Weak Gravitational Lensing of Intercluster Filaments: Shear Amplitudes, Critical Surface Densities and Segment Masses

Weak gravitational lensing is the only filament probe that weighs total mass directly, dark and baryonic alike. This paper computes the lensing budget for a stated stacked detection: an excess surface density of 1.0 solar mass per square parsec at a projected radius of one megaparsec around the filament axis, for lenses at redshift 0.4 and sources at redshift 1.0. The critical surface density for that geometry is 2.75e+03 solar masses per square parsec, so the tangential shear at one megaparsec is 0.0003641 — a distortion of a few parts in ten thousand, far below any single-filament measurement and accessible only by stacking thousands of systems. Integrating the stated profile, falling as inverse radius between 0.3 and 2 megaparsecs, over a ten-megaparsec segment gives a segment mass of 1.07e+14 solar masses and a line mass of 1.07e+13 solar masses per megaparsec, of which the cosmic baryon share is 1.67e+12. The angular diameter distances entering the geometry, 1.15e+03 megaparsecs to the lens and 1.7e+03 to the sources, are computed by numerical integration over the stated expansion history.