The Search for Ho

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Cosmological Parameters:

• Ho --> more precision --> physical differences in stars/galaxies

• --> no real convergence for the last 20 years though most studies favor in the range 0.1--0.3

• --> A fashion statement these days but, there are data driven reasons to believe its non-zero

• What are the ages of Globular Clusters now that the solar neutrino problem may be resolved?

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Choices of Cosmological Models (Five Options):

1. The Sandage Model:
   • H = 50
   • The ages of globular clusters are T = 16+/- 1 Gyr
   • = 0.1
   • All Baryonic Universe

2. The de Vaucouleurs/Aaronson Model
   • H = 100
   • The ages of globular clusters are not well known but must be around 10 billion yars
   • The Universe has to be open
   • All the Mass is in Galaxies

3. The Overlapping Error Bar Model:
   • H = 75
   • The age of globular clusters is 12--15 years
   • is 0.1--1.0
   • There may or may not be lots of dark matter

4. The Inflationary Model:
   • H = 50
   • The ages of globular clusters are 12-13 Gyr
   • = 1.0000000000000
   • Dark Matter Dominated Universe

5. The 90's Data Driven Cosmology
   • H = 70--90
   • Globular Cluster Ages: 15--17 Gyr
   • --> 0.1 --0.3
   • Quasi-dark matter dominated
   • Inflation is satisified with non-zero
   The Distance Scale Ladder:

   

   The basic philosophy of the distance scale ladder is to use one distance measuring technique to calibrate another that can be used to larger distances. All systematic errors associated with each step are cumulative in the final result! This sucks but we are stuck with it.

   • The First Rung: Calibration of the lower main sequence from stellar parallax. This is fairly secure, and most recent HIPPARCHOS data confirms no systematic error in the position of the lower main sequence.

     The parallax horizon is about 25 pc (not very big). But this region does contain a representative sample of low mass stars.

   • The game is now the following: Suppose we can identify a kind of star that is a "standard candle" (constant and universal luminosity). If one of those stars existed in the parallax sample, we would be done, but it does not. So we need to determine a distance, by some technique, to one of these stars in order to calibrate its absolute luminosity. Here is the magic star
     

     Cepheids are pulsationally unstable and hence change their radius in a periodic manner. As the radius changes so does the luminosity of the star. The rate of change of the radius is correlated with the luminosty through some real physics!

   • To do this requires determining the distance to a cluster of stars that contains these objects. This is fraught with difficulty and even worse, no nearby cluster contains the kind of object we are looking for. But we have to begin somewhere and the two clusters which are used are the Pleides and Hyades clusters.

   There are two ways to determine the distances to these clusters:
   • Main Sequence Fitting --> find the position of the lower main sequence in some nearby cluster in apparent flux space. Using the calibrated sample of lower main sequence stars that are available from Trignometric parallax, one can determine at what distance the calibrated sample would have the same range of apparent fluxes as the lower main sequence in the nearby cluster.

     Hence the distance can be determined. In the case of the Hyades and Pleidaes clusters, they are young and still have thier upper main sequence stars as well. These stars are generally missing from the nearby parallax sample. Since the upper main sequence is significantly brighter than the lower main sequence, those stars can be detected in more distant clusters, where the lower main sequence stars are too faint to detect. It is these more distant clusters that contain Cepheids.

     Caveats:

     • The luminosity of upper main sequence stars is more strongly effected by variations in heavy element abundances than lower main sequence stars. Thus, clusters of different abundances than the Pleideas of Hyades might have systematic errors in distance.

     • In the conventional HR diagram, (B-V) vs V, the lower main sequence is quite vertical. Thus small errors in photometry or spectral type measures translate into significant errors in luminosity. This is why you need the whole lower main sequence represented and not just a few stars.

     • Nearby clusters of stars have large angular extents across the sky. The Pleideas for instance is about 2 degrees across. On this scale, the amount of foreground reddening between the observer and the individual stars is variable. Thus, one can't assume a constant reddening and reddening variations across the extent of the cluster become another source of error and are difficult to measure.

   • Moving Cluster Method.

     Hyades distance measurements

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