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Independent constraints on local non-Gaussianity from the peculiar velocity and density fields

Primordial, non-Gaussian perturbations can generate scale-dependent bias in the galaxy distribution. This in turn will modify correlations between galaxy positions and peculiar velocities at late times, since peculiar velocities reflect the underlying matter distribution, whereas galaxies are a biased tracer of the same. We study this effect, and show that non-Gaussianity can be constrained by comparing the observed peculiar velocity field to a model velocity field reconstructed from the galaxy density field assuming linear bias. The amplitude of the spatial correlations in the residual map obtained after subtracting one velocity field from the other is directly proportional to the strength of the primordial non-Gaussianity. We construct the corresponding likelihood function use it to constrain the amplitude of the linear flow $β$ and the amplitude of local non-Gaussianity $f^{\rm NL}_{\rm local}$. Applying our method to two observational data sets, the Type-Ia supernovae (A1SN) and Spiral Field \textit{I}-band (SFI++) catalogues, we obtain constraints on the linear flow parameter consistent with the values derived previously assuming Gaussianity. The marginalised 1-D distribution of $|f^{\rm NL}_{\rm local}|$ does not show strong evidence for non-zero $f^{\rm NL}_{\rm local}$, and we set 95% upper limits $|f^{\rm NL}_{\rm local}|<51.4$ from A1SN and $|f^{\rm NL}_{\rm local}|<92.6$ from SFI++. These limits on $f^{\rm NL}_{\rm local}$ are as tight as any set by previous large-scale structure measurements. Our method can be applied to any survey with radial velocities and density field data, and provides an independent check of recent CMB constraints on $f^{\rm NL}_{\rm local}$, extending these to smaller spatial scales.