20. The ideal distance indicator

In an extragalactic context the requirements for an ideal distance indicator are indeed demanding:

1. High luminosity is a pre-requisite, given the enormous distances that must be bridged in passing out of the Milky Way, beyond the Local Group and eventually into regions of pure and undisturbed Hubble flow.

2. The ideal distance indicator (be it derived from a luminosity or a measure of size) needs to have the lowest possible intrinsic dispersion. Low-precision distance indicators all eventually run afoul of bias at large distances where only the largest and/or intrinsically brightest objects fall into limiting-case samples. Blindly calibrated against the mean these exceptional objects always end up underestimating distances, if not properly corrected for selection effects.

3. A secure empirical calibration requires that examples of the distance indicator be found locally so that detailed and repeated tests can be made at high signal-to-noise, before applications are made at the limits of detectability.

4. In order to anticipate problems, predict trends, and understand exceptions, a firm theoretical basis for the distance indicator is required. In the consideration of many distance indicators a theoretical understanding is all too often lacking.

5. Lacking a detailed theoretical understanding of the distance indicator, one might require that a demonstrable empirical proof that the luminosity (or size) being used is insensitive to (or at least can be easily corrected for) known effects. Age differences, chemical composition variations, population size, environment differences and, of course, interstellar reddening are just a few of the known outstanding variables that should be considered.

6. The ideal distance indicator should also be universally available. It should be found in spiral galaxies, ellipticals and irregulars, if clusters, groups and the field are to be equally sampled without bias. This universality constraint obviously weighs heavily against Population I distance indicators, because of the lack of any significant star formation in elliptical and S0 galaxies at the present time.

7. Singular events are to be avoided. The hope is to find a distance indicator that has more than an occasional or unpredictably fleeting presence in a galaxy, but rather that it is abundant and always found whenever and wherever it is needed. Follow-up observations or applying new technology is problematic for one-time, historical events. Supernovae of all types suffer from this problem.

8. Finally, the identification of the ideal distance indicator should be unambiguous. Two, three or more types and sub-types of the distance indicator, each having subtle differences in their properties inevitably require additional observations to resolve differences. Cepheids (Classical Population I versus Population II W Virginis stars) suffered from this flaw early in the history of their calibration; supernovae suffer from the (growing) diversity of types to this very day (compare the observations required, as the singular event is unfolding, to definitively distinguish between a supernova of SN Type II as opposed to a supernova of SN Type Ia [Branch-Normal], for example).