An Inconsistency in standard Maximum Likelihood Estimation of Bulk Flows

Abstract

Maximum Likelihood estimation of the bulk flow from radial peculiar motions of galaxies, generally assumes a constant velocity field inside the survey volume. The assumption is inconsistent with the definition of the bulk flow as the average of the peculiar velocity field over the relevant volume. This follows from a straightforward mathematical relation between the bulk flow of a sphere and the velocity potential on its surface. The inconsistency exists also for ideal data with exact radial velocities and full spatial coverage. Based on the same relation we propose a simple modification to correct for this inconsistency.

References in corpus (7)

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Cited by in corpus (12)

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• Evaluating bulk flow estimators for CosmicFlows-4 measurements
• Gamma-Ray Bursts as Sources of Strong Magnetic Fields
• Local Hole revisited: evidence for bulk motions and self-consistent outflow
• The redshift dependence of the inferred $H_0$ in a local void solution to the Hubble tension
• Easily Interpretable Bulk Flows: Continuing Tension with the Standard Cosmological Model
• On methods of estimating cosmological bulk flows
• The Peculiar Velocity Correlation Function
• Uneven flows: On cosmic bulk flows, local observers, and gravity
• Testing Bayesian reconstruction methods from peculiar velocities
• Gravitational potential wells and the cosmic bulk flow
• Improved Methods for Estimating Peculiar Velocity Correlation Functions Using Volume Weighting