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ASTRONOMERS and geophysicists share a common handicap. Neither can see
directly inside the object they study. The interiors of stars are completely
shielded from view: astronomers can see less than 0.01 per cent of our Sun,
the star we know best. Most of the Earth is also out of reach. The deepest
oil wells and mines barely scratch the surface of our planet. The Earth’s
core, separated from us by only a few thousand kilometres, might as well
be light years away. Despite this, geophysicists have a fairly detailed
idea of the internal structure of the Earth, carefully pieced together through
seismology, the study of earth tremors. In recent years, the discovery of
vibrations on the surface of the Sun and a few other stars has inspired
astronomers to adopt a similar approach. This new breed of stellar seismologists
hopes to uncover some of the secrets hidden in the centres of distant stars.

Those secrets are well protected. Radiation generated in the nuclear
furnace at the core of a star has to struggle to the surface, constantly
being absorbed by atoms and re-emitted in random directions. It can take
a million years for a trail of photons to reach the outermost layers of
the star and escape into space. So, a photon that manages to escape no longer
carries any information about the star’s deep interior. It can give information
only about the surface gas in which it was last regenerated. As a result,
almost everything astronomers know about the interiors of stars is indirect;
they have to work from theory and the external properties.

Our nearest star, the Sun, is the best understood. Astronomers have
measured its size, mass, brightness, surface temperature and composition
to a relatively high degree of accuracy. Using these data, and the laws
of physics, theorists have constructed models of the solar interior which
reproduce the outer properties. Astronomers have a great deal of confidence
in the overall framework of these models, because the laws governing matter
and radiation do not tolerate much leeway. But before the advent of stellar
seismology, there was only one direct test of the theory: to measure the
Sun’s output of particles known as neutrinos and see if the observations
matched the predictions from the models. They were significantly different.

Neutrinos are subatomic particles born of fusion reactions in the centre
of the Sun. Having zero charge, possibly zero mass, and very high energy,
neutrinos interact so little with matter that most would pass easily through
a light year of solid lead. Oblivious of the 700 000 kilometres of hydrogen
and helium gas in their way, these cosmic bullets shoot out of the Sun in
seconds. They should accurately reflect the conditions under which they
were created in its core. In 1970, an American physicist, Raymond Davis,
began to log the number of solar neutrinos passing through a sensitive detector
buried in a gold mine in South Dakota; he found only a third of the flux
predicted by the theory. Something was clearly wrong with the models, or
current understanding of high-energy physics, or both.

There are several ways in which astronomers can adjust the models to
account for the measured flux of neutrinos and still produce a Sun that
looks like the one we see. Without at least one more independent check,
however, there was no way of narrowing the field of contending solutions.
Ironically, 10 years before the first solar neutrino left its trace in Davis’s
underground tank, a team of astronomers made a discovery that would eventually
open a new window on the interior of the Sun, and may, one day, lead to
the solution to the neutrino problem.

Robert Leighton and his colleagues at the California Institute of Technology
hoped to study the turbulent motions of gases at the Sun’s surface by tracking
subtle shifts in its spectral lines induced by the doppler effect. Light
emitted by gas moving away from an observer is shifted to longer wavelengths,
becoming redder; approaching gas seems to radiate blue-shifted light. Leighton’s
team knew that the upper layers of the Sun were in constant upheaval and,
like all solar astronomers at the time, they expected the variations to
occur purely at random. But, superimposed on the chaotic churning, the researchers
were surprised to find regular pulsations that repeated in cycles of about
five minutes. The entire surface of the Sun appeared to be rippling in this
fashion. There was no obvious global pattern to the pulsations, and it was
always changing, but all parts of the Sun showed the five-minute cycle.

The ‘five-minute solar oscillations’ remained a mystery for years, until
theorists realised that the complex surface vibrations could be described
in terms of sound waves bouncing back and forth through the inside of the
Sun. The waves are probably produced by the very turbulence that Leighton
originally wanted to study. Once astronomers recognised the nature of the
oscillations, they were quick to grasp the implications. Here, finally,
was a powerful tool for probing the invisible interior of the Sun.

Solar seismology, or helioseismology, like its terrestrial counterpart,
relies heavily on the principles of refraction. In the Earth, pressure waves
from an earthquake bend towards new directions when they strike the boundary
between, say, the mantle and the denser core. The Sun is gaseous and lacks
such sharp discontinuities, but its temperature, density and composition
change between its surface and the core. Because the speed of sound depends
on the temperature and average mass of the particles in a gas, gradual changes
with depth will bend the path of a sound wave. Eventually, this refraction
will direct a sound wave descending into the Sun onto an upward path, towards
the surface.

An individual sound wave will be trapped between the surface and the
interior of the Sun at a depth set by the speed of sound at that point.
Circumnavigating the Sun within these acoustic cavities, the waves resonate,
as if in a musical instrument. In simpler terms, they cause the Sun to ring.
Astronomers ‘listen’ to this silent ringing across the vacuum of space by
studying the telltale motions of the surface, minute changes in the size
of the solar disc or the Sun’s brightness.

Because the waves are simply fluctuations in pressure transmitted through
the gas, the patterns of vibration they produce at the Sun’s surface are
dubbed pressure- or p-modes. The simplest p-mode is one in which the sound
wave has a wavelength so large that all parts of the Sun expand and contract
in unison. The most complicated seen so far divides the surface into a grid
of about a thousand oscillating segments. Each mode can vibrate with shorter
periods as well. These are the equivalents of musical overtones and astronomers
have adopted the same term for them.

Astronomers estimate that the Sun vibrates simultaneously in at least
10 million p-modes and their corresponding overtones. The pattern and period
of each mode arise from waves penetrating to a specific depth beneath the
Sun’s surface. The many modes enable helioseismologists to chart how the
speed of sound changes with depth below the surface and how quantities such
as temperature, composition and internal rotation vary within the Sun. All
this is new information about the interior of this otherwise familiar star.

The seismic observations and the standard theory appear to agree to
within a few per cent, but the differences are greater than the precision
of the data, precision that continues to improve as helioseismologists introduce
new instruments and observing strategies. As Roger New describes in ‘Watching
the wobbling Sun’ next week, American and French groups are now establishing
arrays of small telescopes worldwide to keep nearly constant vigils on the
Sun. Studies will also continue from space, an ideal vantage point for continuously
monitoring the Sun above the clouds and turbulence of the Earth’s atmosphere.

Astronomers are also looking elsewhere. Many of the phenomena seen in
the Sun, for example, sunspots, flares and magnetic fields, have their counterparts
in other stars; a comparative study will tell them more about both the Sun
and stars in general. But if the Sun were at the distance of even the nearest
other star, astronomers would not be able to detect its oscillations using
present techniques. They would no longer be able to distinguish the velocities
of different areas of the star’s surface, for the Sun’s disc would be visible
as only a point of starlight, with the millions of vibrations almost completely
cancelling out each other.

Some researchers, undaunted, are taking up this challenge. Groups at
the University of Birmingham, the Astrophysical Institute of the Canaries
at Tenerife, and the Observatory of Nice have started looking for oscillations
in nearby stars that resemble the Sun. The French group has harnessed the
light-gathering power of two of the world’s largest optical telescopes:
the Soviet 6-metre giant deep in the Caucasus Mountains and the 3.6-metre
Canada-France-Hawaii telescope on the island of Hawaii. To date, their best
efforts have yielded no convincing evidence of rapid oscillations in any
other star similar to the Sun.

Astronomers still think that these type of stars are excellent candidates,
mainly because there is at least one that does oscillate – our Sun. But
beggars cannot afford to be choosers, and astronomers had long ago widened
their search to include very different types of stars.

Stellar seismologists hunting for stars that ring can take heart from
the fact that such stars should be quite common. In fact, most stars should
vibrate if kicked (an astronomer would say ‘pulsate if excited’) in the
right way. But like a bell struck only once, the ringing would die out quickly,
and astronomers would have little chance to spot it.

But under special circumstances, the ringing can continue for a long
time. If the vibrations are big and simple enough, the brightness of the
star can change substantially, partly because its surface area varies, but
also because the expansions and contractions alter the temperature at its
surface in step with the oscillations. This accounts for many of the variable
stars that astronomers have discovered over the centuries.

One process that can keep the ringing going involves helium, the second
most abundant element in stars, after hydrogen. Helium atoms stripped of
one electron (He⁺) are very efficient at absorbing large amounts of the
radiation flowing outward from the centre of a star. They are part of the
gauntlet that photons in a star must run on their journey to the surface.
When a He+ ion absorbs radiation, it loses its one remaining electron to
become a bare helium nucleus (a He²⁺ ion). This form of ionised helium
is all but transparent to light.

The two kinds of ionised helium have very different effects on the flow
of radiation from a star’s centre. He+ absorbs radiation, and stems the
flow of energy. The outward pressure of the dammed radiation makes the star
swell. But during the absorption, the He+ ions change to He**2+ ions, which
are transparent. Consequently, the radiation streams through, without exerting
pressure, so the gas is free to collapse towards the centre of the star
under the force of gravity, and the star shrinks. Ionised helium can, therefore,
act as a ‘valve’ which will either dam or release the flow of energy, and
keep the star pulsating for millions of years.

All stars contain ionised helium, but not all pulsate. For the mechanism
to work, the layer of ionised helium must lie at a specific depth, and be
at the correct temperature. For this reason, the most prominent pulsating
stars, though spanning a wide range of size and luminosity, all have nearly
the same temperature. Astronomers refer to this narrow band of temperature
as the ‘instability strip’. Variable stars that fall in the strip include
(in order of decreasing brightness) the Cepheids, RR Lyrae stars, with periods
of days and weeks, and the delta Scuti stars, with cycles of hours.

It is no coincidence that, among these ringing stars, the brightest
have the longest vibration periods. Stars of the same size have higher luminosities
if they have higher temperatures, because hotter gas glows more intensely.
Conversely, a bigger star is brighter than a smaller star at the same temperature,
simply because it has more surface to radiate into space. Stars in the instability
strip are all at about the same temperature, so the brighter ones must be
larger. Just as a large bell rings at a low pitch whereas a tiny one will
tinkle, larger stars tend to vibrate with longer periods than their smaller
kin. The giant Cepheids, dozens of times larger than the Sun, are in this
sense the Big Bens of ringing stars. Pulsators such as delta Scuti might
be likened to hand bells in comparison.

The stars of the instability strip are of tremendous importance to astrophysics.
Astronomers exploit the bell-like relationship between the size of a star
and its period, together with the link between size and luminosity, to translate
the period of pulsation and apparent brightness of a Cepheid into its distance
from the Earth. Because Cepheids are bright enough to be visible in other
galaxies, astronomers use their vibrations to calibrate the entire scale
of distance outside our Galaxy.

Regrettably, they are not quite so useful as subjects for stellar seismology.
Cepheids may ring more ‘loudly’ than the Sun (in that their oscillations
are thousands of times as large) but they almost always vibrate in pure
monotone, that is, with just one p-mode. It is the Sun’s rich melody of
many high-pitched modes which provides the detailed information about its
interior.

Stellar seismology is a powerful tool nonetheless. Theory predicts that
the various p-modes and their overtones should have frequencies that are
almost equally spaced along the spectrum. Astronomers do indeed find this
frequency signature in the solar oscillations. The frequencies of the different
modes depend on the time it takes a wave to cross the diameter of the star.
The bigger the star, the smaller the spacing between modes. On the other
hand, the small deviations from equal spacing are most sensitive to variations
in the speed of sound near the centre of the star. This is where thermonuclear
reactions convert hydrogen into helium, slowly modifying the composition
of the gas. As the star grows older, the rate at which the speed of sound
changes with depth also changes. The distinctive signatures of rapid oscillations
can define the size and age of a distant star and help astronomers to understand
more clearly how it evolves.

Astronomers found rapid oscillations suitable for seismology in a star
other than the Sun, more than 20 years ago. In 1968, Arlo Landolt of Louisiana
State University announced that a rather obscure star, Haro-Luyten Taurus
76, was varying in brightness with a period of about 12.5 minutes. HL Tau-76
is a white dwarf: a hot, extremely dense star roughly the size of the Earth
but with almost as much mass as the Sun. It started out very much like the
Sun, but after a long life, which included expansion into a red giant and
the ejection of its outer layers into space, the star collapsed to its present
size. Most white dwarfs cannot collapse any further, because electrons in
them are packed together as tightly as they can be; they repel each other
strongly.

Such a compact star should be one of the tiniest, and tinniest, of stellar
bells, ringing at a very high pitch. Astronomers thought that white dwarfs
might vibrate and that they should have short periods. But their calculations
predicted periods of only a few seconds, much too short to account for Landolt’s
findings. For this reason, scientists at that time rejected the notion that
HL Tau-76 was pulsating and turned instead to more exotic explanations.
They toyed with such notions as stellar flares ignited by regular approaches
of an unseen companion star. None was satisfactory. The discovery of other
oscillating white dwarfs with periods from 5 to 15 minutes gave the problem
a greater sense of urgency. One such star might be dismissed as a unique
stellar misfit; a dozen demand serious attention. The solution was soon
found. As with the solar oscillations, it depended on waves trapped beneath
the star’s surface, but this time they were not pressure waves.

If you drop a pebble into a pond, it starts two types of wave in the
water: a sound wave that travels rapidly through the pond announcing the
splash, and a much slower wave visible on the surface as the familiar concentric
ripples. A stellar version of the second wave, moving well below the speed
of sound, could trigger slower vibrations in white dwarfs, with the kind
of periods that Landolt saw. This type of wave depends on the buoyancy of
gas resisting the gravitational pull from the centre of the star, so the
resulting lower-pitched vibrations are called gravity- or g-modes.

The music of the stars

Like p-modes, g-modes have their own distinctive pattern of periods
(or frequencies). Although a star like HL Tau-76 might appear to vibrate
with only one period, a long series of observations will often reveal complicated
changes in the amplitude of the oscillation. This modulation suggests that
there are several vibrations with very similar periods; you can hear a similar
‘beating’ effect by playing musical notes that are nearly identical at the
same time. If the oscillation data are analysed mathematically, the patterns
of the separate notes can be decoded. The match between the observed and
theoretical signatures of oscillations confirms that at least some white
dwarfs are ringing in low-pitched g-modes. In one instance, the analysis
of the g-mode pattern in a white dwarf gives an estimate of its mass to
within 2 per cent, a precision unheard of for any star other than the Sun.
The oscillations in white dwarfs have also given astronomers a clue to another
great unknown, the age of the Universe itself .

Although the discovery of rapid vibrations in the Sun was unexpected,
and the appearance of g-modes in white dwarfs was a surprise to astronomers
prepared for something else altogether, a third type of rapidly oscillating
star caught observers and theorists completely off guard. They happened
in a class of stars in which lasting vibrations were not merely unexpected,
they were expressly forbidden by the accepted theory of the pulsations.

These ‘Ap’ stars have very strong magnetic fields (the ‘A’ is part of
a spectral classification scheme; the ‘p’ means that these stars are peculiar,
and do not quite fit in the standard A class). In theory, this field should
calm the turbulence normally found in stellar atmospheres. One side effect
of this enforced stability is that gravity will make helium sink into the
sea of lighter hydrogen gas surrounding it. Without helium ions, there should
be no ionisation valve to drive the large-scale vibrations. Because Ap stars
do not have helium in their upper atmospheres, they are unlikely to pulsate,
even though many have temperatures which place them in the instability strip.
Indeed, researchers looking for variations in brightness with periods of
a few hours found no sign of vibrations. Observation and theory were in
total agreement: Ap stars do not ring. This view was so widely held that
astronomers seeking new pulsators would often select Ap stars as benchmarks
against which they could gauge the variations in the light coming from other
stars in their search.

One such astronomer was Donald Kurtz, whose studies of the light variations
of delta Scuti stars had brought him to the edge of the Great Karoo desert,
site of the South African Astronomical Observatory, which is renowned for
its pristine skies. In the spring of 1978, Kurtz allowed his small telescope
to linger on an Ap star for a little longer than usual. The photometer he
was using to measure the intensity of the starlight showed that this supposedly
constant star was oscillating, with a period of a few minutes. The oscillations
were small by stellar standards – barely 1 per cent of the total brightness
of the star – but huge compared to those of the Sun.

The oscillations were surprising enough, but the short period was the
real puzzle. No one would have thought a star that was twice the diameter
of the Sun could ring so rapidly and with such vigour. It was rather like
watching a musician play the tuba and hearing it produce the high-pitched
strains of a piccolo.

The list of rapidly oscillating Ap (roAp) stars has since grown to 14.
There is now little doubt that they are in fact ringing. In 1986, I was
a member of a Canadian team that finally succeeded in measuring the subtle
movements of the surface of an Ap star associated with its variations in
brightness. We used the Canada-France-Hawaii Telescope, equipped with an
instrument also used to search for very small wobbles in a star’s velocity
caused by planets in orbit around it. Even before this breakthrough, Kurtz,
I, and others had studied those brightness variations in sufficient detail
to reveal the characteristic signature of p-mode oscillations. The roAp
stars are the only stars that we know of which vibrate in a similar way
to the Sun.

In many respects, these stars are strikingly different from the Sun,
with their intense magnetic fields, calm outer atmospheres and peculiar
surface compositions. Compared with the white dwarfs, however, the Sun and
Ap stars are close relatives. Both are what astronomers refer to as ‘main
sequence’ stars, which continue to fuse hydrogen into helium in their cores.
And both have oscillations that can be described by p-mode theory, although
how the roAp stars manage to keep on vibrating is still a mystery.

Some of the differences between these stars and the Sun are being used
for discovery in ways previously impossible even for the Sun. The vibration
patterns in an roAp star line up with its powerful magnetic field. This
subtly alters the signature of the p-modes. Precise measurements of these
effects tell astronomers, for the first time, something about the strength
of the magnetic field beneath a star’s surface.

To date, stellar seismologists have available only a handful of Ap stars,
a few white dwarfs, and a lone but familiar solar-type star, the Sun. That
situation may soon change. Observers are stepping up their efforts to find
new pulsators. Instrument experts are designing and building better devices
to aid in the hunt. Theorists are busy calculating models in anticipation
of data to come.

All this enthusiasm borders on brashness. As the natures of solar and
stellar oscillations become better defined, so do the limits of what they
can tell us. But any field which in its fledgling years has tackled issues
as diverse as the solar neutrino puzzle, stellar magnetism and the age of
the Universe might be forgiven an early touch of overconfidence.

* * *

White dwarfs ring up the age of the Universe

UNFORTUNATELY for astronomers interested in the connection between the
Sun and other stars, white dwarfs tell them little about stars like the
Sun, except perhaps painting a more vivid picture of the fate that awaits
our star in a few billion years. In one unusual application, however, the
seismology of white dwarfs is shedding some light on one of the most basic
questions posed by astronomy: How old is our Universe? A white dwarf is
a dead star. With its nuclear fires extinguished, all that remains is a
slow inexorable cooling to blackness. The hottest and brightest white dwarfs
radiate their heat most quickly; those with the lowest surface temperature
and brightness cool more gradually and remain visible for billions of years.

As long ago as 1959, astronomers were aware that the faintest white
dwarfs, still visible in deep space, should be the oldest. They may be almost
as old as the Galaxy itself. If astronomers could clearly identify this
group of stars and determine how long it took for them to cool to their
present state, it might set an accurate limit on the age of the Galaxy and,
in turn, the Universe itself.

A recent census of stars near the Sun conducted with sensitive electronic
detectors revealed fewer than expected white dwarfs that are fainter than
about 30 millionths of the Sun’s luminosity.

Donald Winget of the University of Texas and his collaborators assert
that this cutoff in brightness marks the first generation of white dwarfs
formed in the disc of the Galaxy. They say that there are no white dwarfs
fainter than this limit because there has not been enough time in the history
of the Galaxy for any star to cool to a luminosity less than this. The sharpness
of the cutoff reflects how all white dwarfs behave in a similar way as they
cool. But such strict conformity is not too surprising for compact stars.
If people were squeezed into balls a hundredth of their normal size, they
too would probably lose most of their individuality.

All that was then needed to estimate the age of the Universe was a measurement
of how long this group of white dwarfs had been cooling. Here is where seismology
of the oscillations plays a crucial role. The vibration period of a star
is sensitive to its size, but it also depends on its temperature. Most white
dwarfs have already collapsed as much as they can, so their sizes are constant.
In contrast, their temperatures will drop as time passes.

As a white dwarf cools slowly, the period of vibration increases and
the frequency decreases. They slow down at a minuscule rate; astronomers
speak in terms of seconds per century. They need many years of careful observation
before the growing lag in a star’s vibrational clock begins to show itself.
Astronomers have been helped by the fact that they need to dedicate only
comparatively small and cheap telescopes, with mirrors as small as 60 centimetres
across, to such a long-term project.

Armed with seismological estimates of changes in period, Winget’s group
calculated how long their proposed first generation of white dwarfs had
been cooling. Then, using theories of the evolution of stars and galaxies,
and simple arithmetic, they arrived at an age for the Universe: about 10.3
thousand million years.

If all the assumptions, some admittedly controversial, are correct,
then the Universe is at least several billion years younger than most astronomers
believe. Debate over this age will continue for some time. In the meantime,
the clock provided by white dwarf cooling, and calibrated by stellar seismology,
is capable of precision few other techniques can equal. And it achieves
this with data from some of the smallest research telescopes used by astronomers.
Cosmology is no longer the exclusive domain of the world’s giant telescopes.

—â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä” Age of the oldest
white 9000 million years, dwarfs in the Galaxy + /- 800 million
years + + Time for a star to evolve 300
million years, into this type of white + 800 or – 100 dwarf
million years + + Time between big bang
between 1000 and 2000 and formation of stars million years in galactic
discs = = —â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”
Age of the Universe 10 300 million years +/- 2200 million years
—â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”â¶Ä”

Jaymie Matthews is an NSERC and Killam Postdoctoral Fellow in the Geophysics
and Astronomy Department, University of British Columbia, Vancouver, Canada.
He specialises in the study of roAp stars.