How is the Cepheid yardstick validated?
I assume the Cepheid yardstick is validated by parallax measurements, but parallax is only useful to measure distances to stars within a limited volume of space.
Actually, the Cepheid yardstick is generally validated by methods other than parallax measurements. Methods to determine distances in astronomy are numerous, and each has its strengths and weaknesses. For a complete and accurate treatment of the subject, I highly recommend reading chapter 7 of Binney and Merrifield's Galactic Astronomy (Princeton University Press).
Question 1: How many Cepheids (approximately) are available within this volume?
Parallax measurements are currently reliable out to about 200 parsecs, or 800 light-years from the Sun (note: this is going to change drastically in the next 10 years with new parallax satellites that are being launched. Parallaxes of objects 1000 times more distant will be measured). Within this 200 parsecs, there are at best a handful of cepheid variables. The nearest one, Delta Cephei, was the variable used to first calibrate the Cepheid Yardstick. This yardstick can be used to indicate distances out to the Virgo Cluster.
Question 2: Is there any other way to independently validate the Cepheid yardstick?
Fortunately for us, there are other ways to calibrate the Cepheid Yardstick; I'll only go over the most popular ones here.
Perhaps the most direct method of verifying it comes from proper motion measurements of water masers in nearby galaxies (for example, in the nearby spiral NGC4258). The masers are regions of intense emission from water molecules, most often found in very dense regions in galactic nuclei. If the masing "spots" are located in a rotating disk, then using very high angular resolution images (from the Very Long Baseline Array or VLBI) it is possible to measure their proper motion, or the speed with which they move across the sky. If you take the maximum radial velocity observed to be the true velocity of the masers, then from the proper motion measurements you can derive a distance. This method is very elegant, but you need to know the geometry of the masing regions for it to work: consequently, the only convincing distance measurement using this method is for NGC 5248.
Another way to calibrate the cepheid yardstick is to use "open clusters" of stars (in our own galaxy). Depending on the cluster's distance from the Sun, it will either be moving towards or away from us. In analogy to a stop sign increasing in angular size as you approach it on the road, the angular size of the cluster will increase or decrease as well; this, combined with the radial velocity of the cluster, can be used to estimate its distance. If there are cepheid variables in the clusters as well, then the distance using the open cluster method can be compared to that obtained from the Cepheid.
Finally, there are a host of other indirect methods to find distances in the same range as Cepheid variables: the luminosity functions of globular clusters and of planetary nebulae are thought to have a common standard deviation or spread, which can be used as a distance indicator; other variable stars such as novae or RR Lyrae stars may be used in a similar manner to Cepheids; A type of supernova called 1A is thought to have a "universal" peak brightness which may be used to estimate distance; the kinematics of spiral and elliptical galaxies (called the Tully-Fisher and Faber-Jackson relations, respectively) may be used, and the list goes on. It is generally a combination of all of these methods that is used to estimate the distances to galaxies and clusters.
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