From: phfrom@nyx.uni-konstanz.de (Hartmut Frommert)
Subject: Re: Age of the galaxy (was: stars & carbon)
Organization: Dept. of Physics, University of Constance
Date: Wed, 29 Jul 1992 08:55:17 GMT

DOCTORJ@SLACVM.SLAC.STANFORD.EDU (Jon J Thaler) writes:

>[..]  There are two competing
>models for the dark matter that is postulated to make up the bulk of the
>mass in the universe: "hot" and "cold" dark matter.  [..]
>It seems that if one were able to
>measure the age of galaxies and other objects, just as one can measure
>the ages of stars, this would provide evidence for one model or the other.

You canNOT measure the age of an individual star in an easy way but only
say that, e.g. a Red Giant of 1 solar mass is 13--14 GYs old, while a
main sequence star of 30 solar masses can't be older than a few million
years. What you CAN calculate, from stellar evolution theory, is the 
Hertzsprung-Russell (HR) diagram of a star *cluster*, you must give only
the initial chemical composition (and age): 

Assume that all stellar masses in the reasonable range (approx < 0.1 .. 30 
solar masses) are present in the cluster, calculate the position in the HRD, 
i.e. temperature and luminousity, for each mass at a given age. Proceed for 
a reasonable amount of time. Then compare with the measured color-magnitude 
diagram of the cluster under consideration. 

There are TWO essential points that allow this procedure:

1. On the Main Sequence, the massive stars are at the hot (blue) and luminous
   end (luminiousity ~ mass^(3..4)), the least massive on the cold (red) and
   faint.

2. At a certain age t_{ms}, depending on the stellar mass 
   (t_{ms} ~ mass^(2..3)) and the initial chemical composition, each star 
   will leave the mean sequence to become a Red Giant. This occurs when all 
   hydrogene in the center is burnt to Helium. Massive, i.e. blue and 
   luminous stars reach this point in shorter time than red, so that only
   the fainter and redder part of the main sequence is present in an older
   cluster. So you can calculate the age of the cluster from what is left
   from the main sequence.

A perhaps surprising fact turned out to be that at least most (if not all) 
globular clusters of our Galaxy have roughly the same age (13..15 GY).
This coincides with the age of some elliptical galaxies determined in the
same way.

As far as I know there are no other more accurate methods for calculating 
the age of a cosmic object (besides planetary nebulae/SN remnants..).

>So what I want to know is, can one measure, with a minimum of cosmological
>input, the ages of galaxies and other large objects?  Knowing the answer
>would be very interesting.

Quite true. But in standard cosmology all initial objects 
(1st generation stars, globular clusters, galaxies, and clusters of galaxies)
are rapidly formed in a rather short period of time (which is proven by the
fact that galaxies at high redshift (z=4) look the same as in our cosmic 
neighborhood) -- only few (1..3) GYs compared to the age of the universe
(> 13..15 GY). Note: z=4 implies that the universe had then 1/5 the size than
today, corresponding to an age of less than 10 percent it has now. All age
determinations are hardly that accurate (think of interstellar extinction,
e.g., which limits the color and magnitude determination accuracy).
--
 Hartmut Frommert, Physics, Univ of Constance, | + Whale killing is murder. +
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