We discuss the origin of galactic angular momentum and the statistics of the present-day spin distribution. It is expected that the galaxy spin axes are correlated with the intermediate principal axis of the gravitational shear tensor. This allows one to reconstruct the shear field and thereby the full gravitational potential from the observed galaxy spin fields. We use the direction of the angular momentum vector without any information of its magnitude, which requires a measurement of the position angle and inclination on the sky of each disk galaxy. We present the maximum likelihood shear inversion procedure, which involves a constrained linear minimization. The theory is tested against numerical simulations. We find the correlation strength of nonlinear structures with the initial shear field and show that accurate large-scale density reconstructions are possible at the expected noise level.

We present a theoretical study of galaxy spin correlation statistics, with detailed technical derivations. We also find an expression for the spin-density crosscorrelation, and apply that to the Tully galaxy catalog. The observational results appear qualitatively consistent with the theoretical predictions, yet the error bars are still large. However, we expect that currently ongoing large surveys such as the Sloan Digital Sky survey (SDSS) will enable us to make a precision measurement of these correlation statistics in the near future. These intrinsic galaxy alignments are expected to dominate over the weak lensing signal in SDSS, and we present the detailed algorithms for the density reconstruction for this case.These observables are tracers of the galaxy-gravity interaction, which may provide us deeper insights into the galaxy formation and large scale matter distribution as well.Subject headings: galaxies:statistics -large-scale structure of universe Recently Lee & Pen (2000, hereafter LP00) pointed out that the 1st-order linear perturbation theory predicts preferential alignments of the galaxy spin axis along with the 2nd principal axis of the local gravitational shear tensor, and suggested a unique statistical model that uses the galaxy spin axis as a tool to reconstruct the initial density field. Their theory is based on two basic assumptions: First, the spin axis of a galaxy aligns well with that of

Statistics of lensed arcs in clusters of galaxies serve as a powerful probe of both the non-sphericity and the inner slope of dark matter halos. We develop a semi-analytic method to compute the number of arcs in triaxial dark matter halos. This combines the lensing cross section from the Monte Carlo ray-tracing simulations, and the probability distribution function (PDF) of the axis ratios evaluated from cosmological N-body simulations. This approach enables one to incorporate both asymmetries in the projected mass density and elongations along the line-of-sight analytically, for the first time in cosmological lensed arc statistics. As expected, triaxial dark matter halos significantly increase the number of arcs relative to spherical models; the difference amounts to more than one order of magnitude while the value of enhancement depends on the specific properties of density profiles. Then we compare our theoretical predictions with the observed number of arcs from 38 X-ray selected clusters. In contrast to the previous claims, our triaxial dark matter halos with inner density profile ρ ∝ r −1.5 in a Lambda-dominated cold dark matter (CDM) universe reproduces well the observation. Since both the central mass concentration and triaxial axis ratios (minor to major axis ratio ∼ 0.5) required to account for the observed data are consistent with cosmological N-body simulations, our result may be interpreted to lend strong support for the collisionless CDM paradigm at the mass scale of clusters.

We report a direct observational evidence for the existence of the galaxy spin alignments with the real space tidal field. We calculate the real space tidal field from the real space density field reconstructed recently from the Two Mass Redshift Survey (2MRS) by Erdogdu et al. in 2006. Using a total of 12122 nearby spiral galaxies from the Tully Galaxy Catalog, we calculate the orientations of their spin axes relative to the 2MRS tidal field. We find a clear signal of the intrinsic correlations between the galaxy spins and the intermediate principal axes of the tidal shears. The null hypothesis of no correlation is rejected at 99.99% confidence level. We also investigate the dependence of the intrinsic correlations on the galaxy morphological type and the environment. It is found that (i) the intrinsic correlation depends weakly on the morphological type of the spiral galaxies but tends to decrease slightly as the type increases; (ii) it is stronger in the high-density regions than in the low-density regions. The observational result is quantitatively consistent with analytic prediction based on the tidal torque theory. It is concluded that the galaxy spin orientations may provide in principle a new complimentary probe of the dark matter distribution.