Overview

The first part of this chapter is devoted to a brief description of the methods and terminology employed in Bayesian inference and can be read as a stand-alone introduction on how to do Bayesian analysis. Following a review of the basics in Section 3.2, we consider the two main inference problems: parameter estimation and model selection. This includes how to specify credible regions for parameters and how to eliminate nuisance parameters through marginalization. We also learn that Bayesian model comparison has a built-in “Occam's razor,” which automatically penalizes complicated models, assigning them large probabilities only if the complexity of the data justifies the additional complication of the model. We also learn how this penalty arises through marginalization and depends both on the number of parameters and the prior ranges of these parameters.

We illustrate these features with a detailed analysis of a toy spectral line problem and in the process introduce the Jeffreys prior and learn how different choices of priors affect our conclusions. We also have a look at a general argument for selecting priors for location and scale parameters in the early phases of an investigation when our state of ignorance is very high. The final section illustrates how Bayesian analysis provides valuable new insights on systematic errors and how to deal with them.

I recommend that Sections 3.2 to 3.5 of this chapter be read twice; once quickly, and again after seeing these ideas applied in the detailed example treated in Sections 3.6 to 3.11.

The goal of science is to unlock nature's secrets. This involves the identification and understanding of nature's observable structures or patterns. Our understanding comes through the development of theoretical models which are capable of explaining the existing observations as well as making testable predictions. The focus of this book is on what happens at the interface between the predictions of scientific models and the data from the latest experiments. The data are always limited in accuracy and incomplete (we always want more), so we are unable to employ deductive reasoning to prove or disprove the theory. How do we proceed to extend our theoretical framework of understanding in the face of this? Fortunately, a variety of sophisticated mathematical and computational approaches have been developed to help us through this interface, these go under the general heading of statistical inference. Statistical inference provides a means for assessing the plausibility of one or more competing models, and estimating the model parameters and their uncertainties. These topics are commonly referred to as “data analysis” in the jargon of most physicists.

We are currently in the throes of a major paradigm shift in our understanding of statistical inference based on a powerful theory of extended logic. For historical reasons, it is referred to as Bayesian Inference or Bayesian Probability Theory. To get a taste of how significant this development is, consider the following: probabilities are commonly quantified by a real number between 0 and 1.

Galactic scale phenomena relevant to life on a terrestrial planet are reviewed. The habitability of the Earth for complex life is surprisingly dependent on a diverse collection of processes ranging from Galactic chemical evolution to Galactic nuclear activity to comet impacts. The combined effect of these is to restrict the time and space that complex life can exist on a terrestrial planet. That region in the Milky Way is termed the Galactic Habitable Zone.

Introduction

The introduction of the Circumstellar Habitable Zone (CHZ) concept in the late 1950s (Huang 1959) and later refinements (Hart 1979; Kasting et al. 1993; Franck et al. 2000) have permitted the study of life in the universe to be systematized to some degree. However, discussion of habitability on the scale of the Milky Way Galaxy has received less attention. Trimble (1997a) considered habitability in the context of Galactic chemical evolution. Clarke (1981) discussed the possible effects on habitability of a Seyfert-like outburst in the Galactic center. In addition, many papers have been written about the possible threats to life by nearby supernovae (e.g. Ellis & Schramm 1995). While these studies have been helpful studies, they do not attempt to systematize the concept of habitability on the Galactic scale.

Before beginning any discussion about habitability, it is important to be up front about assumptions regarding life. As in CHZ studies, we assume Earth-like life in exploring Galactic-scale habitability constraints.

I examine some recent findings in cosmology and their potential implications for the emergence of life in the Universe. In particular, I discuss the requirements for carbon-based life, anthropic considerations with respect to the nature of dark energy, the possibility of time-varying constants of nature, and the question of the rarity of intelligent life.

Introduction

The progress in cosmology in the past few decades leads also to new insights into the global question of the emergence of intelligent life in the Universe. Here I am not referring to discoveries that are related to very localized regions, such as the detection of extrasolar planetary systems, but rather to properties of the Universe at large.

In order to set the stage properly for the topics to follow, I would like to start with four observations with which essentially all astronomers agree. These four observations define the cosmological context of our Universe.

1. (i) Ever since the observations of Vesto Slipher in 1912–1922 (Slipher 1917) and Hubble (1929), we know that the spectra of distant galaxies are redshifted.

2. (ii) Observations with the Cosmic Background Explorer (COBE) have shown that, to a precision of better than 10−4, the cosmic microwave background (CMB) is thermal, at a temperature of 2.73 K (Mather et al. 1994).

3. (iii) Light elements, such as deuterium and helium, have been synthesized in a high-temperature phase in the past (e.g. Gamow 1946; Alpher, Bethe, & Gamow 1948; Hoyle & Tayler 1964; Peebles 1966; Wagoner, Fowler, & Hoyle 1967).

4. […]

A planetary system may undergo significant radial rearrangement during the early part of its lifetime. Planet migration can come about through interaction with the surrounding planetesimal disk and the gas disk—while the latter is still present—as well as through planet-planet interactions. We review the major proposed migration mechanisms in the context of the planet formation process, in our Solar System as well as in others.

Introduction

The word planet is derived from the Greek word “planetes,” meaning wandering star. Geocentric views of the Universe held sway until the Middle Ages, when Copernicus and Kepler developed a better phenomenological explanation of planetary wanderings, which with small modifications has withstood the test of time. Kepler's first law of planetary motion states that planets travel along elliptical paths with one focus at the Sun. Thus, although planets wander about the sky, in this model their orbits remain fixed and they do not migrate. In his physical model of the Solar System, Newton theorized that planets gradually altered one another's orbits, and he felt compelled to hypothesize occasional divine intervention to keep planetary trajectories well-behaved over long periods of time. In the early 1800s, Poisson pointed out that planetary-type perturbations cannot produce secular changes in orbital elements to second order in the mass ratio of the planets to the Sun, but Poincare's work towards the end of the 19th century suggests that the Solar System may be chaotic.

It is becoming increasingly clear, based on a combination of observational, theoretical, and laboratory studies, that the interstellar medium (ISM) is not chemically “inert.” Instead, it contains a variety of distinct environments in which chemical synthesis and alteration are constantly occurring under the aegis of a number of different processes. The result of these different processes is an interstellar medium rich in chemical diversity. The discussion found here will concentrate on those materials and molecular species built from the elements C, H, O, and N, with particular emphasis on those compounds that may be of prebiotic interest. Furthermore, there is excellent evidence that the products of interstellar chemistry are not restricted solely to the ISM, but that some fraction of these materials survive the transition from interstellar dense clouds to planetary surfaces when new stars and planets form in these clouds. This raises the interesting possibility that molecules created in the interstellar medium may play a role in the origin and evolution of life on planetary surfaces.

Introduction

A variety of organic and volatile compounds are now known or suspected to exist in a number of different space environments including stellar outflows, the diffuse interstellar medium, dense molecular clouds, and protostellar nebulae.

Stellar nucleosynthesis of heavy elements, followed by their subsequent release into the interstellar medium, enables the formation of stable carbon compounds in both gas and solid phases. Spectroscopic astronomical observations provide evidence that the same chemical pathways are widespread both in the Milky Way and in external galaxies. The physical and chemical conditions—including density, temperature, ultraviolet radiation and energetic particle flux—determine reaction pathways and the complexity of organic molecules in different space environments. Most of the organic carbon in space is in the form of poorly-defined macromolecular networks. Furthermore, it is also unknown how interstellar material evolves during the collapse of molecular clouds to form stars and planets. Meteorites provide important constraints for the formation of our Solar System and the origin of life. Organic carbon, though only a trace element in these extraterrestrial rock fragments, can be investigated in great detail with sensitive laboratory methods. Such studies have revealed that many molecules which are essential in terrestrial biochemistry are present in meteorites. To understand if those compounds necessarily had any implications for the origin of life on Earth is the objective of several current and future space missions. However, to address questions such as how simple organic molecules assembled into complex structures like membranes and cells, requires interdisciplinary collaborations involving various scientific disciplines.

Introduction

Life in the Universe is the consequence of the increasing complexity of chemical pathways which led to stable carbon compounds assembling into cells and higher organisms.

Transits of the planets Mercury and especially Venus have been exciting events in the development of astronomy over the past few hundred years. Just two years ago the first transiting extra-solar planet, HD 209458b, was discovered, and subsequent studies during transit have contributed fundamental new knowledge. From the photometric light curve during transit one obtains a basic confirmation that the radial velocity detected object is indeed a planet by allowing precise determination of its mass and radius relative to these stellar quantities. From study of spectroscopic changes during transit it has been possible to probe for individual components of the transiting planets atmosphere. Planet transits are likely to become a primary tool for detection of new planets, especially other Earth-like planets with the Kepler Discovery Mission. Looking ahead, the additional aperture of the James Webb Space Telescope promises to allow the first possibility of studying the atmosphere of extra-solar Earth-analogue planets, perhaps even providing the first evidence of direct relevance to the search for signs of life on other planets.

Transits in history

Transits happen when an obscuring body passes in between us, the observers, and a background luminous source. Historically, both of the planets interior to Earth in the solar system have been observed while transiting the Sun. Mercury transits the Sun from our perspective frequently, Venus transits the Sun from the vantage point of the moving Earth only twice in every 130 years given current orbits.

Interstellar material surrounding an extrasolar planetary system interacts with the stellar wind to form the stellar astrosphere, and regulates the properties of the interplanetary medium and cosmic ray fluxes throughout the system. Advanced life and civilization developed on Earth during the time interval when the Sun was immersed in the vacuum of the Local Bubble and the heliosphere was large, and probably devoid of most anomalous and galactic cosmic rays. The Sun entered an outflow of diffuse cloud material from the Sco-Cen Association within the past several thousand years. By analogy with the Sun and solar system, the Galactic environment of an extrasolar planetary system must be a key component in understanding the distribution of systems with stable interplanetary environments, and inner planets which are shielded by stellar winds from interstellar matter (ISM), such as might be expected for stable planetary climates.

Introduction

Our solar system is the best template for understanding the properties of extrasolar planetary systems. The interaction between the Sun and the constituents of its galactic environment regulates the properties of the interplanetary medium, including the influx of interstellar matter (ISM) and galactic cosmic rays (GCR) onto planetary atmospheres. In the case of the Earth, the evolution of advanced life occurred during the several million year time period when the Sun was immersed in the vacuum of the Local Bubble (Frisch & York 1986, Frisch 1993). Here we use our understanding of our heliosphere to investigate the astrospheres around extrasolar planetary systems.

The search for Earth-like extrasolar planets is in part motivated by the potential detection of spectroscopic biomarkers. Spectroscopic biomarkers are spectral features that are either consistent with life, indicative of habitability, or provide clues to a planet's habitability. Most attention so far has been given to atmospheric biomarkers, gases such as O2, O3, H2O, CO, and CH4. Here we discuss surface biomarkers. Surface biomarkers that have large, distinct, abrupt changes in their spectra may be detectable in an extrasolar planet's spectrum at wavelengths that penetrate to the planetary surface. Earth has such a surface biomarker: the vegetation “red edge” spectroscopic feature. Recent interest in Earth's surface biomarker has motivated Earthshine observations of the spatially unresolved Earth and two recent studies may have detected the vegetation red edge feature in Earth's hemispherically integrated spectrum. A photometric time series in different colors should help in detecting unusual surface features in extrasolar Earth-like planet spectra.

Introduction

One hundred extrasolar giant planets are currently known to orbit nearby sun-like stars. These planets have been detected by the radial velocity method and so, with the exception of the one transiting planet, only the minimum mass and orbital parameters are known. Many plans are underway to learn more about extrasolar planets' physical properties from ground-based and space-based observations and via proposed or planned space missions. Direct detection of scattered or thermally emitted light from the planet itself is the only way to learn about a variety of the planet's physical characteristics.

Gravitational microlensing offers a powerful technique to search for extra-solar planets around lensing stars via short-timescale amplifications produced by the planet on the microlensing lightcurve. This method is technologically simple, can be carried out with a network of relatively small ground-based telescopes, and is sensitive down to earth-mass planets.

More than 100 microlensing events towards the Galactic bulge have been monitored by the PLANET collaboration to look for such planetary signals. No clear planetary signal has been detected, which implies that less than 33% of the lensing stars have Jupiter-mass planets with orbital radii of 1.5–4 AU. Since other techniques are currently not sensitive to the outer portion of these orbital radii, these are the best current limits on extra-solar planets at these orbital separations.

Isolated planetary-mass objects can also reveal themselves as short timescale microlensing events in a monitoring program. Lack of such short-timescale events in the MACHO and EROS database towards the LMC suggests that the contribution of planetary-mass objects is less than 10% of the halo dark matter.

Gravitational microlensing as a tool

Uranus is roughly a 6th magnitude object, and is almost a naked-eye object. Yet it was discovered only in 1791, long after the telescope was invented, and it took a great astronomer like Sir William Herschel to do so (at least by some accounts). Uranus was the last planet to be discovered by its direct light.

The Space Telescope Science Institute Symposium on “Astrophysics of Life” took place during 6–9 May 2002. Unlike other astrobiology symposia, the emphasis here was on astronomical observations and astrophysical research. With the discovery of more than a hundred extrasolar planets on one hand, and recent progress in the understanding of the evolution of the universe on the other, the “astro” part of astrobiology has advanced to the forefront of astronomical investigation.

These proceedings represent only a part of the invited talks that were presented at the symposium. We thank the contributing authors for preparing their manuscripts.

We thank Sharon Toolan of ST ScI for her help in preparing this volume for publication.