This chapter presents a selection of image processing techniques that are more specific to astronomy. Again, vita brevis, ars longa – more techniques have been invented than any individual can master, and I make no attempt to be exhaustive.

You do not have to master every known technique in order to get good pictures. Keep in mind that there are many ways to achieve almost identical results. Indeed, in the next few years I expect a shakedown and simplification as astrophotographers unclutter their digital toolboxes.

Combining images

Why do we combine images? To build up the signal while rejecting the noise. The key idea is that the random noise is different in each image and therefore will partly cancel out when they are stacked (Figure 14.1). To be precise, the signal-to-noise ratio in the sum or average of √N images is times as good as in one image by itself.

How images are combined

Sum

The most obvious way to combine corresponding pixel values is to add them. This is like making a multiple exposure in a camera; every image contributes something to the finished product.

The problem with adding (summing) is that the resulting pixel values may be too high. If you are working with 16-bit pixels, then the maximum pixel value is 65 535; clearly, if you add two images that have 40 000 in the same pixel, the result, 80 000, will be out of range.

Introduction

Space exploration has allowed us over the last 40 years to visit most of the different types of bodies that constitute the Solar System (which we define as comprising all those objects under the gravitational influence of the Sun). We have reached all the planets, except Pluto, and consequently most of their satellites, by means of fly-bys, orbital injection (Venus, Mars, Jupiter and Saturn), landing (the Moon, Venus, Mars and Titan) and probe sounding (Jupiter). We have sent vehicles to asteroids and comets (fly-bys), with impacts on the asteroid Eros and Comet Temple 1, and we have samples returned from the Moon, and from meteorites coming from Mars and the asteroid belt. All this has provided a large quantity of information, so the reader can find a large number of books dealing with the Solar System as a whole, or reviewing the properties of each individual constituent (Gehrels 1976, 1979; Burns 1977; Wilkening 1982; Morrison 1982; Hunten et al. 1983; Gehrels & Matthews 1984; Greenberg & Brahic 1984; Burns & Matthews 1986; Chamberlain & Hunten 1987; Kerridge & Matthews 1988; Vilas, Chapman & Matthews 1988; Atreya, Pollack & Matthews 1989; Binzel, Gehrels & Matthews 1989; Kieffer et al. 1992; Cruikshank 1995; Lewis 1997; Bougher, Hunten & Phillips 1997; Shirley & Fairbridge 1997; Beatty, Collins Petersen & Chaikin 1999; Weissman, McFadden & Johnson 1999; de Pater & Lissauer 2001; Cole &Woolfson 2002; Bertotti, Farinella & Vokrouhlicky 2003; McBride & Gilmour 2003; Encrenaz et al. 2004; Bagenal, Dowling & McKinnon 2004).

Witnessing the discovery

What happened to the theory of star and planet formation when almost ten years ago, in October 1995, Mayor and Queloz (1995) announced that they had found a planet, in a four day orbit around the fifth magnitude star 51 Pegasi? Theory at this time was preparing for the discovery of extrasolar planets in orbits around common main-sequence stars. Yet the first discoveries seemed to lie well in the future, not to be expected before the start of the new, the third, millennium.

Introduction

In the following sections an overview of the main methods of extrasolar planet detection is presented. This is not a historical review – an excellent review, for example, can be found in Perryman (2000) and the 469 references therein. It is also not an up-to-date listing of extrasolar planet detections or candidates; these can be found at the comprehensive site of the Extrasolar Planets Encyclopedia by J. Schneider (www.obspm.fr/encycl/encycl.html). In this chapter we do, however, describe in a general manner each detection method and examine the general astrophysical parameters each technique measures as well as its present measurement limitations. We mention some secondary detection methods that may find application in the near future and what additional parameters may be derived through the acquisition of data from several methods combined.

Motivation and context

The hypothesis of the formation of planets in our Solar System from a solar nebula, in a flattened gaseous disc in differential rotation, is more than two centuries old. This approach was first proposed by Kant around 1755 and then developed by Laplace (1796). The idea came in a natural way from the observation of the planet configuration in our Solar System: they turn in the same direction, on quasi-circular orbits, in a quasi-common plane.

Introduction

In this chapter, I have tried to present an overview of the topic of planetary habitability. This topic can be broken down into three related questions: (1) what are the factors that have kept the Earth habitable throughout most of its lifetime? (2) what has caused our neighbouring planets, Mars and Venus, to be uninhabitable? and (3) what are the chances that habitable planets exist around other main sequence stars, and how might we tell if they are inhabited? I will briefly address each question, recognizing that it will be impossible to do justice to any of them in the space of one short chapter. References to the relevant literature are provided, and this should allow the interested reader to pursue these topics further.

Contemplating the existence and character of ‘other worlds’ has a long history, giving rise to an ample body of philosophical and artistic works. But only in 1995 could we begin to put these musings on a scientific basis, with the detection of the first extrasolar planet by Michel Mayor and collaborators at Geneva Observatory. Since that time, the field of extrasolar planets (exoplanets for short) has undergone extremely rapid development and has delivered some of the most exciting results in astronomy. Research today on exoplanets has established itself as a major branch of current astronomy. The growing importance of this field can be shown from the rising number of publications in the field. Starting with a few scattered papers over ten years ago, currently about 2% of all of the papers published in astronomy deal with extrasolar planets. Similarly, the number of projects searching for extrasolar planets has risen from five in 1995 to over 70 at present. Training in exoplanets may therefore be considered very valuable for young researchers. Due to the novelty of the subject, new research groups are frequently still being formed, giving excellent opportunities for participation by qualified personnel.

With exoplanetary science essentially starting in 1995 and with its very rapid development in the following years, this topic has hardly found its way into the astronomy/astrophysics curricula taught at universities. There are still relatively few lecturers familiar with the topic.

Introduction: the search for habitable worlds

The search for habitable terrestrial planets raises considerable scientific and philosophical interest.

Introduction

Finding extrasolar planets is good; learning something about their intrinsic properties is much better. Planets that are known only from their radial velocity signatures can be studied only in a limited sense: we can put a fairly reliable lower limit on their masses, and we can know the size and shape of their orbits. Transiting planets offer opportunities for more complete characterization: we can measure their radii with some precision, and in principle we can learn something of their temperature structure and of their atmospheres. For this reason, this review deals almost entirely with transiting planets. The plan of the paper is as follows: Section 3.2 introduces the basic geometrical and astrophysical ideas relating to transiting planets, and establishes the relationships among them.

Introduction

Beginning with the discovery by Mayor & Queloz (1995) of a giant planet, 51 Pegasi b, the number of planets orbiting solar-type stars has now reached 137. Most of the planets have been discovered by the Geneva and California & Carnegie groups using a Doppler technique. This sample size is now sufficient to search for various statistical trends linking the properties of planetary systems and those of their parent stars. It has been suggested that one of the key factors relevant to the mechanisms of planetary system formation is the metallicity of protoplanetary matter (Pollack et al. 1996). Note that in the context of this paper we consider as ‘metals’ all elements except H, He, Li, Be and B.

Chemical abundance studies of planet hosts are based on high signal-to-noise (S/N) and high resolution spectra. Many targets have been observed by more than one group, allowing useful crosschecks of their analyses and spectra.

Introduction

Brown dwarfs populate the mass domain between that of very low-mass stars and giant planets. They share some characteristics with stars and others with planets. Current models of stellar evolution predict a minimum mass of ∼ 73 MJup for stable hydrogen burning to take place in the interior of a solar metallicity self-gravitating object (e.g. Baraffe et al. 1998). This is the mass generally adopted in defining the frontier between stars and brown dwarfs for solar metallicity. Because of the lack of hydrogen burning, brown dwarfs progressively cool and dim.

In the first section of this chapter we explain why the problem of quantum gravity cannot be ignored in present-day physics, even though the available accelerator energies lie way beyond the Planck scale. Then we define what a quantum theory of gravity and all interactions is widely expected to achieve and point out the two main directions of research divided into the perturbative and non-perturbative approaches. In the third section we describe these approaches in more detail and finally in the fourth motivate our choice of canonical quantum general relativity as opposed to other approaches.

Why quantum gravity in the twenty-first century?

It is often argued that quantum gravity is not relevant for the physics of this century because in our most powerful accelerator, the LHC to be working in 2007, we obtain energies of the order of a few 103 GeV while the energy scale at which quantum gravity is believed to become important is the Planck energy of 1019 GeV. While that is true, it is false that nature does not equip us with particles of energies much beyond the TeV scale; we have already observed astrophysical particles with energy of up to 1013 GeV, only six orders of magnitude away from the Planck scale. It thus makes sense to erect future particle microscopes not on the surface of the Earth any more, but in its orbit. As we will sketch in this book, even with TeV energy scales one might speculate about quantum gravity effects in the close future with γ-ray burst physics and the GLAST detector.