So far, we have seen how do we measure the spacial scale of the universe, which
is simply one over a Hubble constant. What about its temporal scale? What's the
age of the universe? It turns out that we actually can't measure the age of the
universe directly. However, what we can do is measure lower
limits to the ages of all these things we can find.
And, then presumably the age of the universe is just a little more than that.
Several different possibilities exist. The first one.
Is the globular star clusters, These are believed to be formed over very short
time interval in the early universe and all stars in them have essentially the
same age. Understanding the ages of star clusters
or stellar populations is the basic fundamental thing in stellar evolution
theory. So in principle we understand how the
changes, by looking at their color magnitude.
The second kind of thing that we can look at are white dwarfs.
Again, these are inert, incandescent cores of low-mass stars that are now
slowly cooling down. The cooling theory is fairly well
understood, and by observing apparent luminosity function of white dwarf stars,
you can estimate how old the, how old are the oldest ones.
Another thing we can do, is estimate the age of the heavy elements, created in
stars. Very high mass, elements, will tend to be
radioactively unstable. And, if we can find long lived isotopes,
of some of those elements, and measure their alter abundances, we can estimate
the age of those elements, which presumably came from supernova
explosions. Some of the very first stars.
This is very similar to the carbon dating that's often used on planet Earth.
That is somewhat model-dependent, because it depends on when the Supernova were
exploding, but the upper limit of that would, again give the lower limit, the
age of the universe. And finally, we could model Stellar
populations, in a similar way that we model, star clusters.
But that turns out to be much complicated, and, it's really not used to
constrain the age the universe. The fundamental measurement here, is
estimating the ages of globular clusters, which are almost as old, as our galaxy
itself. This is based on a well established and
well tested theory of stellar evolution, which predicts so called Isograms which
is color magnitude diagrams and the paths that, main sequence and the giant branch
will have, at any given time. They look like this, the main sequence
turn-off, moves to ever lower masses. Lower luminosity as time goes on, and
then stars ascend the giant branch. So, by measuring where the main sequence
turnoff is, and where the giant branch is, we can fit the models and find out
how old the cluster is. Likewise, the difference between the
turnoff, and the position of the horizontal branch is another age
indicator. The isograms will depend slightly, on the
chemical composition of stars in the cluster.
So there are many uncertainties, in those estimates but the biggest one of them
all, is the uncertainty in the distance to the globular clusters.
Stellar evolution models are pretty good but in detail, there's still some minor
uncertainties that need to be resolved. The exact effects of the different
abundances of chemical elements and diffusion from stellar course in which
they are made towards the surface and so on.
Those also contribute to the uncertainty and the estimate of ages of globular
clusters. Nevertheless,
measuring ages of globular clusters was probably one of the more reliable
cosmological measurements for many years, certainly more so than any other
cosmological parameters until the 1990s. The key point here was to calibrate
exactly where the main sequences are, and this became possible only after Hipparcos
satellite measured the actual paraloxes and distances to some metal core stars
which defined the metal core main sequence that can be then applied to
globular star clusters. Different groups have done that and
typically the results they get, are the ages of globular clusters, on the order
of 12 to 13 billion years. Which is very close to what we now know
is the actual age of the universe of about 13.7 billion years.
Here is a probability distribution of globular cluster ages that take into
account all of the sources of uncertainty and so on.
Clusters could have different ages and probably do so that will contribute to
the spread as well. So the peak of this distribution is
indeed where it should be. A little more than 13 giga years ago
which allowed for a few hundred million years for galaxy and clusters to form.
Of course there are no clusters older than the universe itself.
The fact that the distribution has a high end tail is simply indicative of the
errors in age estimates. The next method is estimating the ages of
white dwarfs. They are fairly well understood, and they
are cooling a very orderly fashion. So the faintest white dwarfs that we can
find are probably the coolest, the ones that had been cooling for the longest
period of time, and they can constrain the age of the cluster, or galactic disk,
in which they are found. Again, theories fairly well understood.
In over-all sense, but there's still details that need to be ironed out.
Probably the best way to do this is in star clusters, where again, we know the
population of white dwarfs all have the same age.
And because they're really faint, and clusters are crowded, we need Hubble
Space Telescope to do this. Here is an example of the first
measurement of this kind in the upper right you see a little segment called the
main sequence. In the center is the white dwarf cooling
sequence, and you can see it stops at some point.
Those are the oldest and the coolest white dwarfs in the cluster and their
position determines the edge. So this method produced results which are
perfectly consistent with those from. Main sequence, isochrome feeding, and
that's, very different physics, so it's very encouraged.
Here is the observed luminosity function, of y dwarfs, in this particular cluster.
Meaning, their distribution of the luminosity's.
You can see that there is a, fairly sharp cutoff, at the faint end, which is,
indicative, what the h really is. An entirely different approach, uses ages
of chemical elements. Heavy chemical elements that must have
been produced in super nova explosions of say per supernovae often have unstable
isotopes. And their radioactive decay can be used
to age data the elements themselves. Because the age of the universe is about
13 billion years. You need radioactive decays that are
commensurate with it. Again, measured in billion, billions of
years. There are such isotopes like thorium and
uranium, there is also ranium and osmium, and a few others.
And so you need, something that has a radioactive half-life, decay time of life
time. But that, unfortunately, also means that
it will be really hard to measure, in the laboratory, what the half-life decay time
is. So doing this for variety of different
isotopes then provides the estimate of the age of the oldest, supernova
explosions, all this chemical elements in our galaxy.
The abundances of these elements are done by very high resolution, high signal to
noise spectroscopy of all the stars we can find.
The [INAUDIBLE] are very subtle and that measurements are very hard.
Nevertheless, they've been done over the years and results are shown.
So for one particular star shown here. There are ratios of several isotopes that
are being used to estimate the age of the elements that made a star.
And the average of it is remarkably close to what we now know is the actual age of
the universe. And it's also essentially the same as the
age as measured for globular clusters and for white dwarfs.
This is just 1 star, doing it for many stars improves the result.
And so, to recap. We have, now, a fairly good idea of what
the age of the universe it. Or at least the lower limit to it.
Using several completely different methods.
Which rely on different physics, different assumption, and different
measurements. And they all agree.
It's because of that we think we got it right.
Moreover this is also in perfect agreement with age of the universe
deduced from measurement of other cosmological parameters to which we'll
come later. Next time we will address the question
of, is the universe actually expanding? You think we would have probably figured
this one out by now, but it's good to be sure.