CosmicFlows4: Galaxy Distances & Flow Mapping

• CosmicFlows4 is a hierarchical distance-and-flow database that integrates redshift-independent measurements from over 55,000 galaxies using eight distinct methodologies.
• It employs Bayesian Markov chain Monte Carlo and group-based calibration to harmonize data, yielding precise peculiar velocity estimates and reconstructed density fields.
• The database underpins diverse cosmological analyses, including local cosmography, growth-rate inference, bulk-flow estimation, and constrained simulations.

The CosmicFlows4 Database, usually denoted Cosmicflows-4 or CF4, is the fourth major release in the Cosmicflows program: a hierarchical distance-and-flow database designed to convert heterogeneous redshift-independent distance measurements into a coherent map of departures from uniform cosmic expansion. In its core catalog form, CF4 compiles distances for 55,877 galaxies, organizes them into 38,065 groups in the abstract and 38,057 groups in the published catalog section, merges eight distance methodologies through Bayesian Markov chain Monte Carlo procedures, and provides derived peculiar-velocity quantities for grouped systems (Tully et al., 2022). In a broader operational sense, CF4 also denotes a public ecosystem of component catalogs, grouped tables, mock-survey realizations, and reconstructed three-dimensional density and velocity fields used for cosmography, growth-rate inference, bulk-flow estimation, and multiscale statistical analysis (Courtois et al., 2022).

1. Program lineage and scientific purpose

CF4 emerged from a program whose original stated objective was to determine galaxy distances for about 30,000 galaxies with systematic errors below 2%, thereby enabling a velocity field dense enough to constrain reconstructions of the local mass distribution and simulations of the local universe. The early Cosmic Flows roadmap already defined the central dynamical relation as

$V_{obs} = H_{0} * d + V_{pec},$

and treated the Extragalactic Distance Database (EDD) as the public infrastructure for combining observations, cross-calibrating distance indicators, reconciling duplicate measurements, grouping galaxies, and separating peculiar velocities from observed recessional velocities (Courtois et al., 2012).

That early architecture matters directly for CF4. It established three persistent design principles: first, the database is intrinsically multi-method rather than tied to a single distance indicator; second, group structure is not merely an auxiliary annotation but a core device for suppressing nonlinear motions and cross-linking calibrations; third, the end product is not just a distance table but a dynamical data system intended to support reconstructed velocity and density fields, attractor/repeller analysis, and constrained simulations (Courtois et al., 2012).

Cosmicflows-3 already demonstrated the transition from a distance compilation to a grouped, method-flagged, public database, expanding from 8,188 to 17,669 entries and explicitly anticipating a later release with a much larger all-sky infrared Tully–Fisher sample based on WISE (Tully et al., 2016). CF4 supersedes that release by combining a much larger spiral-galaxy Tully–Fisher/Baryonic Tully–Fisher component, massive northern-hemisphere SDSS Fundamental Plane coverage, recalibrated 6dFGSv distances, expanded supernova samples, and a denser local anchor network (Tully et al., 2022).

2. Catalog structure, scope, and measurement methodologies

CF4 is simultaneously a galaxy-level and group-level database. The individual-galaxy table preserves per-object measurements and method-specific distance moduli, while the grouped tables provide averaged distances and derived velocities for physically associated systems. Grouping follows the 1PGC convention, in which a group is named by the PGC number of its dominant member; beyond roughly $3000\ {\rm km\,s^{-1}}$, the preferred framework is the 2MASS-redshift-survey-based catalog of Tully (2015), while nearer systems use a separate nearby-group catalog, and more distant SDSS FP and supernova objects can be attached to Tempel et al. SDSS groups where needed (Tully et al., 2022).

The compilation reaches to a hard upper cutoff of $z=0.1$. Its coverage is dense and relatively uniform within $\sim 8000\ {\rm km\,s^{-1}}$ apart from the Zone of Avoidance, reasonably dispersed within $16{,}000\ {\rm km\,s^{-1}}$, and increasingly anisotropic at larger distances because the SDSS FP sample dominates one sector of the sky. This anisotropy is a structural feature of the database rather than a secondary nuisance: TF, FP, SN Ia, SBF, and local resolved-stellar-population distances contribute on different angular footprints, redshift intervals, and host-galaxy populations (Tully et al., 2022).

The eight methodologies entering the final CF4 assembly, together with the roles stated in the release paper, are summarized below.

Method	Final contribution	Typical role or scale
TF / BTFR	12,223 galaxies in 10,188 groups	Spiral-galaxy distances; $\sim 20\%-25\%$ accuracy
Fundamental Plane	42,223 galaxies in 27,691 groups	Early-type distances; to $z=0.1$; $\sim 20\%-25\%$
Type Ia supernovae	1008 galaxies in 945 groups	Deep, precise overlap component; about $7\%$
Surface brightness fluctuations	480 galaxies in 227 groups	Early-type precision distances; $\sim 5\%$
Type II supernovae	94 galaxies in 94 groups	Ancillary long-range component; $3000\ {\rm km\,s^{-1}}$0
TRGB	489 galaxies	Local anchor; mostly within 10 Mpc; $3000\ {\rm km\,s^{-1}}$1
Cepheids / CPLR	76 systems	Local anchor; $3000\ {\rm km\,s^{-1}}$2 Mpc; $3000\ {\rm km\,s^{-1}}$3
Masers	6 distances	Geometric anchor; includes NGC 4258

The dominant long-range components are TF/BTFR for spirals and FP for ellipticals, with SN Ia functioning as a particularly important overlap set because it is both deep and relatively precise. Smaller SBF and SN II samples provide additional cross-links, while TRGB, Cepheids, and masers impose the absolute scale (Tully et al., 2022). A plausible implication is that CF4 should be understood less as a monolithic survey than as an overlap network whose statistical strength comes from cross-calibration density as much as from raw object count.

3. Primary measurement subsystems and component catalogs

The spiral-galaxy subsystem of CF4 is built on a substantial HI and photometric infrastructure. The Tully–Fisher calibration paper states that the project aimed to measure distances for more than $3000\ {\rm km\,s^{-1}}$4 spiral galaxies out to $3000\ {\rm km\,s^{-1}}$5, using new HI linewidth information primarily from ALFALFA, SDSS $3000\ {\rm km\,s^{-1}}$6 photometry, WISE $3000\ {\rm km\,s^{-1}}$7 photometry, and inclinations measured with the Galaxy Inclination Zoo interface (Kourkchi et al., 2020). The operative linewidth variable is $3000\ {\rm km\,s^{-1}}$8, corrected to the inclination-adjusted quantity

$3000\ {\rm km\,s^{-1}}$9

and the inverse Tully–Fisher relation is written as

$z=0.1$0

That calibration used 648 galaxies in 20 clusters and 94 zero-point calibrators, and enabled multiband CF4 distances with typical single-galaxy accuracy of about $z=0.1$1 over the field sample of interest (Kourkchi et al., 2020).

The dedicated CF4 Tully–Fisher catalog then released distances for 9792 spiral galaxies within $z=0.1$2, starting from a broader candidate set of 19,905 potential spirals and applying quality cuts on HI linewidths, morphology, inclination, photometry, luminosity, and outlier status. HI data were drawn from four sources—ADHI, ALFALFA, Springob/Cornell, and the Pre Digital HI catalog—and harmonized onto the ADHI linewidth system. Corrected magnitudes were formed as

$z=0.1$3

and the final operational distances used calibrated $z=0.1$4 relations together with empirical cross-band regularization; when WISE photometry was unavailable, a random-forest model was used to infer support quantities needed for attenuation correction (Kourkchi et al., 2020). This component is therefore both a distance catalog and a value-added measurement database containing reduced kinematic, photometric, attenuation, inclination, and quality metadata.

The HI side of that subsystem depends on the All Digital HI catalog (ADHI), the homogenized 21-cm linewidth repository maintained within EDD. A 2021 update reported that ADHI contained 18,874 galaxies, of which 15,433 had good-quality data for Tully–Fisher use, after adding 385 new good GBT measurements, 889 good Nançay remeasurements, and identifying 1,515 additional ALFALFA $z=0.1$5 galaxies likely adequate for TF work. The preferred width measure remained $z=0.1$6, transformed toward $z=0.1$7 and ultimately used as the rotational input for CF4 distances (Dupuy et al., 2021). This suggests that CF4’s spiral-galaxy distances are inseparable from a longer-running HI standardization program rather than being produced by a single release-specific observing campaign.

On the early-type side, CF4’s largest single component is the Fundamental Plane sample: 42,223 galaxy distances in 27,691 groups, dominated by 34,045 SDSS FP objects and 7099 6dFGSv galaxies. The release paper emphasizes two notable calibration adjustments: 6dFGSv required a brighter effective magnitude limit, $z=0.1$8, to flatten shell-averaged Hubble parameters and reduce a spurious southern bulk-flow bias, and SDSS FP required a correction for group-richness bias via separate FP fits as a function of richness (Tully et al., 2022).

4. Homogenization, grouping, absolute scale, and released tables

CF4’s defining technical feature is staged statistical homogenization. Within each methodology, each subsample is placed on a common internal scale by allowing a global modulus offset,

$z=0.1$9

and inferring the offsets $\sim 8000\ {\rm km\,s^{-1}}$0 in a Bayesian framework with flat priors. The total posterior is sampled with emcee using 128 chains of length 10,000, with the first 1,000 steps discarded as burn-in (Tully et al., 2022). The individual subsamples are not merged directly into a single flat table at the outset; instead, they are first bound within method, then translated to group distances, and only then cross-registered between methods.

Grouping is central to this process. After internal method merging, the five volume-filling methods—TF, FP, SBF, SN Ia, and SN II—are converted to weighted group distances and merged again by MCMC, using grouped SN Ia as the temporary reference because it is deep, precise, and overlaps well with both TF and FP. The group framework provides the principal cross-calibration nodes; the paper highlights, for example, the rich overlap structure in Coma and Virgo, and reports 694 FP–TF intersecting groups (Tully et al., 2022). This is one of the clearest respects in which CF4 differs from a conventional survey catalog: many of its strongest constraints are group-mediated rather than galaxy-by-galaxy.

The absolute scale is imposed only after the five-method network is internally coherent. TRGB, Cepheids/CPLR, and masers are held fixed as anchors, and the final zero-point step uses 121 galaxy matches after rejecting three outliers and four Local Group objects. The resulting shift is

$\sim 8000\ {\rm km\,s^{-1}}$1

and the final assembly is stated to be compatible with

$\sim 8000\ {\rm km\,s^{-1}}$2

with a formal statistical uncertainty of about $\sim 8000\ {\rm km\,s^{-1}}$3 but a likely systematic uncertainty of order $\sim 8000\ {\rm km\,s^{-1}}$4 (Tully et al., 2022). The paper explicitly notes that calibrating through SN Ia alone would instead favor about $\sim 8000\ {\rm km\,s^{-1}}$5, so the adopted CF4 scale retains a few-percent systematic ambiguity.

The public release is organized around three principal tables hosted through EDD: All CF4 Individual Distances, CF4 All Groups, and CF4 All Group Velocities. The individual table contains 55,877 galaxies and stores PGC, 1PGC, T17 identifiers, $\sim 8000\ {\rm km\,s^{-1}}$6, final combined DM, method-specific moduli and uncertainties, and celestial, galactic, and supergalactic coordinates. The group table contains 38,057 groups and stores weighted-average group distance moduli, systemic $\sim 8000\ {\rm km\,s^{-1}}$7, and per-method contribution counts and grouped moduli. The velocity table adds luminosity distances, $\sim 8000\ {\rm km\,s^{-1}}$8, $\sim 8000\ {\rm km\,s^{-1}}$9, $16{,}000\ {\rm km\,s^{-1}}$0, $16{,}000\ {\rm km\,s^{-1}}$1, peculiar velocities, $16{,}000\ {\rm km\,s^{-1}}$2, $16{,}000\ {\rm km\,s^{-1}}$3, and SGX/SGY/SGZ coordinates (Tully et al., 2022).

The adopted peculiar velocity in the group catalog is a ramped combination of the Davis–Scrimgeour and Watkins–Feldman estimators: $16{,}000\ {\rm km\,s^{-1}}$4

$16{,}000\ {\rm km\,s^{-1}}$5

$16{,}000\ {\rm km\,s^{-1}}$6

The database is public through the Extragalactic Distance Database at https://edd.ifa.hawaii.edu, continuing the earlier Cosmic Flows policy that EDD is open without password [(Tully et al., 2022); (Courtois et al., 2012)].

5. Reconstructed fields, mocks, and higher-level data products

CF4 is not only a tabular distance catalog. A 2022 companion paper publicly released three-dimensional reconstructions of the local-universe gravitational field derived from the CF4 catalog of about 56,000 galaxy distances and its subsample of 1,008 Type Ia supernovae. In practice, the released products are $16{,}000\ {\rm km\,s^{-1}}$7 grids to $16{,}000\ {\rm km\,s^{-1}}$8, corresponding to about $16{,}000\ {\rm km\,s^{-1}}$9, for the grouped CF4 sample, the ungrouped galaxy sample, and the supernova subsample; the release also includes voxelized standard-deviation grids estimated from 10,000 Hamiltonian Monte Carlo realizations (Courtois et al., 2022). The reconstruction uses a Bayesian forward model with a $\sim 20\%-25\%$0CDM Gaussian prior, Wiener-filter constrained realizations, and a sampled nonlinear-dispersion term $\sim 20\%-25\%$1, with reported mean values of $\sim 20\%-25\%$2 for grouped CF4, $\sim 20\%-25\%$3 for ungrouped CF4, and $\sim 20\%-25\%$4 for the supernova sample (Courtois et al., 2022).

Those field products support direct cosmological measurements. The same study reports $\sim 20\%-25\%$5 for ungrouped CF4, $\sim 20\%-25\%$6 for grouped CF4, and $\sim 20\%-25\%$7 for the CF4 SNIa subsample in the abstract, while also noting slightly different values in the body text depending on separation range. It quotes a grouped-catalog bulk flow of $\sim 20\%-25\%$8 at $\sim 20\%-25\%$9, and effective $z=0.1$0 values of $z=0.1$1, $z=0.1$2, and $z=0.1$3 for grouped CF4, ungrouped CF4, and the CF4 supernova sample respectively (Courtois et al., 2022). The release URL is given as https://projets.ip2i.in2p3.fr//cosmicflows/.

A different high-level product is the grouped-CF4 Wiener-filter/constrained-realization reconstruction corrected with the Bias Gaussianization correction. That analysis uses the grouped CF4 database as of 17 May 2023, decomposes it into 6dFGS, SDSS, and “others,” and studies the cumulative bulk velocity $z=0.1$4 and mean overdensity $z=0.1$5 out to $z=0.1$6. It concludes that CF4 without 6dFGS is consistent with cosmic variance within $z=0.1$7, whereas the 6dFGS component dominates the signal beyond $z=0.1$8, driving the bulk-flow profile to roughly a $z=0.1$9 excess at $\sim 20\%-25\%$0 and the mean-overdensity profile to about a $\sim 20\%-25\%$1 deficiency near $\sim 20\%-25\%$2 (Hoffman et al., 2023).

CF4 has also acquired a mock-survey layer. The CF4 Tully–Fisher sample, described in one analysis as a full-sky catalog of 9790 galaxies and one of the key components of the future full CF4 catalog, was paired with a mock-generation algorithm based on 250 L-PICOLA dark-matter simulations, each split into 8 observer-centered cubes, for 2000 mock CF4TF catalogs in total. These mocks were tuned to reproduce the luminosity selection, survey geometry, clustering, redshift distribution, and log-distance-ratio error distribution of the real sample, and were used to validate $\sim 20\%-25\%$3MLE estimates of bulk flow and shear (Qin et al., 2021). The paper states that the real CF4TF catalog was downloaded from EDD and that the mock catalogs would be shared on reasonable request.

By 2026, public CF4-derived products were being treated as three-dimensional grid-space fields in their own right. A multiscale statistical analysis used the public CF4 reconstructed density-contrast cube $\sim 20\%-25\%$4 and peculiar-velocity cube $\sim 20\%-25\%$5, derived from an underlying database of $\sim 20\%-25\%$6 galaxies organized into $\sim 20\%-25\%$7 groups. The grids are provided on a $\sim 20\%-25\%$8 Cartesian mesh covering a $\sim 20\%-25\%$9 cube, with spacing $7\%$0; the survey covers 94% of the sky for $7\%$1, uses six distance indicators, has median fractional distance uncertainty $7\%$2, and adopts $7\%$3 for Local-Group-frame peculiar velocities (Grosdidier et al., 6 Mar 2026). The paper is explicit that these cubes are reconstructed, smoothed, prior-regularized products rather than unsmoothed matter fields.

6. Scientific uses, debates, and limitations

CF4 has been used to measure low-order moments of the local flow field, reconstruct the large-scale velocity field, and test the consistency of local dynamics with $7\%$4CDM. Using the CF4TF catalog and realistic mocks, one study found a bulk flow of $7\%$5 with an additional cosmic variance of $7\%$6 at effective depth $7\%$7, directed toward $7\%$8, and concluded that both bulk and shear moments are consistent with concordance $7\%$9CDM (Qin et al., 2021). The same paper emphasizes that CF4TF’s nearly all-sky geometry and its companion mocks make it suitable for future covariance estimation in peculiar-velocity power-spectrum and two-point analyses.

Other analyses have reached more tension-oriented conclusions. A minimum-variance bulk-flow study using the grouped CF4 catalog reported amplitudes of $\sim 5\%$0 at $\sim 5\%$1 and $\sim 5\%$2 at $\sim 5\%$3, with quoted $\sim 5\%$4CDM tail probabilities of $\sim 5\%$5 and $\sim 5\%$6 respectively, and argued that the added SDSS and BTFR depth in CF4 increased the apparent tension relative to CF3 (Watkins et al., 2023). The grouped Wiener-filter analysis, however, interpreted the largest deviations more cautiously, emphasizing that the anomaly is strongly tied to the anisotropic 6dFGS contribution and concluding that the field is somewhat atypical but shows no compelling tension with the model (Hoffman et al., 2023). These papers therefore frame one of the main CF4 controversies: whether the large-scale bulk-flow signal is principally cosmological or partly a product of heterogeneous depth and sky coverage.

A separate debate concerns statistical homogeneity in reconstructed CF4 fields. The 2026 cube analysis found two regimes in structure functions, with small scales dominated by reconstruction smoothing and a larger-scale regime characterized by $\sim 5\%$7, $\sim 5\%$8, and

$\sim 5\%$9

over $3000\ {\rm km\,s^{-1}}$00–$3000\ {\rm km\,s^{-1}}$01, implying $3000\ {\rm km\,s^{-1}}$02. It concluded that CF4 does not show a clear approach to $3000\ {\rm km\,s^{-1}}$03 over the probed range, while also stressing that the result is limited by smoothing, finite volume, anisotropic sampling, and prior-driven behavior in poorly constrained regions (Grosdidier et al., 6 Mar 2026). The important misconception addressed there is that CF4 reconstructed cubes can be treated as direct matter fields; the paper states repeatedly that they are low-pass, regularized reconstructions.

Several limitations are therefore intrinsic to the CF4 database. It is not a uniformly selected survey with a single known selection function; it is a cross-calibrated synthesis with methodology-dependent footprints, systematics, and depth. Individual TF and FP distances retain $3000\ {\rm km\,s^{-1}}$04 errors, so peculiar velocities of single objects are noisy. Grouping mitigates virial contamination but does not erase inter-subsample calibration concerns. The release paper itself warns that peculiar-velocity interpretation is complex and beyond the scope of the catalog paper, and later reconstruction papers repeatedly note that their outer volumes are prior-dominated, their small scales are smoothing-dominated, and their largest anomalies are sensitive to the angular structure of the input database (Tully et al., 2022, Courtois et al., 2022, Hoffman et al., 2023).

In that sense, the “CosmicFlows4 Database” is best understood not as a single static file or a modern API-defined portal, but as a layered research infrastructure: EDD-hosted galaxy and group tables, method-specific component catalogs, HI and photometric support databases, mock survey realizations, and public reconstructed field products. That layered structure was already implicit in the original Cosmic Flows program, which linked curated distance data, grouped velocity products, and local-universe simulations through a common calibration-aware database design (Courtois et al., 2012).