DESI DR1: Peculiar Velocity & Bright Galaxy Surveys

• The paper introduces a comprehensive analysis of DESI DR1 surveys, accurately calibrating peculiar velocities using Fundamental Plane and Tully-Fisher relations.
• It demonstrates robust distance measurements through advanced calibration, quality control, and targeted outlier rejection strategies.
• The study provides precise constraints on the growth rate and Hubble constant by jointly analyzing clustering and peculiar velocity data.

The DESI DR1 Peculiar Velocity and Bright Galaxy Surveys comprise an extensive observational program using the Dark Energy Spectroscopic Instrument to map the local universe's large-scale structure, directly measure galaxy distances via the Fundamental Plane and Tully-Fisher relations, infer peculiar velocities, and thereby constrain cosmological parameters such as the growth rate of structure and the Hubble constant. DESI DR1 delivers the largest samples to date of both redshift and peculiar velocity tracers, leveraging advanced calibration, quality-control, and analysis methodologies. The joint analysis of the PV and BGS samples enables precise tests of gravity and cosmology at $z \lesssim 0.1$.

1. Survey Architecture and Data Samples

The Bright Galaxy Survey (BGS) and Peculiar Velocity Survey (PVS) under DESI DR1 form complementary programs. The BGS targets over $5.5 \times 10^6$ galaxies selected from DESI Legacy Imaging, with a subset of $415,523$ galaxies at $z < 0.1$ used in clustering and PV analyses, selected by $r$-band magnitude and absolute magnitude ($M_r < -17.7$). The sky footprint covers $\simeq 10,000\, \mathrm{deg}^2$ with nearly uniform number density for $z < 0.1$ (Qin et al., 2 Dec 2025, Turner et al., 2 Dec 2025).

The PVS delivers $104,840$ galaxy distance measurements, including $96,758$ Fundamental Plane (FP) early-type ellipticals and $8,082$ Tully-Fisher (TF) late-type spirals, all with high signal-to-noise relative distances (Carr et al., 2 Dec 2025, Douglass et al., 2 Dec 2025). The FP sample is restricted to $0.0033 < z_{\mathrm{obs}} < 0.10$; TF sample to $z_{\mathrm{obs}} > 0.0166$. Peculiar velocities are calibrated to absolute scales via external calibrators.

Quality control includes detailed cuts and cleaning: $4\sigma$ outliers in log-distance ratio $\eta$ are removed, and TF galaxies with $z > 0.05$ are excluded from cosmological analyses due to systematic behavior (Lai et al., 2 Dec 2025, Turner et al., 2 Dec 2025). The resulting PV catalog for joint cosmology contains $76,616$ galaxies at $z_{\mathrm{eff}} = 0.07$.

2. Distance Indicators: Fundamental Plane and Tully-Fisher Calibration

Relative distances are inferred via two scaling relations:

• Fundamental Plane (FP): Utilizes central velocity dispersion $\sigma_0$, effective radius $R_e$, and mean surface brightness $I_e$:

$$\log_{10} R_e = a \log_{10} \sigma_0 + b \log_{10} I_e + c$$

Photometry is from DESI Legacy Imaging Surveys, spectroscopic data from DESI. FP distances are calibrated using a 3D Gaussian maximum-likelihood fit including measurement errors and selection cuts (Carr et al., 2 Dec 2025, Douglass et al., 2 Dec 2025).

• Tully-Fisher (TF): For spirals, optical rotational velocity $V_{\mathrm{rot}}$ at $0.4\,R_{26}$ (26 mag arcsec$^{-2}$ isophote) is measured from redshift differences between fibers placed at galaxy center and at $0.4\,R_{26}$:

$$M_r = a \, \log_{10} \left( \frac{V(0.4R_{26})}{V_0} \right) + b$$

Calibration uses $10,262$ galaxies, jointly fitting redshift bins $0.03 < z < 0.1$ for a global slope ($a = -7.22 \pm 0.01$), intercepts, and intrinsic scatter ($\sigma_{\mathrm{int}} = 0.466 \pm 0.001$ mag), ensuring robust cross-redshift calibration (Douglass et al., 2 Dec 2025).

Zero-point calibration is anchored via group catalogs linking DESI PV galaxies to external absolute distance calibrators (SH0ES/Pantheon+ Type Ia SNe, SBF, masers, Cepheids). Group-linked calibration increases the number of PV calibrators, decreasing zero-point uncertainty (Carr et al., 2 Dec 2025).

3. Peculiar Velocity Estimation and Catalogs

After zero-point calibration, the FP and TF relations yield relative comoving distances for each galaxy. The log-distance ratio

$$\eta = \log_{10} \frac{D(z_{\mathrm{CMB}})}{\bar{D}}$$

is computed for cosmological modeling, with propagated uncertainties including measurement errors, intrinsic scatter, and zero-point systematics. Peculiar velocities are derived via

$v_{\mathrm{pec}} = cz_{\mathrm{CMB}} - H_0 D$

where $H_0$ is anchored to the external calibrator scale (Douglass et al., 2 Dec 2025, Carr et al., 2 Dec 2025).

DESI releases both full catalogs (all measured galaxies) and main cosmology samples (after quality and completeness cuts). Random catalogs with matched redshift and angular distributions are provided for clustering and power-spectrum analyses (Douglass et al., 2 Dec 2025).

Comprehensive catalog properties—sky coverage, redshift range, completeness—are optimized for both velocity and clustering analyses.

4. Cosmological Analysis: Growth Rate and Hubble Constant

Joint analysis of BGS clustering and PV enables direct, independent constraint on the normalized linear growth rate $f\sigma_8$, velocity correlation functions, and the expansion rate $H_0$.

Growth rate measurement:

• Power Spectrum Fitting: Simultaneous modeling of auto-density ($P^{\delta}_0$, $P^{\delta}_2$), momentum ($P^{p}_0$), and cross ($P^{\delta p}_1$) moments. Robust fitting to DESI DR1 yields $f\sigma_8 = 0.440^{+0.080}_{-0.096}$ at $z_{\mathrm{eff}} = 0.07$ (Qin et al., 2 Dec 2025).
• Maximum Likelihood Fields: Gaussian likelihood on joint gridded density and log-distance data achieves a precision $$f\sigma_8 = 0.483^{+0.080}_{-0.043}\mathrm{(stat)} \pm 0.018\mathrm{(sys)}$$ (Lai et al., 2 Dec 2025).
• Correlation Functions: Non-linear models fit to two-point functions of density and velocity tracers yield $f\sigma_8 = 0.391^{+0.080}_{-0.081}$ (Turner et al., 2 Dec 2025).
• These methods, combined using appropriate correlation treatments, yield a consensus $f\sigma_8(z=0.07) = 0.450 \pm 0.055$, consistent with Planck $+\Lambda$CDM ($f\sigma_8 = 0.449 \pm 0.008$ at $z=0.07$). The associated growth index measurement $γ = 0.58 \pm 0.11$ matches General Relativity expectations (Qin et al., 2 Dec 2025, Lai et al., 2 Dec 2025).

Hubble constant:

• Absolute Zero-point Calibration: Anchoring FP/TF distances with SN Ia and SBF calibrators across group catalogs yields $$H_0 = 73.7 \pm 0.06\ (\mathrm{stat}) \pm 1.1\ (\mathrm{sys})\ \mathrm{km\,s}^{-1}\,\mathrm{Mpc}^{-1}$$. SBF calibration, and joint SBF+SN, give consistent results (Carr et al., 2 Dec 2025).
• Uncertainty Budget: Dominant uncertainties arise from absolute calibration rather than sample size. Group catalog linking, FP-TF alignment, and full covariance treatment ensure results are robust to methodological choices.

Future DR2 expects larger overlaps with primary calibrators, enabling sub-percent $H_0$ measurements.

5. Methodological Developments and Systematic Controls

DESI PV analyses integrate several technical advancements:

• Multi-fiber spectroscopic velocity measurement methodology for TF, with rigorous error floor, inclination correction, and photometric systematics (Milky Way dust, internal extinction, cross-survey zero-points) (Douglass et al., 2 Dec 2025).
• FP fitting via 3D Gaussian maximum-likelihood estimation incorporating full measurement error covariance (Carr et al., 2 Dec 2025).
• Data cleaning removes statistically significant outliers, systematics-affected galaxies, and applies conservative high-redshift cuts to TF (Lai et al., 2 Dec 2025, Turner et al., 2 Dec 2025).
• Random catalogs and angular mask weighting mitigate large-scale clustering and selection biases.
• End-to-end simulations validate the analytic covariance matrices, likelihoods, and statistical estimators across all principal cosmological pipelines (Qin et al., 2 Dec 2025, Lai et al., 2 Dec 2025, Turner et al., 2 Dec 2025).

Inter-method comparison confirms mutual consistency within $1\sigma$. Combined fits and covariance accounting yield robust consensus cosmological parameters.

6. Impact, Comparisons, and Future Prospects

The DESI DR1 PV+BGS program surpasses previous velocity surveys (e.g., 6dFGSv, SDSS PV, CF4 ALFALFA) in sample size, sky coverage, and measurement precision. The intrinsic scatter of the TF relation ($0.466$ mag) matches or improves earlier optical calibrations (Douglass et al., 2 Dec 2025).

Comparison to SDSS–MaNGA H$\alpha$ velocities shows no systematic offset or trend after inclination correction (Douglass et al., 2 Dec 2025). Log-distance ratios $\eta$ are near-Gaussian, simplifying cosmological inference.

Low-redshift consensus $f\sigma_8$ from DESI DR1 agrees closely with Planck $\Lambda$CDM and shows no evidence of modified gravity or anomalous growth (joint fit $\gamma = 0.58 \pm 0.11$ vs. GR prediction $\gamma = 0.55$) (Lai et al., 2 Dec 2025, Qin et al., 2 Dec 2025, Turner et al., 2 Dec 2025).

Future DR2 and full DESI PV samples will enable percent-level measurements of both $f\sigma_8$ and $H_0$, direct calibration to Cepheids/TRGB distances, improved systematics control, and velocity field studies across the local universe.

7. Tables: Principal Survey Properties

Survey/Method	Sample Size	Redshift Range	$f\sigma_8$ (central value)	$H_0$ (km s$^{-1}$ Mpc$^{-1}$)
BGS clustering	415,523	$0.01 < z < 0.10$	–	–
Fundamental Plane (FP)	96,758	$0.0033 < z < 0.10$	–	–
Tully-Fisher (TF)	8,082	$z_{\mathrm{obs}} > 0.0166$	–	–
Combined PV analysis	76,616	$z_{\mathrm{eff}} = 0.07$	$0.450 \pm 0.055$	$73.7 \pm 1.1$

This comprehensive survey architecture, calibration, and analysis pipeline establishes DESI DR1 PV+BGS as a definitive resource for local cosmological inferences, setting the stage for next-generation velocity-based cosmology.