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 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)

b = 2x - 1

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 t_o = 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

   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 = 2^4.6/14.05*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.

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/L^0.7. 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

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 t_o > 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.

© 1997-2005 Edward L. Wright.

How Old is the Universe?

Until recently, astronomers estimated that the Big Bang occurred between 12 and 14 billion years ago. To put this in perspective, the Solar System is thought to be 4.5 billion years old and humans have existed as a species for a few million years. Astronomers estimate the age of the universe in two ways: 1) by looking for the oldest stars; and 2) by measuring the rate of expansion of the universe and extrapolating back to the Big Bang; just as crime detectives can trace the origin of a bullet from the holes in a wall. Older Than the Oldest Stars? Astronomers can place a lower limit to the age of the universe by studying globular clusters. Globular clusters are a dense collection of roughly a million stars. Stellar densities near the center of the globular cluster are enormous. If we lived near the center of one, there would be several hundred thousand stars closer to us than Proxima Centauri, the star nearest to the Sun. Text Link to the HST press release describing this image The life cycle of a star depends upon its mass. High mass stars are much brighter than low mass stars, thus they rapidly burn through their supply of hydrogen fuel. A star like the Sun has enough fuel in its core to burn at its current brightness for approximately 9 billion years. A star that is twice as massive as the Sun will burn through its fuel supply in only 800 million years. A 10 solar mass star, a star that is 10 times more massive than the Sun, burns nearly a thousand times brighter and has only a 20 million year fuel supply. Conversely, a star that is half as massive as the Sun burns slowly enough for its fuel to last more than 20 billion years. All of the stars in a globular cluster formed at roughly the same time, thus they can serve as cosmic clocks. If a globular cluster is more than 20 million years old, then all of its hydrogen burning stars will be less massive than 10 solar masses. This implies that no individual hydrogen burning star will be more than 1000 times brighter than the Sun. If a globular cluster is more than 2 billion years old, then there will be no hydrogen-burning star more massive than 2 solar masses. The oldest globular clusters contain only stars less massive than 0.7 solar masses. These low mass stars are much dimmer than the Sun. This observation suggests that the oldest globular clusters are between 11 and 18 billion years old. The uncertainty in this estimate is due to the difficulty in determining the exact distance to a globular cluster (hence, an uncertainty in the brightness (and mass) of the stars in the cluster). Another source of uncertainty in this estimate lies in our ignorance of some of the finer details of stellar evolution. Presumably, the universe itself is at least as old as the oldest globular clusters that reside in it. Extrapolating Back to the Big Bang An alternative approach to estimating is the age of the universe is to measure the “Hubble constant”. The Hubble constant is a measure of the current expansion rate of the universe. Cosmologists use this measurement to extrapolate back to the Big Bang. This extrapolation depends on the history of the expansion rate which in turn depends on the current density of the universe and on the composition of the universe. If the universe is flat and composed mostly of matter, then the age of the universe is 2/(3 Ho) where Ho is the value of the Hubble constant. If the universe has a very low density of matter, then its extrapolated age is larger: 1/Ho If the universe contains a form of matter similar to the cosmological constant, then the inferred age can be even larger. Many astronomers are working hard to measure the Hubble constant using a variety of different techniques. Until recently, the best estimates ranged from 65 km/sec/Megaparsec to 80 km/sec/Megaparsec, with the best value being about 72 km/sec/Megaparsec. In more familiar units, astronomers believe that 1/Ho is between 12 and 14 billion years. An Age Crisis? If we compare the two age determinations, there is a potential crisis. If the universe is flat, and dominated by ordinary or dark matter, the age of the universe as inferred from the Hubble constant would be about 9 billion years. The age of the universe would be shorter than the age of oldest stars. This contradiction implies that either 1) our measurement of the Hubble constant is incorrect, 2) the Big Bang theory is incorrect or 3) that we need a form of matter like a cosmological constant that implies an older age for a given observed expansion rate. Some astronomers believe that this crisis will pass as soon as measurements improve. If the astronomers who have measured the smaller values of the Hubble constant are correct, and if the smaller estimates of globular cluster ages are also correct, then all is well for the Big Bang theory, even without a cosmological constant. WMAP Can Measure the Age of the Universe Measurements by the WMAP satellite can help resolve this crisis. If current ideas about the origin of large-scale structure are correct, then the detailed structure of the cosmic microwave background fluctuations will depend on the current density of the universe, the composition of the universe and its expansion rate. WMAP has been able to determine these parameters with an accuracy of better than 5%. Thus, we can estimate the expansion age of the universe to better than 5%. When we combine the WMAP data with complimentary observations from other CMB experiments (ACBAR and CBI), we are able to determine an age for the universe closer to an accuracy of 1%. The expansion age measured by WMAP is larger than the oldest globular clusters, so the Big Bang theory has passed an important test. If the expansion age measured by WMAP had been smaller than the oldest globular clusters, then there would have been something fundamentally wrong about either the Big Bang theory or the theory of stellar evolution. Either way, astronomers would have needed to rethink many of their cherished ideas. But our current estimate of age fits well with what we know from other kinds of measurements: the Universe is about 13.7 billion years old!