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We describe a simple model that explains the qualitative and (approximate) quantitative features of the distribution of orbital velocities of merging pairs of dark matter haloes. Our model considers a primary dark matter halo as a perturber in a background of secondary haloes with velocities described by linear theory. By evaluating the ensemble of secondary haloes on orbits within the perturbing halo's 'loss cone' we derive the distribution of orbital parameters of these captured haloes. This model is able provide qualitative explanations for the features of this distribution as measured from N -body simulations, and is in approximate quantitative agreement with those measurements. As the velocity dispersion of the background haloes is larger on smaller scales our model predicts an overall increase in the characteristic velocities of merging haloes, relative to the virial velocities of those haloes, in lower mass systems. Our model also provides a simple explanation for the measured independence of the orbital velocity distribution function on redshift when considered at fixed peak height. By connecting the orbital parameter distribution to the underlying power spectrum our model also allows for estimates to be made of the effect of modifying that power spectrum, for example by including a truncation at large wavenumber. For plausible warm dark matter models, we find that this truncation has only a small effect on the predicted distributions. [ABSTRACT FROM AUTHOR]

To date at least 10 highly flattened planes of dwarf galaxies are claimed to have been discovered in the Local Universe. The origin of these planes of galaxies remains unknown. One suggestion is that they are related to the large-scale structure of the cosmic web. A recent study found that the normal of a number of these dwarf galaxy planes is very closely aligned with the eigenvector of the shear tensor corresponding to the direction of greatest collapse obtained by reconstructing the full velocity field in the linear regime. Here we extend that work by both considering an additional 5 planes beyond the five examined previously and examining the alignment with respect to the quasi-linear field, a more sophisticated reconstruction, which is a better approximation on smaller (quasi-linear) scales. Our analysis recovers the previous result while not finding a significantly tight alignment with the additional five planes. However, the additional five plane normals also do not appear to be randomly oriented. We conclude that this could be due either to the normals of the new planes being poorly defined and described; the quasi-linear field at those locations being poorly constrained; or different formation mechanisms for the orientation of planes of dwarf galaxies. [ABSTRACT FROM AUTHOR]