Locally Biased Galaxy Formation and Large Scale Structure

We examine the influence of the morphology-density(MD) relation and a wide range of simple models for biased galaxy formation on statistical measures of large scale structure. We contrast the behavior of local biasing models, in which the efficiency of galaxy formation is determined by density, geometry, or velocity dispersion of the local mass distribution, with that of non-local biasing models, in which galaxy formation is modulated coherently over scales larger than the galaxy correlation length. If morphological segregation of galaxies is governed by a local MD relation, then the correlation function of E/S0 galaxies should be steeper and stronger than that of spiral galaxies on small scales, as observed, while on large scales the correlation functions of E/S0 and spiral galaxies should have the same shape but different amplitudes. Similarly, all of our local bias models produce scale-independent amplification of the correlation function and power spectrum in the linear and mildly non-linear regimes; only a non-local biasing mechanism can alter the shape of the power spectrum on large scales. Moments of the biased galaxy distribution retain the hierarchical pattern of the mass moments, but biasing alters the values and scale-dependence of the hierarchical amplitudes S3 and S4. Pair-weighted moments of the galaxy velocity distribution are sensitive to the details of the biasing prescription. The non-linearity of the relation between galaxy density and mass density depends on the biasing prescription and the smoothing scale, and the scatter in this relation is a useful diagnostic of the physical parameters that determine the bias. Although the sensitivity of galaxy clustering statistics to the details of biasing is an obstacle to testing cosmological models, it is an asset for testing galaxy formation theories.Comment: 47 pages including 17 Figures, submitted to Ap

Asymptotic behaviour of two-point functions in multi-species models

We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the $SU(3)$-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.Comment: 45 pages, 1 figur

Local Dynamics and Strong Correlation Physics I: 1D and 2D Half-filled Hubbard Models

We report on a non-perturbative approach to the 1D and 2D Hubbard models that is capable of recovering both strong and weak-coupling limits. We first show that even when the on-site Coulomb repulsion, U, is much smaller than the bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D. Consequently, the Hubbard model at half-filling is always in the strong-coupling non-perturbative regime. For both large and small U, we find that the population of nearest-neighbour singlet states approaches a value of order unity as $T\to 0$ as would be expected for antiferromagnetic order. We also find that the double occupancy is a smooth monotonic function of U and approaches the anticipated non-interacting limit and large U limits. Finally, in our results for the heat capacity in 1D differ by no more than 1% from the Bethe ansatz predictions. In addition, we find that in 2D, the heat capacity vs T for different values of U exhibits a universal crossing point at two characteristic temperatures as is seen experimentally in a wide range of strongly-correlated systems such as $^3He$, $UBe_3$, and $CeCu_{6-x}Al_x$. The success of this method in recovering well-established results that stem fundamentally from the Coulomb interaction suggests that local dynamics are at the heart of the physics of strongly correlated systems.Comment: 10 pages, 16 figures included in text, Final version for publication with a reference added and minor corrections. Phys. Rev. B, in pres

Constrained simulations of the local universe: I. Mass and motion in the Local Volume

It has been recently claimed that there is no correlation between the distribution of galaxies and their peculiar velocities within the Local Volume (LV), namely a sphere of R=7/h Mpc around the Local Group (LG). It has been then stated that this implies that either locally dark matter is not distributed in the same way as luminous matter, or peculiar velocities are not due to fluctuations in mass. To test that statement a set of constrained N-body cosmological simulations, designed to reproduce the main observed large scale structure, have been analyzed. The simulations were performed within the flat-Lambda, open and flat matter only CDM cosmogonies. Two unconstrained simulations of the flat-Lambda and open CDM models were performed for comparison. LG-like objects have been selected so as to mimic the real LG environment. The local gravitational field due to all halos found within each LV is compared with the exact gravitational field induced by all matter in the simulation. We conclude that there is no correlation between the exact and the local gravitational field obtained by pairwise newtonian forces between halos. Moreover, the local gravitational field is uncorrelated with the peculiar velocities of halos. The exact gravitational field has a linear correlation with peculiar velocities but the proportionality constant relating the velocity with gravitational field falls below the prediction of the linear theory. Upon considering all matter inside the LVs, the exact and local gravitational accelerations show a much better correlation, but with a considerable scatter independent on the cosmological models. The main conclusion is that the lack of correlation between the local gravitation and the peculiar velocity fields around LG-like objects is naturally expected in the CDM cosmologies.Comment: 10 pages, 19 figures. Accepted for publication in MNRA

Classification of local realistic theories

Recently, it has shown that an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment (two-setting model), works only for the specific set of settings in the given experiment, but cannot construct a local realistic model for the values of a correlation function, given in a {\it continuous-infinite} settings Bell experiment (infinite-setting model), even though there exist two-setting models for all directions in space. Hence, two-setting model does not have the property which infinite-setting model has. Here, we show that an explicit two-setting model cannot construct a local realistic model for the values of a correlation function, given in a {\it only discrete-three} settings Bell experiment (three-setting model), even though there exist two-setting models for the three measurement directions chosen in the given three-setting experiment. Hence, two-setting model does not have the property which three-setting model has.Comment: To appear in Journal of Physics A: Mathematical and Theoretica

The Abundance of Molecular Hydrogen and its Correlation with Midplane Pressure in Galaxies: Non-Equilibrium, Turbulent, Chemical Models

Observations of spiral galaxies show a strong linear correlation between the ratio of molecular to atomic hydrogen surface density R_mol and midplane pressure. To explain this, we simulate three-dimensional, magnetized turbulence, including simplified treatments of non-equilibrium chemistry and the propagation of dissociating radiation, to follow the formation of H_2 from cold atomic gas. The formation time scale for H_2 is sufficiently long that equilibrium is not reached within the 20-30 Myr lifetimes of molecular clouds. The equilibrium balance between radiative dissociation and H_2 formation on dust grains fails to predict the time-dependent molecular fractions we find. A simple, time-dependent model of H_2 formation can reproduce the gross behavior, although turbulent density perturbations increase molecular fractions by a factor of few above it. In contradiction to equilibrium models, radiative dissociation of molecules plays little role in our model for diffuse radiation fields with strengths less than ten times that of the solar neighborhood, because of the effective self-shielding of H_2. The observed correlation of R_mol with pressure corresponds to a correlation with local gas density if the effective temperature in the cold neutral medium of galactic disks is roughly constant. We indeed find such a correlation of R_mol with density. If we examine the value of R_mol in our local models after a free-fall time at their average density, as expected for models of molecular cloud formation by large-scale gravitational instability, our models reproduce the observed correlation over more than an order of magnitude range in density.Comment: 24 pages, 4 figures, accepted for publication in Astrophys. J, changes include addition of models with higher radiation fields and substantial clarification of the narrativ