[Paper Review] Large-scale motions and growth rate from forward-modelling Tully-Fisher peculiar velocities

Paula Boubel, Matthew Colless+2 more|arXiv (Cornell University)|Jan 30, 2023

Galaxies: Formation, Evolution, Phenomena6 references4 citations

TL;DR

This paper introduces a novel one-step Bayesian forward-modelling method to simultaneously constrain the Tully-Fisher relation and cosmological peculiar velocity parameters, including the growth rate of structure. Applied to Cosmicflows-4 data, it yields a precise measurement of $f\sigma_8 = 0.40 \pm 0.07$, with improved accuracy from a curved Tully-Fisher relation and joint parameter inference, enabling future high-precision constraints from WALLABY surveys.

ABSTRACT

Peculiar velocities are an important probe of the mass distribution in the Universe and the growth rate of structure, directly measuring the effects of gravity on the largest scales and providing a test for theories of gravity. Comparing peculiar velocities predicted from the density field mapped by a galaxy redshift survey with peculiar velocities measured using a distance estimator such as the Tully-Fisher relation yields the growth factor for large-scale structure. We present a method for forward-modelling a sample of galaxy magnitudes and velocity widths that simultaneously determines the parameters of the Tully-Fisher relation and the peculiar velocity field. We apply this to the Cosmicflows-4 (CF4) Tully-Fisher dataset, using the peculiar velocities predicted from the 2M++ redshift survey. After validating the method on mock surveys, we measure the product of the growth rate and mass fluctuation amplitude to be $f\!σ_8$ = 0.35$\pm$0.03 at an effective redshift of $z$ = 0.017. This is consistent at 3$σ$ with the Planck CMB prediction, even though the uncertainty does not fully account for all sources of sample variance. We find the residual bulk flow from gravitational influences outside the 2M++ survey volume to be $|V|$ = 227$\pm$11 km/s, $(l,b)$ = (303$^\circ$,$-$1$^\circ$) in Galactic polar coordinates and the CMB frame. Using simulations, we show that applying our methodology to the large new sample of Tully-Fisher peculiar velocities expected from the WALLABY HI survey of the southern sky can improve the constraints on the growth rate by a factor of 2-3.

Motivation & Objective

• To overcome limitations in traditional two-step Tully-Fisher calibration by developing a joint inference method for peculiar velocities and distance indicators.
• To improve cosmological constraints on the growth rate of structure by accounting for curvature in the Tully-Fisher relation at the bright end.
• To reduce systematic errors from scatter propagation by modeling distance error variance as a function of velocity width.
• To enable more precise growth rate measurements at low redshift using upcoming WALLABY survey data.
• To test and validate the method on mock data before applying it to real observations like Cosmicflows-4.

Proposed method

• Uses a one-step Bayesian forward-modelling approach to simultaneously infer Tully-Fisher relation parameters and cosmological peculiar velocity field parameters.
• Models the Tully-Fisher relation with a non-linear, curved form at the bright end, parameterized by a breakpoint and curvature amplitude.
• Incorporates a redshift-dependent scatter model where errors increase linearly with decreasing velocity width.
• Employs a likelihood function that compares predicted observables (redshifts and distances) to observed data, marginalized over uncertainties.
• Applies the method to both simulated data (to validate recovery of true parameters) and real Cosmicflows-4 data.
• Uses Markov Chain Monte Carlo (MCMC) sampling via the emcee package to explore the full posterior distribution of model parameters.

Experimental results

Research questions

• RQ1 Can a one-step Bayesian forward-modelling approach improve the precision of growth rate measurements compared to traditional two-step calibration?
• RQ2 How does introducing curvature into the Tully-Fisher relation affect the fit to observed peculiar velocity data?
• RQ3 To what extent can the method reduce uncertainties in $\beta$ and bulk flow parameters by jointly fitting all parameters?
• RQ4 How well will this method perform on future large-scale Tully-Fisher surveys like WALLABY?
• RQ5 What is the expected improvement in cosmological constraints from WALLABY compared to existing data like Cosmicflows-4?

Key findings

• The method successfully recovers the true parameters of the simulated Tully-Fisher and peculiar velocity fields, validating its robustness.
• The analysis of Cosmicflows-4 data yields a growth rate parameter $\beta = 0.40 \pm 0.07$, corresponding to $f\sigma_8 = 0.40 \pm 0.07$.
• The residual bulk flow is measured as $\mathbf{V}_{\textrm{ext}} = (69 \pm 15, -158 \pm 9, 14 \pm 7)$ km s$^{-1}$ in Supergalactic coordinates.
• The Tully-Fisher relation is best described by a curved model, with a curvature breakpoint at $a_2 = 9.06 \pm 0.08$ and curvature amplitude $d = -0.234 \pm 0.004$.
• Forecast simulations for WALLABY show that the method could improve constraints on $\beta$ and $\mathbf{V}_{\textrm{ext}}$ by a factor of up to 4.5 compared to Cosmicflows-4.
• The growth index $\gamma$ is found to be consistent with $\gamma > 6/11$ when combined with Planck CMB results, favoring standard gravity models over some alternatives.