Lagrangian bias in the local bias model

It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field. We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function. This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function. In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions. Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit. In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space. We discuss why things are more complicated in practice. We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not. We use the Lognormal model to illustrate many of our findings.Comment: 14 pages, published on JCA

Accelerated learning at masters’ level: problem based learning of diagnostic reasoning skills by physician associate students

Physician Associates (PA) complete a two year postgraduate course, and are expected to graduate with diagnostic skills equivalent to those of newly qualified doctors who have completed a five year course. BSMS has utilised Problem Based Learning (PBL) in an attempt to accelerate the acquisition of these skills by PAs. Weekly PBL sessions were conducted during year 1 of the PA course, focusing on the ‘top 20’ core conditions within the curriculum. Alongside this, students had weekly clinical exposure in General practice. In order to assess the impact of this strategy the ‘Diagnostic Thinking Inventory‘ (DTI) developed by Bordage et al. (1990) was conducted three times across year 1 and the results compared to standardised data for medical students and doctors. This found that PA students had a significantly higher baseline score in terms of flexibility of thinking (equivalent to newly qualified doctors engaged in foundation training) and structure of memory (equivalent to third year medical students). Results showed a statistically significant improvement in structure of memory across year 1: achieving an improvement in score which took over four years to achieve in medical students. This appears to suggest that PBL can facilitate increased assimilation of diagnostic reasoning skills within postgraduate learners. Keywords: Physician Associate, Diagnostic Reasoning, Problem Based Learning, Postgraduate

An accurate tool for the fast generation of dark matter halo catalogues

We present a new parallel implementation of the PINpointing Orbit Crossing-Collapsed HIerarchical Objects (PINOCCHIO) algorithm, a quick tool, based on Lagrangian Perturbation Theory, for the hierarchical build-up of dark matter (DM) haloes in cosmological volumes. To assess its ability to predict halo correlations on large scales, we compare its results with those of an N-body simulation of a 3 h−1 Gpc box sampled with 20483 particles taken from the MICE suite, matching the same seeds for the initial conditions. Thanks to the Fastest Fourier Transforms in the West (FFTW) libraries and to the relatively simple design, the code shows very good scaling properties. The CPU time required by PINOCCHIO is a tiny fraction (∼1/2000) of that required by the MICE simulation. Varying some of PINOCCHIO numerical parameters allows one to produce a universal mass function that lies in the range allowed by published fits, although it underestimates the MICE mass function of Friends-of-Friends (FoF) haloes in the high-mass tail. We compare the matter–halo and the halo–halo power spectra with those of the MICE simulation and find that these two-point statistics are well recovered on large scales. In particular, when catalogues are matched in number density, agreement within 10 per cent is achieved for the halo power spectrum. At scales k > 0.1 h Mpc−1, the inaccuracy of the Zel’dovich approximation in locating halo positions causes an underestimate of the power spectrum that can be modelled as a Gaussian factor with a damping scale of d = 3 h−1 Mpc at z = 0, decreasing at higher redshift. Finally, a remarkable match is obtained for the reduced halo bispectrum, showing a good description of non-linear halo bias. Our results demonstrate the potential of PINOCCHIO as an accurate and flexible tool for generating large ensembles of mock galaxy surveys, with interesting applications for the analysis of large galaxy redshift surveys

On the reliability of merger-trees and the mass growth histories of dark matter haloes

We have used merger trees realizations to study the formation of dark matter haloes. The construction of merger-trees is based on three different pictures about the formation of structures in the Universe. These pictures include: the spherical collapse (SC), the ellipsoidal collapse (EC) and the non-radial collapse (NR). The reliability of merger-trees has been examined comparing their predictions related to the distribution of the number of progenitors, as well as the distribution of formation times, with the predictions of analytical relations. The comparison yields a very satisfactory agreement. Subsequently, >.........Comment: A&SS Accepte

Merger rates of dark matter haloes: a comparison between EPS and N-body results

We calculate merger rates of dark matter haloes using the Extended Press-Schechter approximation (EPS) for the Spherical Collapse (SC) and the Ellipsoidal Collapse (EC) models. Merger rates have been calculated for masses in the range $10^{10}M_{\odot}\mathrm{h}^{-1}$ to $10^{14}M_{\odot}\mathrm{h}^{-1}$ and for redshifts $z$ in the range 0 to 3 and they have been compared with merger rates that have been proposed by other authors as fits to the results of N-body simulations. The detailed comparison presented here shows that the agreement between the analytical models and N-body simulations depends crucially on the mass of the descendant halo. For some range of masses and redshifts either SC or EC models approximate satisfactory the results of N-body simulations but for other cases both models are less satisfactory or even bad approximations. We showed, by studying the parameters of the problem that a disagreement --if it appears-- does not depend on the values of the parameters but on the kind of the particular solution used for the distribution of progenitors or on the nature of EPS methods. Further studies could help to improve our understanding about the physical processes during the formation of dark matter haloes.Comment: 29 pages, 9 figure

Probing Primordial Non-Gaussianity with Large-Scale Structure

We consider primordial non-Gaussianity due to quadratic corrections in the gravitational potential parametrized by a non-linear coupling parameter fnl. We study constraints on fnl from measurements of the galaxy bispectrum in redshift surveys. Using estimates for idealized survey geometries of the 2dF and SDSS surveys and realistic ones from SDSS mock catalogs, we show that it is possible to probe |fnl|~100, after marginalization over bias parameters. We apply our methods to the galaxy bispectrum measured from the PSCz survey, and obtain a 2sigma-constraint |fnl|< 1800. We estimate that an all sky redshift survey up to z~1 can probe |fnl|~1. We also consider the use of cluster abundance to constrain fnl and find that in order to be sensitive to |fnl|~100, cluster masses need to be determined with an accuracy of a few percent, assuming perfect knowledge of the mass function and cosmological parameters.Comment: 15 pages, 7 figure

On the spin distributions of Λ\LambdaCDM haloes

We used merger trees realizations, predicted by the extended Press-Schechter theory, in order to study the growth of angular momentum of dark matter haloes. Our results showed that: 1) The spin parameter $\lambda'$ resulting from the above method, is an increasing function of the present day mass of the halo. The mean value of $\lambda'$ varies from 0.0343 to 0.0484 for haloes with present day masses in the range of $10^9\mathrm{h}^{-1}M_{\odot}$ to $10^{14}\mathrm{h}^{-1}M_{\odot}$. 2)The distribution of $\lambda'$ is close to a log-normal, but, as it is already found in the results of N-body simulations, the match is not satisfactory at the tails of the distribution. A new analytical formula that approximates the results much more satisfactorily is presented. 3) The distribution of the values of $\lambda'$ depends only weakly on the redshift. 4) The spin parameter of an halo depends on the number of recent major mergers. Specifically the spin parameter is an increasing function of this number.Comment: 10 pages, 8 figure

Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant

We present semi-analytical solutions to the background equations describing the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius. Hence, these solutions describe the complete space time of a collapsing spherical object in an expanding universe. In the appendix we present for completeness a solution of the Friedmann equations in the additional presence of radiation, only valid for the Robertson-Walker metric.Comment: 23 pages, one figure. Numerical module for evaluation of the solutions released at http://web.physik.rwth-aachen.de/download/valkenburg/ColLambda/ Matches published version, published under Open Access. Note change of titl

Quinstant Dark Energy Predictions for Structure Formation

We explore the predictions of a class of dark energy models, quinstant dark energy, concerning the structure formation in the Universe, both in the linear and non-linear regimes. Quinstant dark energy is considered to be formed by quintessence and a negative cosmological constant. We conclude that these models give good predictions for structure formation in the linear regime, but fail to do so in the non-linear one, for redshifts larger than one.Comment: 9 pages, 14 figures, "Accepted for publication in Astrophysics & Space Science

Cross-Correlation of the Cosmic Microwave Background with the 2MASS Galaxy Survey: Signatures of Dark Energy, Hot Gas, and Point Sources

We cross-correlate the Cosmic Microwave Background (CMB) temperature anisotropies observed by the Wilkinson Microwave Anisotropy Probe (WMAP) with the projected distribution of extended sources in the Two Micron All Sky Survey (2MASS). By modelling the theoretical expectation for this signal, we extract the signatures of dark energy (Integrated Sachs-Wolfe effect;ISW), hot gas (thermal Sunyaev-Zeldovich effect;thermal SZ), and microwave point sources in the cross-correlation. Our strongest signal is the thermal SZ, at the 3.1-3.7 \sigma level, which is consistent with the theoretical prediction based on observations of X-ray clusters. We also see the ISW signal at the 2.5 \sigma level, which is consistent with the expected value for the concordance LCDM cosmology, and is an independent signature of the presence of dark energy in the universe. Finally, we see the signature of microwave point sources at the 2.7 \sigma level.Comment: 35 pages (preprint format), 8 figures. In addition to minor revisions based on referee's comments, after correcting for a bug in the code, the SZ detection is consistent with the X-ray observations. Accepeted for publication in Physical Review