BASILISK IV. No $S_8$ Tension with Satellite Kinematics

TL;DR

We address the $S_8$ tension by combining satellite-kinematics data with the galaxy luminosity function through Basilisk, a Bayesian hierarchical forward-modeling framework that disentangles the galaxy–halo connection from cosmology. The method first tightly constrains the conditional luminosity function (CLF) from SDSS satellite kinematics and then uses the CLF posterior as a prior to predict the galaxy LF under different $(\Omega_{\rm m},\sigma_8)$, comparing to the observed LF to infer cosmology while marginalizing over baryonic physics. Tests on realistic mocks show unbiased recovery of input cosmology and a characteristic degeneracy along $\sigma_8\Omega_{\rm m}^2$, reflecting the mass function sensitivity to a wide halo-mass range. Applying the approach to SDSS-DR7 yields $\Omega_{\rm m}=0.324\pm0.012$, $\sigma_8=0.775\pm0.063$, and $S_8=0.81\pm0.05$, in excellent agreement with Planck and showing no $S_8$ tension; the strongest constraint is $\sigma_8(\Omega_{\rm m}/0.3)^2=0.91\pm0.05$. The results are robust to reasonable variations in baryonic corrections and underline the critical role of the satellite radial profile, offering a path to leverage upcoming surveys to constrain baryonic physics while testing cosmology.

Abstract

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.

Figures (12)

• Figure 1: The SDSS data used by Basilisk$\,\,$ to constrain the galaxy-halo connection. The panels in the left-hand column show the projected phase-space distribution of secondaries, while the right-hand panels show their multiplicity distributions. To highlight the dependence on the luminosity of the primary, the data is split in three consecutive bins of $L_{\rm pri}$ that contain equal numbers of primaries, with the brightest (faintest) subsample shown at the top (bottom). Note, the velocity dispersion of the secondaries is higher for the more luminous primaries, which also contain, on average, more secondaries, implying that they reside in more massive halos.
• Figure 1: Constraints on the $S_8$ parameter for different variations of the assumed galaxy-halo connection model. The differences in the CLF models are indicated in the text corresponding to each constraint. The green star with errorbars corresponds to our fiducial model adopted throughout the main text, which is identical to the one shown in Fig. \ref{['fig:Cosmo_Constraint']}. Note that the $S_8$ inference is robust to changes in the (flexibility) of the CLF model.
• Figure 2: The $3\times 3$ panels on the left show how baryonic effects impact satellite kinematics for three different halo masses (different columns). From top to bottom, the panels show radial profiles of total mass density, enclosed mass, and the resultant line-of-sight velocity dispersion of satellite galaxies modelled as a massless tracer population. Solid and dashed curves correspond to the dark matter only (DMO) case and the case in which baryonic effects have been taken into account, respectively. The gray shaded regions in the lower panels indicate where Basilisk$\,\,$ does not have data, due to secondary selection cuts; inner radii are excluded because of fiber collisions, while outer radii are excluded to minimize the impact of interlopers. The top right-hand panels plots $f_{\rm eject}$, the fraction of baryons ejected from halos in the EAGLE$\,\,$ simulation as a function of the DMO virial mass, which is the most relevant parameter controlling the impact of baryonic effects in our analysis of satellite kinematics. The gray-shaded region envelopes the range of $f_{\rm eject}(M)$ models considered in this study (see Section \ref{['sec:subsec:varying_baryon']}). For the fiducial baryonic prescription of B25, which includes the adiabatic response of the dark matter, that ratio of interest $(\overline{\sigma}_{\rm hydro}/\, \overline{\sigma}_{\rm DMO})$ is shown in the bottom-right panel, labelled " Basilisk's input". The coloured circles correspond to the 3 different halo masses shown in the panels on the left.
• Figure 3: Top 3 rows show Basilisk's inference of galaxy-halo connection parameters from the mock data discussed in the text for 9 different cosmologies. Each set of histograms shows the posterior distributions of the parameters for a specific cosmology, as indicated on the top of each panel. The cyan shaded regions show the amounts of variation of the posterior distributions across all 9 cosmologies shown here. All posterior distributions are shifted by the true value of the input parameter used to create the mock, and scaled by the standard deviation of the posterior distribution. All posterior inferences are statistically consistent with the truth (red vertical line in each panel), irrespective of the cosmology. The narrow width of the cyan shaded regions demonstrates that the inferred posteriors have only a very weak cosmology-dependence. As described in the text, the combined posterior of these 9 cosmologies serves as the prior in our cosmological inference procedure. Bottom row shows the 90 percent confidence intervals of the predicted luminosity functions using the CLF posteriors for each of the 9 cosmologies, all computed using the halo mass function for $\Omega_{\rm m} = 0.30$ and $\sigma_8 = 0.82$. Each one is compared to the luminosity function predicted for the true cosmology (gray shaded region in each of these 3 panels), to demonstrate that they almost perfectly overlap.
• Figure 4: Basilisk's cosmology inference based on mock data. The contours mark the 68 and 95 percent confidence intervals, and are in perfect agreement with the cosmology of the SMDPL simulation used to create the mock data, shown by the black square. The gray points on a $3\times 3$ grid shows the set of 9 cosmologies used to infer the combined $P({\cal G})$, that acts as the prior in the cosmology inference. The brown dashed curve is the locus for constant $S_8 = 0.8323$, the true value in the SMDPL simulation. As is evident from the other loci of constant $S_8$ shown as light-brown dotten lines, the constraints on $S_8$ are of the order of $\sim 8$ (15) percent at 68 (95) percent confidence. Note, though, that Basilisk's inference is degenerate along the direction $\sigma_8 \Omega_{\rm m}^2$ (brown dot-dashed curve), rather than $\sigma_8 \Omega_{\rm m}^{0.5}$. The accuracy with which our analysis constrains $\sigma_8 \Omega_{\rm m}^2$ is $\sim 6$ percent (68 percent confidence).