The intrinsic inclination of galaxies embedded in cosmic sheets and its cosmological implications: An analytic calculation

We investigate analytically a large-scale coherence in the orientation of galaxies embedded in two-dimensional sheetlike structures in the framework of tidal torque theory. Assuming that the galaxy spin and the surrounding matter fields are intrinsically aligned in accordance with the tidal torque model, we first derive analytically the probability distribution of the galaxy position angles and evaluate the degree of their inclinations relative to the plane of the sheet. Then, we apply our analytic approach to the nearby spiral galaxies in the Local Supercluster and provide theoretical explanations about why and to what degree the nearby spiral galaxies are inclined relative to the supergalactic plane. Finally, we conclude that the observed large-scale coherence in the orientation of nearby spiral galaxies relative to the supergalactic plane can be quantitatively understood in terms of the intrinsic galaxy alignment predicted by the tidal torque theory and that the spins of luminous galaxies might be more strongly aligned with the surrounding matter than with the underlying dark halos. If applied to large-scale surveys like the Sloan Digital Sky Survey, our analytic approach will allow us to measure accurately the strength of the intrinsic galaxy alignment, which plays the role of statistical error in weak lensing searches and can be used as a fossil record to reconstruct cosmology.