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 sheet-like structures in the frame of the 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 spirals in the Local Super Cluster, and provide theoretical explanations about why and to what degree the nearby spirals are inclined relative to the supergalatic plane. Finally, we conclude that the observed large-scale coherence in the orientation of nearby spirals relative to the supergalactic plane can be quantitatively understood in terms of galaxy intrinsic alignment predicted by the tidal torque theory, and that the spins of luminous galaxies might be more strongly aligned with the surrounding matter than the underlying dark halos. If applied to large scale surveys like Sloan Digital Sky Survey (SDSS), our analytic approach will allow us to measure accurately the strength of galaxy intrinsic alignment which plays a role of statistical error in weak lensing searches and can be used as a fossil record to reconstruct cosmology. Subject headings: cosmology:theory — large-scale structure of universe