[Paper Review] DESI Peculiar Velocity Survey -- Fundamental Plane

Khaled Saïd, Cullan Howlett+53 more|arXiv (Cornell University)|Aug 25, 2024

Inertial Sensor and NavigationEngineering108 references9 citations

TL;DR

Describes the initial Fundamental Plane analysis within the DESI Peculiar Velocity Survey using Survey Validation data to measure distances and peculiar velocities of early-type galaxies, and derives H0 from FP zero-point calibration.

ABSTRACT

The Dark Energy Spectroscopic Instrument (DESI) Peculiar Velocity Survey aims to measure the peculiar velocities of early and late type galaxies within the DESI footprint using both the Fundamental Plane and optical Tully-Fisher relations. Direct measurements of peculiar velocities can significantly improve constraints on the growth rate of structure, reducing uncertainty by a factor of approximately 2.5 at redshift 0.1 compared to the DESI Bright Galaxy Survey's redshift space distortion measurements alone. We assess the quality of stellar velocity dispersion measurements from DESI spectroscopic data. These measurements, along with photometric data from the Legacy Survey, establish the Fundamental Plane relation and determine distances and peculiar velocities of early-type galaxies. During Survey Validation, we obtain spectra for 6698 unique early-type galaxies, up to a photometric redshift of 0.15. 64\% of observed galaxies (4267) have relative velocity dispersion errors below 10\%. This percentage increases to 75\% if we restrict our sample to galaxies with spectroscopic redshifts below 0.1. We use the measured central velocity dispersion, along with photometry from the DESI Legacy Imaging Surveys, to fit the Fundamental Plane parameters using a 3D Gaussian maximum likelihood algorithm that accounts for measurement uncertainties and selection cuts. In addition, we conduct zero-point calibration using the absolute distance measurements to the Coma cluster, leading to a value of the Hubble constant, $H_0 = 76.05 \pm 0.35$(statistical) $\pm 0.49$(systematic FP) $\pm 4.86$(statistical due to calibration) $\mathrm{km \ s^{-1} Mpc^{-1}}$. This $H_0$ value is within $2σ$ of Planck Cosmic Microwave Background results and within $1σ$, of other low redshift distance indicator-based measurements.

Motivation & Objective

• Motivate the use of direct peculiar velocity measurements to improve constraints on the growth rate of structure and H0.
• Establish a Fundamental Plane relation from DESI FP data using velocity dispersion and photometry.
• Assess data quality of DESI stellar velocity dispersions and implement a robust FP fitting with selection effects.
• Calibrate FP zero-point using Coma cluster distances to estimate the Hubble constant.
• Provide an early catalogue of FP-based distances and peculiar velocities from DESI SV data.

Proposed method

• Use central velocity dispersion (sigma0) and r-band photometry from DESI Legacy Imaging Surveys to construct the Fundamental Plane: log Re = a log sigma0 + b log Ie + c.
• Compute angular to physical effective radius Re with theta_e from r-band half-light radius and ellipticity, then convert to kpc h^-1 at z in CMB frame.
• Estimate Ie from model flux in r-band, incorporating corrections (evolution, dimming, K-correction) and angular size, via log Ie = 0.4(Msun_r - m_r - 0.85 zcmb) - log(2 pi theta_e^2) + 4 log(1+zhelio) + 2 log(206265/10).
• Measure sigma0 and uncertainties with pPXF using the DESI blue-arm spectra and Indo-U.S. template library; use full-depth DESI spectra for final sigma0 when available.
• Fit the FP parameters (a, b, c) with a 3D Gaussian maximum likelihood method that accounts for measurement errors and selection
• Perform FP zero-point calibration using absolute distances to the Coma cluster to derive H0.

Experimental results

Research questions

• RQ1 What is the Fundamental Plane for the DESI FP galaxy sample given DESI photometry and SV spectroscopy?
• RQ2 How do velocity dispersion measurement quality and selection cuts affect FP distances and peculiar velocities?
• RQ3 What FP-derived distances and peculiar velocities can be obtained for early-type galaxies in the DESI footprint during Survey Validation?
• RQ4 What H0 value emerges from FP zero-point calibration using Coma cluster distances, and how does it compare to Planck and other low-z indicators?

Key findings

• 6698 FP galaxies identified in SV data after cross-matching with photometric selection and quality cuts.
• 64% of observed FP galaxies have relative velocity dispersion errors below 10%; the fraction rises to 75% for spectroscopic redshifts z < 0.1.
• FP fit yields H0 = 76.05 ± 0.35 (stat) ± 0.49 (systematic FP) ± 4.86 (statistical due to calibration) km s^-1 Mpc^-1.
• The H0 value is within 2 sigma of Planck CMB results and within 1 sigma of other low-z distance-indicator measurements.
• The study demonstrates the viability of DESI SV data for FP-based distance and peculiar velocity measurements and FP zero-point calibration using Coma distances.
• The analysis uses a 3D Gaussian maximum likelihood FP fitting that incorporates measurement uncertainties and selection effects.