Numerical action reconstruction of the dynamical history of dark matter haloes in N-body simulations

We test the ability of the numerical action method (NAM) to recover the individual orbit histories of mass tracers in an expanding universe, given the masses and redshift-space coordinates at the present epoch. The mass tracers are represented by dark matter (DM) haloes identified in a region of radius 26 h(-1) of a high-resolution N-body simulation of the standard Lambda cold dark matter (CDM) cosmology. Since previous tests of NAM at this scale have traced the underlying distribution of DM particles rather than extended haloes, our study offers an assessment of the accuracy of NAM in a scenario which more closely approximates the complex dynamics of actual galaxy haloes. We show that NAM can recover the present-day halo distances with typical distance errors of less than 3 per cent and radial peculiar velocities with a dispersion of similar to 130 km s(-1). The accuracy of individual orbit reconstructions was limited by the inability of NAM, in some instances, to correctly model the positions of haloes at early times solely on the basis of the redshifts, angular positions and masses of the haloes at the present epoch. Improvements in the quality of NAM reconstructions may be possible using the present-day three-dimensional halo velocities and distances to further constrain the dynamics. This velocity data is expected to become available for nearby galaxies in the coming generations of observations by Space Interferometry Mission (SIM) and Global Astrometric Interferometer for Astrophysics (GAIA).