Inviscid smoothed particle hydrodynamics

In smoothed particle hydrodynamics (SPH), artificial viscosity is necessary for the correct treatment of shocks, but often generates unwanted dissipation away from shocks. We present a novel method of controlling the amount of artificial viscosity, which uses the total time derivative of the velocity divergence as shock indicator and aims at completely eliminating viscosity away from shocks. We subject the new scheme to numerous tests and find that the method works at least as well as any previous technique in the strong-shock regime, but becomes virtually inviscid away from shocks, while still maintaining particle order. In particular sound waves or oscillations of gas spheres are hardly damped over many periods

Weakening dark matter cusps by clumpy baryonic infall

We consider the infall of a massive clump into a dark matter halo as a simple and extreme model for the effect of baryonic physics (neglected in gravity-only simulations of large-scale structure formation) on the dark matter. We find that such an infalling clump is extremely efficient in altering the structure of the halo and reducing its central density: a clump of 1 per cent the mass of the halo can remove about twice its own mass from the inner halo and transform a cusp into a core or weaker cusp. If the clump is subsequently removed, mimicking a galactic wind, the central halo density is further reduced and the mass removed from the inner halo doubled. Lighter clumps are even more efficient: the ratio of removed mass to clump mass increases slightly towards smaller clump masses. This process becomes more efficient the more radially anisotropic the initial dark matter velocities are. While such a clumpy infall may be somewhat unrealistic, it demonstrates that the baryons need to transfer only a small fraction of their initial energy to the dark matter via dynamical friction to explain the discrepancy between predicted dark matter density profiles and those inferred from observations of dark-matter-dominated galaxies

The alignment of the second velocity moment tensor in galaxies

We show that provided the principal axes of the second velocity moment tensor of a stellar population are generally unequal and are oriented perpendicular to a set of orthogonal surfaces at each point, then those surfaces must be confocal quadric surfaces and the potential must be separable or Stäckel. This is true under the mild assumption that the even part of the distribution function (DF) is invariant under time reversal vi → −vi of each velocity component. In particular, if the second velocity moment tensor is everywhere exactly aligned in spherical polar coordinates, then the potential must be of separable or Stäckel form (excepting degenerate cases where two or more of the semiaxes of ellipsoid are everywhere the same). The theorem also has restrictive consequences for alignment in cylindrical polar coordinates, which is used in the popular Jeans Anisotropic Models (JAM) of Cappellari. We analyse data on the radial velocities and proper motions of a sample of ∼7300 stars in the stellar halo of the Milky Way. We provide the distributions of the tilt angles or misalignments from both the spherical polar coordinate systems. We show that in this sample the misalignment is always small (usually within 3°) for Galactocentric radii between ∼6 and ∼11 kpc. The velocity anisotropy is very radially biased (β ≈ 0.7), and almost invariant across the volume in our study. Finally, we construct a triaxial stellar halo in a triaxial NFW dark matter halo using a made-to-measure method. Despite the triaxiality of the potential, the velocity ellipsoid of the stellar halo is nearly spherically aligned within ∼6° for large regions of space, particularly outside the scale radius of the stellar halo. We conclude that the second velocity moment ellipsoid can be close to spherically aligned for a much wider class of potentials than the strong constraints that arise from exact alignment might suggest

The alignment of the second velocity moment tensor in galaxies

We show that provided the principal axes of the second velocity moment tensor of a stellar population are generally unequal and are oriented perpendicular to a set of orthogonal surfaces at each point, then those surfaces must be confocal quadric surfaces and the potential must be separable or Stäckel. This is true under the mild assumption that the even part of the distribution function (DF) is invariant under time reversal vi → −vi of each velocity component. In particular, if the second velocity moment tensor is everywhere exactly aligned in spherical polar coordinates, then the potential must be of separable or Stäckel form (excepting degenerate cases where two or more of the semiaxes of ellipsoid are everywhere the same). The theorem also has restrictive consequences for alignment in cylindrical polar coordinates, which is used in the popular Jeans Anisotropic Models (JAM) of Cappellari. We analyse data on the radial velocities and proper motions of a sample of ∼7300 stars in the stellar halo of the Milky Way. We provide the distributions of the tilt angles or misalignments from both the spherical polar coordinate systems. We show that in this sample the misalignment is always small (usually within 3°) for Galactocentric radii between ∼6 and ∼11 kpc. The velocity anisotropy is very radially biased (β ≈ 0.7), and almost invariant across the volume in our study. Finally, we construct a triaxial stellar halo in a triaxial NFW dark matter halo using a made-to-measure method. Despite the triaxiality of the potential, the velocity ellipsoid of the stellar halo is nearly spherically aligned within ∼6° for large regions of space, particularly outside the scale radius of the stellar halo. We conclude that the second velocity moment ellipsoid can be close to spherically aligned for a much wider class of potentials than the strong constraints that arise from exact alignment might suggest