Predicting the peculiar velocities of nearby PSC-z galaxies using the Least Action Principle

Abstract

We use the Least Action Principle to predict the peculiar velocities of PSC-z galaxies inside $cz=2000$\km. Linear theory is used to account for tidal effects to $cz=15000$\km, and we iterate galaxy positions to account for redshift distortions. As the Least Action Principle is valid beyond Linear theory, we can predict reliable peculiar velocities even for very nearby galaxies (ie $cz \leq 500$\km). These predicted peculiar velocities are then compared with the observed velocities of 12 galaxies with Cepheid distances. The combination of the PSC-z galaxy survey (with its large sky coverage and uniform selection), with the accurate Cepheid distances, makes this comparison relatively free from systematic effects. We find that galaxies are good tracers of the mass, even at small ($\leq 10$\mpc) scales; and under the assumption of no biasing, $0.25 \leq β\leq 0.75$ (at 90% confidence). We use the reliable predicted peculiar velocities to estimate the Hubble constant \ho from the local volume without ``stepping up'' the distance ladder, finding a confidence range of 65-75\kmM (at 90% confidence).