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We study the alignment of dark matter haloes with the cosmic webcharacterized by the tidal and velocity shear fields. We focus on the alignmentof their shape, angular momentum and peculiar velocities. We use a cosmologicalN-body simulation that allows to study dark matter halos spanning almost fiveorders of magnitude in mass ($10^{9}$-$10^{14}$) $h^{-1}$$M_{\odot}$ andspatial scales of $(0.5$-$1.0)$ $h^{-1}$ Mpc to define the cosmic web. We findthat the halo shape presents the strongest alignment along the smallest tidaleigenvector, e.g. along filaments and walls, with a signal that gets strongeras the halo mass increases. In the case of the velocity shear field onlymassive halos $>10^{12}$ $h^{-1}$$M_{\odot}$ tend to have their shapes alignedalong the largest tidal eigenvector; that is, perpendicular to filaments andwalls. For the angular momentum we find alignment signals only for halos moremassive than $10^{12}$ $h^{-1}$$M_{\odot}$ both in the tidal and velocity shearwebs where the preferences are for it to be parallel to the middle eigenvector;perpendicular to filaments and parallel to walls. Finally, the peculiarvelocities show a strong alignment along the smallest tidal eigenvector for allhalo masses; halos move along filaments and walls. In the velocity shear thesame alignment is present but weaker and only for haloes less massive than$10^{12}$ $h^{-1}$$M_{\odot}$. Our results clearly show that the two differentalgorithms we used to define the cosmic web describe different physical aspectsof non-linear collapse and should be used in a complementary way to understandthe effect of the cosmic web on galaxy evolution.

Cosmic web alignments with the shape, angular momentum and peculiar velocities of dark matter haloes