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

TL;DR

This paper integrates prompt cusps—steep inner-density remnants formed from early primordial peaks—into the SASHIMI semi-analytic framework to produce a fully hierarchical, environment-dependent calculation of dark matter annihilation boosts. By embedding one prompt cusp per first-generation subhalo and tracking their survival through subhalo hierarchies and tidal stripping, the authors show rapid convergence of the substructure contribution after a few levels and demonstrate that prompt cusps can raise Milky-Way–sized halo boosts to around an order of magnitude above subhalo-only expectations, with B ≈ O(10) at z=0 for fiducial cusp-occupation parameters. The study also reveals that their fiducial boosts are roughly an order of magnitude lower than universal-average peak-based estimates, underscoring the importance of coupling cusp formation statistics to merger-tree evolution and environment. Overall, the work provides a physically grounded, hierarchical prediction for cusp-enhanced annihilation signals and offers a public code extension to SASHIMI for future refinement and comparison with microhalo simulations. The results highlight that hierarchical processing and environment dependence can significantly shape indirect-detection expectations for WIMP-like dark matter.

Abstract

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 \textsc{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 $B\sim O(10)$ 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 an order of magnitude, 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.

Figures (4)

• Figure 1: Mass-normalized annihilation luminosity parameters at $z=0$ including hierarchical substructure up to $\mathrm{sub}^4$-subhalos, shown as functions of the host-halo mass $M_{\rm host}$. The dot-dashed, dashed, and solid curves show the contributions from the smooth host-halo component, the total subhalo population, and the total prompt-cusp population, respectively (i.e., $J_{\rm host}/M_{\rm host}$, $J_{\rm sh,,total}/M_{\rm host}$, and $J_{\rm cusp,,total}/M_{\rm host}$), for the fiducial choice of $f_{\rm cusp}=0.25$ and $f_{\rm surv,stripped}=1$. The dotted curve shows the intrinsic cusp annihilation efficiency, $\langle J_{\rm cusp}\rangle/\langle M_{\rm cusp}\rangle$.
• Figure 2: Annihilation boost factor $B = B_{\rm sh}+B_{\rm cusp}$ at $z=0$ including hierarchical substructure up to $\mathrm{sub}^4$-subhalos, shown as a function of the host-halo mass $M_{\rm host}$. The colored bands correspond to different choices of the cusp-occupation fraction $f_{\rm cusp}$ (0.25, 0.5, and 1 from bottom to top). For each $f_{\rm cusp}$, the band width reflects uncertainty in the survival of cusps associated with the stripped region, parametrized by $f_{\rm surv,stripped}\in[0,1]$: the lower (upper) edge assumes $f_{\rm surv,stripped}=0$ ($1$). The dotted curve shows the baseline prediction without prompt cusps ($B = B_{\rm sh}$).
• Figure 3: Dependence of the total boost factor $B$ on the depth of hierarchical substructure included in the model. Curves show results at $z=0$ for $n=0,\ldots,4$ (from bottom to top), where $n$ denotes inclusion up to $\mathrm{sub}^n$-subhalos. The dotted curve shows the corresponding reference prediction without prompt cusps (for $n=4$).
• Figure 4: Redshift dependence of the total boost factor $B$ as a function of host-halo mass $M_{\rm host}$. Solid curves include prompt cusps, while dotted curves show the corresponding no-cusp baseline, for $z=0,1,2$, and 3 (from top to bottom at high masses).