Halo stochasticity from exclusion and nonlinear clustering

We explore the noiseless Burgers dynamics in the inviscid limit, the so-called "adhesion model" in cosmology, in a regime where (almost) all the fluid particles are embedded within pointlike massive halos. Following previous works, we focus our investigations on a "geometrical" model, where the matter evolution within the shock manifold is defined from a geometrical construction. This hypothesis is at variance with the assumption that the usual continuity equation holds but, in the inviscid limit, both models agree in the regular regions. Taking advantage of the formulation of the dynamics of this "geometrical model" in terms of Legendre transforms and convex hulls, we study the evolution with time of the distribution of matter and the associated partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass distribution derives from a triangulation in Lagrangian space, while the dual Voronoi-like tessellation in Eulerian space gives the boundaries of empty regions with shock nodes at their vertices. We then emphasize that this dynamics actually leads to halo fragmentations for space dimensions greater or equal to 2 (for the inviscid limit studied in this paper). This is most easily seen from the properties of the Lagrangian-space triangulation and we illustrate this process in the two-dimensional (2D) case. In particular, we explain how pointlike halos only merge through three-body collisions while two-body collisions always give rise to two new massive shock nodes (in 2D). This generalizes to higher dimensions and we briefly illustrate the three-dimensional case. This leads to a specific picture for the continuous formation of massive halos through successive halo fragmentations and mergings.

Using the conditional luminosity function — the luminosity distribution of galaxies in a dark matter halo as a function of the halo mass — we present an empirical model to describe the redshift evolution of the rest B-band galaxy luminosity function (LF). The model is compared to various estimates of the LF, in rest UV and B bands, out to a redshift of 6, including estimates of LFs of galaxy types separated to red and blue galaxies. Using the observed LFs out to z~ 5, we present a general constraint on the redshift evolution of the central galaxy-halo mass relation. The increase in the number density of luminous galaxies, at the bright end of the LF, can be explained as due to a brightening of the luminosity of galaxies present in dark matter halo centres, relative to the luminosity of central galaxies in similar mass haloes today. The lack of strong evolution in the faint end of the LF, however, argues against a model involving pure-luminosity evolution at all halo mass scales. The increase in luminosity at the bright end compensates the rapid decline in the number density of massive haloes as the redshift is increased. The decline in group to cluster-mass dark matter haloes out to a redshift of ~2 is not important as the central galaxy luminosity flattens at halo masses around 1013 M⊙. At redshifts ~2–3, however, the density of bright galaxies begins to decrease due to the rapid decline in the number density of dark matter haloes at mass scales around and below 1013 M⊙. Based on a comparison of our predictions to the measured ultraviolet (UV) LF of galaxies at redshifts ~3, we estimate the probability distribution of halo masses to host Lyman break galaxies (LBGs). This probability for galaxies brighter than AB-absolute magnitudes of -21, with a number density of ~5 × 10−3h3 Mpc−3, peaks at a halo mass of ~7 × 1011h−1 M⊙ with a 68 per cent confidence level of (4–21) × 1011h−1 M⊙. These estimates are consistent with the mass estimates for LBGs using two-point clustering statistics and recent estimates of halo masses based on spectroscopic observations. For galaxies brighter than AB-absolute magnitudes of -21 at z~ 6, the halo mass scale is a factor of ~2 smaller; the LF predictions at z~ 6 are consistent with measured estimates in the literature. Based on the models, we also predict the LF of galaxies at redshifts greater than 6 and also the bias factor of galaxies at redshifts greater than 3; these predictions will soon be tested with observational data. In general, to explain high-redshift LFs, galaxies in dark matter haloes around 1012 M⊙ must increase in luminosity by a factor of ~4–6 between today and redshift of 6.

Recent work on quasar clustering suggests a degeneracy in the halo occupation distribution constrained from two-point correlation functions. To break this degeneracy, we make the first empirical measurement of the mean occupation function (MOF) of quasars at $z \sim 0.2$ by matching quasar positions with groups and clusters identified in the MaxBCG sample. We fit two models to the MOF, a power law and a 4-parameter model. The number distribution of quasars in host halos is close to Poisson, and the slopes of the MOF obtained from our best-fit models (for the power law case) favor a MOF that monotonically increases with halo mass. The best-fit slopes are $0.53 \pm 0.04$ and $1.03\pm 1.12$ for the power law model and the 4-parameter model, respectively. We measure the radial distribution of quasars within dark matter halos and find it to be adequately described by a power law with a slope $-2.3 \pm 0.4$. We measure the conditional luminosity function (CLF) of quasars and show that there is no evidence that quasar luminosity depends on host halo mass, similar to the inferences drawn from clustering measurements. We also measure the conditional black hole mass function (CMF) of our quasars. Although the results are consistent with no dependence on halo mass, we observe a slight indication of downsizing of the black hole mass function. The lack of halo mass dependence in the CLF and CMF shows that quasars residing in galaxy clusters have characteristic luminosity and black hole mass scales.

Modern models predict that galaxies do not evolve in isolation, but exist in haloes of dark matter and gas, embedded in the large-scale cosmic web. To build a self-consistent model for how galaxies form and evolve, it is vital to understand how galaxies regulate their formation through interaction with the circumgalactic medium that surrounds them, and at present the nature and impact of these interactions is poorly-constrained by both theory and observations. This thesis presents new insights into how galaxies affect their surroundings through feedback processes, the impact of the properties of the CGM on galaxy evolution, and how the properties of galaxy-CGM ecosystems are fundamentally connected to the assembly histories of their dark matter haloes. I begin by examining the origin of scatter in the relationship between the gas fraction and mass of dark matter haloes hosting present-day ~L* central galaxies in the EAGLE simulations. The scatter is uncorrelated with the accretion rate of the central galaxy's black hole (BH), but correlates strongly and negatively with the BH's mass, implicating differences in the expulsion of gas by active galactic nucleus (AGN) feedback, throughout the assembly of the halo, as the main cause of scatter. Haloes whose central galaxies host undermassive BHs also tend to retain a higher gas fraction, and exhibit elevated star formation rates (SFRs). Diversity in the mass of central BHs stems primarily from diversity in the dark matter halo binding energy, as these quantities are strongly and positively correlated at fixed halo mass, such that ~L* galaxies hosted by haloes that are more (less) tightly-bound develop central BHs that are more (less) massive than is typical for their halo mass. Variations in the halo gas fraction at fixed halo mass are reflected in both the soft X-ray luminosity and thermal Sunyaev-Zel'dovich flux, suggesting that the prediction of a strong coupling between the properties of galaxies and their halo gas fractions can be tested with measurements of these diagnostics for galaxies with diverse SFRs but similar halo masses. I then examine the connection between the properties of the CGM and the quenching and morphological evolution of central galaxies in both the EAGLE and IllustrisTNG simulations. The simulations yield very different median CGM mass fractions as a function of halo mass, with low-mass haloes being significantly more gas-rich in IllustrisTNG than in EAGLE. Nonetheless, in both cases the scatter in the CGM mass fraction at fixed halo mass is strongly correlated with the specific star formation rate and the kinematic morphology of central galaxies. This feedback elevates the CGM cooling time, preventing gas from accreting onto the galaxy to fuel star formation, and thus establishing a preference for quenched, spheroidal galaxies to be hosted by haloes with low CGM mass fractions for their mass. In both simulations, the CGM mass fraction correlates negatively with the host halo's intrinsic concentration, and hence with its binding energy and formation redshift, primarily because early halo formation fosters the rapid early growth of the central black hole (BH). This leads to a lower CGM mass fraction at fixed halo mass in EAGLE because the BH reaches high accretion rates sooner, whilst in IllustrisTNG it occurs because the central BH reaches the mass threshold at which AGN feedback is assumed to switch from thermal to kinetic injection earlier. Despite these differences, there is consensus from these state-of-the-art simulations that the expulsion of efficiently-cooling gas from the CGM is a crucial step in the quenching and morphological evolution of central galaxies. The above results suggest a connection between the assembly histories of dark matter haloes and the properties of their galaxy-CGM ecosystems. I clearly demonstrate this connection by performing a controlled and systematic experiment in which I adjust the assembly history of a single EAGLE halo hosting a moderately star-forming Milky Way-like galaxy by ``genetically modifying its initial conditions, keeping all other variables fixed. Shifting the halo assembly history to earlier times increases the integrated feedback injected by the AGN, ejecting a greater fraction of the CGM baryons and leading to the quenching and morphological transformation of the central galaxy. These effects can only have originated from differences in the assembly history of the halo, providing compelling evidence for this novel picture of the self-regulation of galaxy formation.

Sparse regression algorithms have been proposed as the appropriate framework to model the governing equations of a system from data, without needing prior knowledge of the underlying physics. In this work, we use sparse regression to build an accurate and explainable model of the stellar mass of central galaxies given properties of their host dark matter (DM) halo. Our data set comprises 9521 central galaxies from the EAGLE hydrodynamic simulation. By matching the host haloes to a DM-only simulation, we collect the halo mass and specific angular momentum at present time and for their main progenitors in 10 redshift bins from z = 0 to z = 4. The principal component of our governing equation is a third-order polynomial of the host halo mass, which models the stellar-mass–halo-mass relation. The scatter about this relation is driven by the halo mass evolution and is captured by second- and third-order correlations of the halo mass evolution with the present halo mass. An advantage of sparse regression approaches is that unnecessary terms are removed. Although we include information on halo specific angular momentum, these parameters are discarded by our methodology. This suggests that halo angular momentum has little connection to galaxy formation efficiency. Our model has a root mean square error (RMSE) of 0.167log10(M*/M⊙), and accurately reproduces both the stellar mass function and central galaxy correlation function of EAGLE. The methodology appears to be an encouraging approach for populating the haloes of DM-only simulations with galaxies, and we discuss the next steps that are required.

In this dissertation we analyse the dark matter substructure dynamics within a series of high-resolution cosmological galaxy clusters simulations generated with the N-body code MLAPM. Two new halo finding algorithms were designed to aid in this analysis. The first of these was the 'MLAPM-halo-finder' MHF), built upon the adaptive grid structure of MLAPM. The second was the 'MLAPM-halo-tracker' (MHT), an extension of MHF which allowed the tracking of orbital characteristics of gravitationally bound objects through any given cosmological N-body-simulation. Using these codes we followed the time evolution of hundreds of satellite galaxies within the simulated clusters. These clusters were chosen to sample a variety of formation histories, ages, and triaxialities; despite their obvious differences, we and striking similarities within the associated substructure populations. Namely, the radial distribution of these substructure satellites follows a 'universal' radial distribution irrespective of the host halo's environment and formation history. Further, this universal substructure profile is anti-biased with respect to the underlying dark matter profile. All satellite orbits follow nearly the same eccentricity distribution with a correlation between eccentricity and pericentre. The destruction rate of the substructure population is nearly independent of the mass, age, and triaxiality of the host halo. There are, however, subtle differences in the velocity anisotropy of the satellite distribution. We find that the local velocity bias at all radii is greater than unity for all halos and this increases as we move closer to the halo centre, where it varies from 1.1 to 1.4. For the global velocity bias we find a small but slightly positive bias, although when we restrict the global velocity bias calculation to satellites that have had at least one orbit, the bias is essentially removed. Following this general analysis we focused on three specific questions regarding the evolution of substructures within dark matter halos. Observations of the Virgo and Coma clusters have shown that their galaxies align with the principal axis of the cluster. Further, a recent statistical analysis of some 300 Abell clusters confirm this alignment, linking it to the dynamical state of the cluster. Within our simulations the apocentres of the satellite orbits are preferentially found within a cone of opening angle 40 degrees around the major axis of the host halo, in accordance with the observed anisotropy found in galaxy clusters. We do, however, note that a link to the dynamical age of the cluster is not well established. Further analysis connects this distribution to the infall pattern of satellites along the filaments, rather than some 'dynamical selection' during their life within the host's virial radius. We then focused our attention on the outskirts of clusters investigating the socalled 'backsplash population', i.e. satellite galaxies that once were inside the virial radius of the host but now reside beyond it. We and that this population is significant in number and needs to be appreciated when interpreting empirical galaxy morphology-environmental relationships and decoupling the degeneracy between nature and nurture. Specifically, we and that approximately half of the galaxies with current clustercentric distance in the interval 1- 2 virial radii of the host are backsplash galaxies which once penetrated deep into the cluster potential, with 90% of these entering to within 50% of the virial radius. These galaxies have undergone significant tidal disruption, losing on average 40% of their mass. This results in a mass function for the backsplash population different to those galaxies infalling for the first time. We further show that these two populations are kinematically distinct and should be observable spectroscopically. Finally we present a detailed study of the real and integrals-of-motion space distributions of a disrupting satellite obtained from one of our self-consistent highresolution cosmological simulations. The satellite has been re-simulated using various analytical halo potentials and we and that its debris appears as a coherent structure in integrals-of-motion space in all models ('live' and analytical potential) although the distribution is significantly smeared for the live host halo. The primary mechanism for the dispersion is the mass growth of the host. However, when quantitatively comparing the effects of 'live' and time-varying host potentials we conclude that not all of the dispersion can be accounted for by the steady growth of the host's mass. We ascribe the remaining differences to additional effects in the 'live' halo such as non-sphericity of the host and interactions with other satellites, which have not been modelled analytically.

We compute the mass function of galactic dark matter halos for different values of the warm dark matter (WDM) particle mass m X and compare it with the number density of ultra-faint galaxies derived from the deepest UV luminosity function available so far at redshift z ≈ 2. The magnitude limit M UV = −13 reached by such observations allows us to probe the WDM mass functions down to scales close to or smaller than the half-mass mode mass scale ∼109 M ⊙. This allowed for an efficient discrimination among predictions for different m X which turn out to be in practice independent of the star formation efficiency η adopted to associate the observed UV luminosities of galaxies to the corresponding dark matter halo masses. Adopting a conservative approach to take into account the existing theoretical uncertainties in the galaxy halo mass function, we obtain a robust limit m X ≥ 1.8 keV for the mass of thermal relic WDM particles when comparing with the measured abundance of the faintest galaxies, while m X ≥ 1.5 keV is obtained when we compare with the Schechter fit to the observed luminosity function. The corresponding lower limit for sterile neutrinos depends on the modeling of the production mechanism; for instance m sterile ≳ 4 keV holds for the Shi–Fuller mechanism. We discuss the impact of observational uncertainties on the above bound on m X . In the cold dark matter (CDM) limit m X ≫ 1 keV ?> we recover the generic CDM result that very inefficient star formation efficiency is required to match the observed galaxy abundances. As a baseline for comparison with forthcoming observational results from the Hubble Space Telescope Frontier Field project, we provide predictions for the number density of faint galaxies with M UV = −13 for different values of the WDM particle mass and of the star formation efficiency η, which are valid up to z ≈ 4.

Halo models provide a simple and computationally inexpensive way to investigate the connection between galaxies and their dark matter haloes. However, these models rely on the assumption that the role of baryons can easily be parametrized in the modelling procedure. We aim to examine the ability of halo occupation distribution (HOD) modelling to reproduce the galaxy clustering found in two different hydrodynamic simulations, Illustris and EAGLE. For each simulation, we measure several galaxy clustering statistics on two different luminosity threshold samples. We then apply a simple five parameter HOD, which was fit to each simulation separately, to the corresponding dark matter-only simulations, and measure the same clustering statistics. We find that the halo mass function is shifted to lower masses in the hydrodynamic simulations, resulting in a galaxy number density that is too high when an HOD is applied to the dark matter-only simulation. However, the exact way in which baryons alter the mass function is remarkably different in the two simulations. After applying a correction to the halo mass function in each simulation, the HOD is able to accurately reproduce all clustering statistics for the high luminosity sample of galaxies. For the low luminosity sample, we find evidence that in addition to correcting the halo mass function, including spatial, velocity, and assembly bias parameters in the HOD is necessary to accurately reproduce clustering statistics.

In this work we investigate the generation of mock halo catalogues based on perturbation theory and non-linear stochastic biasing with the novel patchy code. In particular, we use Augmented Lagrangian Perturbation Theory (ALPT) to generate a dark matter density field on a mesh starting from Gaussian fluctuations and to compute the peculiar velocity field. ALPT is based on a combination of second order LPT (2LPT) on large scales and the spherical collapse model on smaller scales. We account for the systematic deviation of perturbative approaches from N-body simulations together with halo biasing adopting an exponential bias model. We then account for stochastic biasing by defining three regimes: a low-, an intermediate- and a high-density regime, using a Poisson distribution in the intermediate regime and the negative binomial distribution – including an additional parameter – to model over-dispersion in the high-density regime. Since we focus in this study on massive haloes, we suppress the generation of haloes in the low-density regime. The various non-linear and stochastic biasing parameters, and density thresholds, are calibrated with the large BigMultiDark N-body simulation to match the power spectrum of the corresponding halo population. Our model effectively includes only five parameters, as they are additionally constrained by the halo number density. Our mock catalogues show power spectra, in both real- and redshift-space, which are compatible with N-body simulations within about 2 per cent up to k ∼ 1 h Mpc−1 at z = 0.577 for a sample of haloes with the typical Baryon Oscillation Spectroscopic Survey (BOSS) CMASS (constant stellar mass galaxy sample) galaxy number density. The corresponding correlation functions are compatible down to a few Mpc. We also find that neglecting over-dispersion in high-density regions produces power spectra with deviations of 10 per cent at k ∼ 0.4 h Mpc−1. These results indicate the need to account for an accurate statistical description of the galaxy clustering for precise studies of large-scale surveys.

Several observations reveal that dwarf galaxy Segue 1 has a dark matter (DM) halo at least ∼200 times more massive than its visible baryon mass of only ∼103 M⊙. The baryon mass is dominated by stars with perhaps an interstellar gas mass of ≲13 M⊙. Regarding Segue 1 as a dwarf disc galaxy by its morphological appearance of long stretch, we invoke the dynamic model of Xiang-Gruess, Lou & Duschl (XLD) to estimate its physical parameters for possible equilibria with and without an isopedically magnetized gas disc. We estimate the range of DM mass and compare it with available observational inferences. Due to the relatively high stellar velocity dispersion compared to the stellar surface mass density, we find that a massive DM halo would be necessary to sustain disc equilibria. The required DM halo mass agrees grossly with observational inferences so far. For an isopedic magnetic field in a gas disc, the ratio f between the DM and baryon potentials depends strongly on the magnetic field strength. Therefore, a massive DM halo is needed to counteract either the strong stellar velocity dispersion and rotation of the stellar disc or the magnetic Lorentz force in the gas disc. By the radial force balances, the DM halo mass increases for faster disc rotation.

We present a detailed investigation of the changing relationship between galaxies and the dark matter haloes they inhabit from z~1.2 to the present day. We do this by comparing precise galaxy clustering measurements over 133 deg2 of the "Wide" component of the CFHT Legacy Survey (CFHTLS) with predictions of an analytic HOD model where the number of galaxies in each halo depends only on the halo mass. Starting from a parent catalogue of ~ 3x10^6 galaxies at i'_AB < 22.5 we use accurate photometric redshifts calibrated using ~ 10^4 spectroscopic redshifts to create a series of type-selected volume-limited samples covering 0.2 < z < 1.2. Our principal result, based on clustering measurements in these samples, is a robust determination of the luminosity-to-halo mass ratio and its dependence on redshift and galaxy type. For the full sample, this reaches a peak at low redshifts of Mh,peak = 4.5x10^11 h^-1 M_sun and moves towards higher halo masses at higher redshifts. For redder galaxies the peak is at higher halo masses and does not evolve significantly over the entire redshift range of our survey. We also consider the evolution of bias, average halo mass and the fraction of satellites as a function of redshift and luminosity. Our observed growth of a factor of ~ 2 in satellite fraction between z~1 and z~0 is testament to the limited role that galaxy merging plays in galaxy evolution for ~ 10^12 h^-1 M_sun mass haloes at z<1. Qualitatively, our observations are consistent with a picture in which red galaxies in massive haloes have already accumulated most of their stellar mass by z~1 and subsequently undergo little evolution until the present day. The observed movement of the peak location for the full galaxy population is consistent with the bulk of star-formation activity migrating from higher mass haloes at high redshifts to lower mass haloes at lower redshifts.

We characterize the luminosity distribution, halo-mass dependence, and redshift evolution of red galaxies in galaxy clusters using the SDSS Data Release 8 redMaPPer cluster sample. We propose a simple prescription for the relationship between the luminosity of both red central and red satellite galaxies and the mass of their host halos, and show that this model is well fit by the data. Using a larger galaxy cluster sample than previously employed in the literature, we find that the luminosities of red central galaxies scale as , with A L = 0.39 ± 0.04, and that the scatter of the red central galaxy luminosity at fixed M 200b ( ) is dex, with the error bar including systematics due to mis-centering of the cluster finder, photometry, and photometric redshift estimation. Our data prefers a positive correlation between the luminosity of red central galaxies and the observed richness of clusters at a fixed halo mass, with an effective correlation coefficient . The characteristic luminosity of red satellites becomes dimmer from z = 0.3 to z = 0.1 by ∼20% after accounting for passive evolution. We estimate the fraction of galaxy clusters where the brightest red galaxy is not the central to be P BNC ∼ 20%. We discuss implications of these findings in the context of galaxy evolution and the galaxy–halo connection.

We present 2-D stellar kinematics of M87 out to R = 238" taken with the integral field spectrograph VIRUS-P. We run a large set of axisymmetric, orbit-based dynamical models and find clear evidence for a massive dark matter halo. While a logarithmic parameterization for the dark matter halo is preferred, we do not constrain the dark matter scale radius for an NFW profile and therefore cannot rule it out. Our best-fit logarithmic models return an enclosed dark matter fraction of 17.2 +/- 5.0 % within one effective radius (R_e ~ 100"), rising to 49.4 (+7.2,-8.8) % within 2 R_e. Existing SAURON data (R < 13"), and globular cluster kinematic data covering 145" < R < 540" complete the kinematic coverage to R = 47 kpc. At this radial distance the logarithmic dark halo comprises 85.3 (+2.5,-2.4) % of the total enclosed mass of 5.7^(+1.3)_(-0.9) X 10^(12) M_sun making M87 one of the most massive galaxies in the local universe. Our best-fit logarithmic dynamical models return a stellar mass-to-light ratio of 9.1^(+0.2)_(-0.2) (V-band), a dark halo circular velocity of 800^(+75)_(-25) kms, and a dark halo scale radius of 36^(+7)_(-3) kpc. The stellar M/L, assuming an NFW dark halo, is well constrained to 8.20^(+0.05)_(-0.10) (V-band). The stars in M87 are found to be radially anisotropic out to R ~ 0.5 R_e then isotropic or slightly tangentially anisotropic to our last stellar data point at R = 2.4 R_e where the anisotropy of the stars and globular clusters are in excellent agreement. The globular clusters then become radially anisotropic in the last two modeling bins at R = 3.4 R_e and R = 4.8 R_e. As one of the most massive galaxies in the local universe, constraints on both the mass distribution of M87 and anisotropy of its kinematic components strongly informs our theories of early-type galaxy formation and evolution in dense environments.

In the standard picture of disc galaxy formation, baryons and dark matter receive the same tidal torques, and therefore approximately the same initial specific angular momentum. However, observations indicate that disc galaxies typically have only about half as much specific angular momentum as their dark matter haloes. We argue this does not necessarily imply that baryons lose this much specific angular momentum as they form galaxies. It may instead indicate that galaxies are most directly related to the inner regions of their host haloes, as may be expected in a scenario where baryons in the inner parts of haloes collapse first. A limiting case is examined under the idealised assumption of perfect angular momentum conservation. Namely, we determine the density contrast Delta, with respect to the critical density of the Universe, by which dark matter haloes need to be defined in order to have the same average specific angular momentum as the galaxies they host. Under the assumption that galaxies are related to haloes via their characteristic rotation velocities, the necessary Delta is ~600. This Delta corresponds to an average halo radius and mass which are ~60% and ~75%, respectively, of the virial values (i.e., for Delta = 200). We refer to this radius as the radius of baryonic collapse R_BC, since if specific angular momentum is conserved perfectly, baryons would come from within it. It is not likely a simple step function due to the complex gastrophysics involved, therefore we regard it as an effective radius. In summary, the difference between the predicted initial and the observed final specific angular momentum of galaxies, which is conventionally attributed solely to angular momentum loss, can more naturally be explained by a preference for collapse of baryons within R_BC, with possibly some later angular momentum transfer.

The growth and properties of galaxies are thought to be closely connected to the ones of their host dark matter haloes. Despite the importance of this so-called galaxy–halo connection, the potential role of dark matter haloes in regulating observed galaxy properties remains yet to be fully understood. In this work, we derive the ages, metallicites, and [Mg/Fe] abundances from optical spectra from the Sloan Digital Sky Survey of nearby central galaxies, and study them in terms of their host haloes. We investigate how the scatter in the stellar-to-halo mass relation and the velocity dispersion–halo mass relation correlates with these stellar population parameters. In addition, we also study the differences when distinguishing between different galaxy morphologies and environments. We find that the ages and chemical enrichment of galaxies are not fully determined by their stellar masses or velocity dispersion, but also depend on the mass of the host haloes. Our findings suggest that the velocity dispersion is the best proxy of the stellar population parameters with halo mass playing a secondary yet noticeable role. We interpret that the origin of the correlation between the scatter of these relations and the ages and metallicities might be related to different halo formation times.