1. Introduction

Astrobiology is undergoing something of a phase transition. In the past two decades, it has progressed from broad discussions hamstrung by limited data, such as Fermi's first formulation of his classic Paradox (see Brin 1983 and Cirkovic 2009 for more detail), towards an era of burgeoning empiricism, driven largely by two separate observational astrophysical programs.

The first is the search for planets around other stars, begun in earnest with the first detection of a planet around the solar type star 51 Pegasi (Mayor et al., 1995). These discoveries have since led to a growing program devoted to exoplanet detection, with several methods of identifying planets populating diverse parameters. With 422 exoplanets so far detected, astronomers are receiving their first glimpse at data on the available niches for life in the Galaxy - while at the same jettisoning assumptions collected over the centuries when the only known planets to exist were those in our Solar System.

Secondly, missions in the Solar System itself have increased our knowledge of our neighbours. For example, Cassini has illustrated the commonalities between the Saturnian regular satellites and Earth - the presence of hydrocarbon lakes and watery matrices on Titan (e.g. Naganuma and Sekine, 2010; Stofan et al 2007), or geysers on Enceladus (Chela-Flores 2010; Parkinson et al 2007; Spencer and Grinspoon 2007). Discoveries such as these, coupled with our understanding of the adaptability of extremeophiles, erode the concept of the stellar habitable zone (Hart 1979, Kasting et al 1993) as the only locale in a star system where amenable conditions for life exist. Given the fact that microorganisms have been discovered even in the most life-neutralizing environments, from miles beneath the earth, at the bottom of the ocean, within radioactive waste, and in below zero temperatures within snow packs and ice, the notion of "habitability" as a discrete quantity for a celestial body is increasing difficult to apply even to the Earth (Spiegel et al 2008).

Prior to the discovery of the first extrasolar planets, and the subsequent identification of those within "habitable zones" most astrobiologists had to rely on simple algorithms such as Drakeʼs equation so as to compensate for the extreme paucity of data. Drake's elegant equation has led to some interesting statistical results (e.g. Maccone 2009). However, its simplicity prevents the useful incorporation of current observations.

Therefore, given the avalanche of recent discoveries, and as the old pillars of an isolated, unique, geocentric Earth at the center of the biological universe have now fallen, the onus is on theorists to fashion a modern coherent theory of Life in the Universe. Today's astrobiologists are at a distinct advantage compared to their predecessors, as numerical astrophysics and current astrophysical data allows the construction of more sophisticated models which are sufficiently constrained to be informative.

This paper will highlight some of the latest works in numerical astrophysics and will demonstrate how numerical simulations at many astrophysical size scales, have important implications for numerical astrobiology.

2. Drakeʼs Equation and Fermiʼs Paradox

Fermiʼs Paradox and Drakeʼs Equation have set the standards against which all numerical astrobiological analysis is judged. Fermiʼs Paradox is expertly reviewed in Brin (1983) and Cirkovic (2009), so only a brief summary appears here.

The paradox begins with the lack of evidence for extraterrestrial life/intelligence. If we estimate the expected timescale for crossing the Galaxy (as Fermi himself did, on the metaphorical back of an envelope), we come to a value of around 10⁸ years. Given that the Galaxy has been in existence and developing life forms for over ten times that value, Fermi was led to the question: "where is everybody?".

However, as it has been correctly pointed out (Brin 1983; Cirkovic 2009) the calculation of this crossing timescale is somewhat perilous, containing as it does a plethora of hidden assumptions - what is the average crossing velocity? What course would extraterrestrial vehicles plot through the Galaxy? What motivation would a civilization have to carry out such a task? What if highly advanced extraterrestrials are not like humans? What if they are like ants, bees? Consider also that for much of human civilization communication did not involve radio transmission. Advanced civilizations have come and gone, building the great pyramids and the great wall of China, and yet they never sent a radio signal into space. If extraterrestrials had been listening then, they might conclude the Earth did not possess intelligent life. It would be a mistake to make the same assumption about life on other planets. Attempting to solve this paradox has provided the driving force for the field of astrobiology for the last fifty years, and a number of answers to the paradox have been formulated (Cirkovic 2009; Crater 2009).

While Fermiʼs Paradox requires quantitative analysis to be posed, arguably the foundation and cornerstone of numerical astrobiology is Drakeʼs Equation. The formulation is simple: begin by counting all the stars in the Galaxy to create a sample set. Then begin removing stars from the sample set if they do not meet certain criteria, e.g. if they do not host planets, if they do not host Earthlike planets, if they do not harbour inhabited planets etc. The final tally represents the total number of communicating civilizations in the Galaxy.

The mathematical result is elegantly simple:

The terms on the right hand side are, respectively: the mean star formation rate; the fraction of stars that could support habitable planets ; the fraction of stars that host planetary systems; the number of planets in each system that are potentially habitable; the fraction of habitable planets where life originates and becomes complex; the fraction of life-bearing planets that bear intelligence the fraction of intelligence bearing planets where technology can develop, and the mean lifetime of a technological civilization within the detection window. The first few terms are inherently astrophysical, and much progress has been made towards constraining them fully. However, the simplicity of Drakeʼs Equation is both its greatest strength and its greatest weakness. It is essentially axiomatic, but it was formulated in a time when we were ignorant of planetary systems beyond our own: we are now faced with a wealth of data which proves difficult to distill into a few dimensionless parameters. The next sections detail progress chiefly in the first few terms of Drakeʼs Equation, looking at a series of size scales.

3. Galactic Scale Simulations - Niches and Timescales

The computational cost of simulating Galaxies with resolutions down to planetary scales is prohibitive in most cases. The usual resort of numerical astrophysicists is to run one of two types of numerical simulation. "N Body" simulations follow the evolution of N particles (where N is typically of order 10⁵ to 10⁶) under the effect of forces such as gravity.

"Hydrodynamic" simulations are more sophisticated in that they model the effects of gravity, pressure and other forces on a fluid, by replacing the fluid by a set of grid cells or particles representing the fluid elements. These two techniques have been effective in simulating phenomena from the dark matter distribution of the Universe (the famous "Cosmic Web", e.g. Teyssier et al 2009), the birth of star clusters (e.g. Price and Bate 2009) to the evolution of stellar systems (e.g. Forgan and Rice 2009) and everything in between. The interested reader should consult Bodenheimer et al (2007) for an excellent overview of these numerical methods. However, these simulation techniques are limited by how many particles or grid cells are used, and cannot simulate an entire Galaxy down to the level of individual planets (at this time). Therefore, studies of interest for astrobiology and SETI focus on much simpler "static" simulations which discard much of the dynamics. This allows the modelling of billions of stars and planets without significantly increasing the computer runtime. Vukotic and Cirkovic (2007, 2008) used such models coupled with the concept of "global regulation mechanisms" (Annis 1999) to challenge Carterʼs classic argument against SETI. By allowing galactic gamma ray bursts (GRBs) to impede life across the entire Galaxy at the same instant in history, their numerical work demonstrates that the astrophysical timescale (e.g. the lifetime of a Main Sequence star such as the Sun) and the biological timescale required for the formation of intelligent life become correlated, undermining Carterʼs principal assumption that they are in fact uncorrelated (Cirkovic et al 2009). The age of the Galaxy is therefore the incorrect timescale to adopt for Fermiʼs Paradox, and should instead be the time from the last "resetting event". Being much shorter than the galaxy crossing timescale, the Paradox is then resolved.

Similar work has been carried out using current exoplanet data and theory in an attempt to compare hypotheses for life on a Galactic playing field (Forgan 2009, Forgan and Rice 2010). The method generates a Galaxy of planets, and allows life to form according to some hypothesis which establishes the criteria that must be met for life to form (planet surface temperature, stellar type, chemical composition etc). The simulation is then rerun several times, and the results averaged to identify statistical fluctuations. Unfortunately, statistical incompleteness in exoplanet data and uncertainty in the origin of life prevent models of this type from providing concrete predictions of the multiplicity of life in the Galaxy. What they do provide is twofold: firstly, they can compare two different hypotheses in terms of their relative trends; secondly, they provide an alternative to the Drake Equation, where each individual exoplanet discovery can be folded in intuitively to the input, and results can be presented as a function of space and time. This is particularly useful for testing models such as the "phase transition" model, where the number of civilizations in the galaxy increases from a low to a high value in a short time frame, another potential solution to Fermiʼs Paradox (Cirkovic and Vukotic 2008). As future studies of exoplanets grow, this method will be able to provide observational constraints on the current zoo of hypotheses for life, based on the available planetary architectures that exist.

The work of Cotta and Morales (2009) also deserves mentioning in this section. While their galactic model is perhaps the simplest of all, they pursue a devilishly complex problem, regarding the exploration of the Galaxy by remote probes. This has always been an important point in the discussion of Fermiʼs Paradox, as probes vastly decrease the timescale in which intelligent civilizations can make themselves known to us (Cirkovic 2009). However, the dynamics of how a fleet of probes explores a region of space is not obvious, being heavily dependent on the algorithm by which individual probes must select their course and survey pattern. Relying on previous study of an analogous problem, known as the "vehicle routing problem" (c.f. Toth and Vigo 2001), they use similar heuristic algorithms and extensive numerical simulation to simulate the routing procedure for a fleet of probes, giving them a star map and leaving them to construct an economical route to visit all star systems in the least time. They conclude that the non-detection of any such probes limits their potential number to less than 1000 in the Galaxy for any given epoch (and even less if they leave significant traces of their presence as they go). While the first steps with a simple model, it is an admirable attempt to address what is a demanding problem at the heart of current debate on extraterrestrial intelligence.

4. Solar System Creation and Life - Surviving Planet Formation and Asteroid Impact

Although lifeʼs origin is unknown, but assuming life is widespread, the survivability of complex life in a star system will be sensitive to the distribution of planetary and other astral bodies in it. In particular, the interactions between planets and asteroids, comets and other leftover debris from the planet formation phase will be crucial to the continuity of life. Positively, the transfer of organisms from one celestial body to the other - as current panspermia theory suggests - requires this interaction (Arrhenius 2009; Joseph 2009a), and may indicate that microbes participate in the generation of planetary atmospheres, climate, and environment, thus contributing to its habitability for more complex life forms (Joseph 2009b). Negatively, impacts from such objects onto an inhabited planet can decrease its habitability and its biodiversity significantly, potentially causing mass extinctions amongst metazoans (Barbee and Nuth 2009; Isvoranu and Badescu 2009; Napier 2009; Raup and Sepkoski 1982) or eradicating them entirely, with the only possible survivors being the extremophiles.

N Body simulations of planetary systems have a long and distinguished history (von Hoerner 1960,1963, Aarseth 2003), and are an important tool for planet formation theorists to determine the physical and dynamical processes that sculpt planetary systems. Key in much of these simulations is the presence of a disc of debris left over from the planet formation process, collected into dynamical groups, such as the asteroid belt which separates Mars and Jupiter. Astrobiologists have begun studying the effects of different planetary architectures on this leftover debris - particularly if they may come within close proximity of inhabited planets.

Broadly considered, some of this debris may be the remnants of planets expelled during the red giant phase of a solar system's death (Joseph 2009a). Current theory holds that our sun and solar system were created from a nebular cloud following the supernova of another star. Yet other supernova's may have perturbed that nebular cloud stimulating star formation. Although considered controversial, it is possible that as stars lose mass planets orbiting those stars may be ejected billions of years before supernova (Joseph 2009a). Yet other planets may be shattered. Atmosphere's and oceans ripped from these planets by powerful red giant solar winds may also be deposited in the nebular cloud (Joseph 2009a) thereby contributing to the creation of comets and the Oort cloud. According to current theories of panspermia, much of this debris, including comets, could contain microbial life. It is now well established that bacteria can survive journeys through space including the ejection from and reentry through the atmosphere to a planet's surface (Burchella et al., 2001; Burchell et al. 2004; Horneck et al. 1994, 1995, 2001; Mastrapaa et al. 2001; Nicholson et al. 2000). As this debris strikes Earth and other planets, some of these life forms may survive and may take up residence on these planets (Joseph 2009a). We know that Mars and our own planet experienced a period of heavy bombardment for over 700 billion years, therefore, according to theories of panspermia, life may have been deposited on these planets early in their respective histories (Joseph 2009a). If true, then the same mechanisms could be applied to other planets.

If asteroids and comets were to strike the modern Earth, the consequences could eradicate all but microbial life (Barbee and Nuth 2009; Isvoranu and Badescu 2009; Napier 2009). Therefore, instead of delivering life, these astral bodies could end life, leaving only microbes in their wake.

Horner, Jones and Chambers have studied the influence of Jupiter on three separate groups of objects in our Solar System - the asteroid belt between Mars and Jupiter (Horner and Jones 2008), the Centaur objects of the Kuiper Belt (Horner and Jones 2009) and the distant Oort Cloud beyond Pluto (Horner et al. 2010). Jupiter has long been thought of as a protector of Earth, capturing potential impactors in its gravitational well, effectively shielding Earth from increased bombardment and frequent mass extinctions and allowing intelligent life to successfully develop. This supposition was put to the test by running a series of around ten separate N Body simulations of the Solar System, containing around 10⁵ particles, one particle for each of the four giant planets, and the rest for the asteroids/comets being studied. They varied Jupiterʼs mass in each simulation, from zero Jupiter masses (i.e. no Jupiter) to 2 Jupiter masses. They then measured the number of objects being deflected towards the inner solar system during the simulation (a duration of around ten million years). While Jupiterʼs presence can increase the rate of impacts from relatively nearby objects such as the asteroids in the belt between Mars and Jupiter and the Centaurs of the Kuiper Belt (compared to it not being present), it decreases the rate of impacts from the more distant Oort Cloud objects, showing that the survivability of complex or intelligent life on worlds like ours is sensitive to the planetary system it resides in, with a relationship that is not intuitively obvious.

5. Planetary Scale Simulations - Climate Models and Habitability

If life survives in other systems besides our own, then what will we see as observers? The ability of the transit planet detection method to probe the exoplanetʼs atmospheric spectrum (e.g. Tinetti et al 2007, Swain et al 2008) warrants the study of biomarkers - spectral features whose presence indicates chemical species which are most probably generated biotically, e.g. O₂, O₃, CH₄+O₂ or CH₄+O₃ (Lovelock 1975). While biomarkers limit the search to Earthlike organisms only, it is an important starting point in the current dearth of data regarding extraterrestrial life.

Several works have studied the detectability of Earthʼs biomarkers. Arnold et al (2009) simulate the Earthʼs surface and atmosphere using the Biome3.5 model at three epochs in its history - the present, the Last Glacial Maximum (a lower temperature regime), and the Holocene Optimum (a higher temperature regime). The model accounts for a series of components (oceans, ice, continents, grasslands, tundra, woodlands and other vegetation). They use these climate models (in conjunction with cloud cover models) to assess the strength of what is known as the vegetative red edge (VRE), a distinctive increase in spectral reflectance caused by green vegetation at λ ~ 700 nm. They show that the VRE is detectable in all three epochs, despite the extreme changes in climate (depending on the angle of observation - observing above the North Pole during the Last Glacial Maximum obviously produces a much reduced VRE).

Fujii et al (2009) take a slightly different approach, constructing light curves for extrasolar planets consisting of four main components - ocean, soil, vegetation and snow. This requires a scattered light model of the planet, taking into account its spin-orbit angles and observation angle, and scattered light contributions from the atmosphere, land and sea.

These curves are then fitted in an attempt to recover the fractional areas of each of the four components. While they admit there are several assumptions and simplifications that require improvement (the lack of clouds, for example), their work provides a means for observers to evaluate their data (alongside model-independent work, such as Cowan et al.'s (2009) measurements of Earth light curves). These techniques may also be extended to exomoons (Kalteneger 2009), potentially detectable using current instruments (Kipping et al 2009).

Perhaps most importantly, simulations of "pseudo-Earths" with differing rotation rates and land ocean ratios by Spiegel et al (2008) have shown that "conventional" habitability can be found in somewhat exotic circumstances. They show that habitability can only occur for a fraction of a terrestrial planetʼs orbit, or a fraction of its surface only (after all, the Earthʼs surface is not 100% habitable in its own right). This is reflected in Lammer et al. (2009)ʼs classification system for habitable planets, which shows that simply being an Earthlike planet is not sufficient for it to share the same level of habitability as the Earth itself (Lal 2010).

6. Discussion and Conclusions

The field of numerical astrobiology, while nascent, is growing apace from the contributions of numerical astrophysics as well as substantial contributions from other computational disciplines such as bio-informatics, evolutionary dynamics and network theory.

This paper highlights only a small fraction of recent advances in numerical astrophysics which have direct consequences for numerical astrobiology. We have moved from the simple analyses of Drake and Fermi into deeper understandings of how Life may be distributed in the Universe - glimpses of the complex relationships between species, biosphere, planet, star and galaxy. While we are not much further forward with concrete predictions for SETI, we are far better informed of our ignorance on the subject. Fifty years of subsequent human development have improved our perspective of technological civilization as a whole, while better studies of history are honing our understanding of how civilizations may develop sustainably in the future.

The first discovery of biomarkers will herald the new science of observational astrobiology, but we might also receive our first detections of life from unexpected sources - the most prominent being the future surveys of low frequency radio astronomy observatories such as the Low Frequency Array (LOFAR), and its successor, the larger scale Square Kilometre Array (SKA). While they are designed to detect hydrogen emission at cosmological distances - billions of light years away - they also cover the same frequency bands as those most commonly used by ourselves for telecommunication, radar and other functions. In fact, a human-esque civilizationʼs radio leakage could be detected by the SKA at distances of up to 300 light years (Loeb and Zaldarriaga 2006). The SKA will produce a phenomenal quantity of data, approximately 1 terabyte per minute. To inform any potential search of this data, theory must do all it can to guide observers to the most likely signal locations.

Studies like those referred to in this review are at the cutting edge of this effort, progressing at every astrophysical size scale, folding in new observational results as they arrive. There are also many opportunities for cross-disciplinary activity in all directions. It is the hope of the author that non-specialists reading this will be encouraged to make contacts across the traditional boundaries of science, and further the scientific endeavour of astrobiology.