--- title: Cosmicflows-4 Compilation url: https://www.emergentmind.com/topics/cosmicflows-4-compilation type: topic --- # Cosmicflows-4 Compilation The Cosmicflows-4 (CF4) compilation is the largest and most comprehensive catalog of galaxy distances and inferred peculiar velocities assembled to date, comprising approximately 56,000 galaxies grouped into 38,000 systems. It synthesizes photometric, spectroscopic, and geometric distance indicators to construct a high-fidelity three-dimensional map of the local universe's velocity and density fields, enabling precise cosmological tests and measurements of the Hubble constant and bulk flows. CF4 is the result of systematic data acquisition from multiple international radio and optical surveys, advanced calibration methods, and robust Bayesian statistical merging. ## 1. Dataset Structure and Composition CF4 compiles individual distances for 55,877–56,000 galaxies (depending on the precise cut and grouping protocol) merged into 38,000–38,065 groups, using eight primary methodologies. The catalog brings together three principal subsamples: - **“Others” (CF2-like):**  ~23,000 groups at $cz/100\lesssim120$, distributed nearly isotropically outside the Zone of Avoidance; includes classical Tully–Fisher (TF), Fundamental Plane (FP), and smaller surveys. - **6dFGS:**  ~7,500 groups at $60\lesssim cz/100\lesssim160$; dominant in the Southern Galactic hemisphere. - **SDSS:**  ~7,000 groups at $60\lesssim cz/100\lesssim300$; confined to the Northern Galactic hemisphere. The catalog relies on the following primary tracers and distance methodologies: | Method | Number of Galaxies | Typical Distance Uncertainty | |----------------|---------------------|-------------------------------| | TF/BTFR | 12,412 / 9,967 | 0.3–0.4 mag (15–20%) | | Fundamental Plane (FP) | 42,223 | 0.3 mag (15%) | | SN Ia | 1,008 | 0.1–0.15 mag (5–7%) | | SBF | 480 | 0.05 mag (SBF method) | | SN II | 94 | 0.3 mag (15%) | | TRGB | 489 | — | | Cepheid | 76 | — | | Maser | 6 | — | The sample extends out to $cz\sim24,000$ km s$^{-1}$ ($z\lesssim0.08$), with the SN Ia subsample reaching $z\sim0.05$. Typical individual distance errors for galaxies are $\sim20\%$, corresponding to $\sim2000$ km s$^{-1}$ for $cz/100=100$. ## 2. Distance Indicators and Calibration Protocols The absolute zero-point for all distance measurements is anchored by local geometric methods—chiefly Cepheid period–luminosity relations, Tip of the Red Giant Branch (TRGB) in the color-corrected $I$-band, and water maser distances to NGC 4258. Cross-calibration across methodologies leverages group overlaps using Bayesian Markov Chain Monte Carlo (MCMC) techniques, marginalizing over intrinsic zero-point offsets. ### Tully–Fisher and Baryonic Tully–Fisher For spirals, the TF relation in a given band $\lambda$ is parameterized as $$ M_\lambda = a_\lambda \log_{10} W_{mx}^i + b_\lambda, $$ where $W_{mx}^i$ is the inclination-corrected HI profile width, and $a_\lambda$, $b_\lambda$ are empirically fit. Extensions to the Baryonic TF Relation (BTFR) incorporate the sum of stellar and gas mass: $$ \log_{10}\left(M_b/M_\odot\right) = a + b [\log_{10}(W_{mx}^{i} / \mathrm{km\,s}^{-1}) - 2.5]. $$ Calibration employs a two-step process: (1) cluster regression for the TF/BTFR slope and (2) zero-point alignment using 64 galaxies with independent Cepheid and/or TRGB distances, referenced to LMC and NGC 4258 [2201.13023, 2009.00733, 2004.14499]. ### Fundamental Plane (FP) For early-type galaxies, the FP in SDSS bands is formulated as $$ \log R_e = a \log \sigma + b \langle \mu_e \rangle + c, $$ with $R_e$ the effective radius, $\sigma$ the velocity dispersion, and $\langle \mu_e \rangle$ the mean surface brightness. Uncertainties are controlled via strict photometric and kinematic cuts [2209.11238]. ### Other Methods - **SN Ia**: Standardized using light-curve shape and color corrections, yielding $\sim5\%$ uncertainties. - **Supernova II**: Standardized through expansion velocity and color. - **SBF**: I-band and IR HST calibrations yield $\sim0.05$ mag precision. All methodologies are merged onto a common scale by maximizing the joint likelihood over group/distance correlations, with zero-point priors sampled in the MCMC merging [2209.11238]. ## 3. HI Data Acquisition, Linewidths, and Sample Selection The backbone of TF distances is the All-Digital HI Catalog, aggregating 21 cm width measurements from Parkes, Green Bank Telescope (GBT), and Arecibo (ALFALFA), uniformized through a common reduction pipeline. Key HI width parameter: - $W_{m50}$: Width at 50% of mean flux within the 90% flux window. - Standardization through instrumental, redshift, and turbulence corrections yields $W_{mx}$, corrected for inclination as $W_{mx}^i = W_{mx} / \sin i$. Inclinations are determined via the Galaxy Inclination Zoo (GIZ), a crowdsourced visual classification system, minimizing systematic bias and reducing error floors to 1°–5°, depending on $i$ [2009.00733, 2101.01515, 1411.5719]. Selection criteria for TF inclusion: S/N $>$ 10, $e_W<20$ km s$^{-1}$ in $W_{mx}$, $i>45^\circ$, morphologically classified as Sa or later, and well-determined photometric parameters. ALFALFA widths are harmonized as $W_{mx}=W_{alf}-6$ km s$^{-1}$. Internal extinction corrections exploit both parametric and machine learning (random forest) models, incorporating colors and surface-brightness. ## 4. Grouping Algorithms and Bayesian Merging Galaxies are assigned to groups or clusters via friends-of-friends and virial scaling (using $R_{2t}\propto M^{1/3}$), providing a robust statistical basis for cross-method calibration and error suppression. Bayesian inference treats each methodology's zero-point $\Delta\mu_s$ as a free parameter; the likelihood for group $n$ having distances $DM_n^{(s)}$ from method $s$ is $$ L_n(\{\Delta\mu_s\}) = \prod_s \frac{1}{\sqrt{2\pi\sigma_{n,s}^2}} \exp\left[-\frac{1}{2}\left(\frac{DM_n^{(s)}+\Delta\mu_s-\langle DM \rangle_n}{\sigma_{n,s}}\right)^2\right], $$ with the posterior sampled by the \texttt{emcee} implementation of affine-invariant MCMC [2209.11238]. Group merges are essential for suppressing non-linear virial motions, reducing peculiar-velocity noise, and leveraging overlaps in hybrid clusters (e.g., Coma: $\sim209$ FP, $\sim50$ TF, 7 SN Ia). ## 5. Velocity Field Reconstruction and Statistics Peculiar velocities are extracted for groups via $$ V_{pec}^{ds} = \frac{fV_{cmb} - H_0 d}{1 + H_0 d / c}, $$ with $f=1 + 0.5(1-q_0)z-\ldots$ the relativistic correction, or with alternative logarithmic formulations at large $z$. Reconstruction of the 3D density ($\delta_L$) and velocity ($v$) fields utilizes Bias Gaussianization correction (BGc) to address the lognormal error distribution of distances. After Gaussianizing, the Wiener Filter (WF) and Constrained Realizations (CRs) deliver minimum-variance estimates: $$ s_{WF}(r) = \langle s(r) d^T \rangle \langle dd^T \rangle^{-1} d, $$ with the prior drawn from the linear $\Lambda$CDM power spectrum. Key statistics: - **Mean overdensity:** $\Delta_L(R) = (3/4\pi R^3)\int_{|r|