Peaks and dips in Gaussian random fields: a new algorithm for the shear eigenvalues, and the excursion set theory

We present a new algorithm to sample the constrained eigenvalues of the initial shear field associated with Gaussian statistics, called the `peak/dip excursion-set-based' algorithm, at positions which correspond to peaks or dips of the correlated density field. The computational procedure is based on a new formula which extends Doroshkevich's unconditional distribution for the eigenvalues of the linear tidal field, to account for the fact that halos and voids may correspond to maxima or minima of the density field. The ability to differentiate between random positions and special points in space around which halos or voids may form (peaks/dips), encoded in the new formula and reflected in the algorithm, naturally leads to a straightforward implementation of an excursion set model for peaks and dips in Gaussian random fields - one of the key advantages of this sampling procedure. In addition, it offers novel insights into the statistical description of the cosmic web. As a first physical application, we show how the standard distributions of shear ellipticity and prolateness in triaxial models of structure formation are modified by the constraint. In particular, we provide a new expression for the conditional distribution of shape parameters given the density peak constraint, which generalizes some previous literature work. The formula has important implications for the modeling of non-spherical dark matter halo shapes, in relation to their initial shape distribution. We also test and confirm our theoretical predictions for the individual distributions of eigenvalues subjected to the extremum constraint, along with other directly related conditional probabilities. Finally, we indicate how the proposed sampling procedure naturally integrates into the standard excursion set model, potentially solving some of its well-known problems, and into the ellipsoidal collapse framework. (abridged)Comment: 18 pages, 5 figures, MNRAS in pres

Convolution and deconvolution based estimates of galaxy scaling relations from photometric redshift surveys

In addition to the maximum likelihood approach, there are two other methods which are commonly used to reconstruct the true redshift distribution from photometric redshift datasets: one uses a deconvolution method, and the other a convolution. We show how these two techniques are related, and how this relationship can be extended to include the study of galaxy scaling relations in photometric datasets. We then show what additional information photometric redshift algorithms must output so that they too can be used to study galaxy scaling relations, rather than just redshift distributions. We also argue that the convolution based approach may permit a more efficient selection of the objects for which calibration spectra are required.Comment: 7 pages, 4 figures, accepted for publication in MNRAS; v2 includes a new section and other minor change

The New Horizon Run Cosmological N-Body Simulations

We present two large cosmological N-body simulations, called Horizon Run 2 (HR2) and Horizon Run 3 (HR3), made using 6000^3 = 216 billions and 7210^3 = 374 billion particles, spanning a volume of (7.200 Gpc/h)^3 and (10.815 Gpc/h)^3, respectively. These simulations improve on our previous Horizon Run 1 (HR1) up to a factor of 4.4 in volume, and range from 2600 to over 8800 times the volume of the Millennium Run. In addition, they achieve a considerably finer mass resolution, down to 1.25x10^11 M_sun/h, allowing to resolve galaxy-size halos with mean particle separations of 1.2 Mpc/h and 1.5 Mpc/h, respectively. We have measured the power spectrum, correlation function, mass function and basic halo properties with percent level accuracy, and verified that they correctly reproduce the LCDM theoretical expectations, in excellent agreement with linear perturbation theory. Our unprecedentedly large-volume N-body simulations can be used for a variety of studies in cosmology and astrophysics, ranging from large-scale structure topology, baryon acoustic oscillations, dark energy and the characterization of the expansion history of the Universe, till galaxy formation science - in connection with the new SDSS-III. To this end, we made a total of 35 all-sky mock surveys along the past light cone out to z=0.7 (8 from the HR2 and 27 from the HR3), to simulate the BOSS geometry. The simulations and mock surveys are already publicly available at http://astro.kias.re.kr/Horizon-Run23/.Comment: 18 pages, 10 figures. Added clarification on Fig 6. Published in the Journal of the Korean Astronomical Society (JKAS). The paper with high-resolution figures is available at http://jkas.kas.org/journals/2011v44n6/v44n6.ht

Topology of Luminous Red Galaxies from the Sloan Digital Sky Survey

We present measurements of the genus topology of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) Data Release 7 catalog, with unprecedented statistical significance. To estimate the uncertainties in the measured genus, we construct 81 mock SDSS LRG surveys along the past light cone from the Horizon Run 3, one of the largest N-body simulations to date that evolved 7210^3 particles in a 10815 Mpc/h size box. After carefully modeling and removing all known systematic effects due to finite pixel size, survey boundary, radial and angular selection functions, shot noise and galaxy biasing, we find the observed genus amplitude to reach 272 at 22 Mpc/h smoothing scale with an uncertainty of 4.2%; the estimated error fully incorporates cosmic variance. This is the most accurate constraint of the genus amplitude to date, which significantly improves on our previous results. In particular, the shape of the genus curve agrees very well with the mean topology of the SDSS LRG mock surveys in the LCDM universe. However, comparison with simulations also shows small deviations of the observed genus curve from the theoretical expectation for Gaussian initial conditions. While these discrepancies are mainly driven by known systematic effects such as those of shot noise and redshift-space distortions, they do contain important cosmological information on the physical effects connected with galaxy formation, gravitational evolution and primordial non-Gaussianity. We address here the key role played by systematics on the genus curve, and show how to accurately correct for their effects to recover the topology of the underlying matter. In a forthcoming paper, we provide an interpretation of those deviations in the context of the local model of non-Gaussianity.Comment: 23 pages, 18 figures. APJ Supplement Series 201