Potent reconstruction from mark III velocities

We present an improved version of the POTENT method for reconstructing the cosmological velocity and mass density fields from radial peculiar velociti es, test it with mock catalogs, and apply it to the Mark III Catalog of Gal axy Peculiar Velocities. The method is improved in several ways: (1) the in homogeneous Malmquist bias is reduced by grouping and corrected statistical ly in either forward or inverse analyses of inferred distances, (2) the smo othing into a radial velocity held is optimized such that window and sampli ng biases are reduced, (3) the density field is derived from the velocity h eld using an improved weakly nonlinear approximation in Eulerian space, and (4) the computational errors are made negligible compared to the other err ors. The method is carefully tested and optimized using realistic mock cata logs based on an N-body simulation that mimics our cosmological neighborhoo d, and the remaining systematic and random errors are evaluated quantitativ ely. The Mark III catalog, with similar to 3300 grouped galaxies, allows a reliable reconstruction with fixed Gaussian smoothing of 10-12 h(-1) Mpc ou t to similar to 60 h(-1) Mpc and beyond in some directions. We present maps of the three-dimensional velocity and mass-density fields and the correspo nding errors. The typical systematic and random errors in the density fluct uations inside 40 h(-1) Mpc are +/-0.13 and +/-0.18 (for Omega = 1). In its gross features, the recovered mass distribution resembles the galaxy distr ibution in redshift surveys and the mass distribution in a similar POTENT a nalysis of a complementary velocity catalog (SFI), including such features as the Great Attractor, Perseus-Pisces, and the large void in between. The reconstruction inside similar to 40 h(-1) Mpc is not affected much by a rev ised calibration of the distance indicators (VM2, tailored to match the vel ocities from the IRAS 1.2 Jy redshift survey). The volume-weighted bulk vel ocity within the sphere of radius 50 h(-1) Mpc about the Local Group is V-5 0 = 370 +/- 110 km s(-1) (including systematic errors) and is shown to be m ostly generated by external mass fluctuations. With the VM2 calibration, V- 50 is in a similar direction and reduced to 305 +/- 110 km s(-1).