Eulerian bias and the galaxy density field

We investigate the effects on cosmological clustering statistics of empirical biasing, where the galaxy distribution is a local transformation of the present-day Eulerian density field. The effects of the suppression of galaxy numbers in voids, and their enhancement in regions of high density, are considered, independently and in combination. We compare results from numerical simulations with the predictions of simple analytic models. We find that the bias is generally scale-dependent, so that the shape of the galaxy power spectrum differs from that of the underlying mass distribution. The degree of bias is always a monotonic function of scale, tending to an asymptotic value on scales where the density fluctuations are linear. The scale dependence is often rather weak, with many reasonable prescriptions giving a bias which is nearly independent of scale. We have investigated whether such an Eulerian bias can reconcile a range of theoretical power spectra with the twin requirements of fitting the galaxy power spectrum and reproducing the observed mass-to-light ratios in clusters. It is not possible to satisfy these constraints for any member of the family of CDM-like power spectra in an Einstein - de Sitter universe when normalised to match COBE on large scales and galaxy cluster abundances on intermediate scales. We discuss what modifications of the mass power spectrum might produce agreement with the observational data.Comment: 14 pages, LaTeX (using mn.sty, epsfig), 17 Postscript figures included. Accepted for publication in MNRA

The bias field of dark matter haloes

This paper presents a stochastic approach to the clustering evolution of dark matter haloes in the Universe. Haloes, identified by a Press-Schechter-type algorithm in Lagrangian space, are described in terms of `counting fields', acting as non-linear operators on the underlying Gaussian density fluctuations. By ensemble averaging these counting fields, the standard Press-Schechter mass function as well as analytic expressions for the halo correlation function and corresponding bias factors of linear theory are obtained, thereby extending the recent results by Mo and White. The non-linear evolution of our halo population is then followed by solving the continuity equation, under the sole hypothesis that haloes move by the action of gravity. This leads to an exact and general formula for the bias field of dark matter haloes, defined as the local ratio between their number density contrast and the mass density fluctuation. Besides being a function of position and `observation' redshift, this random field depends upon the mass and formation epoch of the objects and is both non-linear and non-local. The latter features are expected to leave a detectable imprint on the spatial clustering of galaxies, as described, for instance, by statistics like bispectrum and skewness. Our algorithm may have several interesting applications, among which the possibility of generating mock halo catalogues from low-resolution N-body simulations.Comment: 23 pages, LaTeX (included psfig.tex), 4 figures. Few comments and references have been added, and minor typos and errors corrected. This version matches the refereed one, in press in MNRA

Large effect of a small bias field in liquid-crystal magnetic transitions

Most liquid crystals show low sensitivity to magnetic field. However, in this paper we show that a small bias magnetic field not only breaks the symmetry of the ground state, but also plays a crucial role in facilitating the reorientation induced by a large test magnetic field. In particular, a small bias field may alter significantly the strength of the test field needed to observe a given reorientation of the liquid crystal. Moreover, the bias field interacts with other symmetry breaking features of the cell, e.g., pretilt, to change also the qualitative features of the equilibrium state

Time-resolved investigation of magnetization dynamics of arrays of non-ellipsoidal nanomagnets with a non-uniform ground state

We have performed time-resolved scanning Kerr microscopy (TRSKM) measurements upon arrays of square ferromagnetic nano-elements of different size and for a range of bias fields. The experimental results were compared to micromagnetic simulations of model arrays in order to understand the non-uniform precessional dynamics within the elements. In the experimental spectra two branches of excited modes were observed to co-exist above a particular bias field. Below the so-called crossover field, the higher frequency branch was observed to vanish. Micromagnetic simulations and Fourier imaging revealed that modes from the higher frequency branch had large amplitude at the center of the element where the effective field was parallel to the bias field and the static magnetization. Modes from the lower frequency branch had large amplitude near the edges of the element perpendicular to the bias field. The simulations revealed significant canting of the static magnetization and the effective field away from the direction of the bias field in the edge regions. For the smallest element sizes and/or at low bias field values the effective field was found to become anti-parallel to the static magnetization. The simulations revealed that the majority of the modes were de-localized with finite amplitude throughout the element, while the spatial character of a mode was found to be correlated with the spatial variation of the total effective field and the static magnetization state. The simulations also revealed that the frequencies of the edge modes are strongly affected by the spatial distribution of the static magnetization state both within an element and within its nearest neighbors