A Comparison of Semi-Analytic and Smoothed Particle Hydrodynamics Galaxy Formation

We compare the statistical properties of galaxies found in two different models of hierarchical galaxy formation: the semi-analytic model of Cole et al. and the smoothed particle hydrodynamics (SPH) simulations of Pearce et al. Using a `stripped-down' version of the semi-analytic model which mimics the resolution of the SPH simulations and excludes physical processes not included in them, we find that the two models produce an ensemble of galaxies with remarkably similar properties, although there are some differences in the gas cooling rates and in the number of galaxies that populate halos of different mass. The full semi-analytic model, which has effectively no resolution limit and includes a treatment of star formation and supernovae feedback, produces somewhat different (but readily understandable) results. Agreement is particularly good for the present-day global fractions of hot gas, cold dense (i.e. galactic) gas and uncollapsed gas, for which the SPH and stripped-down semi-analytic calculations differ by at most 25%. In the most massive halos, the stripped-down semi-analytic model predicts, on the whole, up to 50% less gas in galaxies than is seen in the SPH simulations. The two techniques apportion this cold gas somewhat differently amongst galaxies in a given halo. This difference can be tracked down to the greater cooling rate in massive halos in the SPH simulation compared to the semi-analytic model. (abridged)Comment: 19 pages, 13 figures, to appear in MNRAS. Significantly extended to explore galaxy progenitor distributions and behaviour of models at high redshift

GALAXY DYNAMICS IN CLUSTERS

We use high resolution simulations to study the formation and distribution of galaxies within a cluster which forms hierarchically. We follow both dark matter and baryonic gas which is subject to thermal pressure, shocks and radiative cooling. Galaxy formation is identified with the dissipative collapse of the gas into cold, compact knots. We examine two extreme representations of galaxies during subsequent cluster evolution --- one purely gaseous and the other purely stellar. The results are quite sensitive to this choice. Gas-galaxies merge efficiently with a dominant central object while star-galaxies merge less frequently. Thus, simulations in which galaxies remain gaseous appear to suffer an ``overmerging'' problem, but this problem is much less severe if the gas is allowed to turn into stars. We compare the kinematics of the galaxy population in these two representations to that of dark halos and of the underlying dark matter distribution. Galaxies in the stellar representation are positively biased (\ie over-represented in the cluster) both by number and by mass fraction. Both representations predict the galaxies to be more centrally concentrated than the dark matter, whereas the dark halo population is more extended. A modest velocity bias also exists in both representations, with the largest effect, $\sigma_{gal}/\sigma_{DM} \simeq 0.7$, found for the more massive star-galaxies. Phase diagrams show that the galaxy population has a substantial net inflow in the gas representation, while in the stellar case it is roughly in hydrostatic equilibrium. Virial mass estimators can underestimate the true cluster mass by up to a factor of 5. The discrepancy is largest if only the most massive galaxies are used, reflecting significant mass segregation.Comment: 30 pages, self-unpacking (via uufiles) postscript file without figures. Eighteen figures (and slick color version of figure 3) and entire paper available at ftp://oahu.physics.lsa.umich.edu/groups/astro/fews Total size of paper with figures is ~9.0 Mb uncompressed. Submitted to Ap.J

Bulge Globular Clusters in Spiral Galaxies

There is now strong evidence that the metal-rich globular clusters (GC) near the center of our Galaxy are associated with the Galactic bulge rather than the disk as previously thought. Here we extend the concept of bulge GCs to the GC systems of nearby spiral galaxies. In particular, the kinematic and metallicity properties of the GC systems favor a bulge rather than a disk origin. The number of metal-rich GCs normalized by the bulge luminosity is roughly constant (i.e. bulge S_N ~ 1) in nearby spirals, and this value is similar to that for field ellipticals when only the red (metal--rich) GCs are considered. We argue that the metallicity distributions of GCs in spiral and elliptical galaxies are remarkably similar, and that they obey the same correlation of mean GC metallicity with host galaxy mass. We further suggest that the metal-rich GCs in spirals are the direct analogs of the red GCs seen in ellipticals. The formation of a bulge/spheroidal stellar system is accompanied by the formation of metal-rich GCs. The similarities between GC systems in spiral and elliptical galaxies appear to be greater than the differences.Comment: 5 pages, Latex, 2 figures, 1 table, Accepted for publication in ApJ Letter

Optimal claim behaviour for third-party liability insurances or to claim or not to claim: that is the question

It is proved that the optimal decision rule to claim or not to claim for damage is of the form: ‘to claim for damage only if its amount exceeds a certain limit’. Optimal critical claim sizes are derived, and a sensitivity analysis is given with respect to changes in (the parameters of) the distributions of the number of claims and the claim size

A halo expansion technique for approximating simulated dark matter haloes

We apply a basis function expansion method to create a time-evolving density/potential approximation of the late growth of simulated N-body dark matter haloes. We demonstrate how the potential of a halo from the Aquarius Project can be accurately represented by a small number of basis functions, and show that the halo expansion (HEX) method provides a way to replay simulations. We explore the level of accuracy of the technique as well as some of its limitations. We find that the number of terms included in the expansion must be large enough to resolve the large-scale distribution and shape of the halo but, beyond this, additional terms result in little further improvement. Particle and subhalo orbits can be integrated in this realistic, time-varying halo potential approximation, at much lower cost than the original simulation, with high fidelity for many individual orbits, and a good match to the distributions of orbital energy and angular momentum. Statistically, the evolution of structural subhalo properties, such as mass, half-mass radius and characteristic circular velocity, are very well reproduced in the HEX approximation over several Gyr. We demonstrate an application of the technique by following the evolution of an orbiting subhalo at much higher resolution than can be achieved in the original simulation. Our method represents a significant improvement over commonly used techniques based on static analytical descriptions of the halo potential