The theme of this book is that the universe in which we live, or think we live, is mostly a thing of our own making. The underlying idea is the distinction between Universe and universes. It is a simple idea having many consequences.

The Universe is everything. What it is, in its own right, independent of our changing opinions, we never fully know. It is all-inclusive and includes us as conscious beings. We are a part or an aspect of the Universe experiencing and thinking about itself.

What is the Universe? Seeking an answer is the endless quest. I can think of no better reply than the admission by Socrates: “all that I know is that I know nothing.” David Hume, a Scottish philosopher in the eighteenth century, in reply to a similar question, said “it admits of no answer” for absolute truth is inaccessible to the human mind. Logan Smith, an expatriate American living in London, expressed his reply in a witty essay Trivia (1902), “I awoke this morning … into the daylight, the furniture of my bedroom – in fact, into the well-known, often-discussed, but to my mind as yet unexplained Universe.”

The universes are our models of the Universe. They are great schemes of intricate thought – grand belief systems – that rationalize the human experience.

Francis Bacon, English courtier and statesman of the late sixteenth and early seventeenth centuries, promoted a philosophy of empirical science and declared, “let every student of nature take this as his rule: that whatever the mind seizes upon with particular satisfaction is to be held in suspicion.” His strong belief in empirical methods of inquiry assured him that witches existed.

Let us look at the witch universe in which this incredulous and illustrious man lived.

Tracing the development of ideas in the long Middle Ages leads the student into a bewildering labyrinth of astonishing beliefs. The works of Jabir ibn Haiyan, court physician in the eighth century to Harun al-Rashid (the caliph of Baghdad famed in The Thousand and One Nights), became widely known for their medical lore and learned alchemy. Jabir was later latinized into Geber, and because of the rigmarole and obfuscation of the numerous works attributed to him, the word Geberish became eventually gibberish.

In the Middle Ages the telluric elements of earth, water, air, and fire exhibited respectively the qualities of cold, wet, dry, and hot. By erudite argumentation the elements accounted for bodily humors of melancholy, phlegm, choler, and blood, which in a marvelous manner corresponded with the characteristics of creation, fall, redemption, and judgment. Acts of the will were governed by God, acts of the intellect by angels, and acts of the body by the celestial orbs. Each person possessed a daemon or genius who acted as a guiding spirit.

“I drew these tides of men into my hands and wrote my will across the sky in stars,” wrote Lawrence of Arabia in The Seven Pillars of Wisdom. Human tides have washed across the globe, crushing nations and carving out empires, led by god-possessed men who sought to write their will across the sky in stars. One such leader was Alexander the Great, who crossed the Hellespont with his cohorts in the fourth century B.C., subjugated Asia Minor and Egypt, vanquished the armies of the Persian Empire, quelled the turbulent forces of Afghanistan, crossed the Hindu Kush, and invaded and defeated the nations of the Punjab.

Eastward flowed Hellenic philosophy and science in the wake of Alexander's conquests; westward flowed oriental philosophy and religion. Westward into the Mediterranean world came the glorious Ahura Mazda – the Zoroastrian Lord of Light embattled with the Lord of Darkness – bringing the belief that the soul is divine and the worship of gods other than the true god a sin. Westward into the Roman legions came the religion of the dying and resurrected martyred god, the triumphant Mithras, bringing the sacramental eating of the flesh of the god and the notions of forgiveness and redemption. Westward came the Babylonian stories of the creation and the flood, the Persian stories of heaven and hell, the last day of judgment, and the resurrection of the dead, all of which shaped the theology and philosophy of the Greco-Roman world in preparation for the rise of Christianity and Islam.

In everyday life we deal with things of sensible size – such as flowerpots and plants – and to understand these ordinary things we explore the worlds of the very small and very large. We delve into molecules and atoms and reach out to the stars and galaxies. Thus, we know that most atoms composing the Earth were made in stars that died long before the birth of the Sun.

This wide realm of nature, of things ranging in size from atoms to galaxies, is ruled not by the gods of antiquity, but by the laws of motion and the push and pull of electrical and gravitational forces. Electrical forces dominate on the scale of molecules and atoms, accounting for much of the intricacy of the very small; gravitational forces dominate on the scale of stars and galaxies, accounting for much of the intricacy of the very large. The exploration of this luxuriant garden of phenomena is in the care of physical sciences such as chemistry, biochemistry, geophysics, and astrophysics.

The great problems lying deep at the foundations of the physical universe are no longer found in this realm that stretches from atoms to galaxies. They are found in the outer realms of nature. When the scale of measurement decreases a hundred thousand times smaller than the size of atoms, and increases a hundred thousand times larger than the size of galaxies, we quit the lush middle realm and enter the outer realms. Here we discover the truly baffling.

The changeover from the magic universe to the mythic universe never reached completion in Australasia and other isolated lands secure from assault. The populations in these lands survived until recent times snug in their halfway magicomythic worlds. Elsewhere, the globe was in uproar with the rise of the mythic universe.

Climate changes and cultural conflicts stirred the swirl of tribal movements. Food hunters and food gatherers turned to herding and farming, and farming communities emerged between ten and twenty thousand years ago in the Middle East, India, China, Africa, Europe, and later in Mesoamerica. Tribes multiplied, merged and became nations. Powerful ruling families attained royal status, and professional priests interpreted the will of the gods. The arts burgeoned into professions and the crafts into industries. Irrigation systems connected rivers to farmlands, and large works such as Stonehenge in Britain and the pyramids in Egypt marked the rise of engineering. Trade flourished over great distances, as between the cities of Sumer and Akkadia in Mesopotamia and the far cities of Mohenjo Daro and Harappa in India.

The mythic universe was well under way more than six thousand years ago with the rise of the great gods in the delta civilizations of the Nile, Euphrates–Tigris, and Indus. “Thou art the Sole One who made all that is, the One and Only who made what existeth,” chanted the Egyptian priests of the New Kingdom in adoration of Amun the god of Thebes.

Historians would love to search the past in a Wellsian time machine and return to tell the “tales of long, long ago, long, long ago” that in the words of Thomas Bayly, a nineteenth century ballad writer, “to us are so dear.” Historians little know that a timeship has been invented by a professor in the Department of Fantasy and Virtual Reality at the University of Massachusetts. In this secret diachronic conveyance we shall take a journey – a safari in time – back to earlier periods of cosmic history.

Let me welcome you aboard with these comments. Moving backward in time is an uncommon way of presenting history, and to avoid the incongruity of a movie show in reverse, I shall occasionally stop the machine and allow time to resume its normal Newtonian flow while gazing at the scenery. I must warn you that our timeship is still in an experimental stage and will not always do exactly what we want. Please fasten your seat belts.

Tentatively I start the timeship in reverse gear and it lurches into motion. Its dials spin alarmingly, and although I slam on the brakes almost immediately, we have already traveled two million years. Through the windows we see hominids striding around in the early Pleistocene. It would be very interesting to stay and see their progress. But we have other more urgent business.

Helioseismology provides us with means to investigate the otherwise invisible solar interior. The seismic approach is indispensable for the study of internal structure and evolution of the sun. It is even more so, however, for the study of dynamical aspects of the sun, because of the lack of other reliable means. The current status of seismology of solar rotation is reviewed and outstanding problems are discussed.

Introduction

In 1984, Douglas Gough started his paper, entitled ‘On the rotation of the Sun’, by pointing out our lack of understanding of the dynamical history of the sun (Gough 1984). The question of how the sun has evolved dynamically, since its arrival on the main sequence, still stands as one of the big questions in astronomy. With an increased level of interest attracted by the issue of how our solar system (and other ‘solar’ systems) formed and evolved, it may be a problem of even greater importance today.

Another big problem regarding the solar rotation is what is behind the solar cycle, and if a dynamo mechanism is responsible, as is generally believed, how it works. Here, too, the problem seems to be recognized in a wider community because of the great interest currently shown towards the solar-terrestrial study.

In tackling both problems, an important key is the dynamical structure of the sun today, and in particular how it rotates. Observational clues are not many.

Telechronohelioseismology (or time-distance helioseismology) is a new diagnostic tool for three-dimensional structures and flows in the solar interior. Along with the other methods of local-area helioseismology, the ring diagram analysis, acoustic holography and acoustic imaging, it provides unique data for understanding turbulent dynamics of magnetized solar plasma. The technique is based on measurements of travel time delays or wave-form perturbations of wave packets extracted from the stochastic field of solar oscillations. It is complementary to the standard normal mode approach which is limited to diagnostics of two-dimensional axisymmetrical structures and flows. I discuss theoretical and observational principles of the new method, and present some current results on large-scale flows around active regions, the internal structure of sunspots and the dynamics of emerging magnetic flux.

Introduction

Telechronohelioseismology (or telechronoseismology) is defined as a subdiscipline of helioseismology by Gough (1996) in his reply to criticism of the term ‘asteroseismology’ (Trimble 1995). Gough argued that, being derived from all classical Greek words, ‘thoroughbred’ telechronohelioseismology should be preferred to ‘oedipal combinations’ of Greek and Latin words. Telechronohelioseismology belongs to a new class of helioseismic measurements, broadly defined as epichorioseismology (also calledlocal-area helioseismology), which provides three-dimensional diagnostics of the solar interior.

Helioseismology is originally basedon interpretation of the frequencies of normal modes of solar oscillation.

Introduction

Although sometimes ignored, there is no doubt that hydrodynamical processes play a central role in virtually all areas of astrophysics. If they are neglected in the analyses of observations and the modelling, the results for any object must become questionable; the same is therefore true of the understanding of basic astrophysical phenomena and processes that result from such investigations.

Investigations of astrophysical fluid dynamics are hampered by both theoretical and observational problems. On the theoretical side it is evident that the systems being studied are so complex that realistic analytical investigations are not possible. Furthermore, the range of scale, extending in the case of stars from the stellar radius to scales of order 100m or less, entirely prevents a complete numerical solution. Observationally, the difficulty is to find data that are sensitive to the relevant processes, without being overwhelmed by other, similarly uncertain, effects. Progress in this field therefore requires a combination of physical intuition combined with analysis of simple model systems, possibly also experiments analogous to astrophysical systems, detailed numerical simulations to the extent that they are feasible, together with a judicious choice of observations and development and application of analysis techniques that can isolate the relevant features. Douglas Gough has excelled in all these areas.

In this brief introduction we make no pretense of reviewing the whole vast field of hydrodynamical processes in astrophysics, or even in stars.

The discovery of extrasolar planets and the determination of their orbital properties have provided golden opportunities for new advancements in the quest to understand the origin and evolution of planets and planetary systems. While their bizarre variety presents a challenge for the existing theories, their ubiquity suggests that planetary formation is a robust process. Combining data obtained from solar system exploration, star formation studies and the searches for extra solar planets, we address some outstanding issues concerning critical processes of grain condensation, planetesimal coagulation, and gas accretion. Some implications of these investigations are: 1) the amount of heavy elements available for planetary formation in protostellar disks is retained at a similar level as that empirically inferred for the primordial solar nebula, through self regulated processes and 2) the critical stages of planet formation, from grain condensation, planetesimal coagulation, to gas accretion, proceed on the timescale of a few million years.

Observations

Ongoing searches of extra solar planets (ESPs) have led to their discovery around ten per cent of the solar-type stars on various target lists (Marcy & Butler 1998). The dynamical properties of many ESPs are very different from those of planets in the solar system. The first ESP discovered, while having a mass (Mp) similar to that of Jupiter (MJ), is located 100 times closer to its host star 51 Peg than Jupiter is to the Sun (Mayor & Queloz 1995). The period (P) distribution of ESPs has a noticeable concentration between 3–7 days.

Pulsation is a common phenomenon in stars. It occurs in a wide range of their masses and in all evolutionary phases, exhibiting large variety of forms. Stochastic driving and just two distinct instability mechanisms are the cause of the widespread phenomenon. The diversity of pulsation properties in stars across the H-R diagram is partially explained in terms of differences in the ranges of unstable modes and in terms nonlinear mechanisms of amplitude limitation. Still a great deal remains to be explained.

Introduction

Excitation of the fundamental radial mode was the essence of the pulsation hypothesis when it was first proposed by Ritter in 1879, as an explanation of periodic variability in stars. Radial symmetry of the motion was confirmed for a number of objects by means of observational tests. Excitation of the same, presumably fundamental, mode in all δ Cephei type stars got support in the discovery of the period-luminosity relation, which at some point seemed unique. Soon, the hypothesis that only the fundamental radial mode may be excited became a dogma like the earlier one that stars do not vary.

Referring to Schwarzschild's (1942) suggestion that RRc stars might be first overtone pulsators, Rosseland (1949) wrote: This hypothesis involves the very difficult problem of how to excite a higher mode to pulsation while leaving the fundamental mode unexcited.

Douglas Gough & Michael McIntyre proposed, in 1998, the first global and self-consistent model of the solar tachocline. Their model is however far more complex than analytical methods can deal with. In order to validate their work and show how well it can indeed represent the tachocline dynamics, I report on progress in the construction of a fully nonlinear numerical model of the tachocline based on their idea. Two separate and complementary approaches of this study are presented: the study of shear propagation into a rotating stratified radiative zone, and the study of the nonlinear interaction between shear and large-scale magnetic fields in an incompressible, rotating sphere. The combination of these two approaches provides good insight into the dynamics of the tachocline.

Introduction

The tachocline was discovered in 1989 by Brown et al.; it is a thin shear layer located at the interface of the uniformly rotating radiative zone and differentially rotating convective zone of the sun. Several issues about these observations remain unclear. Why is the radiative zone rotating uniformly despite the latitudinal shear imposed by the convection zone, and why is the tachocline so thin? How can the tachocline operate the dynamical transition between the magnetically spun-down convection zone and the interior? The first model of the tachocline was presented by Spiegel & Zahn (1992).

There has been a long-standing discrepancy between the number of neutrinos expected from the sun and the number we actually detect. One possible interpretation for this was that our theoretical solar model was wrong. However, recent progress of helioseismology has shown that the real sun is very close to the latest solar models. On the other hand, very recent experiments of neutrino detection provided us evidence for neutrino oscillation. I discuss what we should do and what we can do in this situation for the neutrino physics from the astrophysical side.

Historical review: the solar neutrino problem

The energy source of sunshine (and shining of stars in general) is now thought to be nuclear fusion. To get direct evidence that nuclear reactions are really occurring in the sun is, however, a very challenging task. It takes ∼ 104 years for photons generated by nuclear fusion near the solar centre to reach the solar surface, because the photons interact so frequently with matter in the sun. Hence, the photons by which we can see the sun right now do not tell us the physical state of the present solar core. On the other hand, since neutrinos interact little with matter, unlike photons, and travel at the speed of light, the neutrinos generated by nuclear reactions in the sun reach the earth only eight minutes after they are generated.

The last decade has seen an impressive improvement in the quality and quantity of helioseismic data. While much of the progress has come from a new generation of instruments, such as GONG and MDI, data analysis has also played a major role. In this review I will start with a brief discussion of how the basic analysis of helioseismic data is done. I will then discuss some of the data analysis problems, their influence on our inferences about the Sun and speculate on what improvements may be expected in the near future. Finally I will show a selection of recent results.

Introduction

Until recently most research in helioseismology has used modes in the low (l ≤ 3) and medium (3 < l ≤ 200) degree (l) ranges. Here I will concentrate on the methods and problems in the study of medium-degree modes as well as show selected results. Most studies of modes of high degree (l > 200) have used entirely different analysis methods, such as time-distance analysis, which is discussed elsewhere in this volume (Kosovichev 2003). However, I will touch on some of the issues regarding the analysis of the high-degree modes by methods similar to those used for the medium-degree modes. The reader is also referred to Haber et al. (2002) for results from a technique known as ring diagrams which also uses high-degree modes.

I will start by providing some background material on solar oscillations in Section 17.2.

In this contribution I discuss how recent advances in numerical techniques and computational power can be applied to problems in astrophysical fluid mechanics. As a case in point some results of simulations of radio relics are presented which have provided strong support for a model that explains the origin of these peculiar objects. Radio relics are extended radio sources which do not appear to be associated with any radio galaxy. Here a model is presented which explains the origin of these relics in terms of old plasma that has been compressed by a shock wave. Having taken into account synchrotron, inverse Compton and adiabatic energy losses and gains, the relativistic electron population was evolved in time and synthetic radio maps were made which reproduce the observations remarkably well. Finally, some other examples are discussed where hydrodynamical simulations have proven very useful for astrophysical problems.

Introduction

With the advent of powerful computers and more accurate algorithms, simulations of astrophysical fluids have become increasingly useful. Most fields of astrophysics, such as solar physics, star formation, stellar evolution and cosmology have benefitted greatly from hydrodynamical simulations and hopes for further advances are high.

Essentially, there are two main approaches to the numerical solution of the equations of hydrodynamics: Finite-grid simulations and Smoothed Particle Hydrodynamics (SPH). In the former approach the equations are discretised on a computational mesh before they are solved. The latter method avoids the notion of a mesh and employs particles to track the fluid.

Oscillations and waves in the quiet and active solar atmosphere constitute a zoo of distinct and overlapping phenomena: internetwork oscillations, K-grains, running penumbral waves, umbral oscillations, umbral flashes etc. The distinctive oscillation spectra associated with the network, the internetwork, and sunspots and pores are a strong indicator that the magnetic field has a significant dynamical effect on wave motions. This immediately raises two questions i) Can waves be used as diagnostic indicators of the magnetic field? and ii) Do the different properties of wave motions in various field geometries have consequences for the efficiency of wave-heating in the atmosphere and corona? I will discuss some new numerical calculations of wave propagation in a variety of model atmospheres, which throw some light on these questions.

Introduction

The field of helioseismology has shown how waves which propagate through the deep solar interior can be used to determine the internal properties of the Sun – including its stratification, differential rotation, and sub-surface flow fields. Given the wide variety of waves and oscillations observed in the atmosphere of the Sun, in both Quiet and Active Regions, it is natural to ask whether the structures of these regions can also be determined from a wave analysis.

However, a brief consideration of the problem indicates that there are a number of critical differences between the atmospheric-wave problem and the p-mode problem which make the former vastly more difficult to study.