We show with analytic models that the assumption of uncorrelated intrinsic ellipticities of target sources that is usually made in searches for weak gravitational lensing arising from large‐scale mass inhomogeneities (‘field lensing’) is unwarranted. If the orientation of the galaxy image is determined either by the angular momentum or by the shape of the halo in which it forms, then the image should be aligned preferentially with the component of the tidal gravitational field perpendicular to the line of sight. Long‐range correlations in the tidal field will thus lead to long‐range ellipticity–ellipticity correlations that mimic the shear correlations arising from weak gravitational lensing. We calculate the ellipticity–ellipticity correlation expected if halo shapes determine the observed galaxy shape, and we discuss uncertainties (which are still considerable) in the predicted amplitude of this correlation. The ellipticity–ellipticity correlation induced by angular momenta should be smaller. We consider several methods for discriminating between the weak‐lensing (extrinsic) and intrinsic correlations, including the use of redshift information. An ellipticity–tidal‐field correlation also implies the existence of an alignment of images of galaxies near clusters. Although the intrinsic alignment may complicate the interpretation of field‐lensing results, it is inherently interesting as it may shed light on galaxy formation as well as on structure formation.

The growth of the angular momentum L of protogalaxies induced by tidal torques is reconsidered. We adopt White's formalism and study the evolution of L in Lagrangian coordinates; the motion of the fluid elements is described by the Zel'dovich approximation. We obtain a general expression for the ensemble expectation value of the square of L in terms of the first and second invariant of the inertia tensor of the Lagrangian volume Γ enclosing the protoobject's collapsing mass. We then specialize the formalism to the particular case in which Γ is centred on a peak of the smoothed Gaussian density field and approximated by an isodensity ellipsoid. The result is the appropriate analytical estimate for the rms angular momentum of peaks to be compared against simulations that make use of the Hoffman-Ribak algorithm to set up a constrained density field that contains a peak with given shape. Extending the work of Heavens & Peacock, we calculate the joint probability distribution function for several spin parameters and peak mass M using the distribution of peak shapes, for different initial power spectra. The probability distribution for the rms final angular momentum L 2 f 1/2 on the scales corresponding to common bright galaxies, M ≈ 10 11 M ⊙ , is centred on a value of ≈ 10 67 kg m 2 s −1 , for any cosmologically relevant power spectrum, in line with previous theoretical and observational estimates for L f . Other astrophysical consequences are discussed. In particular, we find that typical values λ 2 1/2 ≈ 0.1 of the dimensionless spin parameter for peaks smoothed on galactic scales and of height ν ∼ 1, usually associated with late type galaxies, may be recovered in the framework of the Gaussian peak formalism. This partially relaxes the importance attributed to dissipative processes in generating such high values of centrifugal support for spiral galaxies. In addition, the values of the specific angular momentum versus massas deduced from observations of rotational velocities and photometric radii of spiral galaxies -are well fitted by our theoretical isoprobability contours. In contrast, the observed lower values for the specific angular momentum for ellipticals of the same mass cannot be accounted for within our linear regime investigation, highlighting the importance of strongly non-linear phenomena to explain the spin of such objects.

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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, extending the recent results by Mo & 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 the bispectrum and the skewness. Our algorithm may have several interesting applications, among which is the possibility of generating mock halo catalogues from low-resolution N-body simulations

We discuss the non-linear evolution of the angular momentum L acquired by protostructures, like protogalaxies and protoclusters, due to tidal interactions with the surrounding matter inhomogeneities. The primordial density distribution is assumed to be Gaussian and the non-linear dynamics of the collisionless mass fluid is followed using Lagrangian perturbation theory. For a Cold Dark Matter spectrum, the inclusion of the leading-order Lagrangian correction terms results in a value of the rms ensemble average L 2 1/2 which is only a factor of 1.3 higher than the corresponding linear estimate, irrespective of the scale. Consequently, the predictions of linear theory are rather accurate in quantifying the evolution of the angular momentum of protostructures before collapse sets in. In the Einstein-de Sitter universe, the initial torque is a good estimate for the tidal torque over the whole period during which the object is spun up.