Void Galaxies Research Articles

Velocity profiles of matter and biased tracers around voids

ABSTRACT The velocity profile of galaxies around voids is a key ingredient for redshift space distortion (RSD) measurements made using the void–galaxy correlation function. In this paper, we use simulations to test whether the velocity profile of the tracers used to find the voids matches the velocity profile of the dark matter around these voids. A mismatch is expected and found in the inner part of voids, where tracers are very sparse. We discuss how this difference is caused by a selection effect where the void centre positions are correlated to the particular realization of the sparse tracers and their spatial distribution. In turn, this then affects the RSD void–galaxy correlation analysis. We show this by evaluating the Jacobian of the real to redshift space mapping using the tracer or matter velocity profile. Differences of the order of 20 per cent in the velocity profile translate into differences of the order of few per cent in the Jacobian. This small discrepancy propagates to the monopole and quadrupole of the void–tracer correlation function, producing modifications of comparable magnitude to those from changes in fσ8 at the level of the statistical uncertainties from current analyses.

Erratum: The completed SDSS-IV extended baryon oscillation spectroscopic survey: geometry and growth from the anisotropic void–galaxy correlation function in the luminous red galaxy sample

Erratum: The completed SDSS-IV extended baryon oscillation spectroscopic survey: geometry and growth from the anisotropic void–galaxy correlation function in the luminous red galaxy sample

Revealing the properties of void galaxies and their assembly using the eagle simulation

ABSTRACT We explore the properties of central galaxies living in voids using the eagle cosmological hydrodynamic simulations. Based on the minimum void-centric distance, we define four galaxy samples: inner void, outer void, wall, and skeleton. We find that inner void galaxies with host halo masses $\lt 10^{12}\,\rm M_{\odot }$ have lower stellar mass and stellar mass fractions than those in denser environments, and the fraction of galaxies with star formation (SF) activity and atomic hydrogen (H i) gas decreases with increasing void-centric distance, in agreement with observations. To mitigate the influence of stellar (halo) mass, we compare inner void galaxies to subsamples of fixed stellar (halo) mass. Compared to denser environments, inner void galaxies with $M_{*}= 10^{[9.0-9.5]}\,\rm M_{\odot }$ have comparable SF activity and H i gas fractions, but the lowest quenched galaxy fraction. Inner void galaxies with $M_{*}= 10^{[9.5-10.5]}\,\rm M_{\odot }$ have the lowest H i gas fraction, the highest quenched fraction and the lowest gas metallicities. On the other hand, inner void galaxies with $M_{*}\gt 10^{10.5}\,\rm M_{\odot }$ have comparable SF activity and H i gas fractions to their analogues in denser environments. They retain the highest metallicity gas that might be linked to physical processes that act with lower efficiency in underdense regions such as AGN (active galaxy nucleus) feedback. Furthermore, inner void galaxies have the lowest fraction of positive gas-phase metallicity gradients, which are typically associated with external processes or feedback events, suggesting they have more quiet merger histories than galaxies in denser environments. Our findings shed light on how galaxies are influenced by their large-scale environment.

Measurements of cosmic expansion and growth rate of structure from voids in the Sloan Digital Sky Survey between redshift 0.07 and 1.0

ABSTRACT We present measurements of the anisotropic cross-correlation of galaxies and cosmic voids in data from the Sloan Digital Sky Survey (SDSS) Main Galaxy Sample, Baryon Oscillation Spectroscopic Survey (BOSS), and extended BOSS luminous red galaxy catalogues from SDSS Data Releases 7, 12, and 16, covering the redshift range 0.07 < z < 1.0. As in our previous work analysing voids in subsets of these data, we use a reconstruction method applied to the galaxy data before void finding in order to remove selection biases when constructing the void samples. We report results of a joint fit to the multipole moments of the measured cross-correlation for the growth rate of structure, fσ8(z), and the ratio DM(z)/DH(z) of the comoving angular diameter distance to the Hubble distance, in six redshift bins. For DM/DH, we are able to achieve a significantly higher precision than that obtained from analyses of the baryon acoustic oscillations and galaxy clustering in the same data sets. Our growth rate measurements are of lower precision but still comparable with galaxy clustering results. For both quantities, the results agree well with the expectations for a Λ cold dark matter model. Assuming a flat Universe, our results correspond to a measurement of the matter density parameter $\Omega _\mathrm{m}=0.337^{+0.026}_{-0.029}$. For more general models, the degeneracy directions obtained are consistent with and complementary to those from other cosmological probes. These results consolidate void–galaxy cross-correlation measurements as a pillar of modern observational cosmology.

Fingerprints of modified gravity on galaxies in voids

ABSTRACT We search for detectable signatures of f(R) gravity and its chameleon screening mechanism in the baryonic and dark matter (DM) properties of simulated void galaxies. The enhancement of the gravitational acceleration can have a meaningful impact on the scaling relations as well as on the halo morphology. The galaxy rotational velocity field (calculated with the velocity of the gas disc and the acceleration fields) deviates from the typical values of the Tully–Fisher Relation in General Relativity (GR). For a given stellar mass, f(R) gravity tends to produce greater maximum velocities. On the other hand, the mass in haloes in f(R) gravity is more concentrated than their counterparts in GR. This trend changes when the concentration is calculated with the dynamical density profile, which takes into account the unscreened outer regions of the halo. Stellar discs interact with the overall potential well in the central regions, modifying the morphology of the screening regions and reshaping them. We find a trend for galaxies with a more dominant stellar disc to deviate further from round screening regions. We find that small haloes are less triaxial and more round in f(R) than their GR counterparts. The difference between halo morphology becomes smaller in f(R) haloes whose inner regions are screened. These results suggest possible observables that could unveil modified gravity effects on galaxies in voids in future cosmological tests of gravity.

Classification of cosmic structures for galaxies with deep learning: connecting cosmological simulations with observations

ABSTRACT We explore the capability of deep learning to classify cosmic structures. In cosmological simulations, cosmic volumes are segmented into voids, sheets, filaments, and knots, according to distribution and kinematics of dark matter (DM), and galaxies are also classified according to the segmentation. However, observational studies cannot adopt this classification method using DM. In this study, we demonstrate that deep learning can bridge the gap between the simulations and observations. Our models are based on 3D convolutional neural networks and trained with data of distribution of galaxies in a simulation to deduce the structure classes from the galaxies rather than DM. Our model can predict the class labels as accurate as a previous study using DM distribution for the training and prediction. This means that galaxy distribution can be a substitution for DM for the cosmic-structure classification, and our models using galaxies can be directly applied to wide-field survey observations. When observational restrictions are ignored, our model can classify simulated galaxies into the four classes with an accuracy (macro-averaged F1-score) of 64 per cent. If restrictions such as limiting magnitude are considered, our model can classify SDSS galaxies at ∼100 Mpc with an accuracy of 60 per cent. In the binary classification distinguishing void galaxies from the others, our model can achieve an accuracy of 88 per cent.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: cosmological implications from multitracer BAO analysis with galaxies and voids

ABSTRACT We construct cosmic void catalogues with the dive void finder upon SDSS BOSS DR12 and eBOSS DR16 galaxy samples with BAO reconstruction, and perform a joint BAO analysis using different types of galaxies and the corresponding voids. The BAO peak is evident for the galaxy–galaxy, galaxy–void, and void–void correlation functions of all data sets, including the ones cross-correlating LRG and ELG samples. Two multitracer BAO fitting schemes are tested, one combining the galaxy and void correlation functions with a weight applied to voids, and the other using a single BAO dilation parameter for all clustering measurements. Both methods produce consistent results with mock catalogues, and on average ∼10 per cent improvements of the BAO statistical uncertainties are observed for all samples, compared to the results from galaxies alone. By combining the clustering of galaxies and voids, the uncertainties of BAO measurements from the SDSS data are reduced by 5–15 per cent, yielding 0.9 per cent, 0.8 per cent, 1.1 per cent, 2.3 per cent, and 2.9 per cent constraints on the distance $D_{_{\rm V}}(z)$, at effective redshifts 0.38, 0.51, 0.70, 0.77, and 0.85, respectively. When combined with BAO measurements from SDSS MGS, QSO, and Lyα samples, as well as the BBN results, we obtain $H_0 = 67.58 \pm 0.91\, {\rm km}\, {\rm s}^{-1}\, {\rm Mpc}^{-1}$, Ωm = 0.290 ± 0.015, and $\Omega _\Lambda h^2 = 0.3241 \pm 0.0079$ in the flat-ΛCDM framework, where the 1σ uncertainties are around 6 per cent, 6 per cent, and 17 per cent smaller respectively, compared to constraints from the corresponding anisotropic BAO measurements without voids and LRG–ELG cross-correlations.

Star Formation Properties of Sloan Digital Sky Survey BOSS Void Galaxies in the Hyper Suprime-Cam Survey

Abstract We utilize the Hyper Suprime-Cam (HSC) Wide Survey to explore the properties of galaxies located in the voids identified from the Baryon Oscillation Spectroscopic Survey up to z ∼ 0.7. The HSC reaches i ∼ 25, allowing us to characterize the void galaxies down to 109.2 solar mass. We find that the revised void galaxy densities, when including faint galaxies in voids defined by bright galaxies, are still underdense compared to the mean density from the entire field. In addition, we classify galaxies into star-forming, quiescent, and green valley populations, and find that void galaxies tend to have slightly higher fractions of star-forming galaxies under the mass and redshift control, although the significance of this result is only moderate (2σ). However, when we focus on the star-forming population, the distribution of the specific star formation rate (sSFR) of void galaxies shows little difference from that of the control galaxies. Similarly, the median sSFR of star-forming void galaxies is also in good agreement with that of the star-forming control galaxies. Moreover, the effective green valley fraction of void galaxies, defined as the number of green valley galaxies over the number of nonquiescent galaxies, is comparable to that of the control ones, supporting the suggestion that void and control galaxies evolve under similar physical processes and quenching frequencies. Our results thus favor a scenario of galaxy assembly bias.

CO-CAVITY pilot survey: Molecular gas and star formation in void galaxies

Context. Voids are the most under-dense large-scale regions in the Universe. Galaxies inhabiting voids are one of the keys for understanding the intrinsic processes of galaxy evolution, as external factors such as multiple galaxy mergers or a dense self-collapsing environment are negligible. Aims. We present the first molecular gas mass survey of void galaxies. We compare these new data together with data for the atomic gas mass (MH I) and star formation rate (SFR) from the literature to those of galaxies in filaments and walls in order to better understand how molecular gas and star formation are related to the large-scale environment. Methods. We observed at the IRAM 30 m telescope the CO(1−0) and CO(2−1) emission of 20 void galaxies selected from the Void Galaxy Survey, with a stellar mass range from 108.5 to 1010.3 M⊙. We detected 15 objects in at least one CO line. We compared the molecular gas mass (MH2), the star formation efficiency (SFE = SFR/MH2), the atomic gas mass, the molecular-to-atomic gas mass ratio, and the specific star formation rate (sSFR) of the void galaxies with two control samples of galaxies in filaments and walls, selected from xCOLD GASS and EDGE-CALIFA, for different stellar mass bins and taking the star formation activity into account. Results. In general, we do not find any significant differences between void galaxies and the control sample. In particular, we do not find any evidence for a difference in the molecular gas mass or molecular gas mass fraction. For the other parameters (SFE, atomic gas mass, molecular-to-atomic gas mass ratio, and sSFR), we also find similar (within the errors) mean values between void and filament and wall galaxies when the sample is limited to star-forming galaxies. We find no evidence for an enhanced sSFR in void galaxies. Some tentative differences emerge when trends with stellar mass are studied: The SFE of void galaxies might be lower than in filament and wall galaxies for low stellar masses, and there might be a trend of increasing deficiency in the HI content in void galaxies compared to galaxies in filaments and walls for higher stellar masses, accompanied by an increase in the molecular-to-atomic gas mass ratio. However, all trends with stellar mass are based on a low number of galaxies and need to be confirmed for a larger sample. Conclusions. The results for the molecular gas mass for a sample of 20 voids galaxies allowed us to make a statistical comparison to galaxies in filaments and walls for the first time. We do not find any significant differences of the molecular gas properties and the SFE, but we note that a larger sample is necessary to confirm this and be sensitive to subtle trends.

Exploring the voids: Luminosity functions and magnetic field

We present semi-analytical models for magnetisation of the void inter-galactic medium (IGM) by outflows from void galaxies. The number density of dark matter haloes in an under-dense region (i.e., void) is obtained using the excursion set method extended for such low density environment. The star formation in such haloes has been estimated, taking account of the negative feedback by supernovae. The galaxy formation/evolution model is tuned to provide the r-band luminosity function, the stellar mass function and also the color of void galaxies as obtained from recent observations. This star formation model is used to study possible outflows from void galaxies driven by the hot thermal gas and cosmic ray pressures. These outflows drag the magnetic fields present in those galaxies to the void IGM. We show that such a model can magnetise ∼30% of the void IGM with the magnetic field strength of 10−12−10−10 G while considering only magnetic flux freezing condition. Along with this, the megapersec size of individual outflows can explain the non-detection of GeV photons in TeV blazars that put a lower limit of 10−16 G for void IGM magnetic field with a Mpc coherent length scale.

Active Galactic Nuclei Abundance in Cosmic Voids

Abstract The abundance of active galactic nuclei (AGN) in cosmic voids is relatively unexplored in the literature, but can potentially provide new constraints on the environmental dependence of AGN activity and the AGN-host coevolution. We investigated AGN fractions in one of the largest samples of optically selected cosmic voids from Sloan Digital Sky Survey Data Release 12 for redshift range 0.2–0.7 for moderately bright and bright AGN. We separated inner and outer void regions based on the void size, given by its effective void radius. We classified galaxies at a distance <0.6 R eff as inner void members and galaxies in the interval 0.6 < R/R eff < 1.3 as outer void galaxies. We found higher average fractions in the inner voids (4.9 ± 0.7)% than for their outer counterparts (3.1 ± 0.1)% at z > 0.42, which clearly indicates an environmental dependence. This conclusion was confirmed upon further separating the data in narrower void-centric distance bins and measured a significant decrease in AGN activity from inner to outer voids for z > 0.42. At low redshifts (z < 0.42), we find very weak dependence on the environment for the inner and outer regions for two out of three bins. We argue that the higher fraction in low-density regions close to void centers relative to their outer counterparts observed in the two higher-redshift bins suggests that more efficient galaxy interactions may occur at a one-to-one level in voids that may be suppressed in denser environments due to higher velocity dispersions. It could also indicate less prominent ram pressure stripping in voids or some intrinsic host or void environment properties.

The Ultraviolet Deep Imaging Survey of Galaxies in the Bootes Void. I. Catalog, Color–Magnitude Relations, and Star Formation

Abstract We present a deep far and near-ultraviolet (FUV and NUV) wide-field imaging survey of galaxies in the Bootes void using the Ultraviolet Imaging Telescope on board AstroSat. Our data reach 5σ limiting magnitudes for point sources at 23.0 and 24.0 AB mag in the FUV and NUV, respectively. We report a total of six star-forming galaxies residing in the Bootes void alongside the full catalog, and of these, three are newly detected in our FUV observation. Our void galaxy sample spans a range of UV colors (−0.35 mag ≤ FUV−NUV ≤ 0.68 mag) and absolute magnitudes (−14.16 mag ≤ M NUV ≤ −18.65 mag). In addition, Sloan Digital Sky Survey and Two Micron All Sky Survey archival data are being used to study UV, optical, and infrared color–magnitude relations for our galaxies in the void. We investigate the nature of bimodal color distribution, morphologies, and star formation of the void galaxies. Most of the galaxies in our sample are fainter and less massive than L* galaxies, with M r > −20 mag. Our analysis reveals a dominant fraction of bluer galaxies over the red ones in the void region probed. The internal and Galactic extinction corrected FUV star formation rates (SFRs) in our void galaxy catalog varies in a large range of 0.05–51.01 M ⊙ yr−1, with a median of 3.96 M ⊙ yr−1. We find a weak effect of the environment on the SFRs of galaxies. Implications of our findings are discussed.

Void Galaxy Distribution: A Challenge for ΛCDM

Abstract We extract void catalogs from the Sloan Digital Sky Survey Data Release 16 (SDSS DR16) survey and also from the Millennium simulation. We focus our comparison on distribution of galaxies brighter than M r < −18 inside voids and study the mean separation of void galaxies, distance from the void center, and the radial density profile. We find that mean separation of void galaxies depends on void size, as bigger voids have lower mean separation in both samples. However, void galaxies in the observation sample seem to have generally larger mean–distance than simulated ones at any given void size. In addition, observed void galaxies tend to reside closer to the void center than those in the simulation. This discrepancy is also shown in the density profile of voids. Regardless of the void size, the central densities of real void profiles are higher than the ones in the predicted simulated catalog.

Recovering the origin of star formation in the central region of I Zw 81

AbstractWe have studied the star formation properties of a massive void galaxy - I Zw 81. We performed 2D structural decomposition on Canada France Hawaii Telescope (CFHT) g- and r-band observation of I Zw 81 using GALFIT. The galaxy consists of an unresolved small bulge, a bar, an inner ring, and a truncated disk. We have used far-ultraviolet (FUV) and near-UV (NUV) observation of Ultraviolet Imaging Telescope (UVIT) onboard AstroSat for our analysis. The NUV–r color map of the lenticular galaxy illustrates a shallow positive color gradient in the profile, implying that the bar and inner ring are more star-forming than the outer disk. The FUV emission is mainly concentrated in the central region of the galaxy. A tidal tail-like feature is detected in the CFHT observations. We infer that bar and minor mergers-like interactions enhance the gas inflow and drive star formation in the center of I Zw 81.

The role of the elaphrocentre in void galaxy formation

ABSTRACT Voids may affect galaxy formation via weakening mass infall or increasing disk sizes, which could potentially play a role in the formation of giant low surface brightness galaxies (LSBGs). If a dark matter halo forms at the potential hill corresponding to a void of the cosmic web, which we denote the ‘elaphrocentre’ in contrast to a barycentre, then the elaphrocentre should weaken the infall rate to the halo when compared to infall rates towards barycentres. We investigate this hypothesis numerically. We present a complete software pipeline to simulate galaxy formation, starting from a power spectrum of initial perturbations and an N-body simulation through to merger-history-tree based mass infall histories. The pipeline is built from well-established, free-licensed cosmological software packages, and aims at highly portable long-term reproducibility. We find that the elaphrocentric accelerations tending to oppose mass infall are modest. We do not find evidence of location in a void or elaphrocentric position weakening mass infall towards a galaxy. However, we find indirect evidence of voids influencing galaxy formation: while void galaxies are of lower mass compared to galaxies in high-density environments, their spin parameters are typically higher. For a fixed mass, the implied disc scale length would be greater. Tangential accelerations in voids are found to be high and might significantly contribute to the higher spin parameters. We find significantly later formation epochs for void galaxies; this should give lower matter densities and may imply lower surface densities of disc galaxies. Thus, void galaxies have higher spin parameters and later formation epochs; both are factors that may increase the probability of forming LSBGs in voids.

Void Galaxies Follow a Distinct Evolutionary Path in the Environmental COntext Catalog

Abstract We measure the environmental dependence, where environment is defined by the distance to the third nearest neighbor, of multiple galaxy properties inside the Environmental COntext (ECO) catalog. We focus primarily on void galaxies, which we define as the 10% of galaxies having the lowest local density. We compare the properties of void and non-void galaxies: baryonic mass, color, fractional stellar mass growth rate (FSMGR), morphology, and gas-to-stellar-mass ratio (estimated from a combination of H i data and photometric gas fractions calibrated with the REsolved Spectroscopy Of a Local VolumE survey). Our void galaxies typically have lower baryonic masses than galaxies in denser environments, and they display the properties expected of a lower mass population: they have more late types, are bluer, have a higher FSMGR, and are more gas-rich. We control for baryonic mass and investigate the extent to which void galaxies are different at fixed mass. Void galaxies are bluer, more gas-rich, and more star-forming at fixed mass than non-void galaxies, which is a possible signature of galaxy assembly bias. Furthermore, we show that these trends persist even at fixed mass and morphology, and we find that voids host a distinct population of early types that are bluer and more star-forming than the typical red and quenched early types. In addition to these empirical observational results, we also present theoretical results from mock catalogs with built-in galaxy assembly bias. We show that a simple matching of galaxy properties to (sub)halo properties, such as mass and age, can recover the observed environmental trends in ECO galaxies.

The Loneliest Galaxies in the Universe: A GAMA and GalaxyZoo Study on Void Galaxy Morphology

The large-scale structure (LSS) of the universe is comprised of galaxy filaments, tendrils, and voids. The majority of the universe’s volume is taken up by these voids, which exist as underdense, but not empty, regions. The galaxies found inside voids are void galaxies and expected to be some of the most isolated objects in the universe. However, their standard morphology remains poorly studied. This study, using the Galaxy and Mass Assembly (GAMA) survey and Galaxy Zoo’s SDSS survey, aims to remedy this. To do so, survey results from GAMA have been plotted using the Sérsic index (n) to analyze morphology, while data from Galaxy Zoo’s crowdsourced study supplies a second analysis. For completeness purposes, we only include void galaxies identified by Alpaslan et al. 2014 with a redshift (z) between .08 and .215 and stellar mass (M*) between 109.35 and 1011.5. We then utilize Kolmogorov-Smirnov (KS) testing for significance. As a result, we conclude that, as supported by previous literature (Kreckel et al. 2014, Beygu et al. 2015, Beygu et al. 2016, Fraser-McKelvie et al. 2016, Pustilnik et al. 2019) , most void galaxies have a disky morphology with Sérsic index n

The Nonvelocity Cosmological Spectral Shift

Beginning from the premise that the universe is static, and that the cosmological redshift is due to a nonconservative tired light effect, the following examines evidence supporting the prediction that photons will progressively blueshift when transiting through the gravity wells of galaxies, galaxy clusters, and superclusters. The presence of such a nonvelocity blueshift effect is seen to make a substantial contribution to Virgo cluster galaxy spectra, sufficient to dramatically decrease the cluster’s velocity dispersion and assessed virial mass and eliminate the need to assume the presence of large quantities of dark matter. The effect is also shown to account for the Fingers-of-God effect and Kaiser pancaking effect seen when the spectra of cluster galaxies are plotted in redshift space. The opposite effect, excessive redshifting of photons passing through cosmic voids is able to explain void elongation in redshift space, and also the subnormal luminosity of void galaxies. The proposed cosmological blueshifting phenomenon also explains the downturn of the slope of the Hubble Flow in the vicinity of the Local Group which projects a negative apparent velocity for photons propagating near the Milky Way. It also offers an explanation for the blueshift of the Andromeda galaxy spectra and for Arp’s findings that the spectra of primary galaxies in a cluster tend to be blueshifted relative to their companion galaxies. These photon energy phenomena are anticipated by the physics of subquantum kinetics which predicts that photons traversing long distances through intergalactic space should undergo nonconservative tired-light redshifting, and that photons passing through gravity potential wells should undergo progressive blueshifting. The latter effect may be visualized as a negative nonvelocity Hubble constant.

Void galaxies follow a distinct evolutionary path in the environmental context catalog

Void galaxies follow a distinct evolutionary path in the environmental context catalog

Extensions to models of the galaxy–halo connection

ABSTRACT We explore two widely used empirical models for the galaxy–halo connection, subhalo abundance matching (SHAM) and the halo occupation distribution (HOD), and compare them with the hydrodynamical simulation IllustrisTNG (TNG) for multiple statistics quantifying the galaxy distribution at $n_{\rm gal}\approx 1.3\times 10^{-3}\, ({\rm Mpc}\,h^{-1})^{-3}$. We observe that in their most straightforward implementations, both models fail to reproduce the two-point clustering measured in TNG. We find that SHAM models that use the relaxation velocity, Vrelax, and the peak velocity, Vpeak, perform best, and match the clustering reasonably well, although neither captures adequately the one-halo clustering. Splitting the total sample into sub-populations, we discover that SHAM overpredicts the clustering of high-mass, blue, star-forming, and late-forming galaxies and underpredicts that of low-mass, red, quiescent, and early-forming galaxies. We also study various baryonic effects, finding that subhaloes in the dark-matter-only simulation have consistently higher values of their SHAM-proxy properties than their full-physics counterparts. We then consider a 2D implementation of the HOD model augmented with a secondary parameter (environment, velocity anisotropy, σ2Rhalf-mass, and total potential) tuned so as to match the two-point clustering of the IllustrisTNG galaxies on large scales. We analyse these galaxy populations adopting alternative statistical tools such as galaxy–galaxy lensing, void–galaxy cross-correlations, and cumulants of the density field, finding that the hydrodynamical galaxy distribution disfavours σ2Rhalf-mass and the total potential as secondary parameters, while the environment and velocity anisotropy samples are consistent with full physics across all statistical probes examined. Our results demonstrate the power of examining multiple statistics for determining the secondary parameters that are vital for understanding the galaxy–halo connection.