1.1. Peculiar Velocities versus H0
What it means to ``measure a galaxy's distance'' depends on whether one is interested in studying peculiar velocities or determining the value of the Hubble constant. A galaxy's peculiar velocity may be estimated given its ``distance'' in km s-1 - the part of its radial velocity due solely to the Hubble expansion. The same object provides an estimate of H0 only if one can measure its distance in metric units such as megaparsecs. What this means in practice is that accurate peculiar velocity studies may be carried out today, despite the fact that H0 remains undetermined at the ~ 20% level.
Another basic distinction between velocity analysis and the search for H0 concerns the distance regimes in which they are optimally conducted. Peculiar velocity surveys are best carried out in the ``nearby'' universe, where peculiar velocity errors are comparable to or less than the peculiar velocities themselves. The characteristic amplitude of the radial peculiar velocity, vp, is a few hundred km s-1 at all distances, whereas the errors we make in estimating vp grow linearly with distance (Section 3). It turns out that the ``break-even'' point occurs at distances of ~ 5000 km s-1. Although we may hope to glean some important information (such as bulk flow amplitudes) on larger scales, our ability to construct an accurate picture of the velocity field is restricted to the region within about 50h-1 Mpc. In the Hubble constant problem, by contrast, peculiar velocities are basically a nuisance. We would like them to be a small fraction of the expansion velocity, so that we incur as small as possible an error by neglecting them. This is best achieved by using comparatively distant objects, d 7000 km s-1, as tracers of the expansion.
On the other hand, to obtain the absolute distances needed to measure H0, we must first calibrate our distance indicators locally ( 2000 km s-1). This is because the distance indicators capable of reaching the ``far field'' ( 7000 km s-1) of the Hubble flow generally have no a priori absolute calibration (cf. Section 1.2). The only reliable distance indicator that can bridge the gap between the Milky Way and the handful of Local Group galaxies whose absolute distances are well-known, and galaxies beyond a few Mpc, is the Cepheid variable method (Section 2), which is limited to distances 2000 km s-1. As a result, Hubble constant measurement is inherently a two-step process: local calibration in galaxies with Cepheid distances, followed by distance measurements in the far field where the effect of peculiar velocities is small. The local calibration step is unnecessary in peculiar velocity studies.
Although peculiar velocity surveys and H0 measurement differ in the ways just discussed, the two problems are, ultimately, closely related. Many distance indicator methods have been and are being used for both purposes. Indeed, a distance indicator calibrated in km s-1 may be turned into a tool for measuring H0 simply by knowing the distances in Mpc to a few well-studied objects to which it has been applied. This Chapter will thus be organized not around the peculiar velocity-H0 distinction, but rather around methods of distance estimation.