  We study the stacked filaments connecting group-mass halo pairs, using
dark-matter-only N-body simulations. We calculate the dark matter over-density
profile of these stacked filaments at different redshifts as a function of the
distance perpendicular to the filament axis. A four-parameter universal
functional form, including three comoving scale radii and one amplitude
parameter (core density), provides a good fit out to a radius of 20 cMpc/h for
stacked filaments over a range of redshifts, lengths and masses. The scale
radii are approximately independent of redshift but increase as power-laws with
the comoving filament length. Lastly, we compare the scaling of the filament
mass measured directly from the simulations to the predicted scaling from the
halo-halo-matter three-point correlation function as a function of redshift and
of the mass of the halo pairs. We find that both measured scalings are similar
to, but somewhat shallower than the predictions, by 10% and 30%, respectively.
These results provide a template to interpret present and upcoming
observational results based on stacking, for example, weak lensing, thermal and
kinetic Sunyaev-Zel'dovich, or X-ray observations.
