One exception to the rule that Cepheids are necessary for tying local and more global distance
determinations is provided by the study of masers, the prototype of which is the maser system in the galaxy
NGC 4258 [23]. This galaxy has a shell of masers which are oriented almost edge-on [96, 50] and
apparently in Keplerian rotation. As well as allowing a measurement of the mass of the central black hole,
the velocity drift (acceleration) of the maser lines from individual maser features can also be measured. This
allows a measurement of absolute size of the maser shell, and hence the distance to the galaxy. This has
become steadily more accurate since the original work [54, 66, 3]. Macri et al. [92] also measure Cepheids
in this object to determine a Cepheid distance (see Figure 3
) and obtain consistency with the
maser distance provided that the LMC distance, to which the Cepheid scale is calibrated, is
48
2 kpc.
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Further discoveries and observations of masers could in principle establish a distance ladder without
heavy reliance on Cepheids. The Water Maser Cosmology Project
(http://www.cfa.harvard.edu/wmcp/index.html) is conducting monitoring and high-resolution imaging
of samples of extragalactic masers, with the eventual aim of a maser distance scale accurate to
3%.
Several other different methods have been proposed to bypass some of the early rungs of the distance scale
and provide direct measurements of distance to relatively nearby galaxies. Many of these are reviewed in the
article by Olling [105].
One of the most promising methods is the use of detached eclipsing binary stars to determine distances
directly [107]. In nearby binary stars, where the components can be resolved, the determination of
the angular separation, period and radial velocity amplitude immediately yields a distance
estimate. In more distant eclipsing binaries in other galaxies, the angular separation cannot
be measured directly. However, the light-curve shapes provide information about the orbital
period, the ratio of the radius of each star to the orbital separation, and the ratio of the stars’
luminosities. Radial velocity curves can then be used to derive the stellar radii directly. If we can
obtain a physical handle on the stellar surface brightness (e.g. by study of the spectral lines)
then this, together with knowledge of the stellar radius and of the observed flux received from
each star, gives a determination of distance. The DIRECT project [16] has used this method
to derive a distance of 964 54 kpc to M33, which is higher than standard distances of
800 – 850 kpc [46, 87]. It will be interesting to see whether this discrepancy continues after further
investigation.
A somewhat related method, but involving rotations of stars around the centre of a distant galaxy, is
the method of rotational parallax [117, 106, 105]. Here one observes both the proper motion
corresponding to circular rotation, and the radial velocity, of stars within the galaxy. Accurate
measurement of the proper motion is difficult and will require observations from future space
missions.
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