Abstract:
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, ∼10% anomalous
signal in the MT component parallel to the line of sight that is present even on large scales RG 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.
