Testing subhalo abundance matching with galaxy kinematics

TL;DR

This paper develops a Bayesian forward model that links ΛCDM halo populations to SPARC disc galaxy kinematics via subhalo abundance matching (SHAM) with a tunable halo response. It jointly constrains the SHAM proxy, intrinsic scatter, halo response, and a halo-level selection based on $V_{ m max,halo}$, comparing predictions to per-galaxy $V_{ m max}$ measurements. Without selection, the model requires extreme halo expansion and a strongly suppressed satellite population, conflicting with clustering; introducing a strong halo selection reconciles kinematics with clustering, yielding mild contraction and $ abla u$ near zero with $\sigma_{ m SHAM} eq 0$, but implies SPARC-like galaxies occupy only the lowest $ imes 16 ext{ per cent}$ of the $V_{ m max,halo}$ distribution at fixed $M_{ m vir}$ and leaves residual tension at low masses. The work demonstrates the power of galaxy-by-galaxy forward modelling and halo selection for constraining the galaxy–halo connection, and points to selection modelling as a crucial ingredient for interpreting kinematic and clustering data from current and future HI surveys.

Abstract

The rotation velocities of disc galaxies trace dark matter halo structure, providing direct constraints on the galaxy--halo connection. We construct a Bayesian forward model to connect the dark matter halo population predicted by $Λ$CDM with an observed sample of disc galaxies (SPARC) through their maximum rotation velocities. Our approach combines a subhalo abundance matching scheme (accounting for assembly bias) with a parameterised halo response to galaxy formation. When assuming no correlation between selection in the SPARC survey and halo properties, reproducing the observed velocities requires strong halo expansion, low abundance matching scatter ($<0.15$ dex at $1σ$) and a halo proxy that strongly suppresses the stellar masses in satellite haloes. This is in clear tension with independent clustering constraints. Allowing for SPARC-like galaxies to preferentially populate low $\Vmax$ haloes at fixed virial mass greatly improves the goodness-of-fit and resolves these tensions: the preferred halo response shifts to mild contraction, the abundance matching scatter increases to $\sint = 0.19^{+0.13}_{-0.11}$ dex and the proxy becomes consistent with clustering. However, the inferred selection threshold is extreme, implying that SPARC galaxies occupy the lowest ${\sim}16$ per cent of the $\Vmaxhalo$ distribution at fixed $\Mvir$. Moreover, even with selection, the inferred scatter remains in statistical disagreement with the low-mass clustering constraints, which are most representative of the SPARC galaxies in our sample. Our analysis highlights the advantage of augmenting clustering-based constraints on the galaxy--halo connection with kinematics and suggests a possible tension using current data.

Figures (7)

• Figure 1: Comparison of forward-modelled (red) and observed SPARC (blue) BTFRs. Model parameters are $\tan^{-1}\alpha = 0.5$, $\sigma_\mathrm{SHAM} = 0.1\,\mathrm{dex}$, $\nu = -1.1$, with no halo selection ($x = 0$).
• Figure 2: Illustration of the halo-level selection on $V_\mathrm{max,halo}$ at fixed $M_\mathrm{vir}$. The solid lines mark the $x = 0$ (orange) and $x = 0.5$ (blue) thresholds, corresponding to the median $V_\mathrm{max,halo}$ at each virial mass. Haloes above this line (higher $V_\mathrm{max,halo}$ at fixed mass) would be excluded.
• Figure 3: Illustration of the likelihood framework. Distribution of predicted $v \equiv \log V_\mathrm{max}$ for galaxy UGC02487 in the baseline model without halo selection ($\tan^{-1}\alpha = 0.0$, $\sigma_\mathrm{SHAM}=0.1$, $x=0.0$, $\nu=-1.1$) in orange, and with added selection ($\tan^{-1}\alpha = 0.0$, $\sigma_\mathrm{SHAM}=0.1$, $x=0.5$, $\nu=-1.1$) in blue, compared to its observed velocity and uncertainty (red). For this example, added selection results in a log-likelihood difference of $\Delta \ln \mathcal{L}(\mathcal{D}_i) \equiv \ln \mathcal{L}(\mathcal{D}_i \mid x=0.5) - \ln \mathcal{L}(\mathcal{D}_i \mid x=0)=0.49$.
• Figure 4: Posterior constraints on the three-parameter model (left) and the four-parameter model with selection on halo properties (right). Contours enclose 39.3, 86.5, and 98.9 per cent of posterior mass (corresponding to $1\sigma$, $2\sigma$, and $3\sigma$ for a 2D Gaussian). Without selection, the data favour extreme SHAM parameters in tension with independent constraints from galaxy clustering. Introducing selection brings all parameters into agreement with clustering, but requires a strong selection threshold ($x = 0.84 \pm 0.04$), meaning SPARC-like galaxies occupy the lowest ${\approx}16$ per cent of the $V_\mathrm{max,halo}$ distribution at fixed $M_\mathrm{vir}$.
• Figure 5: A comparison of the posterior constraints on the SHAM parameters from our SPARC analysis with selection (which assumes mass-independent SHAM parameters), with independent constraints from the clustering analysis of Stiskalek_2021, for their four stellar mass bins (shown above the panels). All posteriors are reweighted to a common flat prior on $\tan^{-1}\alpha$. Contours enclose 39.3, 86.5, and 98.9 per cent of posterior mass (corresponding to $1\sigma$, $2\sigma$, and $3\sigma$ for a 2D Gaussian). The Bayes factor comparing the joint model (in which both datasets constrain the same underlying parameters) to independent models is shown above each panel, with the highest three stellar mass bins showing no more than weak evidence for tension, but the lowest mass bin (which is closest to the SPARC mean mass) indicating strong tension.