The bow whispers to the arrow before it speeds forth - "Your freedom is mine."
iola. Cello. We have an image of spiral galaxies as great stringed instruments, instruments being plucked or bowed, in which the strings of gas and dust typically measure some 100 000 light years across.
The setting: The National Gallery in Canberra.
The occasion: A string trio. Serena McKinney (violin), Katie Kadarauch (viola) and Arnold Choi (cello), who had recently performed at the famed Carnegie Hall. As we sat spellbound listening to the meticulous vibrations of the strings on a Nicolaus Gagliano violin (circa 1760), a Giovanni Grancino viola (circa 1695) and a Carlo Tononi cello (circa 1725), we were transported to magical moments outside of time. One point is, however, strikingly clear: without the bowing of the strings - without the grand bow - there would be no musical tones or harmonics. As in music, so in spiral galaxies do we encounter waves with the full complexity of modes.
No bowing of the strings of the cello, of the violin, of the viola ... no grand bow ... no music. Sitting at the National Gallery in Canberra, what we visually saw was each musician bowing their different strings, but what is actually happening is that multitudes of different sound waves of different frequencies are being produced in the auditorium. It is not a static, but a highly dynamic, interplay. To describe this interplay from a mathematical point of view, one can say that the shape of any bowed string can be represented in terms of an infinite The Grand Bow number of waves or modes. 255
The genius who developed the mathematical technique used in both worlds of music and in our infrared images of galaxies was none other than Jean Baptiste Joseph Fourier, born at Auxerre in France on March 21, 1768. His mother died while Joseph was only nine years old; his father died the following year. Fourier's first schooling was at Pallais' school, run by the music master from the cathedral in Auxerre. There Joseph Fourier studied both Latin and French and showed great promise. At the tender age of thirteen, mathematics became Fourier's chief focus of interest. By the age of 14, Fourier had completed a study of the six volumes of Cours de mathématiques by Bézout. Fourier analysis, Fourier series and Fourier transforms all bear the name of this most talented genius. Notable students of Joseph Fourier included legendaries Gustav Dirichlet and Claude-Louis Navier. Fourier was elected a Fellow of the Royal Society in 1823. When Gustave Eiffel built his famous Parisian Eiffel tower, he included the names of 72 prominent French scientists on plaques around the first stage, and one of these is Joseph Fourier.
Fourier expressed his thoughts:
Mathematical Analysis is as extensive as nature herself.
Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.
Fourier died in 1830; could Fourier ever have imagined that his exquisite mathematical analyses would be used in the 21st century to study symmetries in the disks of galaxies behind Cosmic Shrouds of the Night?
Galaxies, such as the River of the Night, our Milky Way, are highly dynamical entities. One can think of a series of waves of gas propagating through the disk. A simple analogy may be in order. Let us consider a pond of water into the center of which is thrown a stone. Waves of water will propagate outward, hitting the wall of the pool. They will then be reflected, journeying back toward the center of the pool, and so forth. Some of the wave-crests will be enhanced Shrouds of the Night (we term this "constructive interference") while incoming and outgoing waves may essentially
256 "cancel" one another out; mathematically, we call this destructive interference.
The medium in which the waves in the disks of galaxies propagate is twofold: gas and stars. When examining the "backbones of the night" with infrared cameras, we are actually imaging waves of stars moving inwards and outwards of the disk. Ultimately these waves might be reflected off the inner bulge of stars, producing constructive and destructive interference patterns.
The actual material in the mask - the gas - is highly responsive, just like the responsiveness of water in a pond when it reacts to a plunging stone. Some of the most far reaching ideas pertaining to the underlying structure we see in spiral galaxies dates back to 1964, when C.C. Lin and his [then] undergraduate student Frank Shu (who studied under Lin at the Massachusetts Institute of Technology), presented their research work in a paper entitled "On the Spiral Structure of Disk Galaxies." We celebrated the 40th anniversary of that seminal paper at an International Galaxy Conference held in South Africa in 2004.
In our preceding chapter, we carefully noted that when we penetrate shrouds of cosmic dust and peek through these cosmic veils, the patterns we observe in the stars behind the mask can be radically different to that imaged optically in the icing on the cake itself - the dust mask.
In our interpretation of what lies behind Shrouds of the Night, David has worked closely with Giuseppe Bertin in Pisa, one of the mathematicians who developed a theory known as the "modal theory" of spiral structure. In that theory, spiral arms of galaxies may be thought of as the manifestations of sets of traveling waves. Areas of enhanced surface brightness in the infrared may be regarded as regions where waves of principally old stars have constructively interfered with one another.
The players and bowers of our strings on the scales of galaxies spanning possibly a hundred thousand light years - sometimes much more - are varied.
In some examples, the intrusive player may be another galaxy - such as when the galaxy Messier 32 collided almost head-on with the Empress of the Night, the Andromeda Spiral
Galaxy. Disturbances in the wave trains or modes may be very striking indeed, when such The Grand Bow worlds in space (galaxies) collide. The dynamic interplay is analogous to the pizzicato 257
plucking of a string. The player's finger in the Andromeda Spiral would be the interloper Messier 32, which lies external to the "strings" of spiral structure which existed in the disk of the Andromeda Galaxy prior to the collision with Messier 32.
The strings are the Shrouds of the Night: masks of gas and dust, which are highly responsive. In many examples, the bow is the backbone of old stars, inducing waves in the masks. Another efficient bowing mechanism could be the ingestion of gas from vast filamentary wells outside galaxies, renewing spiral forms - which otherwise would die away with time.
In other cases, Nature provides us with a grand bow in the form of a bar of stars - many of these veiled behind their dusty masks. The interplay between a bar of stars and its bowing on the strings (masks of gas and dust in the parent galaxy) is highly dynamic - the presence of bars creates inflows of gas, radially toward the centers of galaxies - such cosmic bows ever draw their masks, creating motions of gas clouds on mammoth scales; motions which, over aeons of time, may actually destroy and then reform the presence of a bar.
What actually occurs as the grand bow itself is played? Gas in the disk is trapped in a spiral-shaped potential well. This gravitational well pulls a young star from its orbit in the neighborhood of a spiral arm. A tug-of-war ensues. The spiral arm pulls the star outward, increasing its radius from the center. However, as the radius increases, its velocity decreases, because of a fundamental law, known as the conservation of angular momentum. Young stars lag behind and begin to pile up, much like a traffic jam on Earth ... creating those fiery lights which so often outline or delineate spiral arm structure seen in the optical images of Hubble and Keeler, for example.
Some spiral pinwheels of the night may present to us lively allegro moltos, others a more tranquil andante; whatever the cosmic orchestra may present to us, we live in an epoch wherein astronomers are able to untangle these spiral modes using Fourier transforms birthed so many years ago, in the mind of Joseph Fourier.
We're now looking at a transition to a possible change in the way we look at galaxies. Sometimes ... we see disks that have a spiral structure that we couldn't have dreamt existed from looking at the optical picture ... we've got a possibility here ofapplying the morphology to a physical framework, perhaps in a way that none of us could have dreamt of before we had the capability of sweeping the dust away from the galaxy in a figurative sense.
What is bowing the gas mask of NGC 309 (Figure 131)? What generates those gargantuan shock-waves of gas, spawning myriads of young stars and blazing regions of ionized hydrogen gas?
What we see optically is the result (not the cause) of a grand bow at work: a small bar and patterns of waves of old stars interacts with a highly complex mask of dust and gas. The grand bow is seen in full action behind the dust shroud!
It is what the hidden grand bow does, which creates the music. As we have repeatedly seen, we cannot, a priori, tell from the music what our Cosmic Fiddler of the Night is up to!
We have noted that, on photographs, NGC 253 is a flocculent spiral galaxy (Figure 140), with fleece-like spiral arms. In the dust penetrated view, the galaxy betrays a remarkably regular pattern: its hidden symmetry, behind the mask, is strikingly revealed. Behind the masks of dust and gas lies the hidden grand bow: a bar, and a regular, classic two-armed spiral.
In our music analogy, the whole is composed of the sum of its parts. We may think of the composer Arvo Part with his tonal technique "tintinnabuli" which produces a profound, mysterious and moving rendering of the Te Deum. Impinging on the ear are the sounds of music akin to a Gregorian chant, with careful use of varying choral forces, strings, piano and "ison," sometimes represented by the organ (the ison is a long drawn-out musical base note). Different choral voices add a profusion of sound to his Te Deum, but the whole is the sum of each part.
Backbones of the night reveal far more restrained structures of stars lying in one or usually at most two spiral arms. Very seldom are backbones of three or four spiral arms imaged behind the mask. Our Local Universe presents astronomers with a ubiquity of low-order modes or waves in the dust-penetrated infrared regime. This is in stark contrast to the myriads of multi-arm features and "spurs" which such ordered backbones may generate in the optical mask. Backbones of the night are generally very much older than the masks of young stars and of dust; while they do their cosmic plucking with care, their lively "allegros" in the mask are often enchanting to behold.
The unique note from a violin, whether it be mellow or jarring, is a product of unique events: these include the characteristics of the violin (for example, what the belly and the back are made of, its thickness, and what the strings are made from), combined with the specific way that the violin has been played by the musician.
Likewise, each galaxy has a unique history, with its own, unique harmonics or modes. It is the music of each galaxy.
From simple tunes and a few simple notes, they expand into fugues by ...
a variety of devices of fragmentation and reassociation, of turning it upside down and back to front; by overlapping these and other variations of it into a range of tonalities; by a profusion of patterns of sequences in time, with always the consequent interplay of sound flowing in an orderly way from the chosen initiating ploy (that is more technically, by inversion, stretto, and canon etc.) Thus does a J.S. Bach create a complex and interlocking harmonious fusion of his seminal material, both through time and at any particular instant, which, beautiful in its elaboration, only reaches its consummation when all the threads have been drawn into the return to the home key of the last few bars - the key of the initial melody whose potential elaboration was conceived from the moment it was Shrouds ofthe Night first expounded.
As we have repeatedly seen, the grand bows are, most often, bars in the disks of spiral galaxies. It is largely from these rotating bars that galaxy taxonomy is born. The diversity of the "bar phenomenon" beckons loud and clear.
A note of caution, pertaining to galaxies masked in their icings of dust in our younger, distant, seemingly chaotic Universe: we cannot, with present technology, penetrate their Shrouds of the Night, simply because they are moving away from us with such enormous speeds, that special filters on-board future space-borne telescopes will be necessary to do such mask penetrations properly.
When astronomers use the traditional near-infrared filters to study such distant galaxies, they invariably sample photons in the ultraviolet region of the galaxy's spectrum! The most distant known galaxies at the time of writing have their ultraviolet region of the spectrum (a wavelength of 0.35 microns) redshifted to about 4 microns in the mid-infrared. This is because the galaxy's entire spectrum has been shifted toward the red end of the spectrum on account of its speed away from us. What is essential is a very large telescope in space (much larger than the Hubble Space Telescope) equipped with special mid-infrared filters (not near-infrared filters, such as those which we have used in this book). Only with such mid-infrared filters can we see these very distant young galaxies in their "restframe near-infrared." Distant galaxies may appear to be highly chaotic and disordered, but this could well be a result of cosmic masks: again, one tends to concentrate on the brilliant light-beacons of young stars, while magnificent symmetries may be simply shrouded by particles of dust, as in our Local Universe. Such are the challenges awaiting the James Webb Space Telescope, to be in an orbit on the far side on the Moon and scheduled to be launched in 2013.
It is clear that many distant galaxies are very dusty indeed; it is intriguing to see just how well dust particles have evidently been manufactured in our early (young) Universe.
In other distant galaxies, peculiarity may remain the norm, for their dust penetrated backbones of older stars may still be in the process of formation. At such primordial epochs, the grand bow may possibly appear to be broken - fragmented. Such bows may be drawing at strings which optically may appear broken, too.
There is a wonderful San story, entitled "The Broken String:"
People were those who Broke for me the string. And so
The place became like this to me, On account of it.
Because the string was that which broke for me. And so
The place does not feel to me, As the place used to feel to me, On account of it. For,
The place feels as if it stood empty before me. Therefore,
The place does not feel pleasant to me, On account of it.
Strings can be broken: on musical instruments, by people; on galactic scales, by multitudes of interactions and mergers. Dust penetrated images of some distant galaxies may remain chaotic when imaged through the eyes of forthcoming space-borne telescopes - perhaps the young Universe is simply the place we are not yet that familiar with - after all, the Universe now, is not the place it used to be.
Penetrating the Mask of Time chapter
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