BASILISK IV. No $S_8$ Tension with Satellite Kinematics

We develop a novel technique to probe the $S_8$ tension, using information from the smallest scales of galaxy redshift survey data. Specifically, we use Basilisk, a Bayesian hierarchical tool for forward modeling the kinematics and abundance of satellite galaxies extracted from spectroscopic data, to first constrain the galaxy-halo connection precisely and accurately. We then demand self-consistency in that the galaxy-halo connection predicts the correct galaxy luminosity function, which constrains the halo mass function and thereby cosmology. Crucially, the method accounts for baryonic effects and is free of halo assembly bias issues. We validate the method against realistic SDSS-like mock data, demonstrating unbiased recovery of the input cosmology. Applying it to the SDSS-DR7, we infer that $Ω_{\rm m} = 0.324 \pm 0.012$, $σ_8 = 0.775 \pm 0.063$ and $S_8 \equiv σ_8 \sqrt{Ω_{\rm m}/0.3} = 0.81 \pm 0.05$, in perfect agreement with the cosmic microwave background constraints from Planck. The most stringent constraint is with regard to the parameter combination $σ_8 (Ω_{\rm m}/0.3)^2$, which we infer to be $0.91 \pm 0.05$. Hence, unlike many low-redshift analyses of large-scale structure data, we find no indication of $S_8$ tension. We demonstrate that these results are robust to reasonable variation in the implementation of baryonification used to model the host halo’s gravitational potentials in response to baryonic processes. We also highlight the importance of correctly modeling the satellite radial profile in any analysis involving small-scale information. Finally, we underscore the hidden potential of this methodology for constraining baryonic physics using data from ongoing and upcoming surveys.

💡 Research Summary

The paper introduces a novel two‑step Bayesian hierarchical framework, called Basilisk, to address the long‑standing S₈ tension between low‑redshift large‑scale‑structure (LSS) measurements and the Planck cosmic‑microwave‑background (CMB) results. In the first step, Basilisk models the abundance and full projected phase‑space distribution (positions and line‑of‑sight velocities) of satellite galaxies from the Sloan Digital Sky Survey (SDSS‑DR7). By fitting the complete satellite kinematics rather than summary statistics, the method simultaneously constrains halo masses, satellite orbital anisotropy, and the galaxy‑halo connection (e.g., central and satellite luminosity–mass relations and their scatter). Crucially, these galaxy‑halo parameters are shown to be essentially independent of the underlying cosmology.

In the second step, the tightly constrained galaxy‑halo connection is used to predict the galaxy luminosity function (LF) for any combination of Ωₘ and σ₈, because the LF directly depends on the halo mass function, which is cosmology‑dependent. Comparing these predictions with the observed SDSS LF yields posterior constraints on Ωₘ and σ₈. The authors validate the pipeline on realistic SDSS‑like mock catalogs, recovering the input cosmology without bias and quantifying both statistical and systematic uncertainties.

Applying the method to the actual SDSS‑DR7 data, they obtain Ωₘ = 0.324 ± 0.012, σ₈ = 0.775 ± 0.063, and S₈ ≡ σ₈√(Ωₘ/0.3) = 0.81 ± 0.05, which is in perfect agreement with the Planck 2018 CMB constraints (S₈ = 0.834 ± 0.016). They also report a tight constraint on the combination σ₈(Ωₘ/0.3)² = 0.91 ± 0.05, the most stringent among low‑z probes. The results are robust to variations in the baryonification model used to account for baryonic feedback effects on halo potentials, and they highlight that incorrect assumptions about the satellite radial profile can lead to significant biases.

Overall, the study demonstrates that small‑scale satellite kinematics contain enough information to break the mass‑anisotropy degeneracy, provide a cosmology‑independent galaxy‑halo connection, and ultimately yield unbiased low‑z cosmological parameters. This approach offers a powerful tool for upcoming surveys (DESI, Euclid, Rubin) to re‑examine the S₈ tension and to constrain baryonic physics simultaneously.