Minkowski Tensors in Redshift Space-Beyond the Plane-parallel Approximation

The Minkowski tensors (MTs) can be used to probe anisotropic signals in a field, and are well suited for measuring the redshift-space distortion (RSD) signal in large-scale structure catalogs. We consider how the linear RSD signal can be extracted from a field without resorting to the plane-parallel approximation. A spherically redshift-space distorted field is both anisotropic and inhomogeneous. We derive expressions for the two-point correlation functions that elucidate the inhomogeneity, and then explain how the breakdown of homogeneity impacts the volume and ensemble averages of the tensor Minkowski functionals. We construct the ensemble average of these quantities in curvilinear coordinates and show that the ensemble and volume averages can be approximately equated, but this depends on our choice of definition of the volume average of a tensor and the radial distance between the observer and field. We then extract the tensor Minkowski functionals from spherically redshift-space distorted, Gaussian random fields and gravitationally evolved dark matter density fields at z = 0 to test if we can successfully measure the Kaiser RSD signal. For the dark matter field, we find a significant, similar to 10% anomalous signal in the MT component parallel to the line of sight that is present even on large scales R (G) greater than or similar to 15 Mpc, in addition to the Kaiser effect. This is due to the line-of-sight component of the MT being significantly contaminated by the Finger of God effect, which can be approximately modeled by an additional damping term in the cumulants.

Automated summary

The Minkowski tensors (MTs) are suitable for measuring the redshift-space distortion (RSD) signal in large-scale structure catalogs. This study explores the extraction of the linear RSD signal from a non-plane-parallel field, which is both anisotropic and inhomogeneous. The analysis includes deriving expressions for the two-point correlation functions, examining the impact of homogeneity breakdown on tensor Minkowski functionals, and testing the ability to measure the Kaiser RSD signal from redshift-space distorted fields.