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Keywords:

  • methods: analytical;
  • large-scale structure of Universe

ABSTRACT

In this paper, we revisit the acquisition of angular momentum of galaxies by tidal shearing and compute the angular momentum variance inline image as well as the angular momentum correlation function CL(r), using tidal torquing in the Zel’dovich approximation as the model for angular momentum build-up. Under the assumption that haloes form at peaks in the density field we determine the protohalo’s inertia from the peak shape and embed it in a tidal field. Inertia and shear are drawn from a random process and we compute the angular momentum variance and correlation function by sampling from a Gaussian distribution which shows the correct covariances between all relevant quantities. We describe the way in which the correlations in angular momentum result from an interplay of long-ranged correlations in the tidal shear and short-ranged correlations in the inertia field. Our description takes care of the relative orientation of the eigensystems of these two symmetric tensors. We propose a new form of the angular momentum correlation function which is able to distinguish between parallel and antiparallel alignment of angular momentum vectors, and comment on implications of intrinsic alignments for weak lensing measurements. We confirm the scaling L/M ∝ M2/3 and find the angular momentum distribution of Milky Way sized haloes to be correlated on scales of ∼1 Mpc h−1. The correlation function can be well fitted by an empirical relation of the form CL(r) ∝ exp(−[r/r0]β).