Justin I. Read

Fundamental differences between SPH and grid methods

We have carried out a comparison study of hydrodynamical codes by investigating their performance in modelling interacting multiphase fluids. The two commonly used techniques of grid and smoothed particle hydrodynamics (SPH) show striking differences in their ability to model processes that are fundamentally important across many areas of astrophysics. Whilst Eulerian grid based methods are able to resolve and treat important dynamical instabilities, such as Kelvin-Helmholtz or Rayleigh-Taylor, these processes are poorly or not at all resolved by existing SPH techniques. We show that the reason for this is that SPH, at least in its standard implementation, introduces spurious pressure forces on particles in regions where there are steep density gradients. This results in a boundary gap of the size of an SPH smoothing kernel radius over which interactions are severely damped.

Cusp-core transformations in dwarf galaxies: observational predictions

The presence of a dark matter core in the central kiloparsec of many dwarf galaxies has been a long standing problem in galaxy formation theories based on the standard cold dark matter paradigm. Recent simulations, based on Smooth Particle Hydrodynamics and rather strong feedback recipes have shown that it was indeed possible to form extended dark matter cores using baryonic processes related to a more realistic treatment of the interstellar medium. Using adaptive mesh renement, together with a new, stronger supernovae feedback scheme that we have recently implemented in the RAMSES code, we show that it is also possible to form a prominent dark matter core within the well-controlled framework of an isolated, initially cuspy, 10 billion solar masses dark matter halo. Although our numerical experiment is idealized, it allows a clean and unambiguous identication of the dark matter core formation process. Our dark matter inner prole is well tted by a pseudo-isothermal prole with a core radius of 800 pc. The core formation mechanism is consistent with the one proposed recently by Pontzen & Governato. We highlight two key observational predictions of all simulations that nd cusp-core transformations: (i) a bursty star formation history (SFH) with peak to trough ratio of 5 to 10 and a duty cycle comparable to the local dynamical time; and (ii) a stellar distribution that is hot with v= 1. We compare the observational properties of our model galaxy with recent measurements of the isolated dwarf WLM. We show that the spatial and kinematical distribution of stars and HI gas are in striking agreement with observations, supporting the fundamental role played by stellar feedback in shaping both the stellar and dark matter distribution.

Mass loss from dwarf spheroidal galaxies: the origins of shallow dark matter cores and exponential surface brightness profiles

Dwarf spheroidal galaxies have shallow central dark matter density profiles, low angular momentum and approximately exponential surface brightness distributions. Through N-body simulations and analytic calculations we investigate the extent to which these properties can be generated from ‘typical’ΛCDM galaxies, which differ in all of these properties, by the dynamical consequences of feedback. We find that, for a wide range of initial conditions, one impulsive mass-loss event will naturally produce a surface brightness profile in the remaining stellar component of a dwarf spheroidal galaxy (dSph) which is well-fitted over many scalelengths by an exponential, in good qualitative agreement with observations of Local Group dSphs. Furthermore, two impulsive mass-loss phases, punctuated by significant gas re-accretion, are found to be sufficient to transform a central density cusp in the dark matter profile into a near-constant density core. This may then provide the missing link between current cosmological simulations, which predict a central cusp in the dark matter density profile, and current observations, which find much shallower central density profiles. We also look at the angular momentum history of dSphs and demonstrate that if these galaxies have spent most of their lifetime in tidal isolation from massive galaxies then they cannot have formed from high angular momentum gas discs.

Thin, thick and dark discs in ΛCDM

In acold dark matter (� CDM) cosmology, the Milky Way accretes satellites into the stellar disc. We use cosmological simulations to assess the frequency of near disc plane and higher inclination accretion events, and collisionless simulations of satellite mergers to quantify the final state of the accreted material and the effect on the thin disc. On average, a Milky Way-sized galaxy has three subhaloes with vmax > 80 km s −1 ; seven with vmax > 60 km s −1 and 15 with vmax > 40 km s −1 merge at redshift z 1. Assuming isotropic accretion, a third of these merge at an impact angle θ 20 ◦ are twice as likely as low-inclination ones. These lead to structures that closely resemble the recently discovered inner and outer stellar haloes. They also do more damage to the Milky Way stellar disc creating a more pronounced flare, and warp; both long-lived and consistent with current observations. The most massive mergers (vmax 80 km s −1 ) heat the thin disc enough to produce a thick disc. These heated thin-disc stars are essential for obtaining a thick disc as massive as that seen in the Milky Way; they likely comprise some ∼50-90 per cent of the thick disc stars. The Milky Way thin disc must reform from fresh gas after z = 1. Only one in four of our sample Milky Way haloes experiences mergers massive and late enough to fully destroy the thin disc. We conclude that thick, thin and dark discs occur naturally within aCDM cosmology.

Haloes gone MAD: The Halo-Finder Comparison Project

We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends, spherical-overdensity and phase-space-based algorithms. We

Does the Fornax dwarf spheroidal have a central cusp or core

ABSTRACT The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbitingat ∼ 1kpc from its centre. In a cuspy CDM halo the globulars would sink to thecentre from their current positions within a few Gyrs, presenting a puzzle as to whythey survive undigested at the present epoch. We show that a solution to this timingproblem is to adopt a cored dark matter halo. We use numerical simulations andanalytic calculations to show that, under these conditions, the sinking time becomesmany Hubble times; the globulars effectively stall at the dark matter core radius. Weconclude that the Fornax dwarf spheroidal has a shallow inner density profile with acore radius constrained by the observed positions of its globular clusters. If the phasespace density of the core is primordial then it implies a warm dark matter particleand gives an upper limit to its mass of ∼ 0.5keV, consistent with that required tosignificantly alleviate the substructure problem.Keywords: galaxies:starclusters — galaxies:dwarfs— galaxies:individual (Fornax)methods: N-body simulations

The local dark matter density

I review current efforts to measure the mean density of dark matter near the Sun. This encodes valuable dynamical information about our Galaxy and is also of great importance for ?direct detection? dark matter experiments. I discuss theoretical expectations in our current cosmology; the theory behind mass modelling of the Galaxy; and I show how combining local and global measures probes the shape of the Milky Way dark matter halo and the possible presence of a ?dark disc?. I stress the strengths and weaknesses of different methodologies and highlight the continuing need for detailed tests on mock data?particularly in the light of recently discovered evidence for disequilibria in the Milky Way disc. I collate the latest measurements of ?dm and show that, once the baryonic surface density contribution ?b is normalized across different groups, there is remarkably good agreement. Compiling data from the literature, I estimate ?b = 54.2 ? 4.9?M?pc?2, where the dominant source of uncertainty is in the H?i gas contribution. Assuming this contribution from the baryons, I highlight several recent measurements of ?dm in order of increasing data complexity and prior, and, correspondingly, decreasing formal error bars. Comparing these measurements with spherical extrapolations from the Milky Way?s rotation curve, I show that the Milky Way is consistent with having a spherical dark matter halo at R0 ? 8 kpc. The very latest measures of ?dm based on ?10?000 stars from the Sloan Digital Sky Survey appear to favour little halo flattening at R0, suggesting that the Galaxy has a rather weak dark matter disc, with a correspondingly quiescent merger history. I caution, however, that this result hinges on there being no large systematics that remain to be uncovered in the SDSS data, and on the local baryonic surface density being ?b ? 55?M?pc?2. I conclude by discussing how the new Gaia satellite will be transformative. We will obtain much tighter constraints on both ?b and ?dm by having accurate 6D phase space data for millions of stars near the Sun. These data will drive us towards fully three dimensional models of our Galactic potential, moving us into the realm of precision measurements of??dm.

THE CAUSES OF HALO SHAPE CHANGES INDUCED BY COOLING BARYONS : DISKS VERSUS SUBSTRUCTURES

Cold dark matter cosmogony predicts triaxial dark matter halos, whereas observations find quite round halos. This is most likely due to the condensation of baryons leading to rounder halos. We examine the halo phase space distribution basis for such shape changes. Triaxial halos are supported by box orbits, which pass arbitrarily close to the density center. The decrease in triaxiality caused by baryons is thought to be due to the scattering of these orbits. We test this hypothesis with simulations of disks grown inside triaxial halos. After the disks are grown we check whether the phase space structure has changed by evaporating the disks and comparing the initial and final states. While the halos are substantially rounder when the disk is at full mass, their final shape after the disk is evaporated is not much different from the initial. Likewise, the halo becomes (more) radially anisotropic when the disk is grown, but the final anisotropy is consistent with the initial. Only if the baryons are unreasonably compact or massive does the halo change irreversibly. We show that the character of individual orbits is not generally changed by the growing mass. Thus, the central condensation of baryons does not destroy enough box orbits to cause the shape change. Rather, box orbits merely become rounder along with the global potential. However, if angular momentum is transferred to the halo, either via satellites or via bars, a large irreversible change in the halo distribution occurs. The ability of satellites to alter the phase space distribution of the halo is of particular concern to galaxy formation simulations since halo triaxiality can profoundly influence the evolution of disks.

The importance of tides for the Local Group dwarf spheroidals

There are two main tidal effects that can act on the Local Group dwarf spheroidals (dSphs): tidal stripping and tidal shocking. Using N-body simulations, we show that tidal stripping always leads to flat or rising projected velocity dispersions beyond a critical radius; it is ∼5 times more likely, when averaging over all possible projection angles, that the cylindrically averaged projected dispersion will rise, rather than be flat. In contrast, the Local Group dSphs, as a class, show flat or falling projected velocity dispersions interior to ∼1 kpc. This argues for tidal stripping being unimportant interior to ∼1 kpc for most of the Local Group dSphs observed so far. We show that tidal shocking may still be important, however, even when tidal stripping is not. This could explain the observed correlation for the Local Group dSphs between central surface brightness and distance from the nearest large galaxy. These results have important implications for the formation of the dSphs and for cosmology. As a result of the existence of cold stars at large radii in several dSphs, a tidal origin for the formation of these Local Group dSphs (in which they contain no dark matter) is strongly disfavoured. In the cosmological context, a naive solution to the missing satellites problem is to allow only the most massive substructure dark matter haloes around the Milky Way to form stars. It is possible for dSphs to reside within these haloes (∼10 10 M� ) and have their velocity dispersions lowered through the action of tidal shocks, but only if they have a central density core in their dark matter, rather than a cusp. A central density cusp persists even after unrealistically extreme tidal shocking and leads to central velocity dispersions which are too high to be consistent with data from the Local Group dSphs. dSphs can reside within cuspy dark matter haloes if their haloes are less massive (∼10 9 M� ) and therefore have smaller

SPHS: smoothed particle hydrodynamics with a higher order dissipation switch

We present a novel implementation of smoothed particle hydrodynamics that uses the spatial derivative of the velocity divergence as a higher order dissipation switch. Our switch – which is second order accurate – detects flow convergence before it occurs. If particle trajectories are going to cross, we switch on the usual SPH artificial viscosity, as well as conservative dissipation in all advected fluid quantities (e.g. the entropy). The viscosity and dissipation terms (that are numerical errors) are designed to ensure that all fluid quantities remain single valued as particles approach one another, to respect conservation laws, and to vanish on a given physical scale as the resolution is increased. SPHS alleviates a number of known problems with ‘classic’ SPH, successfully resolving mixing, and recovering numerical convergence with increasing resolution. An additional key advantage is that – treating the particle mass similarly to the entropy – we are able to use multimass particles, giving significantly improved control over the refinement strategy. We present a wide range of code tests including the Sod shock tube, Sedov–Taylor blast wave, Kelvin–Helmholtz Instability, the ‘blob test’ and some convergence tests. Our method performs well on all tests, giving good agreement with analytic expectations.