The Hierarchical Peak-Patch Picture of Cosmic Catalogues

J.R. Bond (CITA) and S.T. Myers (Caltech/UPenn)

AuthorsTitle/ReprintReference/astro-ph
Bond, J.R., Myers, S.T. (1996a) The Peak-Patch Picture of Cosmic Catalogs. I. Algorithms ApJS, 103, 1-39 (1996)
Bond, J.R., Myers, S.T. (1996b) The Peak-Patch Picture of Cosmic Catalogs. II. Validation ApJS, 103, 41-62 (1996)
Bond, J.R., Myers, S.T. (1996c) The Peak-Patch Picture of Cosmic Catalogs. III. Application to Clusters ApJS, 103, 63-79 (1996)

Abstract for Paper I: Algorithms

We present a picture for large-scale structure formation that describes the formation of virialized cosmological objects as a point process of "peak patches" in the initial (Lagrangian) space. The nonlinear internal dynamics of the collapsing patch is largely decoupled from the linear dynamics of the ensemble of peak-patches in the simulation volume, and a modest set of local field measurement on the patch region suffice to approximately determine the fate of the peak. The candidate peak points are identified using a hierarchy of smoothing operations on the density field. Patch size (and mass) is found by requiring complete collapse of a homogeneous ellipsoid model for internal patch dynamics which includes the important influence of the external tidal field. Exclusion algorithms that prevent peak-patch overlaps trim the candidate list into the final `hierarchical peak' list. The Zeldovich approximation with locally adaptive filtering of the displacement field is used for external dynamics to move the surviving patches to their final state (Eulerian) positions. Thus both statistical and dynamical clustering of the peaks are included. Our technique is the natural generalization of both the Press-Schechter method (to include non-local effects) and the BBKS single-filter peaks theory (to allow a mass spectrum and solve the cloud-in-cloud problem). This method is found to be an efficient algorithm for Monte Carlo construction of 3D catalogues of virialized cosmological objects, such as clusters of galaxies and the initial stages of galaxy formation.

Abstract for Paper II: Validation

We compare hierarchical peak-patch catalogues with groups and clusters constructed using Couchman's adaptive P3M simulations of a `standard' CDM model with amplitude parameter sigma_8 = 1. The N-body groups are found using an identification algorithm based on average cluster overdensity and the peak-patch properties were determined using algorithms from Paper I. We show that the best agreement is obtained if we use (1) density peaks rather than shear eigenvalue peaks as candidate points, (2) ellipsoidal rather than spherical collapse dynamics, thereby including external tidal effects and (3) a binary reduction method as opposed to a full exclusion method for solving the cloud-in-cloud problem of peak theory. These are also the best choices physically. The mass and internal energy distributions of the peaks and groups are quite similar, but the group kinetic energy distribution is offset by about 12% in velocity dispersion, on average. Individual peak-to-group comparisons show good agreement for high-mass, tightly-bound groups, with growing scatter for lower masses and looser binding. The final state (Eulerian) spatial distribution of peak-patches and N-body clusters are shown to be satisfyingly close.

Abstract for Paper III: Application to Clusters

To illustrate the utility of the Peak-Patch method, we construct cluster catalogues covering very large volumes of space for 4 inflation-inspired Gaussian structure formation theories with a critical density in clustering matter and whose sigma_8 normalizations fit the COBE anisotropy measurements. We use these to make deep field X-ray and Sunyaev-Zeldovich maps. Subject to some uncertainties in the internal peak-patch physics and the X-ray data, we find that current X-ray temperature data suggest sigma_8 is within about 15% of 0.7 and the spectrum is flatter than CDM gives, for Einstein-deSitter models. We also find the current X-ray luminosity data are difficult to fit over the entire range with such models.

Abstract for Paper IV: Analytic Methods

An analytic formula for the mass function of peaks which upcross through a critical linear overdensity as a function of mass includes much of the exclusion and agrees extremely well with the Monte Carlo calculations. Tidal effects are included by making the threshold a function of the mean shear. The binding energy of the peaks, including the influence of external tides, can also be calculated very well. Completely modelling the exclusion criteria is not feasible, but useful exclusion functions that act on the upcrossing number density are derived which bracket the simulation results. The clustering properties of peak points can be estimated. We also derive formulas for statistical biasing with first order dynamics.

Note: this paper was never finished! It could have been a contender...

Steven T. Myers