The Role of Images in Astronomical Discovery
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ence). We observe this with water waves on a pond, “giant waves” in the ocean or sound
waves in a room. Electromagnetic waves, light or radio, do the same. A multitude of set-ups,
by way of an interferometer, create interference patterns that can be exploited.
A simple interferometer combines the signals of two antennae. The intensity of the waves
(how strong it is) and their phases (where the wave is) need to be monitored. By analyzing
the structure of the resulting signal after the interference, the angular size of a source, or
the angular distance between two or multiple sources, can be estimated. Even the shape
of a source can be inferred. It suffices to know the wavelength and the dimensions of the
interferometer, i.e. the distance between its collecting elements and their orientation, with
respect to the source under study. A more complex but also more powerful interferometer
can be created by combining the beams of multiple antennae or radio telescopes. This has
not been an easy task, but using this approach, brilliant individuals have managed to design
and build a revolutionary type of imaging radio telescope. Obviously, the appropriate signal
analysis technologies had to be in place.
In the 1960s, groups of British, Dutch, Australian and Canadian radio astronomers
invented the technique by which a few radio telescopes, spread around but interconnected,
could achieve the angular resolution equivalent to that of a large monolithic aperture; they
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called the technique aperture synthesis.15 Instead of using a filled aperture or a very large
single antenna, a number of distributed dishes or smaller antennae were positioned to form
the multiple paired elements of a giant radio interferometer. Some of the telescopes could
be moved on tracks, allowing pairs of different baseline lengths, overall mimicking a larger-
sized telescope with holes in it, that is a partially filled surface. Signals received from each
of the dishes were precisely synchronized to interfere. The arrival of atomic clocks enabled
this high-precision work. There remained only the complex task of disentangling the inter-
ference patterns thus observed.
To do this, radio astronomers used very fast computers, called correlators, to compare
the radio signals, record their phases and their intensities as received from a given point
in the sky and for each separation and orientation of all sets of antenna pairs. To get more
angular coverage, the rotation of the Earth was put to work, following an ingenious proposal
and technique put forward by the British astronomer Martin Ryle (1918–84).16 As the Earth
rotates, the orientation of the different pairs changed with respect to the sky. Multiple pairs
and the continuing change in their orientation generated many signals, and helped to repro-
duce a virtual surface close to a filled surface. Peter Scheuer has written a fine review of the
early days of aperture synthesis.17 However, organizing the multitude of interference pat-
terns recorded for the different pairs, as orientations changed, requires more sophisticated
mathematical tricks. A sort of “image” is obtained, but a further transformation needs to
be applied, as one would need a specially wired brain to make up the real physical images
from these raw data.
A Symphony of Waves
We can use a musical analogy to illustrate another important aspect of wave physics: har-
monics. A musical symphony comprises the sounds of several instruments. By creatively
combining the tunes of wind instruments, strings and percussion, composers, conductors
and musicians produce wonderfully unified melodies. By letting the ear and the mind flow
with the sounds, we forget the individual instruments. We are barely aware that they all con-
tribute to the execution of the piece, coming in at different times and at varying sound levels.
The temporal and intensity variations of the contributions by the groups of instruments are
essential to the quality and impact of the final melody.
Just like musicians, mathematicians have found that natural shapes and phenomena
(fixed or evolving with time) can be represented by the sum of relatively simple periodic
trigonometric functions, sinusoids or cosines, or sine waves (Fig. 7.5). This is harmonic
analysis. The simplest wave is the sinusoidal function that varies regularly over given cycles.
15 W. T. Sullivan, III presents a fine review of early radio in Some Highlights of Interferometry in Early Radio Astronomy, in Radio Interferometry: Theory, Techniques and Applications, T. J. Cornwell and R. A. Perley (editors), Astronomical Society of the Pacific Conference Series, 1991, Vol. 19, pp. 132–149.
16 Martin Ryle, The New Cambridge Radio Telescope, Nature, 1962, Vol. 194, pp. 517–518.
17 P. A. G. Scheuer, The Development of Aperture Synthesis at Cambridge, in W. T. Sullivan, III (editor), The Early Years of Radio Astronomy, Cambridge: Cambridge University Press, 1984, pp. 249–265.
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Fig. 7.5 A square wave reconstructed with four sinusoidals of different amplitudes.
To extract the contributing waves, the signal needs to be decomposed. The decomposition
technique was explored by several mathematicians of the seventeenth and eighteenth cen-
turies. However, it was French mathematician and physicist Jean-Baptiste Joseph Fourier
(1768–1830) who introduced and applied the principle of oscillating functions to natural
phenomena, first to study the propagation of heat in solid bodies.18 It is an interesting aside
that Fourier was also a mentor and strong supporter of the young Jean-François Champol-
lion (1790–1832) who decrypted the texts on the Rosetta stone.
When you listen to a fugue or toccata from Johann Sebastian Bach, instruments enter
a melody at different times; they are phased to create a new melody. The appropriate
18 J.-B. J. Fourier, Théorie analytique de la chaleur, Paris: Chez Firmin Didot, père et fils, 1822.
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gathering of various sinusoids can reconstruct a shape: the coefficients determine their rel-
ative strength, and their phase, i.e. the amount of shift between the various sinusoids.
As illustrated in Fig. 7.5, it is possible to reproduce any geometrical shape by combining
in a weighted fashion an infinite number of sinusoids: it is a matter of adjusting the phases
(that is shifting the waves with respect to each other) and experimenting with their peak
intensities. This is the principle of a Fourier series. Fourier series and their more sophisti-
cated representations, Fourier transforms, are the mathematical tools used to calculate or
extract the spectrum, i.e. the frequencies and amplitudes of the set of sinusoids needed to
reproduce a physical shape or a time variable signal. For example, the spectrum of sinusoids
that reproduces a square box is the function sin ( x)/ x, also called a sinc ( x) function, where x is a fractional or integer value of π.
Fourier series and Fourier transforms have become extremely powerful analytical tools
in many fields. They are applied to a wide range of mathematical, physical and en
gineer-
ing problems, particularly in image processing and signal reconstruction. They play a part
in just about every single high-technology device used today. So when you look around,
remember anything can be reproduced just by a carefully designed sum of sinusoids.
Synthesis of Radio Images
Let us recap. Using several pairs of antennae or radio telescopes at varying separations,
a cosmic source is sampled at different angular scales and resolutions. With N antennae,
there are effectively N( N – 1)/2 usable pairs. For example, the 27 antennae of the Y-shaped
Very Large Array in New Mexico provide 351 simultaneous baselines (see Plate 7.3; see
also the ALMA antennae, Plate 6.1). Letting the Earth’s rotation change the orientation of
the various pairs, the brightness pattern and phase structure can be mapped over different
position angles in the sky. More specifically, it is as if you had assembled a good part of a
very large reflector by strategically positioning your small antennae and letting the rotation
of the Earth fill more and more of the area of the virtual large reflector.
Fast computations run on powerful correlators allow astronomers to construct maps of
the amplitudes and phases of the radio signal received from all sets of pairs of antennae.
Changing the distances between the pair allows the sampling of different spatial separations
(i.e. angular resolution) and the Fourier plane (of frequencies and orientations) is filled
with antennae positioned at as many different baselines and orientations as is operationally
feasible. The whole set of sampled waves, the Fourier plane, can, in our analogy, be called
the full symphony.
An interferometer of this sort, working for several hours, facilitates the measurement
of the Fourier components of the radio brightness distribution, i.e. their spatial frequencies
across a source or the angles at which dominant structures repeat themselves. It is not possi-
ble to get pairs of signals for an infinite number of antennae pairs, separations and orienta-
tions. Incomplete sampling is a fundamental but well-known problem of signal processing,
analysis and reconstruction, as it is not possible to derive all the Fourier components. Math-
ematical tools have been developed to work around the limitation and to reconstruct images
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assuming that a minimum number of configurations are observed. When the observer has
compiled enough Fourier components, he or she does a mathematical conversion called a
Fourier transform to obtain a two-dimensional image. Amazing, indeed.
Imaging by aperture synthesis has improved enormously since the 1960s. Radio
astronomers now produce astonishing radio images of astrophysical objects that compare
in resolution with the best images of optical telescopes on the ground and in space. Fur-
thermore, because radio antennae can be disposed around the surface of the Earth and even
in orbit around it, the angular resolution obtained is the highest of all wavelength regimes,
reaching the microarcsec scale, i.e. 100,000 times better than the best images of the Hubble
Space Telescope. This is an amazing turn-around. However, optical astronomers have not
lagged behind. They are also using interferometry and aperture synthesis. The signals of
optical telescopes separated by a few hundred meters are combined in the same way as for
radio interferometers. However, because of the blurring effect of our turbulent atmosphere,
the technique suffers from limitations that affect radio waves to a lesser degree.
The arrival of aperture synthesis has been revolutionary. The 1974 Nobel Prize in Physics
was awarded to British astronomers Martin Ryle (1918–1984) and Antony Hewish “for
their pioneering research in radio astrophysics: Ryle for his observations and inventions,
in particular of the aperture-synthesis technique, and Hewish for his decisive role in the
discovery of pulsars.” Apart from being visionary, Ryle was a very pragmatic scientist. Peter
Scheuer recalled Ryle telling him about implementing the technique in the early days: “On
engineering topics you shouldn’t write mere theory, you should jolly well build the thing
first.”19
Imaging Cosmic Dragons
Early in the investigation of galaxies, it was found that the centers of some galaxies were
sites of weird phenomena. Already in 1909, the German-born American astronomer Edward
Arthur Fath (1880–1959) had noticed the presence of very strong and broad emission lines
in the spectrum of the nucleus of the spiral galaxy NGC 1068. Fath was an astronomer
at Mount Wilson Observatory. Allan Sandage writes that Fath left the observatory in 1913
because of a conflict with director Walter Adams. “Had he stayed, Fath would have become
the Edwin Hubble of the observatory,” adds Sandage.20 Fath had found that spirals had
spectra like star clusters, but the spiral NGC 1068 in the constellation of Cetus was one
of the exceptions.21 In 1926, Edwin Hubble added a few more galaxies exhibiting central
activity. The American astronomer Carl Keenan Seyfert (1911–1960) carried out a whole
study of this class of objects, hence the name “Seyfert galaxies.”22
19 P. A. G. Scheuer, The Development of Aperture Synthesis at Cambridge, in W. T. Sullivan III (editor), The Early Years of Radio Astronomy, Cambridge: Cambridge University Press, 1984, pp. 249–265.
20 A. R. Sandage, Centennial History of the Carnegie Institution, Volume 1: The Mount Wilson Observatory, Cambridge: Cambridge University Press, 2004, p. 88.
21 E. A. Fath, The Spectra of Some Spiral Nebulae and Globular Star Clusters, Lick Observatory Bulletin, 5, 1909, No. 149, pp. 71–77.
22 C. K. Seyfert, Nuclear Emission in Spiral Nebulae, The Astrophysical Journal, 1943, Vol. 97, pp. 28–40.
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Radio observations were key in revealing the nature of these strange sources. Cygnus
A, first observed by Grote Reber in 1939, was the strongest discrete source of radio waves.
The “radio star” was later identified as a giant elliptical galaxy at a distance of 700 million
light-years. With aperture synthesis, it was shown to be surrounded by two giant radio lobes
of synchrotron radiation, one on each side of the galaxy like a giant butterfly deploying
wings. Cygnus A became the archetype of a fascinating family of extragalactic objects,
radio galaxies (see Plate 7.4).
Indeed, the most impressive astrophysical phenomena seen at radio wavelengths are
these giant radio galaxies: huge clouds of energetic particles, ejected by active galaxies
emitting synchrotron radiation, spewed and ballooning out as colossal lobes of radio emis-
sion. The lobes appear to be roped right into the core or nucleus of the galaxy. The nature
of the central sources or engines remains somewhat mysterious, but is probably explained
as a massive black hole nurturing high-energy processes. Like a particle accelerator, the
galaxy’s central engine sends out energetic electrons and protons in jets extending some-
times to millions of light-years. The precessing jets fan out as spectacular lobes of syn-
chrotron radiation. The majority of the sources are associated with elliptical
galaxies, but
some spirals also harbor an active galactic nucleus. Cygnus A, the most powerful radio
source in our region of the universe, produces several million times more radio energy
than a normal galaxy; its output corresponds to ten times the energy produced at all wave-
lengths by our Milky Way. Quasars are the most energetic and distant members of the
active galactic nuclei family, reaching luminosities 100 times greater than that of the Milky
Way.
Atoms in a Spin
Energetic electrons spiraling along cosmic magnetic field lines are not the sole sources of
radio emission. Hydrogen, the most abundant element in the universe, is an important source
of radio emission, through two different processes (spin transition and bremsstrahlung, dis-
cussed later), which greatly help in the understanding of the physics of cosmic matter. The
first process is a very subtle atomic transition, which is responsible for the extraordinary
radio spectral line at 21 cm (a frequency of 1,420 MHz). This spontaneous transition is of
huge astronomical importance because it arises from neutral hydrogen, the most common
form of the element in the universe; it is produced by atoms of hydrogen at temperatures in
the range of a few to about 100 kelvins.
Let us draw in our mind a simple picture of a hydrogen atom: the positive proton is at the
center of the atom, circled by the light negative electron. Imagine both the electron and the
proton as little spinning tops. These miniature tops have a quantum property that allows their
axes to be either aligned, i.e. their spinning axes pointing in the same quantum direction, or
oppositely aligned – in the analogy of tops, with spin axes pointing in opposite directions.
In the quantum world, these two configurations correspond to two different energy states.
Amazingly, about once every few million years, the electron top flips spontaneously, and
points in the opposite direction to what it was before. The minute flip produces a radio
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photon at a wavelength of 21 cm (1,420 MHz); it is the difference in energy between the two