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Halos of similar mass and redshift exhibit a large degree of variability in their differential properties, such as dark matter, hot gas, and stellar mass density profiles. This variability is an indicator of diversity in the formation history of these dark matter halos that is reflected in the coupling of scatters about the mean relations. In this work, we show that the strength of this coupling depends on the scale at which halo profiles are measured. By analyzing the outputs of the IllustrisTNG hydrodynamical cosmological simulations, we report the radial- and mass-dependent couplings between the dark matter, hot gas, and stellar mass radial density profiles utilizing the population diversity in dark matter halos. We find that for the same mass halos, the scatters in the density of baryons and dark matter are strongly coupled at large scales (r>R₂₀₀), but the coupling between gas and dark matter density profiles fades near the core of halos (r< 0.3R₂₀₀). We then show that the correlation between halo profile and integrated quantities induces a radius-dependent additive bias in the profile observables of halos when halos are selected on properties other than their mass. We discuss the impact of this effect on cluster abundance and cross-correlation cosmology with multiwavelength cosmological surveys.

The underlying physics of astronomical systems govern the relation between their measurable properties. Consequently, quantifying the statistical relationships between system-level observable properties of a population offers insights into the astrophysical drivers of that class of systems. While purely linear models capture behavior over a limited range of system scale, the fact that astrophysics is ultimately scale dependent implies the need for a more flexible approach to describing population statistics over a wide dynamic range. For such applications, we introduce and implement a class of kernel localized linear regression(KLLR)models.KLLRis a natural extension to the commonly used linear models that allows the parameters of the linear model—normalization, slope, and covariance matrix—to be scale dependent.KLLRperforms inference in two steps: (1) it estimates the mean relation between a set of independent variables and a dependent variable and; (2) it estimates the conditional covariance of the dependent variables given a set of independent variables. We demonstrate the model's performance in a simulated setting and showcase an application of the proposed model in analyzing the baryonic content of dark matter halos. As a part of this work, we publicly release a Python implementation of theKLLRmethod.

We apply machine learning (ML), a powerful method for uncovering complex correlations in high-dimensional data, to the galaxy–halo connection of cosmological hydrodynamical simulations. The mapping between galaxy and halo variables is stochastic in the absence of perfect information, but conventional ML models are deterministic and hence cannot capture its intrinsic scatter. To overcome this limitation, we design an ensemble of neural networks with a Gaussian loss function that predict probability distributions, allowing us to model statistical uncertainties in the galaxy–halo connection as well as its best-fitting trends. We extract a number of galaxy and halo variables from the Horizon-AGN and IllustrisTNG100-1 simulations and quantify the extent to which knowledge of some subset of one enables prediction of the other. This allows us to identify the key features of the galaxy–halo connection and investigate the origin of its scatter in various projections. We find that while halo properties beyond mass account for up to 50 per cent of the scatter in the halo-to-stellar mass relation, the prediction of stellar half-mass radius or total gas mass is not substantially improved by adding further halo properties. We also use these results to investigate semi-analytic models for galaxy size in the two simulations, finding that assumptions relating galaxy size to halo size or spin are not successful.

Galaxy cluster masses, rich with cosmological information, can be estimated from internal dark matter (DM) velocity dispersions, which in turn can be observationally inferred from satellite galaxy velocities. However, galaxies are biased tracers of the DM, and the bias can vary over host halo and galaxy properties as well as time. We precisely calibrate the velocity bias, bv – defined as the ratio of galaxy and DM velocity dispersions – as a function of redshift, host halo mass, and galaxy stellar mass threshold ($M_{\rm \star , sat}$), for massive haloes ($M_{\rm 200c}\gt 10^{13.5} \, {\rm M}_\odot$) from five cosmological simulations: IllustrisTNG, Magneticum, Bahamas + Macsis, The Three Hundred Project, and MultiDark Planck-2. We first compare scaling relations for galaxy and DM velocity dispersion across simulations; the former is estimated using a new ensemble velocity likelihood method that is unbiased for low galaxy counts per halo, while the latter uses a local linear regression. The simulations show consistent trends of bv increasing with M200c and decreasing with redshift and $M_{\rm \star , sat}$. The ensemble-estimated theoretical uncertainty in bv is 2–3 per cent, but becomes percent-level when considering only the three highest resolution simulations. We update the mass–richness normalization for an SDSS redMaPPer cluster sample, and find our improved bv estimates reduce the normalization uncertainty from 22 to 8 per cent, demonstrating that dynamical mass estimation is competitive with weak lensing mass estimation. We discuss necessary steps for further improving this precision. Our estimates for $b_v(M_{\rm 200c}, M_{\rm \star , sat}, z)$ are made publicly available.