The role of peculiar velocity uncertainties in standard siren cosmology

TL;DR

This work tackles how peculiar velocity uncertainties and their spatial covariance affect $H_0$ estimates from local distance indicators such as bright sirens. It develops a correlated Gaussian framework for the true and reconstructed velocity fields and derives an analytic marginalisation method to propagate velocity covariance into the $H_0$ posterior, validating the approach with simulated bright-siren data built from the GiggleZ volume and incorporating velocity reconstruction. The results show that ignoring velocity covariance underestimates $H_0$ uncertainties, potentially doubling the error for nearby events with precise distances, while including reconstruction reduces the uncertainty by roughly a factor of two in many cases; the impact is strongest at $D_{ m max}\lesssim 100$ Mpc and for small distance errors. The framework provides a practical tool for standard-siren analyses and can be extended to Type Ia supernovae and other local-distance indicators.

Abstract

Local distance indicators such as standard sirens, in combination with spectroscopic redshift measurements of their host galaxies, allow us to estimate the present-day expansion rate of the Universe parameterised by Hubble's constant, H_0. However, these observed redshifts are systematically modified by the effect of galaxy peculiar velocities. Although these velocities may be estimated from the local density field by the process of velocity-field reconstruction, the intrinsic errors and covariance in these estimates contribute to the error in the H_0 determination. In this paper we demonstrate how the impact of peculiar velocities can be propagated into H_0 measurements from local distance indicators with observed redshifts, incorporating the full covariance of the velocity field induced by bulk flows. We apply our methods to cosmological simulations, testing the importance of this effect in the context of future analyses of gravitational wave sources with electromagnetic counterparts used as bright sirens. We conclude that H_0 errors may be increased by a factor of 2 in comparison with neglecting peculiar velocity covariance, for GW170817-like sirens located within 50 Mpc with 5% distance errors, with the highest impacts expected for sources at nearby distances or with small distance errors. Our analytical methods may also be applied to other local distance indicators, such as Type Ia supernovae.

Figures (5)

• Figure 1: The $H_0$ posterior probability distribution for a bright siren analysis of $N = 10$ sirens distributed to $D_{\rm max} = 100$ Mpc with SNR-scaled distance errors. The narrower black posterior represents the result of an analysis neglecting velocity covariance (Scenario 1 as presented in Sec. \ref{['sec:sim']}), whilst the broader red posterior corresponds to including the full effects of the velocity covariance (Scenario 2). The difference in the $H_0$ error between these two cases gets larger as the siren distance and distance error reduce.
• Figure 2: The recovered values of $H_0$ as a function of the number of sirens observed. We fix the maximum distance from the observer $D_{\rm max} = 100$ Mpc, use SNR-scaled distance errors, and measure $H_0$ for $N = [2,5,10,25,100]$. Results from $H_0$ posteriors derived for a set of independent sirens including reconstruction (Scenario 1) are shown in black, results for correlated sirens including reconstruction (Scenario 2) are shown in red, and results for correlated sirens excluding reconstruction (Scenario 3) are shown in blue. The fiducial value of $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$ for the simulation is shown as a dotted line.
• Figure 3: The fractional error in measurements of $H_0$ as a function of the number of sirens observed. We fix the maximum distance from the observer $D_{\rm max} = 100$ Mpc, and use SNR-scaled distance errors, and measure $\sigma_{H_0}$ for $N = [2,5,10,25,100]$. Results from $H_0$ posteriors derived for a set of independent sirens (Scenario 1) are given by the solid black lines, results from sets of correlated sirens including reconstruction (Scenario 2) are given by the dashed red lines, and results for correlated sirens excluding reconstruction (Scenario 3) are given by the dot-dashed blue lines.
• Figure 4: The fractional error in measurements of $H_0$ as a function of the maximum distance from the observer. We fix the number of bright sirens $N = 10$, and use SNR-scaled distance errors, and measure $\sigma_{H_0}$ for $D_{\rm max} = [50, 100, 150, 200]$ Mpc. The curves are labelled in the same style as Fig. \ref{['fig:h0nsiren']}.
• Figure 5: The fractional error in measurements of $H_0$ as a function of the fractional error in the estimate of the host galaxy luminosity distance. We fix the number of bright sirens $N = 10$ and the maximum distance from the observer $D_{\rm max} = 100$ Mpc, and measure $\sigma_{H_0}$ for $f_{D} = [0.01, 0.02, 0.05,0.10]$. The curves are labelled in the same style as Fig. \ref{['fig:h0nsiren']}.