Mathematics Foundation of America

PINOCCHIO (PINpointing Orbit-Crossing Collapsed Hierarchical Objects) is a new algorithm for identifying dark matter halos in a given numerical realisation of the linear density field in a hierarchical universe (Monaco et al. 2001). It is shown that Lagrangian perturbation theory, and in particular its ellipsoidal truncation, is able to predict accurately the collapse, in the orbit-crossing sense, of generic mass elements. Some points that have undergone orbit crossing are assigned to the network of filaments and sheets that connects the halos; it is demonstrated that this network resembles closely that found in N-body simulations. The code generates a catalogue of dark matter halos with known mass, position, velocity, merging history and angular momentum. It is shown that the predictions of the code are very accurate when compared with the results of large N-body simulations that cover a range of cosmological models, box sizes and numerical resolutions. The mass function is recovered with an accuracy of better than 10 per cent in number density for halos with at least 30-50 particles. A similar accuracy is reached in the estimate of the correlation length r_0. The good agreement is still valid on the object-by-object level, with 70-100 per cent of the objects with more than 50 particles in the simulations also identified by our algorithm. For these objects the masses are recovered with an error of 20-40 per cent, and positions and velocities with a root mean square error of ~1-2 Mpc (0.5-2 grid lengths) and ~100 km/s, respectively. The recovery of the angular momentum of halos is considerably noisier and accuracy at the statistical level is achieved only by introducing free parameters. The algorithm requires negligible computer time as compared with performing a numerical $N$-body simulation.

We have discovered a new Galactic satellite galaxy in the constellation of Sagittarius. The Sagittarius dwarf galaxy is the nearest galaxy known, subtends an angle of $> 10$ degrees on the sky, lies at a distance of $24 \kpc$ from the Sun, $\sim 16 \kpc$ from the centre of the Milky Way. Itis comparable in size and luminosity to the largest dwarf spheroidal, has a well populated red horizontal branch with a blue HB extension; a substantial carbon star population; and a strong intermediate age stellar component with evidence of a metallicity spread. Isodensity maps show it to be markedly elongated along a direction pointing towards the Galactic centre and suggest that it has been tidally distorted. The close proximity to the Galactic centre, the morphological appearance and the radial velocity of 140 km/s indicate that this system must have undergone at most very few close orbital encounters with the Milky Way. It is currently undergoing strong tidal disruption prior to being integrated into the Galaxy. Probably all of the four globular clusters, M54, Arp 2, Ter 7 and Ter 8, are associated with the Sagittarius dwarf galaxy, and will probably share the fate of their progenitor.