The Keck Telescope on Mauna Kea, Haw-aii, has a unique segmented mirror
10 metres across (see ‘Eye at the edge of the Universe’, this issue). Its
first results have just been published in four papers in the 1 January issue
of Astrophysical Journal Letters.

With the aid of its Near Infrared Camera, Keck observed a ‘gravitational
lens system’ called MG1131+0456. The system is a striking example of a massive
galaxy whose gravity acts like a lens, bending and focusing the light of
a more distant quasar to produce a double image of the quasar.

Keck captured images at two infrared wavelengths. Surprisingly, when
Keck observed the system at a wavelength of 2.2 microns, the image of the
double quasar stood out clearly. But at 1.3 microns, it vanished, leaving
only the foreground galaxy. According to James Larkin of the California
Institute of Technology (Caltech) in Pasadena, the most likely explanation
is that the galaxy is impregnated with dust, which blocks the quasar’s
radiation at 1.3 micrometres.

But the real importance of this lens system is that it could help astronomers
to nail down the Hubble constant, the present rate at which galaxies are
moving away from us.

The Hubble constant can be found if both the geometry of the system
and the distance of the quasar are known. It is very rare to see a lensing
galaxy because they are generally too distant and dim. But in this case
astronomers can measure the red shifts of both the galaxy and quasar, enabling
them to plot their relative positions. The distance of the quasar can be
deduced from the fact that the paths of light from these two quasar images
differ in length.

The Near Infrared Camera was also used to study the most distant known
galaxy, 4C41.17. The light from the galaxy has taken billions of years to
reach Earth and shows the object when the Universe was only about 20 per
cent of its current age. Keck’s images reveal galaxy-like objects huddled
near the radio galaxy. They appear to already be half a billion years old,
which could push their time of birth back almost to the big bang, says Tom
Soifer of Caltech.

If the radio galaxy’s companions share its red shift, they could be
the most distant examples of ‘normal’ galaxies and give insight into the
evolution of the early Universe. Radio galaxies such as 4C41.7 are ‘abnormal’
and poorly understood.

The Near Infrared Camera was also used to examine the most luminous
known object, FSC₁0214+4724, 10 billion light year away. Discovered
in 1991, the object appeared to be structureless – perhaps a quasar. But
Keck reveals that the object is not an isolated object but a clump of several
objects. ‘Without Keck, we never would have seen that it’s a group,’ says
Soifer.

The clump could be a galaxy feeding a voracious quasar at its centre.
Quasars are thought to be ‘supermassive’ black holes. Alternatively, the
clump could be two galaxies mingling. Their violent interactions might give
birth to large numbers of bright, new stars, and might also form a quasar.
‘Catching these galaxies in the act, in what looks like an interacting system,
certainly is a novel feature,’ says James Graham of the University of California
at Berkeley.

But Keck’s final discovery could be the most important, says Soifer.
It concerns the so-called faint blue galaxy problem. Recently, scientists
working on the Hawaii Deep Survey, also at Mauna Kea, turned up a conundrum.
They were plotting the number of galaxies in a region of the sky against
their brightness in order to study the distribution of matter in the Universe.
The astronomers found that in the infrared, the number of galaxies levels
off as they become more faint. But in the blue region of the spectrum, the
number of galaxies rises rapidly. This discrepancy flies in the face of
current models of galaxy formation.

These excess blue galaxies, which are hotter and newer than red galaxies,
have moderate red shifts and so are relatively close to us. ‘It suggests
that galaxy formation occurred recently,’ says Lennox Cowie of the University
of Hawaii. ‘That’s not what classical number count models assume. They assume
galaxies formed at a relatively early time.’

The Hawaii Deep Survey images took 80 hours to obtain. But Keck was
able to verify the excess of faint blue galaxies in only a few hours.

In September, six amateurs working under the guidance of Sallie Baliunas
of the Harvard Smithsonian Center for Astrophysics in Cambridge, Massachusetts,
were measuring the light emitted by calcium in nearby stars. A low emission
indicates that the star has a weak magnetic field and, in general, the more
feeble a star’s magnetic field, the older it is.

When Baliunas’s team observed the star HD202537, which is less than
100 light years away, they found its magnetic field to be 30 to 50 per cent
weaker than any Baliunas had ever seen. This corresponds to an age of 19
billion years. Most astronomers believe the Universe to be 10 to 15 billion
years old, so the measurements make the star older than the Universe. ‘Since
that’s ludicrous, this means we have an unusual item on our hands,’ says
Baliunas.

The discovery was an unexpected bonus for the amateurs, who were realising
their ambition to use a large astronomical telescope during the week they
were spending at Mount Wilson through the Smithsonian Research Expedition’s
programme. ‘It was exciting to find something out of context of what’s previously
been detected,’ says Philip Monaghan, one of the participants.

The most likely cause of the discrepancy, according to Baliunas and
her colleague Robert Donahue, is that the star has been misclassified as
a dwarf – a star in its main hydrogen-burning stage, like our Sun. Instead,
it may actually be a red giant, a bright cool star in its later stages.

The calcium emission line of a dwarf is 1 angstrom wide, while a red
giant’s is about 2 angstroms across. If HD202537 is indeed a red giant,
the astronomers would have recorded only half the light emitted by its calcium,
giving the appearance of a very weak magnetic field. But even after widening
the spectral range of their measurement to 2 angstroms, Baliunas and Donahue
say that the star’s magnetic field is still weak.

The definitive test will be to look at the star’s spectrum over a range
of 100 angstroms, in order to reveal other telltale spectral lines that
might show the star to be a red giant.

A number is said to be perfect if the sum of its proper divisors equals
the number itself. For example, 6 is a perfect number because its proper
divisors are 1, 2 and 3. A number is multiply-perfect if the sum of its
divisors equals an integer multiple of the number. The divisors of 120 add
up to 360, so 120 is a multiply-perfect number with an ‘index’ of 3.

Although perfect numbers and their multiply-perfect cousins serve no
practical purpose, they have amused mathematicians and philosophers from
Euler to Descartes. The ancient Greek mathematician Euclid devised a formula
for perfect numbers that end in 6 or 28. But the less well-behaved multiply-perfect
numbers (or multiperfects, as they are known to aficionados of number theory)
do not follow any known pattern. Theorists must use computers to hunt for
larger numbers.

Now Fred Helenius, a mathematician living in Colorado, has developed
a computer program that is yielding a bumper crop of multiperfects. Since
they were first recognised, only about 700 multiperfects have been found
– the largest of which has an index of 8. But Helenius has increased the
total to 1288, and these include 14 monster multiperfects with indices of
9. The largest, which Helenius discovered two months ago, has 588 digits.

According to Rich Schroeppel, a computer programmer at the University
of Arizona in Tucson who has compiled a list of all known multiperfects,
Helenius’s program is a great improvement on previous algorithms, and is
finding multiperfects at a prodigious rate. ‘Before Fred, we knew of only
a dozen multiperfects of index 8,’ says Schroeppel.

He dubbs Helenius’s algorithm the ‘successive adjustment method’. It
starts with a ‘seed’ number – the product of powers of small primes – and
adjusts the number repeatedly to find a multiperfect.

According to theorists, for each index there appears to be a finite
number of multiperfects. There are only 6 numbers known of index 3, 36 of
index 4, and 65 of index 5. However, there are more than 400 known multiperfects
of index 8, almost all of them found by Helenius. ‘One could say I’ve made
a good start on index 8, and the first touch on the far shore of index 9,’
says Helenius.

But the jury is still out on whether the set of multiperfects is finite,
says Schroeppel. As the numbers get larger, they become more sparsely distributed.
‘The open question is whether they thin out to nothing,’ he says.

Helenius’s holy grail is a multiperfect of index 10, a huge number probably
of more than 700 digits, which may require a supercomputer to calculate
in a reasonable amount of time.

‘I was expecting someone with access to more powerful computing facilities
to take this off my hands,’ says Helenius.