Cosmicflows-4 (CF4) Compilation

• The paper compiles a comprehensive database of galaxy distances using eight methodologies to enable precise mapping of local cosmic flows.
• It integrates multi-survey data with rigorous cross-calibration and Bayesian MCMC analyses to minimize systematic errors.
• The CF4 dataset underpins refined estimates of the Hubble constant, bulk flows, and 3D reconstructions of large-scale structure.

The Cosmicflows-4 (CF4) Compilation is a comprehensive database of redshift-independent distance measurements and inferred peculiar velocities for galaxies in the local Universe. Spanning nearly the full sky to redshifts $z \sim 0.1$ and aggregating multiple photometric–kinematic, stellar population, and standard-candle methodologies, CF4 enables transformative analyses of galaxy flows, local cosmic expansion, and large-scale structure. The compilation is characterized by high statistical precision, stringent control of systematics via cross-method calibration, and explicit metadata facilitating public access and independent validation.

1. Catalog Structure and Content

CF4 assembles distance measurements for 55,877 galaxies grouped into 38,065 physical systems, using eight major methodologies: (1) Tully–Fisher (TF) and baryonic Tully–Fisher (BTFR) relations, (2) Fundamental Plane (FP) scaling, (3) Type Ia Supernovae (SNIa) and SNII expansion, (4) surface brightness fluctuations (SBF), (5) Cepheid period–luminosity relation (CPLR), (6) tip of the red giant branch (TRGB), and (7) H$_2$O maser geometric parallaxes (Tully et al., 2022). The core data set comprises the following subsamples:

Methodology	Galaxy Count	Typical Depth (km/s)
TF/BTFR	12,412	≤15,000
FP	42,223	≤30,000
SNIa	1,008	≤30,000
SNII, SBF, CPLR, TRGB, Maser	~1,145	≤5,000–10,000

Each group entry contains sky coordinates, mean redshift, group-averaged distance modulus $\mu$, and associated uncertainties. Cross-identification with external redshift and photometric catalogs (2MASS, SDSS, 6dF, LEDA, Pan-STARRS) ensures maximal completeness outside the Galactic plane ($|b|>10^\circ$) (Valade et al., 2024).

2. Distance Indicators and Calibration Procedures

2.1 Tully–Fisher and Baryonic Tully–Fisher Relations

Spiral galaxy distances are anchored on empirical correlations of absolute magnitude ($M$) or baryonic mass ($M_\mathrm{bar}$) with HI line width ($W_{mx}$), derived from 21 cm spectra (Kourkchi et al., 2020, Kourkchi et al., 2022). The generic calibration is

$$M_\lambda = S_\lambda \left(\log W^i_{mx} - 2.5\right) + \overline{ZP}_\lambda,$$

with $$\log M_b = S_\mathrm{BTFR} \left(\log W^i_{mx} - 2.5\right) + ZP$$. The inclination-corrected width $W^i_{mx} = W_{mx}/\sin i$ is central, with inclinations determined by citizen-science visual assignments (GIZ) (Kourkchi et al., 2020). Bias, curvature, and selection effects are explicitly quantified (e.g., via population simulations and HI-flux selection bias corrections (Kourkchi et al., 2022)). Zero-point calibration is performed with a sample of galaxies possessing independent TRGB and Cepheid distances (Kourkchi et al., 2020), enabling anchoring to an absolute scale.

2.2 Fundamental Plane and Other Methods

Early-type galaxies utilize the FP relation, expressed as

$_2$0

Type Ia supernovae are calibrated via the Phillips relation, and TRGB & CPLR zero-points are tied to geometric maser distances and Gaia-linked Cepheid scales (Tully et al., 2022). Bayesian Markov Chain Monte Carlo (MCMC) analyses are used to merge and cross-calibrate methodologies, minimizing method-dependent systematics and producing universal zero-points.

3. HI Data Compilation and the All-Digital HI (ADHI) Catalog

A critical foundation of the TF and BTFR components, the ADHI database compiles HI line width measurements from:

• Green Bank Telescope (GBT): 628 targets, 385 new TF-quality widths,
• Nançay (NIBLES/KLUN): 1,864 NIBLES, 828 KLUN spectra; 889 TF-quality additions,
• Full 100% ALFALFA (Arecibo): 1,515 additional spectra brought to the ADHI system, yielding a total of 18,874 galaxies, with 16,707 deemed TF-usable ($_2$1 km/s, $_2$2) (Dupuy et al., 2021).

Line widths are homogenized via empirical corrections to $_2$3 and conversions among ALFALFA and ADHI definitions, and all spectra are subjected to uniform reduction, error modeling, S/N cuts, and profile deprojection (Dupuy et al., 2021). The resulting ADHI catalog is disseminated as ASCII and FITS tables, providing profile images and photometric cross-matching (Dupuy et al., 2021).

4. Data Reduction, Grouping, and Statistical Framework

CF4 employs friends-of-friends and hierarchical clustering to assemble galaxy distances into $_2$438,000 groups; group-averaged distances (weighted $_2$5, typical $_2$6 mag) reduce random errors and mitigate virial-motion contamination (Tully et al., 2022, Valade et al., 2024). Merging between methodologies and intra-method datasets is accomplished via Bayesian MCMC over zero-point and error parameters, optimizing consistency across all calibrators (Tully et al., 2022). The full MCMC likelihood incorporates individual $_2$7 uncertainties, redshift errors, and nonlinear velocity-dispersion terms, with systematic selection corrections via empirical or forward-modeling approaches (e.g., density priors for Malmquist bias control) (Courtois et al., 2022).

5. Key Cosmological Results and Applications

5.1 Hubble Constant, Flow Fields, and Bulk Motion

Multiple analyses of CF4 consistently yield:

• $_2$8 (grouped CF4), $_2$9 (ungrouped CF4), $\mu$0 (stat), $\mu$1 km s$\mu$2 Mpc$\mu$3 (sys., variety of methods) (Tully et al., 2022, Kourkchi et al., 2020, Kourkchi et al., 2020, Courtois et al., 2022, Dupuy et al., 2021, Kourkchi et al., 2022).
• Bulk flows measured at $\mu$4 Mpc: $\mu$5 km/s (Courtois et al., 2022), with extended CF4++ augmenting with WALLABY, FAST, and DESI: $\mu$6 km/s, dynamical homogeneity not attained within $\mu$7–$\mu$8 Mpc (Courtois et al., 3 Feb 2025).

5.2 Growth Rate and Large-Scale Structure

From pairwise velocity statistics, the CF4 sample yields $\mu$9 (ungrouped), $|b|>10^\circ$0 (grouped), $|b|>10^\circ$1 (SNIa) (Courtois et al., 2022). Hamiltonian Monte Carlo reconstruction of the density and velocity fields on $|b|>10^\circ$25 Mpc/h scales delivers full 3D maps, permitting the identification of gravitational potential minima—Basins of Attraction—as in the delineation of the Shapley and Sloan Great Wall basins (Valade et al., 2024).

5.3 Anisotropy, Dipole Structure, and Hubble Tension

Spherical harmonic decompositions of local $|b|>10^\circ$3 show a decreasing dipole amplitude, with $|b|>10^\circ$4 falling from $|b|>10^\circ$5 to $|b|>10^\circ$6 km s$|b|>10^\circ$7 Mpc$|b|>10^\circ$8 from the nearest shells to $|b|>10^\circ$9 ($M$0 Mpc). Without peculiar-velocity corrections, this dipole aligns with nearby attractors (Hydra–Centaurus/Shapley); with corrections, the residual dipole is consistent with noise. The found dipole has negligible impact on the global $M$1 tension, with distribution of SNIa hosts uncorrelated with the dipole signal (Salzano et al., 2 Dec 2025).

6. Data Products, Public Access, and Extensions

CF4 and the ADHI/BTFR/TF catalogs are released as ASCII tables and VO-compatible FITS via the Extragalactic Distance Database (EDD) and the NED Distances service, including object-by-object uncertainties and auxiliary meta-information (line width, photometry, inclinations, group assignments) (Dupuy et al., 2021, Kourkchi et al., 2020, Kourkchi et al., 2022). Individual HI profiles (PNG), Pan-STARRS images, and the reconstructed 3D density and velocity fields (Wiener filter, HMC) are available for independent analysis (Courtois et al., 2022). The CF4++ extension incorporates WALLABY, FAST, and DESI-PV data, improving sky coverage, depth, and statistical power for studies of homogeneity and bulk flows (public release at https://github.com/jrmould/fast) (Courtois et al., 3 Feb 2025).

7. Scientific Significance and Systematic Limitations

The CF4 compilation represents the highest-precision, largest-volume, and most methodologically heterogeneous dataset for mapping local Universe kinematics and structure. Its statistical rigor in zero-point calibration, merging, and uncertainty quantification has enabled robust local measurements of $M$2, detection of bulk flows, and three-dimensional dynamical reconstructions. Principal limitations arise from systematic uncertainties in distance scale calibration (e.g., Cepheid/TRGB zero-points), selection and survey incompleteness (Zone of Avoidance, southern-hemisphere coverage pre-WALLABY/FAST), growing uncertainties with distance, and residual dependencies on linear-theory assumptions at large scales. The absence of significant correlations between reconstructed anisotropies and the sample distribution of standard candles reinforces the reliability of CF4-based cosmological inferences, though distinguishing between astrophysical and cosmological origins of detected flows remains a target for further investigation (Salzano et al., 2 Dec 2025).