Interferometric science

Interferometry has already provided many scientific results that could be obtained in no other way. In this chapter, we briefly discuss some of the more prominent results to date. This is not in any way meant to provide a comprehensive review, but is rather only a sampling of the kinds of science that has been done. As interferometry becomes more mature and the new interferometric arrays become operational, the scientific output is expected to increase dramatically, and one hopes that this review will rapidly become out of date!

Stellar measurements and imaging

Stellar diameters and limb darkening

Fundamental understanding of stellar structure and stellar atmospheres depends amongst other things on the accurate determination of stellar diameters. Combined with the measured total flux from the star, the emergent flux density and effective temperature can be directly determined. Consistent models for stellar atmospheres have been created by combining this information with spectroscopic and spectrophotometric measurements. Since the angular diameters of even the supergiant stars are only tens of milliarcseconds and those of the closest main-sequence stars are a few milliarcseconds or less, long-baseline interferometry is the only way of measuring stellar diameters over the full range of spectral types. Measurement of a star's diameter is complicated by the effects of limb darkening. Limb darkening (section 3.2.2) is the apparent change of intensity from the center of the star to its limb.

The development of spectacles (eyeglasses) was a tremendous impetus to the eventual development of the telescope. We do not know who first invented spectacles, but it is thought that they first appeared in Italy between 1285 and 1300. As eyeglasses became more common and more refined, it was perhaps inevitable that someone would figure out how to use lenses to form the first telescope. That happened in 1608, when the German-born Dutch eyeglass maker Hans Lippershey (1570–1619) built the first crude telescopes, not for astronomy, but for military uses.

In May of 1609, the Italian scientist Galileo Galilei (1564–1642) received word of this new magnifying instrument constructed using two lenses and a tube, and at once set about to build his own. In his Sidereus Nuncius (The Starry Messenger; 1610), Galileo describes his first telescope.

Galileo's first telescope could magnify objects just three times, and it was only about an inch in diameter. He soon constructed several more powerful telescopes, beginning at eight times magnification and eventually achieving 30 times.

Searching for extrasolar planets and life

The emerging possibility of searching for life outside the solar system creates a challenging situation for today's civilization. Maybe it is somewhat analogous to that of our Paleolithic ancestors when, roaming along a shoreline, they saw inaccessible off-shore islands and wondered what life forms they could carry. Today's inaccessible islands, which may also carry life forms, are the extrasolar planets, dubbed as “exoplanets,” and man's curiosity about them has pushed NASA and ESA to encourage efforts toward observing exo-Earths. When images of exoplanets are obtained with large telescopes in space, a subsequent step will be the construction of even larger versions designed to obtain images with enough resolved detail to search for life signatures. There are so many possible answers to the question of where life might be sustainable, and therefore where to look for such signs, that it is necessary to define what is called a “habitable zone”: for the purposes of present-day efforts this is considered to be the region where liquid water can exist for at least some part of the time. This defines a rather small shell around any star, which in the case of our solar system includes the planets Venus, Earth and Mars. Of course this definition excludes the possibility of life which has evolved independently of water, but somewhere a line has to be drawn in order to contain the investigation.

What are astronomical spectra good for? For nearly 100 years photographs of low-dispersion spectra have been used to classify stars according to spectral type and luminosity class, determine spectral energy distributions, determine the redshifts and properties of galaxies, and measure emission line ratios in nebulae. High-dispersion spectra have been used to determine precise radial velocities, chemical element abundances in stellar atmospheres and in the interstellar medium, rotational velocities in stars, and magnetic field strengths in stellar atmospheres. We will explore aspects of some of these applications in this chapter.

Low-dispersion spectra are usually presented with absolute flux units on the vertical axis, as we showed in Chapter 5. High-dispersion stellar spectra, however, are usually normalized with respect to the local continuum. The continuum consists of the regions of highest flux that appear continuous except for the intervening absorption lines. Continuum windows are usually available even over a span of a few ångströms in high-dispersion spectra of Sun-like stars. In order to normalize a spectrum, first it is necessary to fit a low-order function through the continuum windows. This can be done by manually selecting the windows or by using a routine that automatically rejects high and low points according to an objective criterion. We show in Figure 13.1 a sample 50 Å region of a high-dispersion spectrum prior to and after continuum normalization. Normalized spectra are used in several of the analysis methods described below.

Visual observations

For thousands of years people recorded what they saw in the sky on rock walls, clay tablets, ivory and papyrus. In more recent times astronomers tried to reproduce on paper the precise patterns of the stars they observed with and without optical aid, some producing accurate and beautiful sky charts. Until the mid nineteenth century the human eye was the only available light detector.

The eye is truly a remarkable organ. Let us describe its structure and the function of some of its important parts in the overall process of vision. Figure 8.1 is a sketch of the right eye as it would appear looking down through the top of the head. The eye is essentially a spherical object that maintains its form by means of its tough outer layer, the sclera. The front center portion of the sclera is the transparent cornea through which all light entering the eye must pass. Behind the cornea is the crystalline lens, and the two are separated by a small amount of clear liquid known as the aqueous humor. The eyeball is filled with a jelly-like substance, the vitreous humor, which also helps it maintain its shape.

Light refracts at the outside surface of the cornea and at all of the interfaces within the eye. In a very real way, then, the optical characteristics of the eye are determined by the cornea, aqueous humor, crystalline lens and the vitreous humor.

Introduction

The idea of using measurements of the correlation between temporal fluctuations in light intensity at different field points was proposed by R. Hanbury Brown as an alternative to interferometry for measuring the spatial coherence function and therefore obtaining stellar data with high resolution. He called it intensity interferometry. Basically, in terms which should by now be familiar to readers of this book, an extended body of angular diameter α, consisting of many incoherently emitting sources, produces a speckled wavefront at the observer in which the speckles have typical size λ/α and typical lifetime τc. A pair of observers separated by a distance considerably less than λ/α are in the same speckle and therefore see the same intensity fluctuations. Observers separated by larger distances are likely to be in different speckles and see fluctuations with lesser correlation. The method was originally used for radio astronomy, in order to overcome the problem of providing identical phase references at two receivers separated by a very long distance (Hanbury Brown et al. 1952). It was then noticed that the measured correlations were immune to severe fluctuations produced by ionospheric instabilities, since these were in a frequency range very different from those of the intensity fluctuations being correlated. This provided the incentive to extend the method to the optical region. One should remember that at that time, the Michelson stellar interferometer was the only interferometric instrument which had provided resolution exceeding the atmospherically limited seeing, having successfully measured the diameters of six stars, and Pease's attempts to extend the baseline from 6 to 15 meters had proved impractical because of problems of atmospheric turbulence and mechanical stability.

One of the important actions that is in nearly all of the foregoing chapters is measurement. We measure time, coordinates, proper motions, parallaxes, magnitudes, the positions of lines in spectra, and shifts in positions of spectral lines, for example. After a measurement has been made we want to know how good the measurement really is, and in order to evaluate our measurements, we must turn to statistics. We would also like to use our measured data to make predictions either within or beyond the range of the measurements. Here we shall describe some of the principles that permit us to achieve these two goals in practical situations.

As an example, let us assume that a student is asked to determine the position of a spectrum line by measuring the distance from some reference position to the line center with a ruler. The smallest divisions on the ruler are one mm apart. We should be able to read the position of the line to within one tenth of a millimeter (0.1 mm). Just as a check the student makes a second setting and reads a new value with the ruler. She tries again and again until she has made fifty tries, and she never makes quite the same reading twice. Which of these many readings should be adopted as the correct one?

In the night sky the stars appear as bright points on a dark spherical surface (Figure 1.1). No such surface really exists, of course, but the concept of a celestial sphere is a useful one that goes back thousands of years. Ptolemy described it and so did Pythagoras and many others. Today we no longer have to worry about the reality of that sphere, and so we eliminate the need for speculation on its composition, radius, thickness and so forth. On the other hand, even though the celestial sphere is not a physical entity, we have many practical uses for the concept. The observer is always at the center of it, and the direction from the observer to any star may be considered to be a radius of the celestial sphere.

The stars are so far very away that we can consider the celestial sphere to be very large and the Earth very small. From the perspective of an observer on the celestial sphere looking back, the entire Earth would appear as a single point. And on the surface of the Earth, when we point to objects in the sky, we don't need to know how far away they are for the purposes of positional astronomy. We need only be concerned with the angles between points on the celestial sphere. That's why a good planetarium fools us into thinking that we are looking at the real sky.

Astronomers, both professional and amateur, have cataloged thousands of variable stars across the celestial sphere. Their periods range from a few minutes to hundreds of days. Some are visible to the naked eye, but most can only be detected with large telescopes. Some behave in an erratic fashion, while others are as predictable as the sunrise. Within this large group there is something for the interests and equipment of every observer, and serious contributions to the overall body of astronomical data can be made by anyone who is willing to exercise care in all phases of the collection of data.

Astronomers have found the study of variable stars to be both pleasant and rewarding. We shall begin this chapter with some information on nomenclature, reference materials and the various classes of variable star. We shall then proceed to discuss methods of analysis of variable star light curves and the determination of precise periods.

Naming variable stars

Variable stars are named in accordance with a scheme that was introduced in the middle of the nineteenth century when variability was first being recognized as a common phenomenon in stars. The originator of the current practice was the German astronomer, Friedrich Argelander, who was mentioned in Chapter 3 as the force behind the BD charts and catalog. In each constellation the first variable to be discovered was identified with the letter “R” followed by the possessive form of the Latin name.

Future ground and space projects

A few decades ago, there appeared to be two distinct evolutionary paths for astronomical imaging instruments: toward larger telescopes and longer-baseline interferometers. A telescope would be based on a single massive monolithic mirror, for which the limiting size appeared to be on the order of 8 m. An interferometer could involve two or more telescopes spaced tens or hundreds of meters apart, possibly up to ten kilometers. More recently, the emphasis in interferometers has turned to larger numbers of subapertures rather than larger sizes or longer baselines, in order to improve (u, v) coverage (e.g. the Magdalena Ridge Observatory Interferometer), and considerable effort is being devoted to planning space interferometers, which will be discussed later in this chapter (section 12.2). On the other hand, following the success of the mosaic mirror Keck telescopes of 10-m diameter, the elements of which are carried by a common pointing mount, projects for larger versions up to 100 m, are now being studied under the generic name “Extremely Large Telescopes” (ELT).

Alternative paths have also emerged. Mosaics of many smaller apertures are also being considered, at scales much larger than ELTs, these being diluted mosaics in which the problems of path-length compensation are overcome by designing the diluted optics as if it were a single giant telescope. In terms of their optical scheme, these mosaics may be considered as “exploded” versions of ELT's and they operate according to the hypertelescope principle (chapter 9).

A qualitative introduction to the basic concepts and ideas

Interferometric astronomy is founded on the basic principles of interference of light waves, which were first conceived in the seventeenth century by Christiaan Huygens, based on experimental evidence by F. M. Grimaldi and Robert Hooke. Interference itself was studied quantitatively in the nineteenth century, beginning with Thomas Young and Augustin Fresnel, and quickly blossomed into the major subject of physical optics. The first application of interference to astronomy was proposed by Hyppolyte Fizeau in the middle of that century.

The purpose of this chapter is to cover the basic ideas of optical interference relevant to astronomy in a qualitative manner. It is followed by two chapters describing the concepts in a more mathematical way. Some of the tools (particularly Fourier analysis), which are essential to detailed understanding of the subject, but may well be quite familiar to many readers, are described in Appendix A.

Young's experiment (1801–3)

This book is about the application of interference to optical astronomy. The possibility of interference is the major distinction between particles and waves as mechanisms for transporting energy and momentum, and the phenomenon of “destructive interference,” in which two disturbances cancel one another out under specific conditions, is peculiar to waves and cannot occur with particles. Although it might seem that energy is somehow being destroyed under these conditions, we always find that the energy which appears to have been lost when two waves interfere destructively appears somewhere else in the system, so that there is, almost miraculously, never any problem with its conservation.

It is safe to say that the spectrograph, a relatively simple instrument, brought about a virtual revolution in astronomy. Although Newton had examined the spectrum of sunlight and Fraunhofer had seen the spectra of a few stars, the spectroscope was not extensively used on telescopes until the latter half of the nineteenth century. Beginning in about 1860, Sir William Huggins in England and Fr. Angelo Secchi in Rome performed their first experiments on the light from the Moon, the planets and the brighter stars. The spectrograph was slowly refined and improved, and eventually it made possible a series of new understandings of the nature of the Sun and stars. First came the identification of a few absorption lines in solar and stellar spectra; then came recognition of several distinct classes of spectra. By the end of the century the construction of spectrographs had been refined to the point that radial velocities could be measured with confidence. Today we have a remarkable understanding of the physical processes that occur in nebulae and the atmospheres of the Sun and stars.

Since the nineteenth century several technological developments have increased the efficiency of the spectrograph, and there have been changes in the means by which the light is dispersed. The general principles of the spectrograph are not complicated, however, and we will outline them below. We shall discuss first the prism and then the grating as dispersive elements. Then we will describe the practical considerations in the design and use of a spectrograph.