, and tidal stripping. We assign prompt cusps to first-generation microhalos and propagate their survival through the merger history, including an explicit treatment of cusps associated with stripped substructure. We find that the substructure hierarchy converges rapidly once a few levels are included, and that prompt cusps can raise the total annihilation boost of Milky-Way–size hosts at $z=0$ to $B\sim 50$ for fiducial cusp-occupation assumptions, compared to a subhalo-only baseline of $B_{\rm sh}\sim\mathrm{few}$. Across a wide range of host masses and redshifts, prompt cusps increase the normalization of $B(M_{\rm host},z)$ while largely preserving its mass and redshift trends. Compared to universal-average, peak-based estimates, our fiducial boosts are lower by about a factor of a few, primarily reflecting a correspondingly smaller inferred cusp abundance in host halos, highlighting the importance of unifying peak-based cusp formation with merger-tree evolution and environmental dependence.

💡 Research Summary

This paper investigates the impact of “prompt cusps”—compact, steep‑density remnants that arise from the earliest density peaks in the primordial matter field—on dark‑matter annihilation signals. Recent ultra‑high‑resolution simulations have shown that a subset of the first‑generation microhalos collapse nearly radially, producing an inner density profile ρ∝r⁻³ᐟ² that persists unless disrupted by later mergers. Because the annihilation rate scales as ρ², such cusps can dramatically boost the gamma‑ray luminosity of a halo despite their tiny masses (∼10⁻⁶ M⊙).

To quantify this effect in a realistic, hierarchical context, the authors embed prompt‑cusp physics into the semi‑analytic substructure framework SASHIMI. SASHIMI generates a weighted catalog of subhalos for any host halo by sampling extended‑Press‑Schechter merger trees, assigning each subhalo an NFW density profile (ρ_s, r_s) and a tidal truncation radius r_t. The new implementation proceeds as follows:

1. Cusp Assignment – Every first‑generation microhalo (the earliest collapsed objects in the tree) receives one prompt cusp. The cusp’s structural parameters (amplitude A, core radius r_core, outer radius r_cusp) are derived from the Gaussian peak statistics of the initial density field. Peaks are characterized by height ν, curvature x, and ellipticity‑prolateness (e, p). Sampling these distributions yields average values ⟨A⟩≈1.5×10⁻⁴ M⊙ pc⁻¹·⁵, ⟨r_core⟩≈2×10⁻⁵ pc, ⟨r_cusp⟩≈1.2×10⁻² pc, and an average cusp mass ⟨M_cusp⟩≈9×10⁻⁷ M⊙. Roughly half of the eligible peaks (f_coll≈0.48) form cusps.

2. Annihilation Luminosity Parameter – For a single cusp the integrated ρ² over r_core < r < r_cusp gives a “J‑parameter” J_cusp≈4.7×10⁻⁶ M⊙² pc⁻³. This is orders of magnitude larger than the J‑value of a typical NFW subhalo of comparable mass.

3. Hierarchical Propagation – As the merger tree evolves, subhalos experience tidal stripping. The authors model cusp survival with a simple, physically motivated probability that depends on the ratio of the subhalo’s truncation radius to the cusp’s outer radius. When a subhalo is stripped, its cusp’s J‑value is multiplied by the survival probability; if the cusp is completely disrupted, its contribution is removed. This procedure is applied recursively to sub‑subhalos and deeper levels, allowing the full hierarchy to be tracked.

4. Convergence and Boost Calculation – The authors find that including three to four levels of substructure is sufficient for the annihilation boost to converge. For a Milky Way‑mass host (M≈10¹² M⊙) at z=0, the total boost factor (including both subhalos and prompt cusps) reaches B≈50, whereas a subhalo‑only calculation yields B≈few. Across a wide range of host masses (10⁸–10¹⁵ M⊙) and redshifts (z=0–6), the presence of cusps raises the normalization of B(M,z) by a factor of ∼2–3 but leaves the mass and redshift scaling slopes essentially unchanged.

5. Comparison with Peak‑Based Estimates – Earlier works that estimated the boost by averaging over peak statistics without accounting for merger‑tree evolution reported larger boosts (often a few hundred). The semi‑analytic approach here produces boosts lower by a factor of a few, reflecting a more realistic, environment‑dependent cusp abundance: many peaks that could form cusps in isolation are either never incorporated into the host or are disrupted during mergers.

6. Implications and Future Work – The study demonstrates that prompt cusps can dominate the annihilation boost in CDM halos, potentially altering interpretations of gamma‑ray background limits and indirect‑detection constraints. However, the current tidal‑survival model is simplified; incorporating baryonic effects (stellar encounters, disk shocking) and more detailed dynamical disruption will be essential. The authors release an updated version of the SASHIMI code with cusp handling, enabling the community to explore non‑cold dark‑matter scenarios (e.g., warm or self‑interacting dark matter) within the same framework.

In summary, by embedding the physics of early‑formed, steep‑density cusps into a hierarchical semi‑analytic model, the paper provides the first self‑consistent, environment‑dependent prediction of dark‑matter annihilation boosts. It shows that prompt cusps can increase the boost by roughly an order of magnitude for Milky Way‑like halos, while preserving the established mass‑ and redshift‑dependence of substructure‑induced enhancements. This work bridges the gap between peak‑theory predictions and realistic merger‑tree evolution, highlighting the importance of small‑scale structure for indirect dark‑matter searches.