Kinematics of the local universe - IX. The Perseus-Pisces supercluster and the Tolman-Bondi model

The matter distribution around the Perseus-Pisces (PP) supercluster is studied by comparing peculiar velocities given by the Kinematics of the local universe (KLUN) galaxy sample to those predicted by Tolman-Bondi (TB) models. To restrict the TB solutions we first solve the mass of the densest part of PP. This part is identified as a sphere at (l; b) = (140.2 degrees, -22.0 degrees), d approximate to 50 h(-1) Mpc having a radius of 15 h(-1) Mpc. This sphere surrounds the main part of the PP ridge and four most prominent clusters of the region. Using virial-like mass estimators we calculate the cluster masses and obtain the upper and lower limits for the mass inside the 15 h(-1) Mpc sphere: M-PP = 4-7 h(-1) 10(15) M-.. This corresponds to a mass overdensity delta (PP) approximate to 4, or rho (PP) = 1 - 2 rho (cr). Mass to light ratios of the clusters are M/L = 200 - 600 h M-./L-., giving mass density ratio Omega (0) = 0.1 - 0.3, if the value of M/L is assumed to be representative elsewhere in the universe. We estimate a radial density distribution around the PP core using two toy models and a smoothed density distribution observed for IRAS galaxies. The cosmological density parameters (Omega (0), Omega (Lambda)) and the PP mass are free parameters in the TB calculations. The KLUN velocities, obtained by Tully-Fisher relation and the normalized distance method, are adjusted by the Local Group (LG) infall velocity towards PP. Comparison of the TB velocities to KLUN data points indicates that the infall velocity v(inf) < 100 km s(-1). Allowing MPP to vary within the limits given above we get constraints for the value of <Omega>(0); Omega (0) = 0.2-0.4 are prefered to the more extreme values, Omega (0) = 0.1 or 1. A choice of either Omega (Lambda) = 1 - Omega (0) or 0 do not cause any significant changes in the results. The validity of the TB model in complex environments is studied with an N-body simulation. There we see that the radially averaged velocity fields around simulated clusters are compatible with the corresponding TB velocities. This confirms the applicability of the TB model around large galaxy concentrations, providing that smoothed density and radially averaged velocity fields are used.