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DOE OSTI2025

A joint analysis of 3D clustering and galaxy × CMB-lensing cross-correlations with DESI DR1 galaxies

The spectroscopic data from DESI Data Release 1 (DR1) galaxies enables the analysis of 3D clustering by fitting galaxy power spectra and reconstructed correlation functions in redshift space. Given low measurements of the amplitude of structure from cosmic shear at z ∼ 1, redshift space distortions (RSD) + Baryon Acoustic Oscillation (BAO) signals from DESI galaxies combined with weak lensing can break degeneracies and provide a tight alternative constraint on the z ∼ 1 amplitude of structure. In this paper we perform joint analyses that combine full-shape + post-reconstruction information from the DESI DR1 BGS and LRG samples along with angular cross-correlations with Planck PR4 and ACT DR6 CMB lensing maps. We show that adding galaxy-lensing cross-correlations tightens clustering amplitude constraints, improving σ 8 uncertainties by 30% over RSD+BAO alone. We also include angular galaxy-galaxy and galaxy-lensing spectra using photometric samples from the DESI Legacy Survey to further improve constraints. Our headline results are σ 8 = 0.803 ± 0.017, Ω m = 0.3037 ± 0.0069, and S 8 = 0.808 ± 0.017. Given DESI's preference for higher σ 8 compared to lower values from BOSS, we perform a catalog-level comparison of LRG samples from both surveys. We test sensitivity to dark energy assumptions by relaxing our ΛCDM prior and allowing for evolving dark energy via the w 0 - w a parameterization. We find our S 8 constraints to be relatively unchanged despite a 3.5σ tension with the cosmological constant model when combining with the Union3 supernova likelihood. Finally we test general relativity (GR) by allowing the gravitational slip parameter (γ) to vary, and find γ = 1.17 ± 0.11 in mild (∼ 1.5σ) tension with the GR value of 1.0.

cosmological parameters from LSS↗
DOE OSTI2023

Velocity Dispersion σ aper Aperture Corrections as a Function of Galaxy Properties from Integral-field Stellar Kinematics of 10,000 MaNGA Galaxies

Abstract The second moment of the stellar velocity within the effective radius, denoted by σ e 2 , is a crucial quantity in galaxy studies, as it provides insight into galaxy properties and their mass distributions. However, large spectroscopic surveys typically do not measure σ e directly, instead providing σ aper , the second moment of the stellar velocity within a fixed fiber aperture. In this paper, we derive an empirical aperture correction formula, given by σ aper / σ e = ( R aper / R e ) α , using spatially resolved stellar kinematics extracted from approximately 10,000 Sloan Digital Sky Survey–Mapping Nearby Galaxies at Apache Point Observatory integral field unit observations. Our analysis reveals a strong dependence of α on the r -band absolute magnitude M r , g – i color, and Sérsic index n Ser , where α values are lower for brighter, redder galaxies with higher Sérsic indices. Our results demonstrate that the aperture correction derived from previous literature on early-type galaxies cannot be applied to predict the aperture corrections for galaxies with intermediate Sérsic indices. We provide a lookup table of α values for different galaxy types, with parameters in the ranges of −18 > M r > −24, 0.4 < g – i < 1.6, and 0 < n Ser < 8. A Python script is provided to obtain the correction factors from the lookup table.

Astronomy & Astrophysics↗
DOE OSTI2022

HIPASS study of southern ultradiffuse galaxies and low surface brightness galaxies

ABSTRACT We present results from an H i counterpart search using the HI Parkes All Sky Survey (HIPASS) for a sample of low surface brightness galaxies (LSBGs) and ultradiffuse galaxies (UDGs) identified from the Dark Energy Survey (DES). We aimed to establish the redshifts of the DES LSBGs to determine the UDG fraction and understand their properties. Out of 409 galaxies investigated, none were unambiguously detected in H i. Our study was significantly hampered by the high spectral rms of HIPASS and thus in this paper we do not make any strong conclusive claims but discuss the main trends and possible scenarios our results reflect. The overwhelming number of non-detections suggest that (a) Either all the LSBGs in the groups, blue or red, have undergone environment aided pre-processing and are H i deficient or the majority of them are distant galaxies, beyond the HIPASS detection threshold. (b) The sample investigated is most likely dominated by galaxies with H i masses typical of dwarf galaxies. Had there been Milky Way (MW) size (Re) galaxies in our sample, with proportionate H i content, they would have been detected, even with the limitations imposed by the HIPASS spectral quality. This leads us to infer that if some of the LSBGs have MW-size optical diameters, their H i content is possibly in the dwarf range. More sensitive observations using the SKA precursors in future may resolve these questions.

Zhou, Yun-Fan↗
DOE OSTI2023

The frequency and sizes of inner bars and nuclear rings in barred galaxies and their dependence on galaxy properties

ABSTRACT Using a volume- and mass-limited (D < 30 Mpc, $\log \, (M_{\star }/M_{\odot })\ge 9.75$) sample of 155 barred S0–Sd galaxies, I determine the fraction with secondary structures within their bars. Some 20 ± 3 per cent have a separate inner bar, making them double-barred; an identical fraction have nuclear rings, with $11^{+3}_{-2}$ per cent hosting both. The inner-bar frequency is a strong, monotonic function of stellar mass: only $4^{+3}_{-2}$ per cent of barred galaxies with $\log \, (M_{\star }/M_{\odot })= 9.75$–10.25 are double-barred, while 47 ± 8 per cent of those with $\log \, (M_{\star }/M_{\odot })\gt 10.5$ are. The nuclear-ring frequency is a strong function of absolute bar size: only $1^{+2}_{-1}$ per cent of bars with semimajor axes <2 kpc have nuclear rings, while $39^{+6}_{-5}$ per cent of larger bars do. Both inner bars and nuclear rings are absent in very late-type (Scd–Sd) galaxies. Inner bar size correlates with galaxy stellar mass, but is clearly offset to smaller sizes from the main population of bars. This makes it possible to define ‘nuclear bars’ in a consistent fashion, based on stellar mass. There are eight single-barred galaxies where the bars are nuclear-bar-sized; some of these may be systems where an outer bar failed to form, or previously double-barred galaxies where the outer bar has dissolved. Inner bar size is even more tightly correlated with host bar size, which is likely the primary driver. In contrast, nuclear ring size is only weakly correlated with galaxy mass or bar size, with more scatter in size than is true of inner bars.

Astronomy & Astrophysics↗
DOE OSTI2023

Constraints on S 8 from a full-scale and full-shape analysis of redshift-space clustering and galaxy–galaxy lensing in BOSS

ABSTRACT We present a novel simulation-based cosmological analysis of galaxy–galaxy lensing and galaxy redshift-space clustering. Compared to analysis methods based on perturbation theory, our simulation-based approach allows us to probe a much wider range of scales, $0.4 \, h^{-1} \, \mathrm{Mpc}$ to $63 \, h^{-1} \, \mathrm{Mpc}$, including highly non-linear scales, and marginalizes over astrophysical effects such as assembly bias. We apply this framework to data from the Baryon Oscillation Spectroscopic Survey LOWZ sample cross-correlated with state-of-the-art gravitational lensing catalogues from the Kilo Degree Survey and the Dark Energy Survey. We show that gravitational lensing and redshift-space clustering when analysed over a large range of scales place tight constraints on the growth-of-structure parameter $S_8 = \sigma _8 \sqrt{\Omega _{\rm m} / 0.3}$. Overall, we infer S8 = 0.792 ± 0.022 when analysing the combination of galaxy–galaxy lensing and projected galaxy clustering and S8 = 0.771 ± 0.027 for galaxy redshift-space clustering. These findings highlight the potential constraining power of full-scale studies over studies analysing only large scales and also showcase the benefits of analysing multiple large-scale structure surveys jointly. Our inferred values for S8 fall below the value inferred from the CMB, S8 = 0.834 ± 0.016. While this difference is not statistically significant by itself, our results mirror other findings in the literature whereby low-redshift large-scale structure probes infer lower values for S8 than the CMB, the so-called S8-tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Biasing from galaxy trough and peak profiles with the DES Y3 redMaGiC galaxies and the weak lensing mass map

We measure the correspondence between the distribution of galaxies and matter around troughs and peaks in the projected galaxy density, by comparing redMaGiC galaxies (0.15 < z < 0.65) to weak lensing mass maps from the Dark Energy Survey (DES) Y3 data release. We obtain stacked profiles, as a function of angle θ, of the galaxy density contrast δ g and the weak lensing convergence κ, in the vicinity of these identified troughs and peaks, referred to as ‘void’ and ‘cluster’ superstructures. The ratio of the profiles depend mildly on θ, indicating good consistency between the profile shapes. We model the amplitude of this ratio using a function $F(\boldsymbol{\eta }, \theta )$ that depends on cosmological parameters $\boldsymbol{\eta }$, scaled by the galaxy bias. We construct templates of $F(\boldsymbol{\eta }, \theta )$ using a suite of N-body (‘Gower Street’) simulations forward-modelled with DES Y3-like noise and systematics. We discuss and quantify the caveats of using a linear bias model to create galaxy maps from the simulation dark matter shells. We measure the galaxy bias in three lens tomographic bins (near to far): $2.32^{+0.86}_{-0.27}, 2.18^{+0.86}_{-0.23}, 1.86^{+0.82}_{-0.23}$ for voids, and $2.46^{+0.73}_{-0.27}, 3.55^{+0.96}_{-0.55}, 4.27^{+0.36}_{-1.14}$ for clusters, assuming the best-fit Planck cosmology. Similar values with ∼0.1σ shifts are obtained assuming the mean DES Y3 cosmology. The biases from troughs and peaks are broadly consistent, although a larger bias is derived for peaks, which is also larger than those measured from the DES Y3 3 × 2-point analysis. This method shows an interesting avenue for measuring field-level bias that can be applied to future lensing surveys.

cosmology: observations↗
DOE OSTI2026

Dark Energy Survey Year 6 results: Galaxy-galaxy lensing

Here, we present galaxy-galaxy lensing measurements from the full six years of data from the Dark Energy Survey (DES Y6), covering 4031 deg 2 and used in the DES Y6 3×2 pt cosmological analysis. We use the Maglim++ lens sample, containing ∼9 million galaxies divided into six redshift bins, and the Metadetection source catalog, including ∼140 million galaxies divided into four redshift bins. The mean tangential shear signal achieves a total signal-to-noise ratio (S/N) of 173, corresponding to a 17% improvement over DES Y3. After applying the scale cuts used in the cosmological analysis, with 𝑅 min =6 Mpc/ℎ (4 Mpc/ℎ) for the linear (nonlinear) galaxy-bias model, the S/N is reduced to 75 (90). A comprehensive suite of validation tests demonstrates that the measurement is robust against observational and astrophysical systematics at the statistical precision required for the DES Y6 analysis. Although not used in the main cosmological analysis, we extract high signal-to-noise geometric shear-ratio measurements from the galaxy-galaxy lensing signal on small angular scales. These measurements provide an internal consistency check on the photometric redshift distributions and shear calibration used in the 3 ×2 pt analysis.

cosmological parameters↗
DOE OSTI2021

Faint galaxies and small halos : probes of galaxy formation and dark matter

This thesis addresses the intersection of dark matter and galaxy formation physics by modeling the faintest galaxies in the Universe in a cosmological context. In the first part of this work, I present an empirical model for the connection between faint galaxies and small dark matter halos. Combining this model with tailored cosmological simulations of Milky Way analogs and state-of-the-art satellite galaxy observations yields new insights into dwarf galaxy formation and hierarchical structure formation. Next, I show that these same dwarf galaxy observations place stringent constraints on microphysical dark matter properties including its warmth, self-interactions, Standard Model interactions, minimum particle mass, and formation epoch. Finally, I describe a unified framework that combines dark matter constraints from dwarf galaxies and strong gravitational lensing, paving the way for next-generation surveys of small-scale cosmic structure to deliver unprecedented insights into dark matter physics.

Nadler, Ethan Oliver↗
DOE OSTI2025

Cosmological Constraints from Full-Scale Clustering and Galaxy-Galaxy Lensing with DESI DR1

We present constraints on cosmic structure growth from the analysis of galaxy clustering and galaxy-galaxy lensing with galaxies from the Dark Energy Spectroscopic Instrument (DESI) Data Release 1. We analyze four samples drawn from the Bright Galaxy Survey (BGS) and the Luminous Red Galaxy (LRG) target classes. Projected galaxy clustering measurements from DESI are supplemented with lensing measurements from the Dark Energy Survey (DES), the Kilo-Degree Survey (KiDS), and the Hyper Suprime-Cam (HSC) survey around the same targets. Our method relies on a simulation-based modeling framework using the AbacusSummit simulations and a complex halo occupation distribution model that incorporates assembly bias. We analyze scales down to $0.4 \, h^{-1} \, \mathrm{Mpc}$ for clustering and $2.5 \, h^{-1} \, \mathrm{Mpc}$ for lensing, leading to stringent constraints on $S_8 = σ_8 \sqrt{Ω_\mathrm{m} / 0.3}$ and $Ω_\mathrm{m}$ when fixing other cosmological parameters to those preferred by the CMB. We find $S_8 = 0.794 \pm 0.023$ and $Ω_\mathrm{m} = 0.295 \pm 0.012$ when using lensing measurements from DES and KiDS. Similarly, for HSC, we find $S_8 = 0.793 \pm 0.017$ and $Ω_\mathrm{m} = 0.303 \pm 0.010$ when assuming the best-fit photometric redshift offset suggested by the HSC collaboration. Overall, our results are in good agreement with other results in the literature while continuing to highlight the constraining power of non-linear scales.

Lange, Johannes U. [American U.] (ORCID:0000000224↗
DOE OSTI2026

Dark Energy Survey Year 6 Results: Galaxy-galaxy lensing

We present galaxy--galaxy lensing (GGL) measurements from the full six years of data from the Dark Energy Survey (DES Y6), covering $4031\,\mathrm{deg}^2$ and used in the DES Y6 $3\times2$pt cosmological analysis. We use the MagLim++ lens sample, containing $\sim 9$ million galaxies divided into six redshift bins, and the Metadetection source catalog, including $\sim 140$ million galaxies divided into four redshift bins. The mean tangential shear signal achieves a total signal-to-noise ratio (S/N) of $173$, corresponding to a $17\%$ improvement over DES Y3. After applying the scale cuts used in the cosmological analysis, with $R_{\min}=6\,\mathrm{Mpc}/h$ ($4\,\mathrm{Mpc}/h$) for the linear (nonlinear) galaxy-bias model, the S/N is reduced to $75$ (90). A comprehensive suite of validation tests demonstrates that the measurement is robust against observational and astrophysical systematics at the statistical precision required for the DES Y6 analysis. Although not used in the main cosmological analysis, we extract high--signal-to-noise geometric shear-ratio measurements from the galaxy--galaxy lensing signal on small angular scales. These measurements provide an internal consistency check on the photometric redshift distributions and shear calibration used in the $3\times2$pt analysis.

Giannini, G. [Barcelona, IEEC; Chicago U., KICP; B↗
DOE OSTI2026

Precision Kinematic Sunyaev--Zel'dovich Measurements Across Halo Mass and Redshift with DESI DR2 and ACT DR6: Part II. Bright Galaxy Survey and Emission-Line Galaxies

We present the first high-significance spectroscopic stacked kinetic Sunyaev-Zel'dovich (kSZ) measurements of circumgalactic gas profiles for both Bright Galaxy Survey (BGS) and Emission Line Galaxy (ELG) tracers, combining DESI Data Release 2 with ACT Data Release 6. Using reconstructed line-of-sight velocities from the DESI galaxies and high-resolution ACT temperature maps, we detect the kSZ signal at high significance, reaching signal-to-noise ratios of up to $\sim$9 for BGS and $\sim$7.5 for ELGs in optimal stellar-mass selections. Together with the LRG measurements presented in Paper I, these constitute the most significant kSZ detections from any spectroscopic survey to date. We perform the analysis in both real and harmonic space, obtaining consistent results. By splitting both tracers into stellar-mass bins, we study the scaling of the kSZ amplitude with galaxy properties. Combining the kSZ measurements with ACT Data Release 6 (DR6) CMB lensing maps enables a joint calibration of the galaxy-halo connection and the gas fractions of host halos. For the BGS galaxies, we observe low gas fractions around the virial radius relative to standard expectations, likely attributable to active galactic nuclei (AGN) activity. We find some evidence for higher-mass halos retaining a larger fraction of their baryons, consistent with more efficient feedback in lower-mass systems. For the ELG sample, dominated by blue, star-forming galaxies, we provide the first detection of the gas distribution in ELG host halos. The ELGs appear to exhibit relatively high gas fractions, which points to the possibility of weaker feedback (due to e.g. low AGN and supernova feedback activity) at their mass scale. Finally, we present generalized Navarro-Frenk-White (GNFW) fits to the harmonic-space measurements, providing a compact parametrization of gas profiles for forward modeling in large-scale structure analyses.

Hadzhiyska, B. [Cambridge U.; Cambridge U., Inst. ↗
DOE OSTI2022

Toward Accurate Modeling of Galaxy Clustering on Small Scales: Constraining the Galaxy-halo Connection with Optimal Statistics

Applying halo models to analyze the small-scale clustering of galaxies is a proven method for characterizing the connection between galaxies and their host halos. Such works are often plagued by systematic errors or limited to clustering statistics that can be predicted analytically. In this work, we employ a numerical mock-based modeling procedure to examine the clustering of Sloan Digital Sky Survey DR7 galaxies. We apply a standard halo occupation distribution (HOD) model to dark matter only simulations with a ΛCDM cosmology. To constrain the theoreStical models, we utilize a combination of galaxy number density and selected scales of the projected correlation function, redshift-space correlation function, group multiplicity function, average group velocity dispersion, mark correlation function, and counts-in-cells statistics. We design an algorithm to choose an optimal combination of measurements that yields tight and accurate constraints on our model parameters. Compared to previous work using fewer clustering statistics, we find a significant improvement in the constraints on all parameters of our halo model for two different luminosity-threshold galaxy samples. Most interestingly, we obtain unprecedented high-precision constraints on the scatter in the relationship between galaxy luminosity and halo mass. However, our best-fit model results in significant tension (>4σ) for both samples, indicating the need to add second-order features to the standard HOD model. To guarantee the robustness of these results, we perform an extensive analysis of the systematic and statistical errors in our modeling procedure, including a first of its kind study of the sensitivity of our constraints to changes in the halo mass function due to baryonic physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The galaxy–halo connection of emission-line galaxies in IllustrisTNG

ABSTRACT We employ the hydrodynamical simulation IllustrisTNG-300-1 to explore the halo occupation distribution (HOD) and environmental dependence of luminous star-forming emission-line galaxies (ELGs) at z ∼ 1. Such galaxies are key targets for current and upcoming cosmological surveys. We select model galaxies through cuts in colour–colour space allowing for a direct comparison with the Extended Baryon Oscillation Spectroscopic Survey and the Dark Energy Spectroscopic Instrument (DESI) surveys and then compare them with galaxies selected based on specific star formation rate (sSFR) and stellar mass. We demonstrate that the ELG populations are twice more likely to reside in lower density regions (sheets) compared with the mass-selected populations and twice less likely to occupy the densest regions of the cosmic web (knots). We also show that the colour-selected and sSFR-selected ELGs exhibit very similar occupation and clustering statistics, finding that the agreement is best for lower redshifts. In contrast with the mass-selected sample, the occupation of haloes by a central ELG peaks at ∼20 per cent. We furthermore explore the dependence of the HOD and the autocorrelation on environment, noticing that at fixed halo mass, galaxies in high-density regions cluster about 10 times more strongly than low-density ones. This result suggests that we should model carefully the galaxy–halo relation and implement assembly bias effects into our models (estimated at ∼4 per cent of the clustering of the DESI colour-selected sample at z = 0.8). Finally, we apply a simple mock recipe to recover the clustering on large scales (r ≳ 1 Mpc h−1) to within 1 per cent by augmenting the HOD model with an environment dependence, demonstrating the power of adopting flexible population models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

SDSS-IV MaNGA: a catalogue of spectroscopically detected strong galaxy–galaxy lens candidates

ABSTRACT We spectroscopically detected candidate emission-lines of 8 likely, 17 probable, and 69 possible strong galaxy–galaxy gravitational lens candidates found within the spectra of $\approx 10\, 000$ galaxy targets contained within the completed Mapping of Nearby Galaxies at Apache Point Observatory survey. This search is based upon the methodology of the Spectroscopic Identification of Lensing Objects project, which extends the spectroscopic detection methods of the BOSS Emission-Line Lensing Survey and the Sloan Lens ACS Survey. We scanned the co-added residuals that we constructed from stacks of foreground subtracted row-stacked-spectra so a sigma-clipping method can be used to reject cosmic rays and other forms of transients that impact only a small fraction of the combined exposures. We also constructed narrow-band images from the signal to noise of the co-added residuals to observe signs of lensed source images. We also use several methods to compute the probable strong lensing regime for each candidate lens to determine which candidate background galaxies may reside sufficiently near the galaxy centre for strong lensing to occur. We present the spectroscopic redshifts within a value-added catalogue (VAC) for data release 17 (DR17) of SDSS-IV. We also present the lens candidates, spectroscopic data, and narrow-band images within a VAC for DR17. High resolution follow-up imaging of these lens candidates are expected to yield a sample of confirmed grade-A lenses with sufficient angular size to probe possible discrepancies between the mass derived from a best-fitting lens model, and the dynamical mass derived from the observed stellar velocities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Dark Energy Survey Year 1 Results: Cosmological Constraints from Cluster Abundances, Weak Lensing, and Galaxy Correlations

We present the first joint analysis of cluster abundances and auto or cross-correlations of three cosmic tracer fields: galaxy density, weak gravitational lensing shear, and cluster density split by optical richness. From a joint analysis (4×2pt+N) of cluster abundances, three cluster cross-correlations, and the auto correlations of the galaxy density measured from the first year data of the Dark Energy Survey, we obtain Ωm=0.305-0.038+0.055 and σ8=0.783-0.054+0.064. This result is consistent with constraints from the DES-Y1 galaxy clustering and weak lensing two-point correlation functions for the flat νΛCDM model. Consequently, we combine cluster abundances and all two-point correlations from across all three cosmic tracer fields (6×2pt+N) and find improved constraints on cosmological parameters as well as on the cluster observable-mass scaling relation. This analysis is an important advance in both optical cluster cosmology and multiprobe analyses of upcoming wide imaging surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Large–scale asymmetry in galaxy spin directions: Analysis of galaxies with spectra in DES, SDSS, and DESI Legacy Survey

Multiple previous studies using several different probes have shown considerable evidence for the existence of cosmological–scale anisotropy and a Hubble–scale axis. One of the probes that show such evidence is the distribution of the directions toward which galaxies spin. The advantage of the analysis of the distribution of galaxy spin directions compared to the cosmic microwave background anisotropy is that the ratio of galaxy spin directions is a relative measurement, and therefore less sensitive to background contamination such as Milky Way obstruction. Another advantage is that many spiral galaxies have spectra, and therefore allow to analyze the location of such axis relative to Earth. This paper shows an analysis of the distribution of the spin directions of over 90K galaxies with spectra. That analysis is also compared to previous analyses using the Earth–based Sloan Digital Sky Survey, Panoramic Survey Telescope and Rapid Response System, and Dark Energy Spectroscopic Instrument Legacy Survey, as well as space–based data collected by Hubble Space Telescope. Finally, the results show very good agreement between the distribution patterns observed with the different telescopes. The dipole or quadrupole axes formed by the spin directions of the galaxies with spectra do not necessarily go directly through Earth.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

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

ABSTRACT We present an analysis of the anisotropic redshift-space void–galaxy correlation in configuration space using the Sloan Digital Sky Survey extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 luminous red galaxy (LRG) sample. This sample consists of LRGs between redshifts 0.6 and 1.0, combined with the high redshift z > 0.6 tail of the Baryon Oscillation Spectroscopic Survey Data Release 12 CMASS sample. We use a reconstruction method to undo redshift-space distortion (RSD) effects from the galaxy field before applying a watershed void-finding algorithm to remove bias from the void selection. We then perform a joint fit to the multipole moments of the correlation function for the growth rate fσ8 and the geometrical distance ratio DM/DH, finding $f\sigma _8(z_\rm {eff})=0.356\pm 0.079$ and $D_M/D_H(z_\rm {eff})=0.868\pm 0.017$ at the effective redshift $z_\rm {eff}=0.69$ of the sample. The posterior parameter degeneracies are orthogonal to those from galaxy clustering analyses applied to the same data, and the constraint achieved on DM/DH is significantly tighter. In combination with the consensus galaxy BAO and full-shape analyses of the same sample, we obtain fσ8 = 0.447 ± 0.039, DM/rd = 17.48 ± 0.23, and DH/rd = 20.10 ± 0.34. These values are in good agreement with the ΛCDM model predictions and represent reductions in the uncertainties of $13{{\ \rm per\ cent}}$, $23{{\ \rm per\ cent}}$, and $28{{\ \rm per\ cent}}$, respectively, compared to the combined results from galaxy clustering, or an overall reduction of 55 per cent in the allowed volume of parameter space.

Nadathur, Seshadri↗