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_Is the Universe Younger than its Oldest Stars?_
_Revised September 20, 1999_
_________________________________________________________________

_Introduction_

Theories in modern cosmology center around the primary interpretation
of cosmological redshift as an indication that the universe is
expanding. If it is expanding outward, then it stands to reason that
it must have started expanding at some point (just run your imaginary
clock backwards), and leads to the notion now widely known as the _big
bang_, the idea that all of the universe we know was born from a
unique event at some time in the past. Classical general relativity is
singular at that event (which means that the natal event cannot be
described either mathematically or physically within the bounds of
classical general relativity).

Current research is trying to combine the very successful ideas of
quantum mechanics with the very successful ideas of general
relativity. But just because these ideas are very successful
independently does not mean that combining them is easy, and the
effort is a long way from finished; for now we are stuck with an
inscrutable _big bang_, followed by an expanding universe.

While the natal event may be beyond our reach, the universe becomes
accessible to our understanding immediately thereafter. We can reach
back through time as close as one Planck time (5.3906×10-44 seconds)
after the _bang_. That being the case, there should be a purely
cosmological way to figure out how old the universe is, or how long it
has been since that inscrutable natal event.

_Introduction to H0_

The Hubble constant (H0) is a measure of the expansion rate of the
universe, commonly given in units of kilometers per second per
megaparsec (km/sec/Mpc or km s-1 Mpc-1). Km/sec is a unit of velocity,
and Mpc is a unit of distance (one parsec = 3.26 light years, so 1 Mpc
= 3.26 million light years, and 1 light year is 9.4606x1015 meters or
5.8787x1012 miles). So H0 measures the expansion velocity of the
universe (km/sec) as a function of the distance (Mpc) from the
observer. Suppose that the value of H0 is 70 km/sec/Mpc. At a distance
of one Mpc, we should see an expansion velocity of 70 km/sec (and the
concordant spectral redshift). At two Mpc we should see a velocity of
140 km/sec. At 3½ Mpc we should see a velocity of 245 km/sec, and so
forth. The larger the distance, the greater the expansion velocity.

Galaxies & galaxy clusters are subject to two kinds of motion, the
cosmological expansion (commonly called the _Hubble Flow_), and local
_turbulent_ motions induced by the gravitational attraction of
surrounding matter. Since the age of the universe is tied to its rate
of expansion, we need to be able to separate those two components of
motion, and consider only the Hubble flow. Since the cosmological
expansion velocity increases with distance, then it stands to reason
that we want to look out as far as we can.

_Cosmology and the Age of the Universe_

If the universe had no mass in it at all, and was therefore totally
_open_, the age of the expanding universe would be expressed as
follows, in terms of the Hubble Constant (H0):

age = 1 / [ H0 x 1.023x10-12 ]

where "age" is the age of the universe in years, and H0 is the Hubble
constant in the usual units of km/sec/Mpc. The scale factor 1.023 x
10-12 is the product of 3.242 x 10-20 (Mpc/km) times 3.154 x 10+7
(sec/year), which is the unit conversion needed to make the age come
out in years.

But of course, we know that the universe is not massless and therefore
fully open because we are in the universe, and we have mass, and so do
the stars and galaxies that we see. So that equation really represents
a limit to the age of the universe. For a given value of H0 we know
that, at least according to standard theory, the universe cannot be
older than the value obtained by that equation.

If the average mass density of the universe is exactly equal to the
_critical density_, then the universe is on average geometrically
flat, and will expand forever. But it will slow its expansion
asymptotically, because of the constant pull of gravity between the
galaxies as they expand, stopping after an infinite time. So in
practice, under such conditions, the universe will expand forever,
slowing all the while. If that is the case, then the age of the
universe is just 2/3 of the age from the equation given above.
Observation indicates that in fact, the average mass density of the
universe is about 20% of the _critical density_, quite a bit short of
the mass density required to get the universe from its massless 1/H0
age to the critical mass age of 2/3 x 1/H0 (that 20% includes all of
the _dark matter_ that we can detect through its gravitational
interactions).

And so we are led to the conclusion that the true age of the universe
lies somewhere between 1/H0 and 2/3 x 1/H0. But H0 is a measurable
quantity, so if we can make some observations that tell us what H0 is,
then we can derive from that an age of the universe. Note that this
age is derived from purely cosmological considerations and does not
involve any reckoning of what stars & galaxies are made of, or how
they are constructed, beyond the fact that they exert gravitational
forces on each other.

_The First HST Value of H0_

Flashback to 1994 when this paper hit the stands:
_________________________________________________________________

_Distance to the Virgo Cluster Galaxy M100 from Hubble Space
Telescope Observations of Cepheids_
by W.L. Freedman _et al._

Nature 371(6500): pp757-762 (1994 October 27)

_Abstract_
Accurate distances to galaxies are critical for determining the
present expansion rate of the Universe or Hubble constant (H0). An
important step in resolving the current uncertainty in H0 is the
measurement of the distance to the Virgo cluster of galaxies. New
observations using the Hubble Space Telescope yield a distance of
17.1±1.8 Mpc to the Virgo cluster galaxy M100. This distance leads
to a value of H0 = 80±17 km s-1 Mpc-1. A comparable value of H0 is
also derived from the Coma cluster using independent estimates of
its distance ratio relative to the Virgo cluster.
_________________________________________________________________

This was the first paper published by the [1]Hubble Space Telescope
Key Project on the Extragalactic Distance Scale; an ambitious effort
to determine the value of the Hubble Constant to within an uncertainty
of ±10%, this project was one of the driving forces behind the desire
to put the [2]Hubble Space Telescope in orbit in the first place.
Coming at a time when just about everybody was happy with a value for
H0 around 65 km/sec/Mpc, 80 was a real eye-opener. If you go back to
the equation and look at what it means for the age of the universe, it
means somewhere between 10 billion and 15.5 billion for a massless
universe (the oldest allowed age range), or between 6.5 billion and 10
billion for a critical mass universe (the youngest allowed age range).
But astronomers at the time thought that the oldest globular clusters
we typically 15 billion years old, at the end of the age range
scratched by this report only for a massless universe. Hence the
appearance of an uncomfortable conflict: the oldest stars that we
could see in the universe seemed to be older even than the universe
itself, hardly a sound scientific idea. Something had to give.

_How Do We Know the Age of a Star?_

Figuring out the age of your favorite star is not so straightforward
in concept as figuring out the age of the universe. While measuring H0
is quite difficult, once you have it, the age of the universe comes
out in one little equation. But not so for stars.

The age of a star is derived through the process of _stellar
evolution_. If we create a mathematical & physical model of the
structure of a star, we quickly discover that stars are not static
objects. Indeed, they can't be static objects. Stars derive their
energy by nuclear fusion (a process we copied to make hydrogen bombs).
The fusion, for instance, of hydrogen nuclei (single protons) into
heavier helium nuclei (2 protons & 2 neutrons) releases more energy
than it takes to get them to fuse in the first place (an _exothermic_
reaction). So if you have a great deal of hydorgen laying around, and
enough energy to get it all to fuse into helium, you can get back out
a lot more energy than you put in. This process of gaining energy via
nuclear fusion becomes less and less efficient as the nuclei get
heavier, until you reach iron. Once you get to iron, it doesn't work
anymore; after iron it takes more energy to make nuclei fuse than you
will get in return (so the reaction is called _endothermic_). The
total amount of nuclear fuel available decreases as the star uses it
up, and so does the distribution of available fuel spread out inside
the star. As those change, the internal temperature, pressure, and
other physical characteristics of the star change radically. This also
changes the visible characteristics at the surface of a star. So, in
general, one can look at a star and see where it is in the course of
its evolution. Note that here, the word _evolution_ refers to the
changes over time of a single star in its own lifetime, and not to the
characteristics of a population over many generations, as the word is
used in _biological evolution_ (where it is said that "individuals do
not evolve, populations do").

By the appropriate application of physics it is possible to follow the
changes in a star's internal structure & chemistry, as well as its
outward appearance, as it ages through its own lifetime. But all of
the details need to be attended to, this is one area where it's hard
to get away with simplifying approximations. Everything counts, and as
a result the computational effort is extraordinary. The advent of
faster and more powerful supercomputers has had a major effect on the
study of stellar evolution.

The easiest things to measure about a star are color, and brightness
as a function of color. The color and temperature are strongly
related, so knowing the color gives the temperature. It turns out that
if you measure the color and brightness of all the stars you can, and
then just plot them all, the result is extremely _non_-random. Stars
do not have just any old color and brightness. The two are distributed
together in a representation we call the _Hertzsprung-Russell
diagram_, or _HR diagram_ for short.

The HR diagram is purely observational. Computational stellar
evolution is the application of a great deal of fundamental physics to
track the myriad of internal properties of a star as it ages through
its own lifetime. The great success story of computational stellar
evolution is that it recreates the observational HR diagram in
exquisite detail, even reproducing what appear to be minor details in
the HR diagram. It is one of the great success stories of modern
science. One of the side effects is that we can compare stars as we
see them to stars as we compute them, and thereby derive the age of a
star from its location on an HR diagram.

That's an outline of how we know what the age of a star is. But note
that this age ignores the cosmological problems of redshift, and is
derived purely through fundamental physics. But on the observational
side, you need to know the _true_ brightness, not just the _apparent_
brightness, and to do that you need to know the true distance to a
star to convert from apparent (observed) brightness to true
brightness, which you would know if you were right next to the star;
distance makes it look dimmer.

There has been a great deal of progress in recent years in
understanding stellar evolution, and in particular the evolution of
_globular cluster stars_, which are amongst the oldest stars that we
know of. They are very far away, and so the distance is harder to
measure and true brightness harder to derive. The European Space
Agency's [3]Hipparcos Mission has used trigonometric parallax
measurements on an unprecendented scale to measure the distances to
over 1,000,000 "nearby" stars, and thereby calibrate the bottom steps
of the distance scale. One of the results was to reset the distance
scale for globular culsters, and thereby the true brightnesses, and
thereby the cluster ages. These results were finally reported in 1998.
_________________________________________________________________

_The Age of globular clusters in light of Hipparcos - Resolving the
age problem_
by B. Chaboyer, P. Demarque, P.J Kernan & L.M Krauss

Astrophysical Journal 494(1)Part 1: pp96-110 (1998 February 10)

We review five independent techniques that are used to set the
distance scale to globular clusters, including subdwarf
main-sequence fitting utilizing the recent Hipparcos parallax
catalog. These data together all indicate that globular clusters
are farther away than previously believed, implying a reduction in
age estimates. We now adopt a best-fit value M-epsilon (RR Lyrae
stars) = 0.39±0.08 (statistical) at [Fe/H] = - 1.9 with an
additional uniform systematic uncertainty of (+ 0.13)(- 0.18). This
new distance scale estimate is combined with a detailed numerical
Monte Carlo study (previously reported by Chaboyer et al.) designed
to assess the uncertainty associated with the theoretical age-
turnoff luminosity relationship in order to estimate both the
absolute age and uncertainty in age of the oldest globular
clusters.

Our best estimate for the mean age of the oldest globular clusters
is now 11.5±1.3 Gyr, with a one-sided 95 % confidence level lower
limit of 9.5 Gyr. This represents a systematic shift of over 2
sigma compared to our earlier estimate, owing completely to the new
distance scale - a shift which we emphasize results not only from
the Hipparcos data. This now provides a lower limit on the age of
the universe that is consistent with either an open universe or
with a flat matter-dominated universe (the latter requiring H0 less
than or equal to 67 km s-1 Mpc-1). Our new study also explicitly
quantifies how remaining uncertainties in the distance scale and
stellar evolution models translate into uncertainties in the
derived globular cluster ages. Simple formulae are provided that
can be used to update our age estimate as improved determinations
for various quantities become available. Formulae are also provided
that can be used to derive the age and its uncertainty for a
globular cluster, given the absolute magnitude of the turnoff or
the point on the subgiant branch 0.05 mag redder than the turnoff.
_________________________________________________________________

This is the most recent full study on the globular cluster age problem
published to date. As you can see from the comments in the abstract,
it's not just Hipparcos distances, but other effects have been updated
as well, such as the effect of metallicity on brightness
determinations (in the jargon of astronomers, anything heavier then
helium is by definition a "metal"). This study puts the ages of the
oldest globular clusters in the range 10.2 to 12.8 billion years.
Since the 1994 HST Key Project age would range roughly from 10 to 15
billion years for an empty universe, and we are at about 20% of the
_critical density_, it would already appear that the major conflict
has been dealt with by advances in "ordinary" astrophysics.

However, that 1994 paper does not represent the end of the HST Key
project effort. Rather, it was the first in a long series of papers
describing their research efforts. In the summer of 1999 the HST key
project announced that it had achieved its goal of determining the
value of H0 with a 10% or better uncertainty.

_The HST Key Project and the Age of the Universe_

In order to fully understand the impact of the HST Key Project on our
understanding of the age of the universe, we have to start with an all
too brief description of the _cosmic distance ladder_. For objects
that are relatively nearby, we can measure the distance directly using
trigonometric parallax. For objects slightly farther away, we use
cepheid class variable stars, which are known to exhibit a fixed
relationship between true brightness and period of variability; we
measure the period, and from that derive a brightness. By comparing
the true brightness to the apparent brightness, we derive the
distance. For objects still farther away, we derive distances from
assumptions based on the more nearby objects. So the chain of
assumptions gets longer the greater the distance gets. The result is
that large distances become more uncertain, and the chain of reasoning
gives rise to the _cosmic distance ladder_. The major impact of the
Hipparcos mission was that it provided the first systematic parallax
distances to a set of cepheid variable stars, thus tying together the
two distance scales at last.

In particular, there are relatively few galaxies that are close enough
for us to get the distance without reference to the redshift (so we
can use those distances to calibrate the relationship between distance
and redshift). Hubble solved the problem by using the [4]100 inch
Hooker telescope at the [5]Mt. Wilson Observatory (at that time the
largest telescope in the world) to observe Cepheid class variable
stars in a few nearby spiral galaxies, such as [6]M31 & [7]M33. A
considerable improvement in observing techniques, imaging, and
telescopes (the [8]Keck I & II telescopes are 4 times the aperature
and 16 times the collecting area of the 100 inch), has allowed modern
astronomers to stretch the cepheid distance scale farther out than
Hubble could. The larger the range of distance we have to compare with
redshift, the better. But a problem still remained.

The problem is that the redshift measure the motion of the galaxy away
from us, but that motion has two components. One of those components
is the expanding universe carrying the galaxy along for the ride. The
other component is local motion induced by the combined gravitational
tug of the galaxies surrounding the observed galaxies. To determine
the rate of expansion of the universe (expressed as H0) we want to
compare distance to the component induced by the expanding universe,
and we want to eliminate the local component. The local component
becomes smaller at greater distances, so if we can measure larger
cepheid distances, we can get a better sampling of the cosmological
expansion, and a better calibration of the relation between
cosmological expansion and distance. And that gives a better value for
H0, and therefore the age of the universe.

The idea behind the HST Key Project was to use the unprecedented
capability of the Hubble Space Telescope to observe and measure
cepheid variable stars in distant galaxies, observations not possible
from underneath the Earth's atmosphere. Five years, 18 galaxies, and
nearly 30 published papers later, the HST Key Project announced in the
summer of 1999 that it had met its goal. They reported H0 = 71±6
km/sec/Mpc. The result is not uncontroversial; the group led by
Sandage & Tammann continues to hold out for a smaller value of H0
(more like 60 km/sec/Mpc), and consequently an older universe.

_Interim Conclusion: The Age of the Universe_

_Fig 1: The Age of the Universe as a Function of the Hubble Constant_

In the discussion on cosmology and the age of the universe, I gave the
equation(s) for figuring out the age of the universe from cosmological
theory, given a measurement of the Hubble Constant. Figure 1 above
shows these two equations plotted on the field of age vs H0; a curve
for 1/H0 and another for 2/3 of that. Remember that the true age of
the universe lies along a curve that is somewhere between these two
curves. The horizontal bar traces out the range of H0 as determined by
the Key Project, 71±6 km/sec/Mpc. The two combine to form a region
bounded on the right & left by the two theoretical curves, and on the
top and bottom by the range of values for H0 as reported by the Key
Project. If the Key Project results are correct, then the true age of
the universe should lie on a curve roughly parallel to the ones on the
right & left, passing through that region.

The vertical bar on figure 1 marks out the range of ages reported for
the oldest globular clusters, as given by the Chaboyer _et al._ paper
cited above. Although their result is derived entirely from the
physics of stellar structure and evolution, with no input from
cosmological theory, the vertical bar cuts right through the prime
region selected by cosmologists as the place where the age of the
universe should be found. It is a tour-de-force triumph for
astrophysics & cosmology; two totally independent indicators for the
age of the universe give concordant results.

But I labeled my conclusions as "_interim_" for good reasons. In 1994
globular cluster stars were generally accepted as the oldest stars we
can see, but that is no longer the case. The last couple of years has
seen an attempt to derive the ages of old metal-poor galactic halo
stars (see for instance, "r-process abundances and chronometers in
metal-poor stars" by J.J. Cowan _et al._, Astrophysical Journal
521(1): 194-205, Part 1, August 10 1999). The few reported ages are in
the 15 billion year range; the cited paper by Cowan _et al._ gives
15.6±4.6 billion years, which covers the rather expansive range of
11.0 billion to 20.2 billion years. The range of ages allowed by the
HST Key Project results falls just short of 15 billion, but the
majority of the bottom half of the uncertainty range cited by Cowan
_et al._ falls within the Key Project range. So even if we include the
halo stars, there is still no major conflict between the cosmological
and astrophysical ages for the universe. And if the accepted value of
H0 should move downward (as Sandage & Tammann and others would have
it), the older halo stars are even easier to accomodate. But the
argument over H0 remains on the table.

_The Bottom Line_

The bottom line is that there is not now a conflict between the
astrophysically determined ages of the oldest stars, and the
cosmologically determined age of the universe. While there was one in
1994 it was predictably short lived. While it made good reading for
the popular press, astronomers were already busy trying to find the
right solution. The result was that the cosmological age moved up (as
H0 moved down), through the addition of more and better data, and the
astrophysical ages moved down, through the addition of more precise
techniques and more detailed models. In short, we learned more about
the problem, and exercised that knowledge to reach a new conclusion.
But I think it is safe to say that the universe is definitely not less
than 10 billion years old, and definitely not more than 20 billion
years old, if the expanding universe and big bang cosmology is
correct.
_________________________________________________________________

Some Key Project Research Papers from 1999

* [9]The Hubble Space Telescope Key Project on the Extragalactic
Distance Scale XXIV:
The Calibration of Tully-Fisher Relations and the Value of the
Hubble Constant
* [10]The HST Key Project on the Extragalactic Distance Scale XXV.
A Recalibration of Cepheid Distances to Type Ia Supernovae and the
Value of the Hubble Constant
* [11]The HST Key Project on the Extragalactic Distance Scale XXVI.
The Calibration of Population II Secondary Distance Indicators and
the Value of the Hubble Constant
* [12]The Extragalactic Distance Scale Key Project XXVII.
A Derivation of the Hubble Constant Using the Fundamental Plane
and Dn-Sigma Relations in Leo I, Virgo, and Fornax
* [13]The HST Key Project on the Extragalactic Distance Scale.
XXVIII.
Combining the Constraints on the Hubble Constant
* [14]The Hubble Constant from the HST Key Project on the
Extragalactic Distance Scale
* [15]The Hubble Constant and the Expansion Age of the Universe

Some Sandage & Tammann Research Papers from 1999

* [16]Cepheid Calibration of the Peak Brightness of SNe Ia --- IX.
SN 1989B in NGC 3627
* [17]The Distance of the Virgo Cluster

Web Sites of Interest

* "[18] How can the oldest stars in the Universe be older than the
Universe?", from the [19]frequently asked questions section of
UCLA professor Ned Wright's [20]cosmology tutorial.
* [21]The Hubble Space Telescope Key Project on the Extragalactic
Distance Scale
* [22]Space Telescope Science Institute
* [23]The Hipparcos Space Astrometry Mission
* [24]Introduction to Cosmology
* [25]Hertzsprung Russell Diagram & Stellar Evolution (by Tim
Thompson)
_________________________________________________________________

Back to [26]Tim Thompson's FAQ Page
Back to [27]Tim Thompson's Home Page
setstats 1

References

1. http://www.ipac.caltech.edu/H0kp/
2. http://marvel.stsci.edu/top.html
3. http://astro.estec.esa.nl/SA-general/Projects/Hipparcos/hipparcos.html
4. http://www.mtwilson.edu/Tour/100inch/
5. http://www.mtwilson.edu/
6. http://www.seds.org/messier/m/m031.html
7. http://www.seds.org/messier/m/m033.html
8. http://www2.keck.hawaii.edu:3636/realpublic/gen_info/gen_info.html
9. http://xxx.lanl.gov/abs/astro-ph/9909269
10. http://xxx.lanl.gov/abs/astro-ph/9908149
11. http://xxx.lanl.gov/abs/astro-ph/9908192
12. http://xxx.lanl.gov/abs/astro-ph/9909222
13. http://xxx.lanl.gov/abs/astro-ph/9909260
14. http://xxx.lanl.gov/abs/astro-ph/9909134
15. http://xxx.lanl.gov/abs/astro-ph/9909076
16. http://xxx.lanl.gov/abs/astro-ph/9904389
17. http://xxx.lanl.gov/abs/astro-ph/9904360
18. http://www.astro.ucla.edu/~wright/cosmology_faq.html#age
19. http://www.astro.ucla.edu/~wright/cosmology_faq.html
20. http://www.astro.ucla.edu/~wright/cosmolog.htm
21. http://www.ipac.caltech.edu/H0kp/
22. http://marvel.stsci.edu/top.html
23. http://astro.estec.esa.nl/SA-general/Projects/Hipparcos/hipparcos.html
24. http://map.gsfc.nasa.gov/html/web_site.html
25. file://localhost/www/sat/files/tim_thompson/hr.html
26. file://localhost/www/sat/files/tim_thompson/faqs.html
27. file://localhost/www/sat/files/tim_thompson/index.html