Clustering Constraints on the Relative Sizes of Central and Satellite Galaxies

We empirically constrain how galaxy size relates to halo virial radius using new measurements of the size- and stellar mass-dependent clustering of galaxies in the Sloan Digital Sky Survey. We find that small galaxies cluster much more strongly than large galaxies of the same stellar mass. The magnitude of this clustering difference increases on small scales, and decreases with increasing stellar mass. Using Halotools to forward model the observations, we test an empirical model in which present-day galaxy size is proportional to the size of the virial radius at the time the halo reached its maximum mass. This simple model reproduces the observed size-dependence of galaxy clustering in striking detail. The success of this model provides strong support for the conclusion that satellite galaxies have smaller sizes relative to central galaxies of the same halo mass. Our findings indicate that satellite size is set prior to the time of infall, and that a remarkably simple, linear size--virial radius relation emerges from the complex physics regulating galaxy size. We make quantitative predictions for future measurements of galaxy-galaxy lensing, including dependence upon size, scale, and stellar mass, and provide a scaling relation of the ratio of mean sizes of satellites and central galaxies as a function of their halo mass that can be used to calibrate hydrodynamical simulations and semi-analytic models.Comment: 12 pages plus an appendix. Submitted to MNRAS. Figure 5 shows that a simple empirical model, with R50 = 0.01Rvir, can accurately reproduce new measurements of size-dependent clustering of SDSS galaxies. Figure 9 shows predictions for the size-dependence of future lensing measurements. Figure 10 provides a diagnostic for hydro sims and SAM

Embedded Implicit Stand-ins for Animated Meshes: a Case of Hybrid Modelling

In this paper we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. This approach is used to model the interaction between an animated mesh object and a viscoelastic substance, normally modelled in implicit form. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented

Fermi's golden rule in a mesoscopic metal ring

We examine the time-dependent non-equilibrium current in a mesoscopic metal ring threaded by a static magnetic flux phi that is generated by a time-dependent electric field oscillating with frequency omega. We show that in quadratic order in the field there are three fundamentally different contributions to the current. (a) A time-independent contribution which can be obtained from a thermodynamic derivative. (b) A term increasing linearly in time that can be understood in terms of Fermi's golden rule. The derivation of this term requires a careful treatment of the infinitesimal imaginary parts that are added to the real frequency omega when the electric field is adiabatically switched on. (c) Finally, there is also a time-dependent current oscillating with frequency 2 omega. We suggest an experiment to test our results.Comment: this is an expanded and completely revised version of our withdrawn manuscript cond-mat/971230

Controlled metamorphosis between skeleton-driven animated polyhedral meshes of arbitrary topologies

Enabling animators to smoothly transform between animated meshes of differing topologies is a long-standing problem in geometric modelling and computer animation. In this paper, we propose a new hybrid approach built upon the advantages of scalar field-based models (often called implicit surfaces) which can easily change their topology by changing their defining scalar field. Given two meshes, animated by their rigging-skeletons, we associate each mesh with its own approximating implicit surface. This implicit surface moves synchronously with the mesh. The shape-metamorphosis process is performed in several steps: first, we collapse the two meshes to their corresponding approximating implicit surfaces, then we transform between the two implicit surfaces and finally we inverse transition from the resulting metamorphosed implicit surface to the target mesh. The examples presented in this paper demonstrating the results of the proposed technique were implemented using an in-house plug-in for Maya™. © 2013 The Authors Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd

Comment Regarding the Functional Form of the Schmidt Law

Star formation rates on the galactic scale are described phenomenologically by two distinct relationships, as emphasized recently by Elmegreen (2002). The first of these is the Schmidt law, which is a power-law relation between the star formation rate and the column density. The other relationship is that there is a cutoff in the gas density below which star formation shuts off. The purpose of this paper is to argue that 1) these two relationships can be accommodated by a single functional form of the Schmidt law, and 2) this functional form is motivated by the hypothesis that star formation is a critical phenomenon, and that as a corollary, 3) the existence of a sharp cutoff may thus be an emergent property of galaxies, as was argued by Seiden (1983), as opposed to the classical view that this cutoff is due to an instability criterion.Comment: 14 pages, 3 figures, in press, New Astronomy. Figs provided in original (png) format as well as ps format for ps/pdf generatio

The Average Star Formation Histories of Galaxies in Dark Matter Halos from z=0-8

We present a robust method to constrain average galaxy star formation rates, star formation histories, and the intracluster light as a function of halo mass. Our results are consistent with observed galaxy stellar mass functions, specific star formation rates, and cosmic star formation rates from z=0 to z=8. We consider the effects of a wide range of uncertainties on our results, including those affecting stellar masses, star formation rates, and the halo mass function at the heart of our analysis. As they are relevant to our method, we also present new calibrations of the dark matter halo mass function, halo mass accretion histories, and halo-subhalo merger rates out to z=8. We also provide new compilations of cosmic and specific star formation rates; more recent measurements are now consistent with the buildup of the cosmic stellar mass density at all redshifts. Implications of our work include: halos near 10^12 Msun are the most efficient at forming stars at all redshifts, the baryon conversion efficiency of massive halos drops markedly after z ~ 2.5 (consistent with theories of cold-mode accretion), the ICL for massive galaxies is expected to be significant out to at least z ~ 1-1.5, and dwarf galaxies at low redshifts have higher stellar mass to halo mass ratios than previous expectations and form later than in most theoretical models. Finally, we provide new fitting formulae for star formation histories that are more accurate than the standard declining tau model. Our approach places a wide variety of observations relating to the star formation history of galaxies into a self-consistent framework based on the modern understanding of structure formation in LCDM. Constraints on the stellar mass-halo mass relationship and star formation rates are available for download at http://www.peterbehroozi.com/data.html .Comment: Revised to match ApJ accepted version, with additional corrections to Figs. 18+19 (superseding published version

A theoretical framework for combining techniques that probe the link between galaxies and dark matter

We develop a theoretical framework that combines measurements of galaxy-galaxy lensing, galaxy clustering, and the galaxy stellar mass function in a self-consistent manner. While considerable effort has been invested in exploring each of these probes individually, attempts to combine them are still in their infancy despite the potential of such combinations to elucidate the galaxy-dark matter connection, to constrain cosmological parameters, and to test the nature of gravity. In this paper, we focus on a theoretical model that describes the galaxy-dark matter connection based on standard halo occupation distribution techniques. Several key modifications enable us to extract additional parameters that determine the stellar-to-halo mass relation and to simultaneously fit data from multiple probes while allowing for independent binning schemes for each probe. In a companion paper, we demonstrate that the model presented here provides an excellent fit to galaxy-galaxy lensing, galaxy clustering, and stellar mass functions measured in the COSMOS survey from z=0.2 to z=1.0. We construct mock catalogs from numerical simulations to investigate the effects of sample variance and covariance on each of the three probes. Finally, we analyze and discuss how trends in each of the three observables impact the derived parameters of the model. In particular, we investigate the various features of the observed galaxy stellar mass function (low-mass slope, plateau, knee, and high-mass cut-off) and show how each feature is related to the underlying relationship between stellar and halo mass. We demonstrate that the observed plateau feature in the stellar mass function at Mstellar~2x10^10 Msun is due to the transition that occurs in the stellar-to-halo mass relation at Mhalo ~ 10^12 Msun from a low-mass power-law regime to a sub-exponential function at higher stellar mass.Comment: 21 pages. Accepted to Ap

Sunyaev-Zel'dovich clusters in millennium gas simulations

Large surveys using the Sunyaev–Zel’dovich (SZ) effect to find clusters of galaxies are now starting to yield large numbers of systems out to high redshift, many of which are new dis- coveries. In order to provide theoretical interpretation for the release of the full SZ cluster samples over the next few years, we have exploited the large-volume Millennium gas cosmo- logical N-body hydrodynamics simulations to study the SZ cluster population at low and high redshift, for three models with varying gas physics. We confirm previous results using smaller samplesthattheintrinsic(spherical)Y500–M500relationhasverylittlescatter(σlog10Y ≃0.04), is insensitive to cluster gas physics and evolves to redshift 1 in accordance with self-similar expectations. Our preheating and feedback models predict scaling relations that are in excel- lent agreement with the recent analysis from combined Planck and XMM–Newton data by the Planck Collaboration. This agreement is largely preserved when r500 and M500 are derived using thehydrostaticmassproxy,YX,500,albeitwithsignificantlyreducedscatter(σlog10Y ≃0.02),a result that is due to the tight correlation between Y500 and YX,500. Interestingly, this assumption also hides any bias in the relation due to dynamical activity. We also assess the importance of projection effects from large-scale structure along the line of sight, by extracting cluster Y500 values from 50 simulated 5 × 5-deg2 sky maps. Once the (model-dependent) mean signal is subtracted from the maps we find that the integrated SZ signal is unbiased with respect to the underlying clusters, although the scatter in the (cylindrical) Y500–M500 relation increases in the preheating case, where a significant amount of energy was injected into the intergalactic medium at high redshift. Finally, we study the hot gas pressure profiles to investigate the origin of the SZ signal and find that the largest contribution comes from radii close to r500 in all cases. The profiles themselves are well described by generalized Navarro, Frenk & White profiles but there is significant cluster-to-cluster scatter. In conclusion, our results support the notion that Y500 is a robust mass proxy for use in cosmological analyses with clusters

Improved Mock Galaxy Catalogs for the DEEP2 Galaxy Redshift Survey from Subhalo Abundance and Environment Matching

We develop empirical methods for modeling the galaxy population and populating cosmological N-body simulations with mock galaxies according to the observed properties of galaxies in survey data. We use these techniques to produce a new set of mock catalogs for the DEEP2 Galaxy Redshift Survey based on the output of the high-resolution Bolshoi simulation, as well as two other simulations with different cosmological parameters, all of which we release for public use. The mock-catalog creation technique uses subhalo abundance matching to assign galaxy luminosities to simulated dark-matter halos. It then adds color information to the resulting mock galaxies in a manner that depends on the local galaxy density, in order to reproduce the measured color-environment relation in the data. In the course of constructing the catalogs, we test various models for including scatter in the relation between halo mass and galaxy luminosity, within the abundance-matching framework. We find that there is no constant-scatter model that can simultaneously reproduce both the luminosity function and the autocorrelation function of DEEP2. This result has implications for galaxy-formation theory, and it restricts the range of contexts in which the mocks can be usefully applied. Nevertheless, careful comparisons show that our new mocks accurately reproduce a wide range of the other properties of the DEEP2 catalog, suggesting that they can be used to gain a detailed understanding of various selection effects in DEEP2.Comment: 24 pages, 13 figures, matches version accepted for publication in ApJS. Catalogs are available for download from the URL referenced in the Appendi

Dynamic response of mesoscopic metal rings and thermodynamics at constant particle number

We show by means of simple exact manipulations that the thermodynamic persistent current $I ( \phi , N )$ in a mesoscopic metal ring threaded by a magnetic flux $\phi$ at constant particle number $N$ agrees even beyond linear response with the dynamic current $I_{dy} ( \phi , N )$ that is defined via the response to a time-dependent flux in the limit that the frequency of the flux vanishes. However, it is impossible to express the disorder average of $I_{dy} ( \phi , N )$ in terms of conventional Green's functions at flux-independent chemical potential, because the part of the dynamic response function that involves two retarded and two advanced Green's functions is not negligible. Therefore the dynamics cannot be used to map a canonical average onto a more tractable grand canonical one. We also calculate the zero frequency limit of the dynamic current at constant chemical potential beyond linear response and show that it is fundamentally different from any thermodynamic derivative.Comment: 19 pages, postscript (uuencoded, compressed