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Bright, pulsating yellow stars called Cepheids have long attracted the
attention of astro-nomers seeking the size and age of the Universe. Cepheids
are cosmic yardsticks: their pulsations reveal exactly how far away they
are. With the latest detectors, astronomers can make observations of Cepheids
which give the distances to nearby galaxies with unprecedented accuracy.
But these observations have also raised a troubling paradox: the Universe
appears to be younger than the oldest objects in it.

The discovery of Cepheids dates back two centuries. On the night of
10 September 1784, the English astronomer Edward Pigott noticed variations
in the brightness of Eta Aquilae, a star lying in the constellation Aquila.
A month later, Pigott’s friend, a 20-year-old deaf-mute named John Goodricke,
detected similar variations in Delta Cephei, in the constellation Cepheus.
Unlike Aquila, Cepheus was far enough north for Goodricke to observe it
all year long. He watched Delta Cephei month after month, observing the
regular rise and fall in its brightness. Astronomers have given the name
Cepheids to all stars whose brightness varies in this characteristic way.

Cepheids periodically swell up and shrink, causing the star’s temperature
to change. These pulsations produce the fluctuations in brightness that
caught the eyes of Pigott and Goodricke. The pattern of the variation is
distinctive. The brightness of a Cepheid rises rapidly to its maximum and
then falls slowly back to its minimum. Some Cepheids pulsate about once
a day, while others take several months. For most Cepheids, this pulsation
period is very stable: Eta Aquilae pulsates exactly once every 7.176779
days.

Cepheids’ great brightness and distinctive variation make them easy
to find. They are so bright that they can be picked out in galaxies other
than our own and are classed as yellow supergiants – stars with the same
colour and temperature as the Sun but which shine hundreds or thousands
of times as brightly. But Cepheids do not exist in all galaxies. A star
passes through the Cepheid stage only if it has several times the mass of
the Sun. These heavy stars die soon after they are born, so only a galaxy
that gives birth to new stars has Cepheids. The Milky Way teems with Cepheids
because it is a vigorous star creator.

MORE THAN A CURIOSITY

This is a boon for astronomers, for Cepheids are more than a curiosity:
they are also high-quality indicators of distance. Astronomers need distance
indicators to work out how fast the Universe is expanding and from this,
how old it is. To describe the rate of expansion of the Universe, astronomers
use a quantity called the Hubble constant, which is expressed in kilometres
per second per megaparsec. (One megaparsec is 3.26 million light years.)
Imagine two galaxies, one of them one megaparsec farther away from Earth
than the other. If the Hubble constant was 80, the more distant galaxy would
be moving away from us 80 kilometres per second faster than the nearer one.

In the same way, the Hubble constant gives the time that has elapsed
since the big bang. A rapidly expanding universe would have been able to
reach its present size faster than one that had been expanding more slowly;
so the faster our Universe expanded, and the higher the Hubble constant,
the younger the Universe must be. Most astronomers believe that the Hubble
constant lies between 50 and 100, but that hardly pins down the age of the
Universe: a universe with a Hubble constant of 50 would be twice as old
as one with a Hubble constant of 100.

To work out the Hubble constant, astronomers need to know how fast particular
galaxies are receding from us and how far away each of them is. Measuring
the rate at which a galaxy is moving away is easily done by determining
the red shifts of these galaxies. The difficult part is knowing how far
away a particular galaxy is, and this is where Cepheids come in.

In the early years of this century, Henrietta Leavitt, an astronomer
at Harvard University, was studying Cepheids in the Small Magellanic Cloud,
one of the 10 galaxies that orbit our own. Like the Milky Way, the Small
Magellanic Cloud gives birth to new stars and has plenty of Cepheids. In
1907, Leavitt reported that she had discovered a remarkable property of
Cepheids: bright ones have longer pulsation periods than faint ones. She
realised that because all Cepheids in the Small Magellanic Cloud are about
the same distance from us, the long-period Cepheids must be intrinsically
brighter than the short-period Cepheids. Knowing how far away the Small
Magellanic Cloud is would allow astronomers to deduce the intrinsic brightness
of a Cepheid with a given period. (The period of any Cepheid reveals its
intrinsic brightness.) From these reference points, they could then measure
the distance of Cepheids in other galaxies. The farther away an object of
a given intrinsic brightness is, the dimmer it will appear. So, by comparing
this with its apparent brightness as seen from Earth, the Cepheid’s distance
can be calculated.

Leavitt’s historic discovery transformed Cepheids from celestial curiosities
into treasured objects. There are several reasons why astronomers prefer
Cepheids to other cosmic yardsticks. The relation between a Cepheid’s period
and its intrinsic brightness is clearly defined, and rests on solid physics:
astronomers understand why big, bright Cepheids vary more slowly than small
faint ones. Cepheids are also stable. Some astronomers use exploding stars
or ‘supernovae’ as distance indicators. But supernovae are one-off events,
and there are no second chances to repeat observations of them when techniques
improve. Cepheids can be observed again and again as astronomers develop
bigger telescopes and better detectors.

Astronomers from Leavitt onwards have observed Cepheids at blue wavelengths,
because most photographic plates are sensitive to blue light. Cepheids fluctuate
more markedly at blue than at red wavelengths, so blue wavelengths are ideal
for discovering Cepheids. But these wavelengths bring problems too. First,
there is the Cepheid variation itself. To determine a Cepheid’s distance,
astronomers must first measure the star’s mean brightness. The less the
star fluctuates, the easier this is to do. At blue wavelengths, a Cepheid
called SU Cygni, in the constellation Cygnus, is 2.4 times as luminous at
its brightest than at its dimmest. But at yellow wavelengths this diminishes
to a factor of 1.9, at red wavelengths to 1.6 and at infrared wavelengths
to 1.2. So from a single observation in the infrared, it is possible to
pinpoint the star’s mean brightness to within 10 per cent.

Another advantage of using red and infrared light is that these wavelengths
penetrate dust, which blocks blue light and can make a Cepheid look fainter
and farther away than it really is. By observing a Cepheid at several wavelengths
– blue, yellow, red, and infrared – astronomers can estimate how much dust
lies between us and the star. Even at red and infrared wavelengths, dust
absorbs some of a Cepheid’s light.

Improvements to detectors over the past decade have allowed astronomers
to put these ideas into action. In place of photographic plates, astronomers
now use charge coupled devices (CCDs), which capture more light across wavelengths
from blue to near infrared. During the late 1980s, good detectors for longer
infrared wavelengths were also developed.

In recent years, astronomers led by Barry Madore of the California Institute
of Technology and Wendy Freedman of the Carnegie Observatories in California
have used these new detectors to observe Cepheids in the Large Magellanic
Cloud, which is the galaxy nearest to our own. From these observations they
determined the intrinsic brightness of Cepheids of a given period. They
assumed that this galaxy is 163 000 light years away, a distance which agrees
with that computed from observations on other pulsating stars, and was also
confirmed last year from measurements of the 1987 supernova in the Large
Magellanic Cloud. Madore and Freedman then turned their telescopes towards
other nearby galaxies to observe their Cepheids and determine their distances.

The closest galaxies belong to the Local Group, a collection of about
30 galaxies that includes Andromeda and the Milky Way. Andromeda has plenty
of Cepheids, and Madore and Freedman determined that its distance is 2.5
million light years, in good agreement with previous values. They also find
that the galaxy M33, the third largest Local Group member, is 2.8 million
light years distant. This agrees with several previous estimates, but puts
M33 a million light years closer to us than some astronomers claimed 10
years ago.

Beyond the Local Group, Madore and Freedman observed Cepheids in the
two nearest galaxy groups. These are the Sculptor group and the M81 group,
which are on opposite sides of us. The Sculptor group, so-called because
most of its members lie in the southern constellation of Sculptor, is the
closer of the two and lies directly south of the Milky Way’s plane. The
king of the Sculptor group is the beautiful edge-on spiral galaxy NGC 253,
which is probably slightly smaller than the Milky Way. The periods of many
Cepheids in the Sculptor group are not known, because the group lies in
the southern hemisphere. There are fewer observatories there, and its Cepheids
have not been observed as thoroughly as those elsewhere. Madore and Freedman
have worked out the distance to only one Sculptor group galaxy, the spiral
NGC 300, which they put at 7 million light years away. Next, they aim to
measure the distances to two other galaxies in the group, NGC 247 and NGC
7793.

The M81 group takes its name from a giant spiral galaxy near the Big
Dipper that is about the same size as our Milky Way. M81 lies in the northern
hemisphere, and its Cepheids have known periods. In the early 1980s, Allan
Sandage at the Carnegie Observatories had argued from observations of Cepheids
at blue wavelengths that M81 was 5 million light years farther away than
NGC 2403, another spiral galaxy in the M81 group. But the new observations
by Madore and Freedman indicate that both galaxies are about 11 million
light years away.

Thanks to Madore and Freedman, astronomers now have good distances to
some of the galaxies in the Local, Sculptor, and M81 groups, but the motion
of these galaxies cannot be used to calculate the Hubble constant. This
is because the galaxies in the Local Group feel the attractive force of
each other’s gravity more than they feel the expansion of the Universe,
which tries to push them apart. The effect is strong enough to cause the
great Andromeda galaxy to move towards us rather than away. Likewise, the
Local Group tugs on the Sculptor and M81 groups, and all three get pulled
towards the Virgo cluster of galaxies, which lies somewhere between 40 and
70 million light years away. Astronomers trying to measure the Hubble constant
have for years had their sights set on the Virgo cluster. This is our
nearest large cluster and the centre of the so-called Local Supercluster,
a huge cigar-shaped conglomeration of galaxies that includes the Milky Way.
The Local, Sculptor and M81 groups all lie near the edge of the Local Supercluster.
The Virgo cluster is far enough away from us to probe the Universe’s expansion
and the gravitational pull of other galaxies on the Virgo cluster is relatively
small. Unfortunately, the distance to the Virgo cluster is poorly known.
If astronomers knew its distance, they would be able to pin down the Hubble
constant to within 10 or 20 per cent.

The problem is that no Cepheids can be seen in the Virgo cluster: it
is so distant that its Cepheids blend in with other stars. So astronomers
must resort to other methods to estimate the distance of Virgo and other
clusters of galaxies – though these methods rely on the most recent distance
information gained from Cepheids. When applied to distant galaxies, these
methods all give a high value for the Hubble constant of around 80 or 85.
This implies that the Universe is young.

Astronomers who believe the Universe is old put more weight on another
method, based on Type Ia supernovae. All Type Ia supernovae arise from exactly
the same kind of star – a white dwarf – so they should all have the same
intrinsic brightness at peak brightness. If this intrinsic brightness were
known, Type Ia supernovae would be excellent indicators of distance. Supernovae
can outshine an entire galaxy and so can be seen far beyond where Cepheids
can be detected. Unfortunately, no Type Ia supernova has recently exploded
in a galaxy with a Cepheid- determined distance. (The 1987 supernova in
the Large Magellanic Cloud was a Type II supernova.)

For estimates of the luminosity of Type Ia supernovae, astronomers have
had to rely heavily on observations made in 1937 of a supernova that exploded
in a small galaxy named IC 4182, which is part of the Local Supercluster
and was thought to be 14 million light years away. Observations of Type
Ia supernovae in more distant galaxies, coupled with the luminosity calculated
for the supernova in IC 4182, yielded a Hubble constant of about 50.

But earlier this year, Michael Pierce of Kitt Peak National Observatory
and his colleagues reported that IC 4182 is really only 8 million light
years away (91av, Science, 4 April). The revised estimate for the
distance gives a Hubble constant of 86 plus or minus 12 – which fits in
well with values of Hubble from other methods tied to the new Cepheid data.

A YOUTHFUL UNIVERSE

High values of the Hubble constant suggest that the Universe is young.
Just how young it is depends on the mass density of the Universe, called
omega (&Ogr;). The gravitational pull of the Universe’s mass retards the
Universe’s expansion, and the critical density of the Universe is when &Ogr;
has a value of 1. If &Ogr; is greater than this, the Universe has so much
mass that it will some day stop expanding and start collapsing. If &Ogr;
is less than 1, the Universe will always expand.

To estimate the age of the Universe, we need to know both the size of
the Hubble constant – that is, the present expansion rate – and the size
of omega. If &Ogr; has any value above zero, the Universe must have been
expanding faster in the past than it is now, because the mass of the Universe
slows its expansion. In the same way, the larger &Ogr; is, the younger the
Universe, for a given Hubble constant. Most astronomers believe &Ogr; lies
between 0.2 and 1.0. If the Hubble constant is 80 and &Ogr; is 0.2, the
Universe is about 10 billion years old. If, on the other hand,&Ogr; is
1.0, then the Universe is only 8 billion years old. Thus, the Universe must
be between 8 and 10 billion years old – if the Hubble constant is 80, and
if standard cosmology is right; in other words, if the big bang did happen
and the age of the Universe depends only on the Hubble constant and &Ogr;.

This leaves us with a big dilemma. It means that the Universe is younger
than the estimated ages of globular star clusters – tightly packed clusters
of old stars, in our Galaxy and others, which are thought to be roughly
15 billion years old. If the Universe is no more than 10 billion years
old, then no 15-billion-year-old objects should exist.

There seem to be four ways out of the dilemma. The first is that estimates
of the ages of globular clusters could be wrong. They are based on standard
theories of stellar structure and evolution, which have other flaws – for
example, they predict that the Sun emits three times as many neutrinos as
it actually does.

A second possibility is that estimates of the Hubble constant are wrong,
that it really is 50 or 60 and that the Universe is some 15 billion years
old. This becomes less likely as astronomers home in on a commonly agreed
value for the Hubble constant. Still, astronomers have previously believed
that they knew the Hubble constant, only to find that they didn’t. And the
best methods for determining the distances of far-off galaxies rely on very
few Cepheid-calibrated galaxies .

Thirdly, we could introduce a ‘fudge factor’ called the cosmological
constant. If the Hubble constant and omega give an age of 10 billion years,
for instance, we could invoke a cosmological constant to say that the Universe
is actually 5 billion years older than it looks. Few astronomers have resorted
to this.

Some might opt for the fourth and most radical option: that the big
bang never happened, in which case age determinations based on an extrapolation
to the time of the big bang are meaningless (‘What if the big bang didn’t
happen?’, New Scientist, 2 March 1991).

Whatever the truth, Cepheids will have a major role in finding it. When
NASA’s Hubble Space Telescope is repaired it should be able to pick out
Cepheids in the Virgo cluster and elsewhere, and pin down their distances.
These cosmic yardsticks are destined to play the key role in resolving one
of the biggest questions in modern astronomy: the age of the Universe.

Ken Croswell is an astronomer in Berkeley, California.

Further reading The Cepheid distance scale, by Barry F. Madore and Wendy
L. Freedman, Publications of the Astronomical Society of the Pacific, vol
103, p 933 (1991).

* * *

How distant is a distant galaxy?

Cepheids can be picked out only in nearby galaxies, so astronomers have
developed several methods to estimate the distance to more remote galaxies
in order to probe the Universe’s expansion. One of the best was developed
during the 1970s by R. Brent Tully of the University of Hawaii and J. Richard
Fisher of the National Radio Astronomy Observatory in West Virginia. The
Tully-Fisher method uses a property of spiral galaxies: The faster a spiral
galaxy rotates, the more intrinsically bright it is. A spiral galaxy’s rotation
speed is easy to measure, and from this and its apparent brightness astronomers
can work out the galaxy’s distance.

To calibrate the Tully-Fisher method, astronomers looked at nearby spiral
galaxies in which Cepheids have been observed. At the moment, there are
only five such galaxies: Andromeda and M33 in the Local Group, NGC 300 in
the Sculptor group, and M81 and NGC 2403 in the M81 group. The Cepheids
reveal the distance of the galaxies, and this can be used to convert their
apparent brightness to intrinsic brightness.

Two newer methods for determining distances to far-off galaxies rely
on even fewer calibrating galaxies. A method developed by George Jacoby
and his colleagues at Kitt Peak National Observatory in Arizona during the
late 1980s and early 1990s uses planetary nebulae. A planetary nebula
forms when a dying star ejects its outer atmosphere. A galaxy’s most luminous
planetary nebulae have a characteristic apparent brightness. If the galaxy’s
distance is known, astronomers can translate this apparent brightness into
an intrinsic brightness and then assume that planetary nebulae in more distant
galaxies have the same intrinsic bright-ness. This method uses two galaxies
with Cepheids: Andromeda and the Large Magellanic Cloud.

The most recent method, proposed by astronomer John Tonry and his colleagues
at the Massachusetts Institute of Technology, uses elliptical galaxies and
the central bulges of spiral galaxies. Both of these look smooth from a
distance but more blotchy close up, rather like the picture on a television
set. Just as you could deduce the distance of the television set from the
smoothness of the picture, Tonry can work out the distances of galaxies,
by comparing them with the bulge of Andromeda and two elliptical galaxies
that orbit it, M32 and NGC 205. Neither M32 nor NGC 205 has Cepheids, but
Tonry assumes both galaxies are the same distance as Andromeda.