We investigate the correlation between nine different dark matter halo properties using a rank correlation analysis and a Principal Component Analysis for a sample of haloes spanning five orders of magnitude in mass. We consider mass and dimensionles
s measures of concentration, age, relaxedness, sphericity, triaxiality, substructure, spin, and environment, where the latter is defined in a way that makes it insensitive to mass. We find that concentration is the most fundamental property. Except for environment, all parameters are strongly correlated with concentration. Concentration, age, substructure, mass, sphericity and relaxedness can be considered a single family of parameters, albeit with substantial scatter. In contrast, spin, environment, and triaxiality are more independent, although spin does correlate strongly with substructure and both spin and triaxiality correlate substantially with concentration. Although mass sets the scale of a halo, all other properties are more sensitive to concentration.
We investigate the physics driving the cosmic star formation (SF) history using the more than fifty large, cosmological, hydrodynamical simulations that together comprise the OverWhelmingly Large Simulations (OWLS) project. We systematically vary the
parameters of the model to determine which physical processes are dominant and which aspects of the model are robust. Generically, we find that SF is limited by the build-up of dark matter haloes at high redshift, reaches a broad maximum at intermediate redshift, then decreases as it is quenched by lower cooling rates in hotter and lower density gas, gas exhaustion, and self-regulated feedback from stars and black holes. The higher redshift SF is therefore mostly determined by the cosmological parameters and to a lesser extent by photo-heating from reionization. The location and height of the peak in the SF history, and the steepness of the decline towards the present, depend on the physics and implementation of stellar and black hole feedback. Mass loss from intermediate-mass stars and metal-line cooling both boost the SF rate at late times. Galaxies form stars in a self-regulated fashion at a rate controlled by the balance between, on the one hand, feedback from massive stars and black holes and, on the other hand, gas cooling and accretion. Paradoxically, the SF rate is highly insensitive to the assumed SF law. This can be understood in terms of self-regulation: if the SF efficiency is changed, then galaxies adjust their gas fractions so as to achieve the same rate of production of massive stars. Self-regulated feedback from accreting black holes is required to match the steep decline in the observed SF rate below redshift two, although more extreme feedback from SF, for example in the form of a top-heavy IMF at high gas pressures, can help.
When averaged over large scales, star formation in galaxies is observed to follow the empirical Kennicutt-Schmidt (KS) law for surface densities above a constant threshold. While the observed law involves surface densities, theoretical models and sim
ulations generally work with volume density laws (i.e. Schmidt laws). We derive analytic relations between star formation laws expressed in terms of surface densities, volume densities, and pressures and we show how these relations depend on parameters such as the effective equation of state of the multiphase interstellar medium. Our analytic relations enable us to implement observed surface density laws into simulations. Because the parameters of our prescription for star formation are observables, we are not free to tune them to match the observations. We test our theoretical framework using high-resolution simulations of isolated disc galaxies that assume an effective equation of state for the multiphase interstellar medium. We are able to reproduce the star formation threshold and both the slope and the normalisation of arbitrary input KS laws without tuning any parameters and with very little scatter, even for unstable galaxies and even if we use poor numerical resolution. Moreover, we can do so for arbitrary effective equations of state. Our prescription therefore enables simulations of galaxies to bypass our current inability to simulate the formation of stars. On the other hand, the fact that we can reproduce arbitrary input thresholds and KS laws, rather than just the particular ones picked out by nature, indicates that simulations that lack the physics and/or resolution to simulate the multiphase interstellar medium can only provide limited insight into the origin of the observed star formation laws.
