Advancing Stellar Streams as a Dark Matter Probe -- I: Evolution of the CDM subhalo population

Stellar streams, long, thin streams of stars, have been used as sensitive probes of dark matter substructure for over two decades. Gravitational interactions between dark matter substructures and streams lead to the formation of low-density ``gaps’’ in streams, with any given stream typically containing no more than a few such gaps. Prior models for the statistics of such gaps have relied on several simplifying assumptions for the properties of the subhalo population in the cold dark matter scenario. With the expected forthcoming increase in the number of streams and gaps observed, this work develops a more detailed model for the statistics of subhalos interacting with streams and tests some of the assumptions made in prior works. Instead of using simple fits to N-body estimates of subhalo population statistics at $z=0$ as in previous work, we make use of realizations of time-dependent subhalo populations generated from an entirely physical model, incorporating structure formation and subhalo orbital evolution, including tidal heating and stripping physics, which has been carefully calibrated to match results of cosmological N-body simulations. We find that this model predicts 20% more gaps (up to 60% for deep gaps) on average in Pal-5-like streams than prior works.

💡 Research Summary

The paper presents a comprehensive, semi‑analytic framework for predicting the statistics of dark‑matter subhalo encounters with stellar streams, with a focus on the Pal 5‑like globular‑cluster stream. The authors argue that previous gap‑statistics studies have relied on overly simplified representations of the subhalo population: they typically use a static z = 0 subhalo mass function derived from N‑body simulations, assume simple density profiles (point mass, Plummer sphere, or unstripped NFW), and treat subhalo orbits in a static Milky Way potential. While these approximations were adequate when only a few streams and gaps were observable, the forthcoming data deluge from the Roman Space Telescope, the Via Project, and other deep surveys will soon provide thousands of streams with sub‑kiloparsec resolution. To fully exploit this data, a more realistic, time‑dependent model of the subhalo population is required.

The authors adopt the Galacticus semi‑analytic galaxy formation code to generate physically motivated merger trees for a Milky Way‑mass halo (M ≈ 10¹² M⊙). The tree is built using the Parkinson et al. (2008) algorithm, resolving progenitor halos down to 10⁵ M⊙. To keep the computational load manageable, low‑mass branches are stochastically sampled with a mass‑dependent probability p(M) = (M/10⁹ M⊙)⁰·⁵⁵ for M < 10⁹ M⊙, and each retained branch is assigned a weight wᵢ that corrects for the undersampling. This weighting scheme reproduces the full, unsampled mass and orbital distributions to within statistical uncertainties.

Each halo is initially assigned an NFW density profile, with concentrations drawn from the Johnson et al. (2021) model based on its assembly history. The orbital parameters at infall are sampled from the cosmological distributions measured by Jiang et al. (2015), including the correlation with host spin. Galacticus then evolves each subhalo forward in time, incorporating dynamical friction, tidal stripping, and a tidal‑heating prescription (Benson & Du 2022). The heating model modifies the inner density, yielding a “tidally stripped NFW” profile that matches high‑resolution N‑body results. The authors emphasize that this treatment captures the gradual erosion of subhalos and the survival of dense cores, which are crucial for determining the strength of stream perturbations.

Gap formation is modeled as an impulsive scattering event. For each subhalo–stream encounter, the relative velocity and impact parameter are used to compute a velocity kick Δv imparted to stream particles. The authors derive analytic expressions for Δv that are valid for a range of density profiles, including point mass, Plummer sphere, pure NFW, and the tidally stripped NFW. After the kick, the perturbed stream orbit is recomputed, and the resulting under‑density region is identified as a gap. The paper explores five profile families (point mass, thin shell, constant‑density sphere, Plummer, and NFW variants) to bracket the possible gap amplitudes; the tidally stripped NFW consistently produces the largest gaps for a given subhalo mass because its central density remains high despite stripping.

To achieve the statistical precision required for future surveys, the authors generate 1.6 × 10⁶ independent realizations of the Milky Way halo and its subhalo population. This massive ensemble reduces the Poisson noise on the predicted gap rate to ≈1 %. Applying the model to a Pal 5‑like stream, they find that the average number of detectable gaps is ≈20 % higher than predicted by Erkal et al. (2016b). For deep gaps (density contrast ≲ 0.5), the increase can be as large as 60 %. The enhancement arises from two main effects: (1) the time‑dependent subhalo mass function includes a larger number of intermediate‑mass subhalos that survive to low redshift, and (2) the tidally stripped NFW profiles retain enough central density to deliver stronger impulsive kicks than the simpler Plummer or point‑mass approximations used previously.

The authors acknowledge several limitations. Their analysis currently restricts subhalo masses to 10⁵–10⁹ M⊙, based on earlier estimates of the “gap‑forming” regime. However, the realistic density profiles suggest that even lower‑mass subhalos could produce observable perturbations, especially in ultra‑cold streams. Moreover, the impulse approximation neglects the finite duration of encounters for very slow, close passages, and the model does not yet incorporate baryonic substructures (e.g., giant molecular clouds, the Galactic bar) that can also generate gaps. Future work will extend the mass range, explore alternative dark‑matter models (warm, self‑interacting), and incorporate more sophisticated treatments of the host potential.

In summary, this paper delivers a state‑of‑the‑art semi‑analytic pipeline that couples physically motivated subhalo evolution with an efficient gap‑formation prescription. By moving beyond static, z = 0 fits and simplistic density profiles, it predicts substantially more gaps in stellar streams, thereby sharpening the toolset for using streams as a probe of the low‑mass end of the dark‑matter subhalo spectrum. The methodology is scalable to the thousands of streams anticipated in the next decade, positioning stellar‑stream gap statistics as a competitive, complementary avenue for testing CDM and its alternatives.