We begin by calibrating the mass-luminosity relation and the H-R diagram based on nearby stars having a reliable parallax. Then we can estimate the distance to Milky Way galactic and globular clusters by the method of cluster fitting. With a great effort the distance to the Magellanic Clouds, the Milky Way's companion galaxies, can be estimated with reasonable confidence. This effort enables the calibration of the period-luminosity relation that applies to Cepheids, W Virginis, and RR Lyrae (cluster) variables. This first calibration step is very important and is a current subject of intense research. Possible improvements include analysis of detached eclipsing binaries and interferometric determination of spectroscopic binary orbits.

[Galaxies are not distributed evenly throughout space but tend to clump in groups like our "poor" Local Group of Galaxies with three large members, our Milky Way, M31, M33, and almost 30 lesser members such as the LMC, SMC, NGC6822 spread over a megaparsec (Mpc). The Virgo cluster with some 3000 members is the nearest moderate cluster at a distance of 15Mpc and the nearest rich cluster is the Coma Cluster with tens of thousands of galaxies spread over 3Mpc at a distance of about 100Mpc. Galaxy clusters can be exploited just like star clusters.]

Cepheid variables have been found in the Virgo Cluster of galaxies at a distance of 15Mpc by the Hubble Space Telescope (HST) but the Cepheids in Coma are still out of reach. But with the galaxies within 15Mpc we can begin to apply "cluster methods" to extend our reach.
The Cepheid P/L relation is given by

Supernovae type Ia [imploding white dwarf stars in a mass exchange binary system] are the brightest reasonably well known standard candle at our disposal. Shining at absolute magnitude -19.5 these candles are easy to see in the Coma cluster (100Mpc is a distance modulus of 35 so at maximum light they would appear at magnitude 15.5). As with all luminosity distances these sources suffer uncertainties due to reddening but the real problem lies in their scarcity and of course the calibration of absolute magnitude at maximum brightness.

The Tully-Fisher technique relies on the observation that the luminosity of a spiral galaxy, more importantly the infra-red luminosity (so the effects of dust are minimized) is related to the total mass of the galaxy. We call this the mass to light ratio M/L. By measuring the rotation curve via the 21cm line and correcting for the tilt of the galaxy the mass and hence absolute infrared magnitude and hence distance modulus obtains. But Tully and fisher found the relation extended to simply the width of the 21cm line, an indication of the maximum rotational speed, much easier to observe than the rotation curve and it would seem just as or even more reliable! Certainly an excellent compliment to the SN Ia.

Planetary Nebulae are a relatively new addition. They are easy to pick out with an appropriate nebular filter (like 500.7 nm) since the light of the central star is mostly UV and the ejected shell fluoresces in discrete recombination lines. The trick here is that any large galaxy has quite a few planetaries and the number of planetaries above a given absolute magnitude seems to be the same for all galaxies. So if you plot N(m)DM vs. m on a (you better hope it is correct) graph of N(M)DM vs. M then the horizontal shift is just the distance modulus m-M. Almost the same as an H-R cluster diagram.

Surface Brightness Fluctuations over elliptical galaxies were shown by John Tonry to be strongly correlated with distance. The reason is that these fluctuations occur when the most luminous stars are resolved. The smoother the image the farther the galaxy. This works out to 100Mpc for earth based telescopes.

For the largest clusters of galaxies it seems safe to say that the brightest giant ellipticals shine at absolute magnitude -24(?) which if true makes them a pretty good candle.

Other less reliable candles include supernovae other than type Ia, luminous supergiants (unless you get the spectrum as well), novae (used to be considered reliable but killed by HST resolving Cepheids in Virgo).

The Expanding Universe (next up)