Earth first formed about 4.6 billion years ago, condensing out of the gases & dust in the proto-Sun's Planetary Disk. But, for about the 1st billion years, the proto-planet was repeatedly pummeled by swarms of Impactors. They deposited gargantuan quantities of energy onto the Earth's surface, keeping it hot, molten, and inhospitable, even to primitive microbes. This period of "Heavy Bombardment" only ended about 3.5 billion years ago*. Around the same time (~3.5 billion years ago), the first Photo-Synthesizing microbes (eg. "Stromatolites") appeared, and began steadily producing Molecular Oxygen (O2), for billions of years. * TLC It Came from Space (VHS) ** Discovery Education Planet Earth (DVD) ; History Channel The Universe -- Astrobiology (DVD) ; James F. Luhr. Earth: the Definitive Visual Guide, pp. 26-29.Now, Earth Life eventually blossomed, into complicated forms, but only after an effective Ozone Layer had finally appeared, to protect the planet from DNA-damaging UV radiation. And, effective Ozone Layers (O3) only arise when Oxygen (O2) concentrations get sufficiently high. That happened, on Earth, about 550 million years ago*, as the end result of about 3 billion years of Oxygenic Photo-Synthesis by those primitive microbes (above). Geologists call this newly Oxygen-rich environment "Earth's Third Atmosphere", and it facilitated the famous "Cambrian Explosion" of Complex Lifeforms at that time**. * History Channel How the Earth was Made (DVD) ** http://en.wikipedia.org/wiki/Earth's_atmosphereBut, Ozone production also depends upon UV radiation reaching the planet's upper atmosphere. The exact equations are quite complicated*. However, if you assume that the "Fast" reactions** are always in equilibrium (mathematically "cancel out"), you obtain the simple yet (seemingly) solid approximation: n(O2) * Fhard ~ n(O3) * Fsoft On the left, the Photo-Dissociation Rate of Molecular Oxygen (O2) by hard UV (< 240 nm) yields 2 Atomic Oxygens (2O). On the right, the Photo-Dissociation Rate of Ozone (O3) by soft UV (240-310 nm) yields 1 Molecular Oxygen & 1 Atomic Oxygen (O2 + O). The Molecular Oxygen from the right side replaces that lost on the left, and we are assuming that the 3 Atomic Oxgens remaining from both sides quickly recombine into Ozone, by "Fast" reactions***. * See: http://en.wikipedia.org/wiki/Ozone ** See: http://en.wikipedia.org/wiki/Ozone-oxygen_cycle *** I have omitted the Reaction Coefficients, which cancel out in the Normalized equations below.Thus, hotter Stars, which produce harder radiation (more Fhard relative to Fsoft), will make more Ozone from less Molecular Oxygen. So, Life on world's in that Star's Habitable Zone need not make as much Molecular Oxygen before their Sun turns it into (sufficient) Ozone. Therefore, complex Life can appear earlier. These Flux Ratios (Fhard to Fsoft) increase with the Star's surface temperature. Specific values can be calculated by appropriately integrating the Planck Function*, using the Incomplete Gamma Function**. For example, our Sun's Flux Ratio is roughly 1/4th. * http://en.wikipedia.org/wiki/Planck's_law ** http://en.wikipedia.org/wiki/Incomplete_gamma_functionWe assume that early Earth Life made Molecular Oxygen at a steady rate. We also assume that other Habitable Planets, by being in their parent Stars' Habitable Zones, receive comparable energy fluxes, for Photo-Synthesis. And, we further assume that those planets are comparably bombarded by impactors, for about 1 billion years, before Life can take root. Finally, we acknowledge those planets' Ozone Layers as having formed, once their Optical Depth of Ozone reaches "one", where "one" is what the Earth's was ~0.5 billion years ago. On Earth, this process took: 1 billion years (impactor bombardments) + 3 billion years (steady Oxygen production) = 4 billion yearsThen, any other Star's "Cambrian Explosion" would happen sooner, or later, depending upon whether its Flux Ratio was greater than, or less than, that of our Sun's. For example, a hotter star, having a Flux Ratio 4x higher, would produce 4x more Ozone from the same Molecular Oxygen concentration. Thus, its advanced Lifeforms could evolve after only 1/4th of the Oxygen production time, or: 1 billion years (impactor bombardments) + (1/4th) x 3 billion years (steady Oxygen production) = 1.8 billion yearsHere, and below, we round all figures to the nearest 0.1 billion years, in acknowledgement of the approximate nature of our calculations. However, while hotter Stars can create complex Lifeforms more quickly, those same Stars will also burn out sooner. Thus, the emergence of advanced Lifeforms rests on the relative rates of these 2 competing processes (birth of complex Life vs. Star death). The results are arranged in the table below. All units are in Solar ratios, save Temperatures (in Kelvins) & Times (in Gigayears). We assume that the Sun (1.0 Msun) lives 10 billion years*: * Strictly speaking, this assumes that all Stars burn only Hydrogen, as in the Sun. Bigger Stars, by burning heavier elements, will live (somewhat) longer than listed. Code (Text): Star-Type Mass Temperature Radius Luminosity Life-Span Time-to-Advanced-Life O 60.0 50,000 15.0 1,400,000 0.00043 1.015 B 18.0 28,000 7.0 20,000 0.009 1.1 A 3.2 10,000 2.5 40 0.8 1.9 F 1.7 7,400 1.3 6 2.8 2.7 G 1.1 6,000 1.1 1.2 9.2 4.0 K 0.8 4,900 0.9 0.4 20 6.4 M 0.3 3,000 0.4 0.04 75 34.6 See: http://zebu.uoregon.edu/~js/ast122/lectures/lec09.html [Broken] CONCLUSION: Complex Lifeforms can only have evolved on Sun-like Stars (F/G/K-Class). For, Life around cool M-Class Stars has yet to make enough Ozone, the Universe itself being only about 15 billion years old. And, hot A/B/O-Class Stars burn out before their "Cambrian Explosions" can even happen. The best candidates are G/K-Class Stars, almost precisely the size of the Sun. Borderline F-Class Stars are an intriguing plausibility, but their "Cambrian Explosions" barely have the half-billion years needed (on Earth) to evolve from Trilobites through Tyrannosaurs to Intelligence.