Cosmic cookery : making a stereoscopic 3D animated movie.

This paper describes our experience making a short stereoscopic movie visualizing the development of structure in the universe during the 13.7 billion years from the Big Bang to the present day. Aimed at a general audience for the Royal Society's 2005 Summer Science Exhibition, the movie illustrates how the latest cosmological theories based on dark matter and dark energy are capable of producing structures as complex as spiral galaxies and allows the viewer to directly compare observations from the real universe with theoretical results. 3D is an inherent feature of the cosmology data sets and stereoscopic visualization provides a natural way to present the images to the viewer, in addition to allowing researchers to visualize these vast, complex data sets. The presentation of the movie used passive, linearly polarized projection onto a 2m wide screen but it was also required to playback on a Sharp RD3D display and in anaglyph projection at venues without dedicated stereoscopic display equipment. Additionally lenticular prints were made from key images in the movie. We discuss the following technical challenges during the stereoscopic production process; 1) Controlling the depth presentation, 2) Editing the stereoscopic sequences, 3) Generating compressed movies in display speci¯c formats. We conclude that the generation of high quality stereoscopic movie content using desktop tools and equipment is feasible. This does require careful quality control and manual intervention but we believe these overheads are worthwhile when presenting inherently 3D data as the result is signi¯cantly increased impact and better understanding of complex 3D scenes

Creating mock catalogues of stellar haloes from cosmological simulations

We present a new technique for creating mock catalogues of the individual stars that make up the accreted component of stellar haloes in cosmological simulations and show how the catalogues can be used to test and interpret observational data. The catalogues are constructed from a combination of methods. A semi-analytic galaxy formation model is used to calculate the star formation history in haloes in an N-body simulation and dark matter particles are tagged with this stellar mass. The tags are converted into individual stars using a stellar population synthesis model to obtain the number density and evolutionary stage of the stars, together with a phase-space sampling method that distributes the stars while ensuring that the phase-space structure of the original N-body simulation is maintained. A set of catalogues based on the Λ cold dark matter Aquarius simulations of Milky Way mass haloes have been created and made publicly available on a website. Two example applications are discussed that demonstrate the power and flexibility of the mock catalogues. We show how the rich stellar substructure that survives in the stellar halo precludes a simple measurement of its density profile and demonstrate explicitly how pencil-beam surveys can return almost any value for the slope of the profile. We also show that localized variations in the abundance of particular types of stars, a signature of differences in the composition of stellar populations, allow streams to be easily identified

Halo merger tree comparison: impact on galaxy formation models

We examine the effect of using different halo finders and merger tree building algorithms on galaxy properties predicted using the GALFORM semi-analytical model run on a high resolution, large volume dark matter simulation. The halo finders/tree builders HBT, ROCKSTAR, SUBFIND, and VELOCI RAPTOR differ in their definitions of halo mass, on whether only spatial or phase-space information is used, and in how they distinguish satellite and main haloes; all of these features have some impact on the model galaxies, even after the trees are post-processed and homogenized by GALFORM. The stellar mass function is insensitive to the halo and merger tree finder adopted. However, we find that the number of central and satellite galaxies in GALFORM does depend slightly on the halo finder/tree builder. The number of galaxies without resolved subhaloes depends strongly on the tree builder, with VELOCIRAPTOR, a phase-space finder, showing the largest population of such galaxies. The distributions of stellar masses, cold and hot gas masses, and star formation rates agree well between different halo finders/tree builders. However, because VELOCIRAPTOR has more early progenitor haloes, with these trees GALFORM produces slightly higher star formation rate densities at high redshift, smaller galaxy sizes, and larger stellar masses for the spheroid component. Since in all cases these differences are small we conclude that, when all of the trees are processed so that the main progenitor mass increases monotonically, the predicted GALFORM galaxy populations are stable and consistent for these four halo finders/tree builders

The host dark matter haloes of [O II] emitters at 0.5 < z < 1.5

Emission line galaxies (ELGs) are used in several ongoing and upcoming surveys (SDSS-IV/eBOSS, DESI) as tracers of the dark matter distribution. Using a new galaxy formation model, we explore the characteristics of [OII] emitters, which dominate optical ELG selections at z ≃ 1. Model [OII] emitters at 0.5 < z < 1.5 are selected to mimic the DEEP2, VVDS, eBOSS and DESI surveys. The luminosity functions of model [OII] emitters are in reasonable agreement with observations. The selected [OII] emitters are hosted by haloes with Mhalo ≥ 1010.3h−1M⊙, with ∼90 per cent of them being central star-forming galaxies. The predicted mean halo occupation distributions of [OII] emitters have a shape typical of that inferred for star-forming galaxies, with the contribution from central galaxies, ⟨N⟩[OII]cen⁠, being far from the canonical step function. The ⟨N⟩[OII]cen can be described as the sum of an asymmetric Gaussian for discs and a step function for spheroids, which plateau below unity. The model [OII] emitters have a clustering bias close to unity, which is below the expectations for eBOSS and DESI ELGs. At z ∼ 1, a comparison with observed g-band-selected galaxy, which is expected to be dominated by [OII] emitters, indicates that our model produces too few [OII] emitters that are satellite galaxies. This suggests the need to revise our modelling of hot gas stripping in satellite galaxies

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

The host dark matter haloes of [O II] emitters at 0.5 < z < 1.5

Emission line galaxies (ELGs) are used in several ongoing and upcoming surveys (SDSS-IV/eBOSS, DESI) as tracers of the dark matter distribution. Using a new galaxy formation model, we explore the characteristics of [OII] emitters, which dominate optical ELG selections at z ≃ 1. Model [OII] emitters at 0.5 < z < 1.5 are selected to mimic the DEEP2, VVDS, eBOSS and DESI surveys. The luminosity functions of model [OII] emitters are in reasonable agreement with observations. The selected [OII] emitters are hosted by haloes with Mhalo ≥ 1010.3h−1M⊙, with ∼90 per cent of them being central star-forming galaxies. The predicted mean halo occupation distributions of [OII] emitters have a shape typical of that inferred for star-forming galaxies, with the contribution from central galaxies, ⟨N⟩[OII]cen⁠, being far from the canonical step function. The ⟨N⟩[OII]cen can be described as the sum of an asymmetric Gaussian for discs and a step function for spheroids, which plateau below unity. The model [OII] emitters have a clustering bias close to unity, which is below the expectations for eBOSS and DESI ELGs. At z ∼ 1, a comparison with observed g-band-selected galaxy, which is expected to be dominated by [OII] emitters, indicates that our model produces too few [OII] emitters that are satellite galaxies. This suggests the need to revise our modelling of hot gas stripping in satellite galaxies

A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an additional vehicular chaos assumption and is derived via a Markovian ansatz for car pairs. This equation is analyzed using simple driver interaction models in the spatial homogeneous case. Velocity distributions in stochastic equilibrium, together with the car density dependence of their moments, i.e. mean velocity and scattering and the fundamental diagram are presented.Comment: 27 pages, 6 figure

Convexity in partial cubes: the hull number

We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some earlier results in the literature. On the other hand we provide a polynomial-time algorithm to determine the hull number of planar partial cube quadrangulations. Instances of the hull number problem for partial cubes described include poset dimension and hitting sets for interiors of curves in the plane. To obtain the above results, we investigate convexity in partial cubes and characterize these graphs in terms of their lattice of convex subgraphs, improving a theorem of Handa. Furthermore we provide a topological representation theorem for planar partial cubes, generalizing a result of Fukuda and Handa about rank three oriented matroids.Comment: 19 pages, 4 figure

Globular cluster formation within the Aquarius simulation

The Aquarius project is a very high-resolution simulation capable of resolving the full mass range of potential globular cluster (GC) formation sites. With a particle mass mp= 1.4 × 104 M¿, Aquarius yields more than 100 million particles within the virial radius of the central halo which has a mass of 1.8 × 1012 M¿, similar to that of the Milky Way. With this particle mass, dark matter concentrations (haloes) that give rise to GCs via our formation criteria contain a minimum of ~2000 particles. Here, we use this simulation to test a model of metal-poor GC formation based on collapse physics. In our model, GCs form when the virial temperatures of haloes first exceed 104 K as this is when electronic transitions allow the gas to cool efficiently. We calculate the ionizing flux from the stars in these first clusters and stop the formation of new clusters when all the baryonic gas of the Galaxy is ionized. This is achieved by adopting reasonable values for the star formation efficiencies and escape fraction of ionizing photons which result in similar numbers and masses of clusters to those found in the Milky Way. The model is successful in that it predicts ages (peak age ~13.3 Gyr) and a spatial distribution of metal-poor GCs which are consistent with the observed populations in the Milky Way. The model also predicts that less than 5 per cent of GCs within a radius of 100 kpc have a surviving dark matter halo, but the more distant clusters are all found in dark matter concentrations. We then test a scenario of metal-rich cluster formation by examining mergers that trigger star formation within central gas discs. This results in younger (~7¿13.3 Gyr), more centrally located clusters (40 metal-rich GCs within 18 kpc from the centre of the host) which are consistent with the Galactic metal-rich population. We test an alternate model in which metal-rich GCs form in dwarf galaxies that become stripped as they merge with the main halo. This process is inconsistent with observed metal-rich globulars in the Milky Way because it predicts spatial distributions that are far too extended