bulk flow from an all space three dimensional peculiar velocity field constrained to match the TF measurements. At large distances  generates a robust bulk flow from the SFI++ that is insensitive to the assumed prior. For comparison, a standard straightforward maximum likelihood estimate leads to very similar results.'
author:
- Adi Nusser
- Marc Davis
bibliography:
- 'bulk\_apj.bib'
title: 'The cosmological bulk flow: consistency with $\Lambda$CDM and $z\approx 0$ constraints on $\sigma_8$ and $\gamma$'
---

Introduction
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Cosmological bulk flows are the peculiar velocities of whole spherical regions around us. Bulk flows are usually considered for sufficiently large spheres where linear expressions for the velocity and density power spectra are valid. This greatly facilitates the calculation of expected bulk flows in cosmological models, in contrast to analyzing the full field field which may involve non-linear effects on small scales [@feldwh10; @abate09; @zarou09; @freu99]. In linear theory, the bulk flow of a sphere is solely determined by the gravitational pull of only the dipole component of the external mass distribution. Bulk flows are, therefore, an unmistakable indicator of distant large mass concentrations should they exist. The exact expression of the bulk flow, $\vB(r)$, of a sphere of radius $r$ is, $$\label{eq:bdef}
