Tuesday, June 12, 2007

193)So how old is the Universe anyway, 6000 years or 14 billion(14,000,000,000) years old?

The recent opening of the Creation Museum in Kentucky, U.S.A. represents the efforts by biblical creationists to promulgate a purely literal exposition of the Genesis passages in the Bible, where the Universe was created in 6 days and is only about 6000 years old:


As a result of the discovery in the late 19th and early 20th centuries of the phenomenon of radioactivity among many elements in Nature, along with other advances, it has been possible to accurately assess the age of many objects in the Universe. Because the radioactive decay of an element is such a precise mathematical process, the most accurate time clocks used in the world today are radioactive atomic time clocks.

Using the decay of radioactive elements as well as other independent techniques, the Universe has been determined to be approximately 14 billion years old, as this paper outlines:

Age of the Universe

There are at least 3 ways that the age of the Universe can be estimated:

1)The age of the chemical elements.
2)The age of the oldest star clusters
3)The age of the oldest white dwarf stars.

Metric note: 1 Gyr=1 Gigayear=1 billion years

The age of the Universe can also be estimated from a cosmological model based on the Hubble constant and the densities of matter and dark energy. This model-based age is currently 13.7 +/- 0.2 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.

1)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. The most definite ages that can be determined this way are ages since the solidification of rock samples. When a rock solidifies, the chemical elements often get separated into different crystalline grains in the rock. For example, sodium and calcium are both common elements, but their chemical behaviours are quite different, so one usually finds sodium and calcium in different grains in a differentiated 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 for more on radioactive dating.

When applied to rocks on the surface of the Earth, the oldest rocks are about 3.8 billion years old. When applied to meteorites, the oldest are 4.56 billion years old. This very well determined age is the age of the Solar System. See the talk.origins age of the Earth FAQ for more on the age of the solar system.

When applied to a mixed together and evolving system like the gas in the Milky Way, no great precision is possible. 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) 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 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, 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. refine the predicted U/Th production ratio and get 14.1 +/- 2.5 Gyr for the age of this star.

2)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 < onclick="return top.js.OpenExtLink(window,event,this)" href="http://xxx.lanl.gov/abs/astro-ph/9509115" target="_blank">Chaboyer, Demarque, Kernan and Krauss (1996, Science, 271, 957) apply this technique to globular clusters 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) 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. give ages between 8.5 and 13.3 Gyr with 12.1 being most likely, while Reid gives ages between 11 and 13 Gyr, and Chaboyer et al. give 11.5 +/- 1.3 Gyr for the mean age of the oldest globular clusters.

3)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. 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 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. have used the HST to measure the ages of white dwarfs in the globular cluster M4, obtaining 12.7 +/- 0.7 Gyr. In 2004 Hansen et al. 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.


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