The Role of Images in Astronomical Discovery Read online

  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

  14:06:02, subject to the Cambridge Core

  .009

  7. A Symphony of Waves

  161

  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.

  14:06:02, subject to the Cambridge Core

  .009

  162

  Part II – Images as Galaxy Discovery Engines

  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.

  14:06:02, subject to the Cambridge Core

  .009

  7. A Symphony of Waves

  163

  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

  14:06:02, subject to the Cambridge Core

  .009

  164

  Part II – Images as Galaxy Discovery Engines

  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.

  14:06:02, subject to the Cambridge Core

  .009

  7. A Symphony of Waves

  165

  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

  14:06:02, subject to the Cambridge Core

  .009

  166

  Part II – Images as Galaxy Discovery Engines

  photon at a wavelength of 21 cm (1,420 MHz); it is the difference in energy between the two