Age of the Universe
===================

There are at least 3 ways that the age of the Universe can be estimated. I will describe

*   The age of the chemical elements.
*   The age of the oldest star clusters.
*   The age of the oldest white dwarf stars.

The age of the Universe can also be estimated from a cosmological model based on the [Hubble constant](./glossary.html#H0) and the densities of matter and dark energy. This model-based age is currently 13.75 +/- 0.1 [Gyr](./glossary.html#Gyr). But this Web page will only deal with actual age measurements, not estimates from cosmological models. The actual age measurements are consistent with the model-based age which increases our confidence in the Big Bang model.

The Age of the Elements
-----------------------

The age of the chemical elements can be estimated using radioactive decay to determine how old a given mixture of atoms is. When a rock solidifies, the chemical elements often get separated into different crystalline grains in the rock. Rubidium and strontium are heavier elements that behave chemically much like sodium and calcium. Thus rubidium and strontium are usually found in different grains in a rock. But Rb-87 decays into Sr-87 with a half-life of 47 billion years. And there is another isotope of strontium, Sr-86, which is not produced by any rubidium decay. The isotope Sr-87 is called _radiogenic_, because it can be produced by radioactive decay, while Sr-86 is non-radiogenic. The Sr-86 is used to determine what fraction of the Sr-87 was produced by radioactive decay. This is done by plotting the Sr-87/Sr-86 ratio versus the Rb-87/Sr-86 ratio. When a rock is first formed, the different grains have a wide range of Rb-87/Sr-86 ratios, but the Sr-87/Sr-86 ratio is the same in all grains because the chemical processes leading to differentiated grains do not separate isotopes. After the rock has been solid for several billion years, a fraction of the Rb-87 will have decayed into Sr-87. Then the Sr-87/Sr-86 ratio will be larger in grains with a large Rb-87/Sr-86 ratio. Do a linear fit of

Sr-87/Sr-86 = a + b\*(Rb-87/Sr-86)

and then the slope term is given by

b = 2x - 1

with _x_ being the number of half-lives that the rock has been solid. See the talk.origins [isochrone FAQ](http://www.talkorigins.org/faqs/isochron-dating.html) for more on radioactive dating.

When applied to a mixed together and evolving system like the gas in the Milky Way, one problem is that there is no chemical separation into grains of different crystals, so the absolute values of the isotope ratios have to be used instead of the slopes of a linear fit. This requires that we know precisely how much of each isotope was originally present, so an accurate model for element production is needed. One isotope pair that has been used is rhenium and osmium: in particular Re-187 which decays into Os-187 with a half-life of 40 billion years. It looks like 15% of the original Re-187 has decayed, which leads to an age of 8-11 billion years. But this is just the mean formation age of the stuff in the Solar System, and no rhenium or osmium has been made for the last 4.56 billion years. Thus to use this age to determine the age of the Universe, a model of when the elements were made is needed. If all the elements were made in a burst soon after the Big Bang, then the age of the Universe would be to = 8-11 billion years. But if the elements are made continuously at a constant rate, then the mean age of stuff in the Solar System is

(to + tSS)/2 = 8-11 Gyr

which we can solve for the age of the Universe giving

   to = 11.5-17.5 Gyr

238U and 232Th are both radioactive with half-lives of 4.468 and 14.05 Gyrs, but the uranium is underabundant in the Solar System compared to the expected production ratio in supernovae. This is not surprising since the 238U has a shorter half-life, and the magnitude of the difference gives an estimate for the age of the Universe. [Dauphas (2005, Nature, 435, 1203)](http://www.nature.com/nature/journal/v435/n7046/full/nature03645.html) combines the Solar System 238U:232Th ratio with the ratio observed in very old, metal poor stars to solve simultaneous equations for both the production ratio and the age of the Universe, obtaining 14.5+2.8\-2.2 Gyr.

### Radioactive Dating of an Old Star

A very interesting paper by Cowan _et al._ (1997, ApJ, 480, 246) discusses the thorium abundance in an old halo star. Normally it is not possible to measure the abundance of radioactive isotopes in other stars because the lines are too weak. But in CS 22892-052 the thorium lines can be seen because the iron lines are very weak. The Th/Eu (Europium) ratio in this star is 0.219 compared to 0.369 in the Solar System now. Thorium decays with a half-life of 14.05 Gyr, so the Solar System formed with Th/Eu = 24.6/14.05\*0.369 = 0.463. If CS 22892-052 formed with the same Th/Eu ratio it is then 15.2 +/- 3.5 Gyr old. It is actually probably slightly older because some of the thorium that would have gone into the Solar System decayed before the Sun formed, and this correction depends on the nucleosynthesis history of the Milky Way. Nonetheless, this is still an interesting measure of the age of the oldest stars that is independent of the main-sequence lifetime method.

A [later paper](http://arXiv.org/abs/astro-ph/9808272) by Cowan _et al._ (1999, ApJ, 521, 194) gives 15.6 +/- 4.6 Gyr for the age based on two stars: CS 22892-052 and HD 115444.

A another star, [CS 31082-001,](http://www.eso.org/outreach/press-rel/pr-2001/pr-02-01.html) shows an age of 12.5 +/- 3 Gyr based on the decay of U-238 \[Cayrel, _et al._ 2001, Nature, 409, 691-692\]. [Wanajo _et al._](http://arxiv.org/abs/astro-ph/0206133) refine the predicted U/Th production ratio and get 14.1 +/- 2.5 Gyr for the age of this star.

The Age of the Oldest Star Clusters
-----------------------------------

When stars are burning hydrogen to helium in their cores, they fall on a single curve in the luminosity-temperature plot known as the H-R diagram after its inventors, Hertzsprung and Russell. This track is known as the main sequence, since most stars are found there. Since the luminosity of a star varies like M3 or M4, the lifetime of a star on the main sequence varies like t=const\*M/L=k/L0.7. Thus if you measure the luminosity of the most luminous star on the main sequence, you get an upper limit for the age of the cluster:

Age < k/L(MS\_max)0.7

This is an upper limit because the absence of stars brighter than the observed L(MS\_max) could be due to no stars being formed in the appropriate mass range. But for clusters with thousands of members, such a gap in the mass function is very unlikely, the age is equal to k/L(MS\_max)0.7. [Chaboyer, Demarque, Kernan and Krauss (1996, Science, 271, 957)](http://xxx.lanl.gov/abs/astro-ph/9509115) apply this technique to [globular clusters](http://antwrp.gsfc.nasa.gov/apod/ap951019.html) and find that the age of the Universe is greater than 12.07 Gyr with 95% confidence. They say the age is proportional to one over the luminosity of the RR Lyra stars which are used to determine the distances to globular clusters. [Chaboyer (1997)](http://xxx.lanl.gov/abs/astro-ph/9605099) gives a best estimate of 14.6 +/- 1.7 Gyr for the age of the globular clusters. But recent Hipparcos results show that the globular clusters are further away than previously thought, so their stars are more luminous. [Gratton _et al._](http://xxx.lanl.gov/abs/astro-ph/9704150) give ages between 8.5 and 13.3 Gyr with 12.1 being most likely, while [Reid](http://xxx.lanl.gov/abs/astro-ph/9704078) gives ages between 11 and 13 Gyr, and [Chaboyer _et al._](http://xxx.lanl.gov/abs/astro-ph/9706128) give 11.5 +/- 1.3 Gyr for the mean age of the oldest globular clusters.

The Age of the Oldest White Dwarfs
----------------------------------

A white dwarf star is an object that is about as heavy as the Sun but only the radius of the Earth. The average density of a white dwarf is a million times denser than water. White dwarf stars form in the centers of red giant stars, but are not visible until the envelope of the red giant is ejected into space. When this happens the ultraviolet radiation from the very hot stellar core ionizes the gas and produces a [planetary nebula](http://antwrp.gsfc.nasa.gov/apod/ap960117.html). The envelope of the star continues to move away from the central core, and eventually the planetary nebula fades to invisibility, leaving just the very hot core which is now a white dwarf. [White dwarf](http://antwrp.gsfc.nasa.gov/apod/ap950910.html) stars glow just from residual heat. The oldest white dwarfs will be the coldest and thus the faintest. By searching for faint white dwarfs, one can estimate the length of time the oldest white dwarfs have been cooling. Oswalt, Smith, Wood and Hintzen (1996, Nature, 382, 692) have done this and get an age of 9.5+1.1-0.8 Gyr for the disk of the Milky Way. They estimate an age of the Universe which is at least 2 Gyr older than the disk, so _to > 11.5 Gyr_.

[Hansen et al.](http://arxiv.org/abs/astro-ph/0205087) have used the HST to measure the [ages of white dwarfs](http://oposite.stsci.edu/pubinfo/pr/2002/10/) in the globular cluster M4, obtaining 12.7 +/- 0.7 Gyr. In 2004 [Hansen et al.](http://arxiv.org/abs/astro-ph/0401443) updated their analysis to give an age for M4 of 12.1 +/- 0.9 Gyr, which is very consistent with the age of globular clusters from the main sequence turnoff. Allowing allowing for the time between the Big Bang and the formation of globular clusters (and its uncertainty) implies an age for the Universe of 12.8 +/- 1.1 Gyr.

Summary
-------

Method	Value [Gyr]	+Errorbar	-Errorbar
Elements	14.5	+2.8	-2.5
Old Stars	14.4	+2.2	-2.2
GC MSTO	     12.2	+1.3	-1.3
GC WDs	        12.8	+1.1	-1.1
Weighted Mean	12.94	+0.75	-0.75

[Edward L. Wright](./b4u-write.html). Last modified 27 Dec 2012
spam fails_task lang_mismatch pii not_appropriate hate_speech sexual_content quality toxicity humor helpfulness creativity violence