Friday, 5 February 2016

How Old is the Milky Way and how do we know that?

Blog Contents and who am I?

(this publication is somewhat more advanced 
than the usual outreach entry)
Please click on a slide to see its bigger image

In previous blogs, I had discussed the use of the radio-isotope dating method for determining the age of the Solar System (and hence of the age of the Earth) and also the age of the Oceanic Crust which established the theory of Plate Tectonics (Continental Drift) on a firm footing.  Radio-isotope dating has really helped geologists in their struggle to understand the history and structure of the earth. Radio-isotope Dating (RD) can also be used to provide an age of our galaxy, the Milky Way.  
The origin of the MW is closely related to the origin of the Universe which has a definite time of creation - the time of the big bang.  The age determined for the MW is similar to the currently accepted age of the Universe and it is generally accepted that formation of galaxies started within about 200 million years after the big bang.  MW is a large diffused structure in which stars are still being created.  Therefore, the age of the MW is best determined by finding the oldest stars and measuring their ages.
When we talk about ages that are billions of years old then it is natural to ask what type of clocks do we use to measure such vast spans of time and how reliable these measurements are.  In this blog, we shall have a critical look at this.
In the case of the Milky Way (MW), the situation is actually quite good. Ages measured by RD are complemented by several other methods that rely on completely different physics and are independent determinations.  Unfortunately, the history of determining an age for the MW is full of inconsistencies and confusion.  However, over the past 20 years or so, the situation has improved remarkably and good agreement is found among the results from different methods. I feel that a consensus value of 12.5 to 13.5 billion years for the age of the oldest stars in our galaxy has been obtained. 

First, let us learn briefly how the Milky Way looks.  It is a large spiral galaxy with a central bulge.  Our Sun is located in the Orion spiral arm about 25000 light years (ly) from the centre of the MW.
Outside the plane of the Milky Way there are globular clusters which contain some of the oldest stars - also called the halo stars.  Stars of all sizes were formed in a globular cluster at the same time and have evolved according to their formation mass.  Heaviest stars have the shortest life and their evolutionary path 
takes them to a supernova stage in a time scale that can be as short as a few million years. Smaller mass stars have much longer evolutionary time and can survive for much more than 20 billion years.     
It is thought that the Milky Way (MW) disk and the globular cluster (GC) stars were formed from a primordial gas cloud. The oldest globular clusters coalesced early on from small-scale density fluctuations in the cloud.  Subsequently the cloud collapsed settling into the disk that is the Milky Way Galaxy with the globular star clusters populating a roughly spherical halo in our galaxy.  This is demonstrated in the slide

Star formation in the Milky Way continues to this day and Open Clusters are regions where new stars are being born. When we talk about the age of the Milky Way, we refer to the oldest objects in it and that is why there is so much interest in determining the age of the old globular clusters to indicate the time when star formation started in the outer regions of the Milky Way. Primordial gas consisted mostly of hydrogen and helium.  Elements up to iron were synthesized in stars with the more massive stars creating elements heavier than iron during their supernova stage.  The oldest stars are deficient in elements heavier than helium (their metallicity is low) with the younger stars progressively increasing in metallicity as the gas clouds continue to acquire heavier elements from the demise of big stars (heavy stars have very short lives of tens of millions of years).

The next slide shows a 2016 study of the time of star formation in different regions of the disk of the Milky Way. Over 70000 red-giant ages are plotted to show that star formation started near the centre of the disk and spread to outer regions of the disk.
red giant
The youngest stars are blue; the oldest are red.
For a determination of the age of the globular clusters,  the faint small mass stars are the best candidates - they have the longest lives and have been shining since their formation with little or no disturbance.  Also during their formation stage, they had obtained elements, including radioactive actinides, that were synthesized in supernovae explosions of massive stars or other catastrophic astrophysical events like neutron star mergers.  More of this later.

Radio-Isotope Dating (RD)
Our Sun is a relatively small star and the Solar System was formed 4.56 Billion Years ago from the gravitational collapse of a low density cloud of matter - the Solar Nebula.  The Solar Nebula would have been enriched in elements synthesized in catastrophic events happening in the neighbourhood regions until the formation of the Sun (the Sun contains more than 99% of the original mass of the nebula) - at which point it became a closed system to further addition of more elements.  The planets, asteroids, meteorites also had their elemental composition frozen 4.56 By ago.  
In RD, the nuclides of interest are those which decay with a half life of the order of the age of the Milky Way - a few billion years (by).   From the slide, we notice that Th-232 (half-life =14 by) and U-238 (half-life = 4.47 by) are useful actinides for dating purposes.  
In a supernova explosion, these two nuclides are created by r-processes.  In a r-process, the neutron flux is very high and nuclides which are rich in neutrons (almost along the neutron drip-line)  are formed in a very short time.  The highest mass nuclide formed is Cf-254 which fissions spontaneously with such high probability that further neutron absorption does not have time to occur.

As soon as they are produced these neutron-rich nuclides start decaying at a rate determined by their half-lives (Half-life is the time for half of the amount of a nuclide to decay).    

First, we shall estimate the age of the MW in a very simple model assuming that  the nucleosynthesis of Th-232 and U-238 happened in one event only.  The production of actinides by r-processes can be calculated from nuclear physics and prevailing physical conditions at the time.  Truran  gives the r-process production ratio in a supernova event of Th-232/U-238 as 1.65+-0.20.  Both Th and U have been decaying since their formation and the present ratio is 3.6

This model would give the lower bound on the age of the galaxy as 9.6 billion years (see slides)

Nucleosynthesis in a single supernova is a very simple, zeroth order but instructive model.  There is lot of evidence that a uniform rate of nucleosysnthesis had happened over the galactic history. Using this more realistic approach Truran arrives at an age of the Milky Way equal to 12.8 +- 3 billion years.

A word of caution must be added here.  The theoretical model used to calculate the production ratio P(Th/U) in r-processes is not totally secure.  Production of neutron-rich nuclei in r-processes follows a path that is far removed from the valley of nuclear stability while the parameters of the nuclear model are fitted to measured properties, like fission probabilities, neutron capture and beta-decay rates,  of available nuclei.  Extrapolation of such nuclear theory parameters can be an uncertain process.  Nicolas Dauphas has used the Th/U ratio in meteorites and data from low-metallicity stars in the halo of the Milky Way to constrain the production ratio P(Th/U) and has obtained a value 1.75 (+ 0.005; - 0.01) and has calculated an age of the Milky Way of 14.5 (+2.8; -2.2) billion years.  This age is consistent with the currently accepted age of the Universe of 13.7 billion years. 

The uncertainty in the RD age is large and we now look to other methods which have been used to estimate an age of the Milky Way

Cooling Rates of White Dwarfs
A white dwarf is the core of a collapsed star. White dwarfs cool slowly and fade away over a time scale of 10 billion years or more. The Universe and the Milky Way (MW) are not old enough for many white dwarfs to have cooled off completely to become invisible black dwarfs. White dwarf temperatures can therefore be used as "cosmic clocks" for an independent estimation of the age of the Milky Way. Where do we find old white dwarfs?

Located 7,000 light-years away in the direction of the constellation Scorpius, M4 is the nearest globular cluster to the Earth. Globular clusters like M4 were born early in the history of the Milky Way. M4 is estimated to be about 13 billion years old and all of its stars that began with 80% or more of the Sun's mass have already evolved to become red giants, followed by a collapse to a white dwarf. (Our Sun will not become a white dwarf for another five billion years.)
M4 globular cluster might contain about 40,000 white dwarfs. Due to their small surface area, White dwarfs are extremely faint but in 1995, Hubble Space Telescope had already  detected more than 75 white dwarfs in a small area of M4.  

A white dwarf contains most of the original mass of a star, that has contracted to an extremely dense object about the size of the Earth.  A tea-spoon full of a white dwarf material would weigh more than a ton. 
The mechanical structure of a white dwarf is sustained by the pressure of degenerate electrons and they do not generate any energy by fusion reactions. This makes the physics of cooling of a white dwarf particularly straightforward.
Because of its small size, high density, and initially hot temperature, it takes more than 10 billion years for a white dwarf to radiate all of its residual heat into space. The science of white dwarf cooling is reasonably well understood and from the spectral profile and temperature, white dwarf age may be estimated. 
In 2004, Harvey Richer measured 600 white dwarfs in globular clusters and found that the oldest were 12.7 +- 0.7 billion years old. The stars which collapsed to form white dwarfs must have taken at least a few hundred million years to complete their life cycle.  This suggests that the age of the globular clusters would be in the region of 13 billion years.
It is interesting to extend this study to see if there is an age difference between the formation of globular clusters and the formation of the Milky Way Galactic Disk.  Brad Hensen and colleagues have found that  the limit of visibility of white dwarfs in M4 is about 10 times fainter than the local Galactic disk white dwarfs.  This demonstrates a significant age difference between the Galactic Disk (7.3 +- 1.5 billion years) and the halo globular cluster M4 (12.7 +- 0.7 billion years).

Main Sequence Turn-Off Stars in Globular Clusters

In the 2003 special issue on Globular Cluster, Krauss and Chaboyer describe how the ages of the oldest metal poor stars in the halo of our galaxy can yield a firm lower limit on the age of the galaxy; thus also for the Universe.

How stars evolve is very well understood and the physics of stellar evolution can confidently explain the life-cycle of stars of different initial masses - particularly the change of luminosity (total power radiated) and surface temperature as a function of time.  The most robust prediction of the stellar evolution model is the time for a star to exhaust the supply of hydrogen in its core, time on the main sequence, and advancing beyond to the turn-off point.  

Globular Clusters are collection of thousands of stars that were born at the same time and are almost at the same  distance from the observation point of the Earth.  This makes interpretation of the luminosity, temperature data of globular cluster stars more straight forward.

Krauss and Chaboyer find the best-fit age of the oldest globular clusters to be 12.6 billion years and give a 95% confidence level lower limit on their age  to be 10.4 billion years but an upper limit of 16 billion years.

By necessity of keeping this blog of reasonable length, I am deciding to conclude this very interesting subject.  There is a great deal of exciting stuff to learn here.  For example:

All methods give an upper bound of the age of the Milky Way that is larger than the age of the Universe.  Universe must have been created first and the numbers do look paradoxical in some ways.  This situation has persisted for about a 100 years.  At one stage in the early 20th Century, The Earth was being measured to be 10 times older than the then accepted age of the Universe.  What do we think of the present situation??
Even if MW is a few hundred million years younger than the Universe, our galaxy must have been one of the first ones to have formed.  Even some of the oldest halo stars observed have been found to contain actinides which can only be synthesized in a supernova type catastrophic astrophysical event and, therefore, are not the oldest stars. 
The age of the universe is dependent on the value of the Hubble constant - a value that has changed by a large factor over the past 100 years.  
The present situation appears much more settled but there are niggling questions and doubts whether we have finally understood the evolution of the galaxies and stars properly.   

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