Yehuda Hoffman

Constrained realizations of Gaussian fields - A simple algorithm

A straightforward method for the construction of constrained realizations of Gaussian fields is presented. Consider a Gaussian random field and its ensemble mean field given a set of constraints. The residual of the field from its mean is statistically independent of the actual numerical value of the constraints. The algorithm is based on a simple construction of this residual field, which is then added to the analytically calculated mean field. This algorithm is exact and involves no iterations.

The structure of voids

Using high resolution N-body simulations we address the problem of emptiness of giant � 20h −1 Mpc–diameter voids found in the distribution of bright galaxies. Are the voids filled by dwarf galaxies? Do cosmological models predict too many small dark matter haloes inside the voids? Can the problems of cosmological models on small scales be addressed by studying the abundance of dwarf galaxies inside voids? We find that voids in the distribution of 10 12 h −1 M⊙ haloes (expected galactic magnitudes � M∗) are almost the same as the voids in 10 11 h −1 M⊙ haloes. Yet, much smaller haloes with masses 10 9 h −1 M⊙ and circular velocities vcirc � 20 km/s readily fill the voids: there should be almost 1000 of these haloes in a 20h −1 Mpc–diameter void. A typical void of diameter 20h −1 Mpc contains about 50 haloes with vcirc > 50 km/s. The haloes are arranged in a pattern, which looks like a miniature Universe: it has the same structural elements as the large-scale structure of the galactic distribution of the Universe. There are filaments and voids; larger haloes are at the intersections of filaments. The only difference is that all masses are four orders of magnitude smaller. There is severe (anti)bias in the distribution of haloes, which depends on halo mass and on the distance from the centre of the void. Large haloes are more antibiased and have a tendency to form close to void boundaries. The mass function of haloes in voids is different from the “normal” mass function. It is much steeper for high masses resulting in very few M33-type galaxies (vcirc � 100 km/s). We present an analytical approximation for the mass function of haloes in voids.

A Dynamical Classification of the Cosmic Web

In this paper, we propose a new dynamical classification of the cosmic web. Each point in space is classified in one of four possible web types: voids, sheets, filaments and knots. The classification is based on the evaluation of the deformation tensor (i.e. the Hessian of the gravitational potential) on a grid. The classification is based on counting the number of eigenvalues above a certain threshold, λth, at each grid point, where the case of zero, one, two or three such eigenvalues corresponds to void, sheet, filament or a knot grid point. The collection of neighbouring grid points, friends of friends, of the same web type constitutes voids, sheets, filaments and knots as extended web objects. A simple dynamical consideration of the emergence of the web suggests that the threshold should not be null, as in previous implementations of the algorithm. A detailed dynamical analysis would have found different threshold values for the collapse of sheets, filaments and knots. Short of such an analysis a phenomenological approach has been opted for, looking for a single threshold to be determined by analysing numerical simulations. Our cosmic web classification has been applied and tested against a suite of large (dark matter only) cosmological N-body simulations. In particular, the dependence of the volume and mass filling fractions on λth and on the resolution has been calculated for the four web types. We also study the percolation properties of voids and filaments. Our main findings are as follows. (i) Already at λth= 0.1 the resulting web classification reproduces the visual impression of the cosmic web. (ii) Between 0.2 ≲λth≲ 0.4, a system of percolated voids coexists with a net of interconnected filaments. This suggests a reasonable choice for λth as the parameter that defines the cosmic web. (iii) The dynamical nature of the suggested classification provides a robust framework for incorporating environmental information into galaxy formation models, and in particular to semi-analytical models.

FLAT-CORED DARK MATTER IN CUSPY CLUSTERS OF GALAXIES

Sand and coworkers have measured the central density profile of cluster MS 213723 with gravitational lensing and velocity dispersion and removed the stellar contribution with a reasonable M/L. The resulting dark matter (DM) distribution within was fitted by a density cusp of with , in an apparent 1 b r ! 50 h kpc r b p 0.35 contradiction to the cold dark matter prediction of . The disagreement worsens if adiabatic compression of b ∼ 1 the DM by the infalling baryons is considered. Following El-Zant, Shlosman, & Hoffman, we argue that dynamical friction acting on galaxies moving within the DM background counters the effect of adiabatic compression by transfering their orbital energy to the DM, thus heating up and softening the cusp. Using N-body simulations we show that indeed the inner DM distribution flattens (with for a cluster like MS 2137 23) when the b ≈ 0.35 galaxies spiral inward. We find as a robust result that while the DM distribution becomes core-like, the overall mass distribution preserves its cuspy nature, in agreement with X-ray and lensing observations of clusters. Subject heading: dark matter — galaxies: clusters: general — galaxies: formation — galaxies: halos

THE VELOCITY FUNCTION IN THE LOCAL ENVIRONMENT FROM ΛCDM AND ΛWDM CONSTRAINED SIMULATIONS

Using constrained simulations of the local universe for generic cold dark matter (CDM) and for 1 keV warm dark matter (WDM), we investigate the difference in the abundance of dark matter halos in the local environment. We find that the mass function (MF) within 20 h –1 Mpc of the Local Group is ~2 times larger than the universal MF in the 109-1013 h –1 M ☉ mass range. Imposing the field of view of the ongoing H I blind survey Arecibo Legacy Fast ALFA (ALFALFA) in our simulations, we predict that the velocity function (VF) in the Virgo-direction region (VdR) exceeds the universal VF by a factor of 3. Furthermore, employing a scheme to translate the halo VF into a galaxy VF, we compare the simulation results with a sample of galaxies from the early catalog release of ALFALFA. We find that our simulations are able to reproduce the VF in the 80-300 km s-1 velocity range, having a value ~10 times larger than the universal VF in the VdR. In the low-velocity regime, 35-80 km s-1, the WDM simulation reproduces the observed flattening of the VF. In contrast, the simulation with CDM predicts a steep rise in the VF toward lower velocities; for V max = 35 km s-1, it forecasts ~10 times more sources than the ones observed. If confirmed by the complete ALFALFA survey, our results indicate a potential problem for the CDM paradigm or for the conventional assumptions about energetic feedback in dwarf galaxies.

A kinematic classification of the cosmic web

A new approach for the classification of the cosmic web is presented. In extension of the previous work of Hahn et al. and Forero-Romero et al., the new algorithm is based on the analysis of the velocity shear tensor rather than the gravitational tidal tensor. The procedure consists of the construction of the shear tensor at each (grid) point in space and the evaluation of its three eigenvectors. A given point is classified to be either a void, sheet, filament or a knot according to the number of eigenvalues above a certain threshold, 0, 1, 2 or 3, respectively. The threshold is treated as a free parameter that defines the web. The algorithm has been applied to a dark matter only simulation of a box of side length 64 h−1 Mpc and N = 10243 particles within the framework of the 5-year Wilkinson and Microwave Anisotropy Probe/Λ cold dark matter (ΛCDM) model. The resulting velocity-based cosmic web resolves structures down to ≲0.1 h−1 Mpc scales, as opposed to the ≈1 h−1 Mpc scale of the tidal-based web. The underdense regions are made of extended voids bisected by planar sheets, whose density is also below the mean. The overdense regions are vastly dominated by the linear filaments and knots. The resolution achieved by the velocity-based cosmic web provides a platform for studying the formation of haloes and galaxies within the framework of the cosmic web.

Testing tidal-torque theory – II. Alignment of inertia and shear and the characteristics of protohaloes

We investigate the cross-talk between the two key components of tidal-torque theory, the inertia (I) and shear (T) tensors, using a cosmological N-body simulation with thousands of well-resolved haloes. We find that the principal axes of I and T are strongly aligned, even though I characterizes the protohalo locally while T is determined by the large-scale structure. Thus, the resultant galactic spin, which plays a key role in galaxy formation, is only a residual due to ∼10 per cent deviations from the perfect alignment of T and I. The T–I correlation induces a weak tendency for the protohalo spin to be perpendicular to the major axes of T and I, but this correlation is erased by non-linear effects at late times, making the observed spins poor indicators of the initial shear field. However, the T–I correlation implies that the shear tensor can be used for identifying the positions and boundaries of protohaloes in cosmological initial conditions – a missing piece in galaxy formation theory. The typical configuration is of a prolate protohalo lying perpendicular to a large-scale high-density ridge, with the surrounding voids inducing compression along the major and intermediate inertia axes of the protohalo. This leads to a transient sub-halo filament along the large-scale ridge, whose subclumps then flow along the filament and merge into the final halo. The centres of protohaloes tend to lie in ∼1σ overdensity regions, but their association with linear density maxima smoothed on galactic scales is vague: only ∼40 per cent of the protohaloes contain peaks. Several other characteristics distinguish protohaloes from density peaks, e.g. they tend to compress along two principal axes while many peaks compress along three axes.

The Laniakea supercluster of galaxies

Galaxies congregate in clusters and along filaments, and are missing from large regions referred to as voids. These structures are seen in maps derived from spectroscopic surveys that reveal networks of structure that are interconnected with no clear boundaries. Extended regions with a high concentration of galaxies are called ‘superclusters’, although this term is not precise. There is, however, another way to analyse the structure. If the distance to each galaxy from Earth is directly measured, then the peculiar velocity can be derived from the subtraction of the mean cosmic expansion, the product of distance times the Hubble constant, from observed velocity. The peculiar velocity is the line-of-sight departure from the cosmic expansion and arises from gravitational perturbations; a map of peculiar velocities can be translated into a map of the distribution of matter. Here we report a map of structure made using a catalogue of peculiar velocities. We find locations where peculiar velocity flows diverge, as water does at watershed divides, and we trace the surface of divergent points that surrounds us. Within the volume enclosed by this surface, the motions of galaxies are inward after removal of the mean cosmic expansion and long range flows. We define a supercluster to be the volume within such a surface, and so we are defining the extent of our home supercluster, which we call Laniakea.

Wiener reconstruction of density, velocity, and potential fields from all sky galaxy redshift surveys

We present a new method for recovering the cosmological density, velocity, and potential fields from all-sky redshift catalogues. The method is based on an expansion of the fields in orthogonal radial (Bessel) and angular (spherical harmonic) functions. In this coordinate system, peculiar velocities introduce a coupling of the radial harmonics describing the density field in redshift space but leave the angular modes unaffected. In the harmonic transform space, this radial coupling is described by a distortion matrix which can be computed analytically within the context of linear theory; the redshift space harmonics can then be converted to their real space values by inversion of this matrix. Statistical noise is mitigated by regularizing the matrix inversion with a Wiener filter. The method yields a minimum variance estimate of the density field in real space. In this coordinate system, the minimum variance harmonics of the peculiar velocity and potential fields are related to those of the density field by simple linear transformations. Tests of the method with simulations of a CDM universe and comparison with previously proposed methods demonstrate it to be a very promising new reconstruction method for the local density and velocity field. A first application to the 1.2 Jy IRAS redshift survey is presented.

The velocity shear tensor: tracer of halo alignment

The alignment of dark matter (DM) halos and the surrounding large scale structure (LSS) is examined in the context of the cosmic web. Halo spin, shape and the orbital angular momentum of subhaloes is investigated relative to the LSS using the eigen- vectors of the velocity shear tensor evaluated on a grid with a scale of 1 Mpc/h, deep within the non-linear regime. Knots, laments, sheets and voids are associated with biased. We nd that larger mass haloes live in regions where the shear is more isotropic, namely the expansion or collapse is more spherical. A correlation is found between the halos shape and the eigenvectors of the shear tensor, with the longest (shortest) axis of the halos shape being aligned with the slowest (fastest) collapsing eigenvector. This correlation is web independent, suggest- ing that the velocity shear is a fundamental tracer of the halo alignment. A similar result is found for the alignment of halo spin with the cosmic web. It has been shown that high mass haloes exhibit a spin ip with respect to the LSS: we nd the mass at which this spin ip occurs is web dependent and not universal as suggested previously. Although weaker than haloes, subhalo orbits too exhibit an alignment with the LSS, providing a possible insight into the highly correlated co-rotation of the Milky Ways satellite system. The present study suggests that the velocity shear tensor constitutes the natural framework for studying the directional properties of the non-linear LSS and of halos and galaxies.