Redshift-space Correlation Function Research Articles

Modelling the redshift-space cluster–galaxy correlation function on Mpc scales with emulation of the pairwise velocity distribution

ABSTRACT We present a method for modelling the cluster–galaxy correlation function in redshift space, down to $\sim$ Mpc scales. The method builds upon the so-called galaxy infall kinematics (GIK) model, a parametric model for the pairwise velocities of galaxies with respect to nearby galaxy clusters. We fit the parameters of the GIK model to a suite of simulations run with different cosmologies, and use Gaussian processes to emulate how the GIK parameters depend upon cosmology. This emulator can then be combined with knowledge of the real-space clustering of clusters and galaxies, to predict the cluster–galaxy correlation function in redshift space, $\xi _\mathrm{cg}^s$. Fitting this model to an observed $\xi _\mathrm{cg}^s$ enables the extraction of cosmological parameter constraints, and we present forecasts for a survey like that currently being done by the Dark Energy Spectroscopic Instrument (DESI). We also perform tests of the robustness of our constraints from fitting to mock data extracted from N-body simulations, finding that fitting to scales $\lesssim 3 \, h^{-1}\, \mathrm{Mpc}$ leads to a biased inference on cosmology, due to model mis-specification on these scales. Finally, we discuss what steps will need to be taken in order to apply our method to real data.

Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6

We present, for the first time, dark matter halo (DMH) mass measurement of quasars at z ∼ 6 based on a clustering analysis of 107 quasars. Spectroscopically identified quasars are homogeneously extracted from the Hyper Suprime-Cam Strategic Survey Program wide layer over 891 deg2. We evaluate the clustering strength by three different autocorrelation functions: projected correlation function, angular correlation function, and redshift–space correlation function. The DMH mass of quasars at z ∼ 6 is evaluated as with the bias parameter b = 20.8 ± 8.7 by the projected correlation function. The other two estimators agree with these values; though, each uncertainty is large. The DMH mass of quasars is found to be nearly constant ∼1012.5 h −1 M ⊙ throughout cosmic time, suggesting that there is a characteristic DMH mass where quasars are always activated. As a result, quasars appear in the most massive halos at z ∼ 6, but in less extreme halos thereafter. The DMH mass does not appear to exceed the upper limit of 1013 h −1 M ⊙, which suggests that most quasars reside in DMHs with across most of the cosmic time. Our results supporting a significant increasing bias with redshift are consistent with the bias evolution model with inefficient active galactic nucleus feedback at z ∼ 6. The duty cycle (f duty) is estimated as 0.019 ± 0.008 by assuming that DMHs in some mass interval can host a quasar. The average stellar mass is evaluated from stellar-to-halo mass ratio as , which is found to be consistent with [C ii] observational results.

The Aemulus Project. V. Cosmological Constraint from Small-scale Clustering of BOSS Galaxies

We analyze clustering measurements of BOSS galaxies using a simulation-based emulator of two-point statistics. We focus on the monopole and quadrupole of the redshift-space correlation function, and the projected correlation function, at scales of 0.1 ∼ 60 h −1 Mpc. Although our simulations are based on wCDM with general relativity (GR), we include a scaling parameter of the halo velocity field, γ f , defined as the amplitude of the halo velocity field relative to the GR prediction. We divide the BOSS data into three redshift bins. After marginalizing over other cosmological parameters, galaxy bias parameters, and the velocity scaling parameter, we find f σ 8(z = 0.25) = 0.413 ± 0.031, f σ 8(z = 0.4) = 0.470 ± 0.026, and f σ 8(z = 0.55) = 0.396 ± 0.022. Compared with Planck observations using a flat Lambda cold dark matter model, our results are lower by 1.9σ, 0.3σ, and 3.4σ, respectively. These results are consistent with other recent simulation-based results at nonlinear scales, including weak lensing measurements of BOSS LOWZ galaxies, two-point clustering of eBOSS LRGs, and an independent clustering analysis of BOSS LOWZ. All these results are generally consistent with a combination of . We note, however, that the BOSS data is well fit assuming GR, i.e., γ f = 1. We cannot rule out an unknown systematic error in the galaxy bias model at nonlinear scales, but near-future data and modeling will enhance our understanding of the galaxy–halo connection, and provide a strong test of new physics beyond the standard model.

Toward Accurate Measurement of Property-dependent Galaxy Clustering. II. Tests of the Smoothed Density-corrected V max Method

We present a smoothed density-corrected V max technique for building a random catalog for property-dependent galaxy clustering estimation. This approach is essentially based on the density-corrected V max method of Cole, with three improvements to the original method. To validate the improved method, we generate two sets of flux-limited samples from two independent mock catalogs with different k + e corrections. By comparing the two-point correlation functions, our results demonstrate that the random catalog created by the smoothed density-corrected V max approach provides a more accurate and precise measurement for both sets of mock samples than the commonly used V max and redshift shuffled methods. For the flux-limited samples and color-dependent subsamples, the accuracy of the projected correlation function is well constrained within 1% on the scale of 0.07–30 h −1 Mpc. The accuracy of the redshift-space correlation function is less than 2% as well. Currently, it is the only approach that holds promise for achieving the goal of high-accuracy clustering measures for next-generation surveys.

Constraining spatial curvature with large-scale structure

We analyse the clustering of matter on large scales in an extension of the concordance model that allows for spatial curvature. We develop a consistent approach to curvature and wide-angle effects on the galaxy 2-point correlation function in redshift space. In particular we derive the Alcock-Paczynski distortion of fσ 8, which differs significantly from empirical models in the literature. A key innovation is the use of the 'Clustering Ratio', which probes clustering in a different way to redshift-space distortions, so that their combination delivers more powerful cosmological constraints. We use this combination to constrain cosmological parameters, without CMB information. In a curved Universe, we find that Ωm, 0=0.26± 0.04 (68% CL). When the clustering probes are combined with low-redshift background probes — BAO and SNIa — we obtain a CMB-independent constraint on curvature: Ω K, 0 = 0.0041-0.0504 +0.0500. We find no Bayesian evidence that the flat concordance model can be rejected. In addition we show that the sound horizon at decoupling is r d = 144.57 ± 2.34 Mpc, in agreement with its measurement from CMB anisotropies. As a consequence, the late-time Universe is compatible with flat ΛCDM and a standard sound horizon, leading to a small value of H 0, without assuming any CMB information. Clustering Ratio measurements produce the only low-redshift clustering data set that is not in disagreement with the CMB, and combining the two data sets we obtain Ω K, 0 = -0.023 ± 0.010.

The DESI N-body simulation project – I. Testing the robustness of simulations for the DESI dark time survey

ABSTRACT Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogues to validate data analysis pipelines and identify potential systematics. We compare three N-body simulation codes, abacus, gadget-2, and swift, to investigate the regimes in which their results agree. We run N-body simulations at three different mass resolutions, 6.25 × 108, 2.11 × 109, and 5.00 × 109 h−1 M⊙, matching phases to reduce the noise within the comparisons. We find systematic errors in the halo clustering between different codes are smaller than the Dark Energy Spectroscopic Instrument (DESI) statistical error for $s\ \gt\ 20\ h^{-1}$ Mpc in the correlation function in redshift space. Through the resolution comparison we find that simulations run with a mass resolution of 2.1 × 109 h−1 M⊙ are sufficiently converged for systematic effects in the halo clustering to be smaller than the DESI statistical error at scales larger than $20\ h^{-1}$ Mpc. These findings show that the simulations are robust for extracting cosmological information from large scales which is the key goal of the DESI survey. Comparing matter power spectra, we find the codes agree to within 1 per cent for k ≤ 10 h Mpc−1. We also run a comparison of three initial condition generation codes and find good agreement. In addition, we include a quasi-N-body code, FastPM, since we plan use it for certain DESI analyses. The impact of the halo definition and galaxy–halo relation will be presented in a follow-up study.

Angular systematics-free cosmological analysis of galaxy clustering in configuration space

ABSTRACT Galaxy redshift surveys are subject to incompleteness and inhomogeneous sampling due to the various constraints inherent to spectroscopic observations. This can introduce systematic errors on the summary statistics of interest, which need to be mitigated in cosmological analysis to achieve high accuracy. Standard practices involve applying weighting schemes based on completeness estimates across the survey footprint, possibly supplemented with additional weighting schemes accounting for density-dependent effects. In this work, we concentrate on pure angular systematics and describe an alternative approach consisting in analysing the galaxy two-point correlation function where angular modes are nulled. By construction, this procedure removes all possible known and unknown sources of angular observational systematics, but also part of the cosmological signal. We use a modified Landy–Szalay estimator for the two-point correlation function that relies on an additional random catalogue where angular positions are randomly drawn from the galaxy catalogue, and provide an analytical model to describe this modified statistic. We test the model by performing an analysis of the full anisotropic clustering in mock catalogues of luminous red and emission-line galaxies at 0.43 < z < 1.1. We find that the model fully accounts for the modified correlation function in redshift space, without introducing new nuisance parameters. The derived cosmological parameters from the analysis of baryon acoustic oscillations and redshift-space distortions display slightly larger statistical uncertainties, mostly for the growth rate of structure parameter fσ8 that exhibits a $50{{\ \rm per\ cent}}$ statistical error increase, but free from angular systematic error.

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

Abstract 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.

Statistical recovery of the BAO scale from multipoles of the beam-convolved 21 cm correlation function

ABSTRACT Despite being designed as an interferometer, the MeerKAT radio array (a Square Kilometre Array pathfinder) can also be used in autocorrelation (‘single-dish’) mode, where each dish scans the sky independently. Operating in this mode allows extremely high survey speeds to be achieved, albeit at significantly lower angular resolution. We investigate the recovery of the baryon acoustic oscillation (BAO) scale from multipoles of the redshift-space correlation function as measured by a low angular resolution 21 cm intensity mapping survey of this kind. Our approach is to construct an analytic model of the multipoles of the correlation function and their covariance matrix that includes foreground contamination and beam resolution effects, which we then use to generate an ensemble of mock data vectors from which we attempt to recover the BAO scale. In line with previous studies, we find that recovery of the transverse BAO scale α⊥ is hampered by the strong smoothing effect of the instrumental beam with increasing redshift, while the radial scale α∥ is much more robust. The multipole formalism naturally incorporates transverse information when it is available however, and so there is no need to perform a radial-only analysis. In particular, the quadrupole of the correlation function preserves a distinctive BAO ‘bump’ feature even for large smoothing scales. We also investigate the robustness of BAO scale recovery to beam model accuracy, severity of the foreground removal cuts, and accuracy of the covariance matrix model, finding in all cases that the radial BAO scale can be recovered in an accurate, unbiased manner.

The n-point streaming model: how velocities shape correlation functions in redshift space

Starting from first principles, we derive the fundamental equations that relate the n-point correlation functions in real and redshift space. Our result generalises the so-called `streaming model' to higher-order statistics: the full n-point correlation in redshift-space is obtained as an integral of its real-space counterpart times the joint probability density of n−1 relative line-of-sight peculiar velocities. Equations for the connected n-point correlation functions are obtained by recursively applying the generalised streaming model for decreasing n. Our results are exact within the distant-observer approximation and completely independent of the nature of the tracers for which the correlations are evaluated. Focusing on 3-point statistics, we use an N-body simulation to study the joint probability density function of the relative line-of-sight velocities of pairs of particles in a triplet. On large scales, we find that this distribution is approximately Gaussian and that its moments can be accurately computed with standard perturbation theory. We use this information to formulate a phenomenological 3-point Gaussian streaming model. A practical implementation is obtained by using perturbation theory at leading order to approximate several statistics in real space. In spite of this simplification, the resulting predictions for the matter 3-point correlation function in redshift space are in rather good agreement with measurements performed in the simulation. We discuss the limitations of the simplified model and suggest a number of possible improvements. Our results find direct applications in the analysis of galaxy clustering but also set the basis for studying 3-point statistics with future peculiar-velocity surveys and experiments based on the kinetic Sunyaev-Zel'dovich effect.

An accurate perturbative approach to redshift space clustering of biased tracers in modified gravity

We extend the scale-dependent Gaussian Streaming Model (GSM) to produce analytical predictions for the anisotropic redshift-space correlation function for biased tracers in modified gravity models. Employing the Convolution Lagrangian Perturbation Theory (CLPT) re-summation scheme, with a local Lagrangian bias schema provided by the peak-background split formalism, we predict the necessary ingredients that enter the GSM, the real-space halo pairwise velocity and the pairwise velocity dispersion. We further consider effective field theory contributions to the pairwise velocity dispersion in order to model correctly its large scale behavior. We apply our method on two widely-considered modified gravity models, the chameleon-screened f(R) Hu-Sawicki model and the nDGP Vainshtein model and compare our predictions against state-of-the-art N-body simulations for these models. We demonstrate that the GSM approach to predict the monopole and the quadrupole of the redshift-space correlation function for halos, gives very good agreement with the simulation data, for a wide range of screening mechanisms, levels of screening and halo masses at z=0.5 and z=1. Our work shows the applicability of the GSM, for cosmologies beyond GR, demonstrating that it can serve as a powerful predictive tool for the next stage of cosmological surveys like DESI, Euclid, LSST and WFIRST.

How to add massive neutrinos to your ΛCDM simulation – extending cosmology rescaling algorithms

ABSTRACT Providing accurate predictions for the spatial distribution of matter and luminous tracers in the presence of massive neutrinos is an important task, given the imminent arrival of highly accurate large-scale structure observations. In this work, we address this challenge by extending cosmology-rescaling algorithms to massive neutrino cosmologies. In this way, a ΛCDM simulation can be modified to provide non-linear structure formation predictions in the presence of a hot component of arbitrary mass, and, if desired, to include non-gravitational modifications to the clustering of matter on large scales. We test the accuracy of the method by comparing its predictions to a suite of simulations carried out explicitly including a neutrino component in its evolution equations. We find that, for neutrino masses in the range Mν ∈ [0.06, 0.3] eV the matter power spectrum is recovered to better than $1{{\ \rm per\ cent}}$ on all scales k < 2 h Mpc−1. Similarly, the halo mass function is predicted at a few per cent level over the range Mhalo ∈ [1012, 1015] h−1 M⊙, and so do also the multipoles of the galaxy two-point correlation function in redshift space over r ∈ [0.1, 200] h−1 Mpc. We provide parametric forms for the necessary transformations, as a function of Ωm and Ων for various target redshifts.

The Aemulus Project. I. Numerical Simulations for Precision Cosmology

Abstract The rapidly growing statistical precision of galaxy surveys has led to a need for ever more precise predictions of the observables used to constrain cosmological and galaxy formation models. The primary avenue through which such predictions will be obtained is suites of numerical simulations. These simulations must span the relevant model parameter spaces, be large enough to obtain the precision demanded by upcoming data, and be thoroughly validated in order to ensure accuracy. In this paper, we present one such suite of simulations, forming the basis for the Aemulus Project, a collaboration devoted to precision emulation of galaxy survey observables. We have run a set of 75 (1.05 h −1 Gpc)3 simulations with mass resolution and force softening of and 20 h −1 kpc, respectively, in 47 different wCDM cosmologies spanning the range of parameter space allowed by the combination of recent cosmic microwave background, baryon acoustic oscillation, and Type Ia supernova results. We present convergence tests of several observables including spherical overdensity halo mass functions, galaxy projected correlation functions, galaxy clustering in redshift space, and matter and halo correlation functions and power spectra. We show that these statistics are converged to 1% (2%) or to the sample variance of the statistic, whichever is larger, for halos with more than 500 (200) particles, respectively, and scales of r > 200 h −1 kpc in real space or k ∼ 3 h Mpc−1 in harmonic space for z ≤ 1. We find that the dominant source of uncertainty comes from varying the particle loading of the simulations. This leads to large systematic errors for statistics using halos with fewer than 200 particles and scales smaller than k ∼ 4 h Mpc−1. We provide the halo catalogs and snapshots detailed in this work to the community at https://AemulusProject.github.io.

The effect of assembly bias on redshift-space distortions

We study potential systematic effects of assembly bias on cosmological parameter constraints from redshift space distortion measurements. We use a semi-analytic galaxy formation model applied to the Millennium N-body WMAP-7 simulation to study the effects of halo assembly bias on the redshift space distortions of the galaxy correlation function. We look at the pairwise velocities of galaxies living in haloes with concentrations and ages in the upper and lower quintiles, and find that the velocity differences between these are consistent with those reported for real-space clustering analyses, i.e. samples with higher clustering also exhibit stronger infall pairwise motions. This can also be seen in the monopole and quadrupole of the redshift-space correlation function. We find that regardless of the method of measurement, the changes in the $\beta$ parameter due to different secondary halo parameters fully tracks the change in the bias Parameter. Hence, assembly bias does not introduce detectable systematics in the inferred logarithmic growth factor.

Structure and dynamics in low-density regions: galaxy–galaxy correlations inside cosmic voids

We compute the galaxy-galaxy correlation function of low-luminosity SDSS-DR7 galaxies $(-20 < M_{\rm r} - 5\log_{10}(h) < -18)$ inside cosmic voids identified in a volume limited sample of galaxies at $z=0.085$. To identify voids, we use bright galaxies with $M_{\rm r} - 5\log_{10}(h) < -20.0$. We find that structure in voids as traced by faint galaxies is mildly non-linear as compared with the general population of galaxies with similar luminosities. This implies a redshift-space correlation function with a similar shape than the real-space correlation albeit a normalization factor. The redshift space distortions of void galaxies allow to calculate pairwise velocity distributions which are consistent with an exponential model with a pairwise velocity dispersion of $w \sim 50-70$ km/s, significantly lower than the global value of $w \sim 500$ km/s. We also find that the internal structure of voids as traced by faint galaxies is independent of void environment, namely the correlation functions of galaxies residing in void-in-void or void-in-shell regions are identical within uncertainties. We have tested all our results with the semi-analytic catalogue MDPL2-\textsc{Sag} finding a suitable agreement with the observations in all topics studied.

The impact of galaxy formation on satellite kinematics and redshift-space distortions

Galaxy surveys aim to map the large-scale structure of the Universe and use redshift space distortions to constrain deviations from general relativity and probe the existence of massive neutrinos. However, the amount of information that can be extracted is limited by the accuracy of theoretical models used to analyze the data. Here, by using the L-Galaxies semi-analytical model run over the MXXL N-body simulation, we assess the impact of galaxy formation on satellite kinematics and the theoretical modelling of redshift-space distortions. We show that different galaxy selection criteria lead to noticeable differences in the radial distributions and velocity structure of satellite galaxies. Specifically, whereas samples of stellar mass selected galaxies feature satellites that roughly follow the dark matter, emission line satellite galaxies are located preferentially in the outskirts of halos and display net infall velocities. We demonstrate that capturing these differences is crucial for modelling the multipoles of the correlation function in redshift space, even on large scales. In particular, we show how modelling small scale velocities with a single Gaussian distribution leads to a poor description of the measure clustering. In contrast, we propose a parametrization that is flexible enough to model the satellite kinematics, and that leads to and accurate description of the correlation function down to sub-Mpc scales. We anticipate that our model will be a necessary ingredient in improved theoretical descriptions of redshift space distortions, which together could result in significantly tighter cosmological constraints and a more optimal exploitation of future large datasets.

The Galaxy Count Correlation Function in Redshift Space Revisited

Abstract In the near future, cosmology will enter the wide and deep galaxy survey era, enabling high-precision studies of the large-scale structure of the universe in three dimensions. To test cosmological models and determine their parameters accurately, it is necessary to use data with exact theoretical expectations expressed in observational parameter space (angles and redshift). The data-driven, galaxy number count fluctuations on redshift shells can be used to build correlation functions on and between shells to probe the baryonic acoustic oscillations and distance-redshift distortions, as well as gravitational lensing and other relativistic effects. To obtain a numerical estimation of from a cosmological model, it is typical to use either a closed form derived from a tripolar spherical expansion or to compute the power spectrum and perform a Legendre polynomial expansion. Here, we present a new derivation of a closed form using the spherical harmonic expansion and proceeding to an infinite sum over multipoles thanks to an addition theorem. We demonstrate that this new expression is perfectly compatible with the existing closed forms but is simpler to establish and manipulate. We provide formulas for the leading density and redshift-space contributions, but also show how Doppler-like and lensing terms can be easily included in this formalism. We have implemented and made publicly available software for computing those correlations efficiently, without any Limber approximation, and validated this software with the CLASSgal code. It is available at https://gitlab.in2p3.fr/campagne/AngPow.

A perturbative approach to the redshift space correlation function: beyond the Standard Model

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model which is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with ⩽ 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpch ⩽ s ⩽ 180Mpc/h. Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.

Measuring neutrino mass imprinted on the anisotropic galaxy clustering

The anisotropic galaxy clustering of large scale structure observed by the Baryon Oscillation Spectroscopic Survey Data Release 11 is analyzed to probe the sum of neutrino masses in the small mν ≲ 1 eV limit in which the early broadband shape determined before the last scattering surface is immune from the variation of mν. The signature of mν is imprinted on the altered shape of the power spectrum at later epoch, which provides an opportunity to access the non-trivial mν through the measured anisotropic correlation function in redshift space (hereafter RSD instead of Redshift Space Distortion). The non-linear RSD corrections with massive neutrinos in the quasi linear regime are approximately estimated using one-loop order terms. We suggest an approach to probe mν simultaneously with all other distance measures and coherent growth functions, exploiting this deformation of the early broadband shape of the spectrum at later epoch. If the origin of cosmic acceleration is unknown, mν is poorly determined after marginalizing over all other observables. However, we find that the measured distances and coherent growth functions are minimally affected by the presence of mild neutrino mass. Although the standard model of cosmic acceleration is assumed to be the cosmological constant, the constraint on mν is little improved. Interestingly, the measured Cosmic Microwave Background (hereafter CMB) distance to the last scattering surface sharply slices the degeneracy between the matter content and mν, and the mν is observed to be mν = 0.19+0.28−0.17 eV which is different from massless neutrino at 68% confidence.

Measuring cosmic velocities with 21 cm intensity mapping and galaxy redshift survey cross-correlation dipoles

We investigate the feasibility of measuring the effects of peculiar velocities in large-scale structure using the dipole of the redshift-space cross-correlation function. We combine number counts of galaxies with brightness-temperature fluctuations from 21 cm intensity mapping, demonstrating that the dipole may be measured at modest significance ($\ensuremath{\lesssim}2\ensuremath{\sigma}$) by combining the upcoming radio survey Canadian Hydrogen Intensity Mapping Experiment with the future redshift surveys of Dark Energy Spectroscopic Instrument (DESI) and Euclid. More significant measurements ($\ensuremath{\lesssim}10\ensuremath{\sigma}$) will be possible by combining intensity maps from the Square Kilometre Array (SKA) with these of DESI or Euclid, and an even higher significance measurement ($\ensuremath{\lesssim}100\ensuremath{\sigma}$) may be made by combining observables completely internally to the SKA. We account for effects such as contamination by wide-angle terms, interferometer noise and beams in the intensity maps, nonlinear enhancements to the power spectrum, stacking multiple populations, sensitivity to the magnification slope, and the possibility that number counts and intensity maps probe the same tracers. We also derive a new expression for the covariance matrix of multitracer redshift-space correlation function estimators with arbitrary orientation weights, which may be useful for upcoming surveys aiming at measuring redshift-space clustering with multiple tracers.