ABSTRACT

Using deep HST/WFC images, originally taken to study faint radio galaxies, we find 81 clear serendipitous galaxy images, of which 34 are pair members. Based on nearby magnitude-limited samples, this is an excess of more than 4σ above the expected number of pair members. We take this result as strong evidence that the galaxy merger rate was higher in the past, and has declined over time.

INTRODUCTION: GALAXY MERGERS AND EVOLUTION

Galaxy interactions and mergers have been implicated as driving galaxy evolution in several ways:

Triggering starbursts, thus making the star-forming history episodic Driving global winds from starbursts, sweeping merger remnants free of gas and dust Transforming galaxy morphology through mergers and tidal impulses Triggering nuclear activity

Counts of local pairs and mergers, plus N-body modelling of orbital decays, suggest that many (perhaps most) present galaxies underwent mergers during cosmic history. This means that the merger rate was probably higher in the past. We are using galaxy and pair counts from deep HST serendipitous fields to constrain the merger rate.

We cannot uniformly trace mergers themselves to large redshifts, because (1) cosmological (1 + z)4 surface-brightness dimming makes the characteristic tidal features too faint for detection and (2) at large redshifts, the disturbed structures can be too small for detection given surface-brightness constraints. We therefore trace the merger rate by studying the evolution of galaxy pairs some of which are the immediate precursors of mergers.

ABSTRACT

In order to study effects of the starburst activity on far-infrared (FIR) colors, we have constructed starburst models which are able to trace FIR color evolution of starburst activity.

INTRODUCTION

The IRAS mission discovered that FIR emission properties of galaxies are significantly altered by starburst activity. Therefore, the FIR properties of galaxies are used to study the nature of starburst activity, in principle. Since, however, it is difficult to know properties of dust grains unambiguously, little effort has been made to construct starburst models which are able to reproduce FIR properties of galaxies (cf. Rowan-Robinson 1992). We here present a simple starburst model capable for calculating FIR emission of starburst galaxies.

MODEL AND RESULTS

The infrared continuum emission comes from dust grains embedded in ionized gas and from those in molecular clouds. The large grains are in thermal equilibrium with the radiation field and radiate as a blackbody with an emissivity Qλ ∝ λ-1. On the other hand, small grains are heated transiently by single UV photons. In our model, emission at 12 and 25 μm mainly comes from small grains in the molecular clouds and large grains in the ionized gas, while emission at 60 and 100 μm comes from large grains in the molecular clouds. The basic concept of our model was given in Mouri and Taniguchi (1992). Our new model is now able to calculate FIR emission from 12 to 100 μm directly and to trace the full phase of starburst evolution. Detailed description will be given elsewhere.

We saw in the previous chapter that the equation governing the evolution of the particle distribution function has the form of a diffusion equation (18.2.19). When starting from the Fokker–Planck equation, it is not obvious why this should be the case.

In this chapter, we consider a homogeneous plasma and assume that the fluctuating electric and magnetic fields can be expressed as a distribution of normal modes of the plasma. We shall find that this approach leads directly to a diffusion equation. In addition, we shall find that the diffusion coefficient is related to the emission and absorption processes for the waves that comprise the normal modes.

Our analysis follows the semi-classical or quasi-quantum-mechanical approach due originally to Ginzburg (1939) and subsequently applied to plasma physics by Smerd and Westfold (1949), Pines and Schrieffer (1962), Melrose (1968) and Harris (1969). Our analysis will be restricted to the case that the unperturbed system contains no magnetic field. For a recent and more complete exposition of this procedure (that includes a possible magnetic field) see Melrose (1980).

Quantum-mechanical description

The relationship between emissivity, absorption and particle diffusion rests upon certain quantum-mechanical relationships. We therefore begin by describing the system in quantum-mechanical terms, taking note of the required relationships, and then making the transition to a classical description.

It is sufficient to consider a simple quantum-mechanical system with discrete energy levels (assumed non-degenerate) of energy E1, E2, …, with particle populations n1, n2,. … (See Fig. 19.1.)

The significance of stellar activity cycles

During the twentieth century, our perception of the fundamental nature of stars and stellar systems has undergone a revolution almost as profound as that initiated by Copernicus in relation to the solar system. In the nineteenth century, a star was regarded as a luminous, spherically symmetric system, for which the only available energy source appeared to be the energy released by gravitational contraction. Unfortunately, simple calculations showed that, on this basis, the Sun's luminous lifetime (the Kelvin-Helmholtz time) was far too short to accommodate the age of geological structures, the development of life, and the evolution of species.

The discovery that nuclear energy could provide the source necessary to prolong the luminous lifetimes of stars by several orders of magnitude was the first significant development in our understanding and provided the background structure for the picture of a star that emerged in the first half of this century: i.e. that of an equilibrium system, in which the internal generation of nuclear energy remained in long-term balance with the radiation emitted at the surface. In this system, it was assumed that hydrostatic pressure balance applied and that the outward temperature gradient was monotonically negative, in conformity with the well-understood principles of thermodynamics.

In February of 1985, an international group of solar astronomers, including both observers and theoreticians, met in Tucson, Arizona, and agreed to plan a series of workshops with the aim of mounting a coordinated study of the new solar cycle, Cycle 22, which was expected to begin in 1986. Meetings were hosted by the California Institute of Technology at the Big Bear Solar Observatory in August of 1986, by Stanford University at Fallen Leaf Lake in May 1987, by the University of Sydney in Sydney, Australia, in January 1989, and by the National Solar Observatory in Sunspot, New Mexico, in October 1991.

This volume does not seek to provide a formal account of the workshop proceedings, which may be found elsewhere. It has, however, been inspired by the intellectual stimulation generated by these meetings and by the many contacts with scientists throughout the world which have followed them.

While making full acknowledgment to the many people whose work and ideas have provided me with excitement and stimulation, I do not wish to imply that this book represents a general consensus. It is not possible to provide a definitive account of the mechanisms underlying cyclic activity at the present time; opinions differ strongly on some aspects, whereas a general bafflement prevails in other areas. It is thus an exciting field, and this volume is intended to set forth a summary of the current state of our understanding of stellar cycles, as interpreted by the author.

The polar fields

The first observations of the Sun's weak polar magnetic fields were obtained in 1915 by Hale at Mount Wilson but, at that time, little attention was paid to their polarities in relation to those of sunspots. In 1957, however, Horace Babcock noted that, at the beginning of Cycle 19, the north polar fields were positive, as were the leader spots of the new cycle in the northern hemisphere. He further noticed that, as the cycle proceeded, the polar fields weakened and, in 1959, the mean magnetic polarity of the north polar field reversed, so that, for a period, the polarity of both polar fields was negative. Eighteen months later, the polarity of the south polar field also changed, so that, at the start of the next cycle (Cycle 20), the polar polarities in each hemisphere again corresponded to those of the leader spots. Similar reversals also occurred shortly after maximum during Cycles 20 and 21. On the basis of these three occurrences, it is now widely assumed that the global polar field of the Sun reverses with a period comparable to that of the sunspot magnetic cycle, but with a phase difference of ∼ 90°.

The polar fields are weak; even at sunspot minimum they are only a few gauss, and their reversals are not well defined. At times during the reversals, the polar regions are covered with weak patches of field of either polarity and the net polarity of the region is uncertain.

Introduction

Although the solar cycle was identified as a sunspot number fluctuation in 1850, and as a magnetic oscillation in 1923, little progress was made in developing theories which might explain the somewhat diverse phenomena associated with it until the latter half of this century. Since 1950, however, several ingenious, and essentially heuristic, models have been proposed, and some have subsequently been supported by more detailed mathematical analyses. Each of these has offered some insight into possible cyclic processes, but none has provided an account consistent with all the available data, or with our current understanding of the physical processes operating within the Sun. Nevertheless, in order to set the stage for later, more mathematical discussions, it may be helpful to review these models briefly in order to see where they have succeeded and to understand how they have failed.

These models may be classified as (i) relaxation models (e.g. Babcock 1961), (ii) forced oscillator models (e.g. Bracewell 1988), or (iii) dynamo wave models (e.g. Parker 1955, Krause and Rädler 1980). Both (i) and (iii) may be regarded as particular examples of the formal mathematical discipline known as dynamo theory, which will be discussed in more detail in Chapter 11. The models to be discussed here have all arisen from attempts to understand the phenomena of the solar cycle and are part of the background against which more recent observational data should be considered.

Introduction

Chapter 5 described the one-dimensional characteristics of the solar activity cycle in terms of variations of the scalar function N(t), where N is a number representing the number of sunspots (or sunspot groups or faculae or any other indicator) and t is the time. The butterfly diagram, shown again in Figure 8.1, provides a two-dimensional characterization of the cycle in terms of a function N(λ, t), where λ is the latitude, a representation which yields additional information of obvious importance to the heuristic models discussed in Chapter 6. (Strictly speaking, the existence of active longitudes emphasizes that N is a function of three variables, N(λ, φ, t), where φ is the Carrington longitude.)

It has been known for ∼ 130 years that the wings of the butterfly diagram overlap to some extent. The overlap is marginal between some cycles, e.g. 18 and 19, but in other cases, e.g. 19 and 20, it extends over ∼ 2 years. Sunspot minimum, therefore, is a point on the one-dimensional plot determined partly by the decay of the old cycle and partly by the rise of the new.

In the one-dimensional approach, all activity lying between successive minima is associated with that particular cycle but, in the two-dimensional approach of the butterfly diagram, active regions of each cycle are distinguished by two properties: latitude and orientation of the magnetic axis (see§ 2.10). Spots of the new cycle should appear at higher latitudes (20° – 40°) and exhibit a reversed magnetic orientation compared with those of the old cycle for a given hemisphere.

Introduction

The measurement and interpretation of the travel times of earthquake signals have been used for many years to study the structure of the Earth's interior. In addition to the classical method, observations of free oscillations have been used since the great Chilean earthquake of 1960, and this branch of seismology has been recently applied to the Sun with considerable success. For a given solar model, the eigenfunctions and eigenfrequencies of the radial velocity perturbations may be calculated by standard methods and compared to the observed frequencies. Improved models of the internal structure of the Sun may be obtained by bringing as many calculated frequencies as possible into agreement with observed frequencies. Such calculations have, for example, forced the rejection of ‘low-Z’ models of the solar interior which, it had been hoped, might resolve the solar neutrino problem (Christensen-Dalsgaard and Gough 1982).

Of particular interest for studies of cyclic phenomena is the rotational modulation of the eigenmode frequencies. Because the eigenfunctions of the many non-radial p-modes exhibit different depth and latitude dependence, the measurement of frequency splittings in the intermediate orders of the waves has led to inferences regarding the internal rotation rate as a function of depth and latitude (Duvall et al. 1986, Brown and Morrow 1987, Morrow 1988, Brown et al 1989, Libbrecht 1989). Surprisingly, these results at first suggested that, within certain error bars, the angular velocity is independent of radial distance across the convection zone; i.e. that the differential rotation (with latitude) at the base of the convection zone is very similar to that at the surface.

Introduction

It is now time to summarize and conclude but, regrettably, it is not possible to follow the King's advice, for the end of this story is not yet in sight. As in any good detective story, both clues and red herrings have been scattered liberally throughout the foregoing chapters. Unlike the novelist, however, we cannot be certain which is which and so cannot now discard the red herrings, marshal the significant clues, and reveal the solution. At best, we can indicate what appear to be the important themes which must form part of the solution and suggest the crucial areas of investigation which may lead to a satisfactory resolution.

Two important questions currently remain without clear and unequivocal answers:

1. (i) Do both cyclic and non-cyclic stellar activity arise as a result of dynamo action and, if so, of what kind (or kinds)?

2. (ii) Is the aperiodicity of solar cyclic activity evidence of a chaotic system, and, if so, can the existence of a strange attractor be demonstrated and its dimension determined?

Until firm answers can be provided for these questions, the problem of cyclic stellar activity remains without a satisfactory solution.

The input from stellar cycles

Because of the more extensive data-base regarding the solar cycle, the discussions in this volume are weighted heavily in that direction, but this in no way implies a greater importance to solar over stellar studies. Although still in their infancy, studies of stellar activity have already made a significant contribution to our understanding of the problem of cyclic activity.

The discovery of sunspots

Although naked-eye observations of sunspots have been recorded sporadically since the first Chinese observations several centuries before the birth of Christ, the year 1611, when sunspots were observed for the first time through the telescope, marks the beginning of the science of astrophysics. Four men share the honour of this discovery: Johann Goldsmid in Holland (1587-1616), Galileo Galilei in Italy (1564-1642), Christopher Scheiner in Germany (1575-1650), and Thomas Harriot in England (1560-1621). It is uncertain which of this international quartet made the first observations, but priority of publication belongs to Goldsmid, or Fabricius, as he is known by his Latinized name. Although his equipment was probably inferior to that of Galileo or of Scheiner, Fabricius made observations of sunspots and used them to infer that the Sun must rotate but did not carry this work beyond these initial observations.

When Scheiner, a Jesuit priest teaching mathematics at the University of Ingolstadt, first observed the spots, he suspected some defect in his telescope. He soon became convinced of their actual existence but failed to persuade his ecclesiastical superiors, who refused to allow him to publish his discovery. This indignity was later shared by the French astronomer, Messier, who in 1780 was similarly prevented from announcing his observation of the return of Halley's comet in that year. Regrettably, such instances of scientific censorship are not uncommon and, in Scheiner's case, played a major role in the controversy that led to the denouncement of Galileo to the Italian inquisition.

Introduction

Although not the most spectacular phenomenon of the solar cycle and undetectable in stellar cycles, the large-scale magnetic field patterns on the Sun play an important role in solar cyclic activity and in the attempts to understand the solar cycle discussed in Chapter 6. In relaxation models such as the Babcock model (see§ 6.2), the reversal of the polar fields by the poleward drift of large-scale fields is crucial, and in the Leighton-Sheeley flux-transport model the large-scale fields arise solely from the decay of active-region fields.

However, magnetic flux emerges at the surface of the Sun in the form of magnetic bipoles whose dimensions range across a wide spectrum, from the largest active regions with dimensions up to 100 000 km, down to the small intra-network elements of order 500 km. Stenflo (1992) has noted that the total flux emerging in the smaller elements exceeds that emerging as large active regions by several orders of magnitude, and there is no a priori reason why regions from the large-scale end of this spectrum should be the only\ contributors to the large-scale field patterns and thus to the reversal of the polar fields.

In this chapter we describe recent studies of the evolution of the large-scale field patterns at the beginnings of Cycles 20, 21, and 22. In Chapter 10 we look at the polar fields near the maximum of Cycle 22.

The solar-stellar connection

Hale's conviction that solar physics is an essential component of astrophysics was shared by some, but unfortunately not by all, astrophysicists. Nevertheless, a further important initiative in this spirit was taken at Mount Wilson in 1966, when, using the 100-inch Hooker telescope, Olin Wilson and his colleagues began a long-term study of 91 cool dwarf stars (Wilson 1978). In 1978 this project (the ‘HK Project’) was transferred to the Mount Wilson 60-inch telescope, which was dedicated entirely to the continuation and extension of this work and has become identified with a particular methodology known as the solar-stellar connection.

Although the Sun permits the detailed two-dimensional study of its activity phenomena, it exhibits only a single set of stellar parameters, since its mass, size, composition, and state of evolution are necessarily fixed at this point of time. On the other hand, stars, as observed from earth, are essentially one-dimensional objects, but they offer a wide range of physical parameters which permit a more thorough testing of theories and conjectures regarding common phenomena than is possible for the Sun alone. The solar-stellar connection aims to bring these two lines of investigation together in order to further our understanding of the properties of the Sun and other late-type stars.

Even before the solar-stellar connection methodology became recognized as such, there were many examples of the successful application of solar results to stellar investigations.

Introduction

The standard concept of the sunspot cycle is of an 11-year variation in the number of sunspots present on the Sun, N(t), at time t. The data from which N(t) must be determined are the daily values of the Zurich sunspot number Rz (defined in §2.5), but, because only half the Sun is visible at any one time, Rz is a measure of the number of spots on the visible hemisphere, and it is not possible, even in principle, to determine N(t) at any instant t. For this reason N(t) must be derived from a time average of Rz over a longer period, such as a Carrington rotation or a calendar year. The variable t is therefore discrete rather than continuous, and the function N(t) is strictly a sequence, Ni, which represents twice the mean value of Rz during the ith time interval.

The sunspot number Rz is not the only scalar quantity that exhibits cyclic variations with an 11-year period. Other such quantities include total sunspot area, active region counts, flare counts, the strength of Call emission, the 10 cm radio flux, the incidence of aurorae, the flux of cosmic rays as measured through certain indicators, and even the widths of terrestrial tree rings. Each of these quantities exhibits a slightly different pattern of variation, and the investigation of the various time series can provide different insights into the nature of the cycle. Such a variety of indicators must, however, raise the question as to what is the fundamental physical variable which generates these variations in secondary phenomena which we call the solar cycle.

Introduction

Chapter 1 discussed the relationship of the solar cycle to the terrestrial environment and offered the hope that a greater understanding of solar and stellar cycles might lead to improved predictions of the parameters of a given solar cycle and, consequently, more reliable forecasts of solar-induced geospheric phenomena.

The more important terrestrial consequences arise during and just after sunspot maximum, when the EUV-UV and total solar irradiance are also at a maximum, along with the probability of occurrence of large solar flares, particle bursts, and solar cosmic rays. These enhanced solar emissions disrupt communications, shorten the orbital lifetimes of satellites in low Earth orbit, cause failure in solid-state components in satellites, and generally introduce major or minor disruptions to our environment (see §1.3). The likelihood of the occurrence of disruptive events follows closely the intensity of the activity cycle, so that accurate forecasting of solar activity on time scales of weeks, months, and years is of considerable importance to those agencies which plan and operate space missions.

Apart from space missions, other possible terrestrial effects of the influence of solar activity are discussed in Chapter 1 and elsewhere in this book. Perhaps the most significant for us and our descendants are the small variations of the solar output which accompany the activity cycle. Although the measured variations are only a few tenths of a per cent, it is generally accepted that, because of the non-linear nature of the interaction of solar radiation with the geosphere (which is poorly understood), the effect of these small fluctuations on our environment may be considerably amplified.

Introduction

Recent work in the theory of non-linear dynamical systems has centred on the concept of chaos, a term that applies to a great variety of situations and configurations. This relatively new subject is fascinating in its own right, and the rapidly growing body of knowledge surrounding it has uncovered a number of characteristics shared by all chaotic systems. The concept has not only achieved an extensive currency throughout the mathematical and scientific communities but has also captured the interest of many in the nonmathematical world, the latter largely due to an excellent popular discussion of the history and basic ideas by James Gleick (1988)

If the dynamics of the solar magnetic field are due to magnetoconvective dynamo action within the Sun, then the activity cycle is governed by the non-linear equations of magnetohydrodynamics, discussed in Chapter 11. A number of investigators have suggested that solar and stellar activity cycles are chaotic phenomena and have begun to explore the implications of cyclic systems which are chaotic.

If stellar activity cycles are indeed examples of chaotic systems, then they will share in the universal characteristics of such systems. In order to discuss the implications for cyclic activity, a brief outline of the relevant concepts in the theory of chaos is called for.