Once planets exist in a system, we need to know if there are some with suitable conditions on their surface: temperature, presence of water, of energy, chemical conditions, etc. This chapter tries to evaluate the probability of this happening. It is factor ne in the Drake equation: among the suitably placed planets, the fraction ne of them which can potentially support life (astronomical factor) (chapitre VIII-1)
The recent discovery of a planet system around a very old star of low metallicity, Kepler-444, 11.2 billions years old, shows that nearby all stars can harbour Earth-sized planets. The explanation may be that the process of formation of the planets does not use all the available rocks and metals, but a (statistically) fixed proportion of the star mass. This may result in nearby all stars having (statistically) the same planet sizes, save some very ancient very low metallicity stars. This makes that the age of the star does not matter in the Drake equation. At a pinch, it is the most recent high-metallicity stars which are more likely to produce «monsters», that is solar systems with giant eccentric planets excluding inhabitable planets.
Moreover, the fact that star much older than the Sun can have planets has an interesting consequence: civilisations may exist since billions of years.
Also, this makes a high potential of finding civilisations in the large halo of old low metallicity population II stars of our galaxy.
So that this contribution to ne is 1 in all cases.
Since all main sequence stars have a «Goldilock zone», their size is not relevant into calculating the probability of life. However we find that their colour is very important. As long as we are in the main sequence stable stars, we have:
-Blue and white stars (O,B,A,F spectra) have a short life span, at least shorter than what life needed to appear on Earth (4.5 billions years). We cannot exclude civilisations appearing much faster, but still we can safely discount them, since they are only 4% of all the stars.
-Yellow stars (G spectrum, like the Sun, or K spectrum) which are suitable without restriction. They count for 20% of the total.
-Red stars (red dwarves) of the M spectrum, are the most numerous, 76%. However their reddish light is less conductive of photosynthesis. Where to place the limit exactly? It is a simple experiment to do: cultivate plants with incandescent lamps. This experiment was made many times by amateurs of illegal weeds, and it works very well with lamps at 3300°K. However wisdom was not really the purpose of these cultivators, so that we do not know the lowest temperature limit (still a simple experiment to do, by an amateur). We can only keep the 3300°K value, and combine it with the temperature range of M stars: from 2400 to 3700°K. Since they are 76% of the total, we get that about 30% of the stars are M stars warmer than 3300°K and able to grow Earth's tropical plants. This is a pessimistic bound, since the exact value is necessarily larger, due to the above experiment not done properly, or the today untestable possibility of photosynthesis adapted to still lower colour temperature.
Then the total is a safe minimum of 50% of the stars able of hosting photosynthesis. This sub-factor counts in ne.
To be noted that all the remaining 50% stars can still host bacteria using volcanic energy sources. But I don't see any mean for developing civilisations without such a vast energy source as photosynthesis. Especially the nervous system itself appeared on Earth only as a consequence of photosynthesis: our power-greedy neurones need the fast energy source of concentrated oxygen.
This star type considerations makes that the best places to search for evolved extraterrestrial life and civilisation are the huge outer halo of our galaxy, or large elliptic galaxies, rather than the stars of the disc, which are our close neighbouring. Unfortunately it is at least thousands light-years away, and this makes them very hard to detect. This alone can explain why we did not found yet.
(Added August 23, 2018) I finally attempted the experiment: cultivating plants in the light of Trappist. This star being among the coldest red dwarves, then if it works any red dwarf can accommodate photosynthesis, and therefore intelligent life. I used incandescent lamps, powered in reduced voltage to get the same temperature as Trappist. As a plant, I used radishes, just because they grow fast (and they are legal, he he he). The experiment worked very well, with plants producing 25 times more dry matter than their seeds, in seven weeks. The main problem was the heat of the lamps, which is also a problem on Trappist. Also radishes grew in stem instead of bulbs, probably a «searching for light» mode.
Including all red dwarfs in the stars likely to host extraterrestrials doubles their number, relative to the values above. This brings our nearest neighbours closer (statistically) by 20%. (I did not updated this figure in the next chapters)
The first planetary systems found were, in a way, exceptions: very large planets, or very close to their sun. The other systems, as the newest discoveries show, are more regular: similar to ours, with planets more or less regularly spaced in a Titus Bode law, in a wide range of distance and temperature, from icy cold to fire. This has an important consequence: in such systems, we are nearby sure to find a rocky planet in the «Goldilock zone», where they receive enough sun to melt the ice, but not as much as boiling it. That makes a close to 1 value for this factor, and even larger, since there can be two planets in the Goldilock zone. Some specialists state 2, but this is an optimistic maximum.
Although, this reasoning holds for Earth-like planets. We can also have moons around large planets, which also increases the value. But giant planets in the Goldilock zone do not appear as very common, so that we can omit this possibility.
Earth is a «clear sky» planet. That is, it has little greenhouse gasses, and the light of the sun reaches the ground directly. There is however the possibility of a very different situation: a thicker atmosphere allows for more greenhouse effect. Such «greenhouse planets» can them harbour life much farther from their sun. The drawback is that the light of the sun is dimmed: less star light, through a thick and cloudy atmosphere. In theory, a planet like Venus, or a moon like Titan, would have life-friendly temperatures if they were, say, in the Asteroid Belt. However the sunlight reaching their ground here would be less than one percent of the Earth level, making photosynthesis impossible. The previous experiments on bad weeds should tell us where is the exact limit, but in a guess we can discount these planets in a pessimistic estimate.
Liquid water needs a relatively narrow range of temperature (which is larger than commonly thought, since salts or «anti-freeze» molecules can keep it liquid as low as -50°C, while high pressure can keep it liquid at hundred degrees). However it is not sure at all that complex life can evolve in very different temperatures than ours. We know fishes living at 0°C, and bacteria living in boiling water, but can complex genomes and brains evolve and function at 110°C, or in brines at -50°C? This is far from demonstrated, and the observed extremes are the birds, at 42°C, and fishes near zero °C. (fishes have slow nervous systems, but this is by lack of oxygen, not from temperature. Their brain can work as fast as ours, but only for short bursts, since their breathing does not allow for a continuous supply of oxygen). This makes only 40% of the 100°C range, and thus only 40% of the Goldilock zone as it is usually calculated. Actually, it can be significantly more, since planets usually exhibit a large range of temperatures (a hot planet can have cold zones, or a cold one can have hot spots). So that if Earth was at 100°C at the equator, Siberia or Antartica would still be cool enough for life to evolve. Inversely, a cool Earth would concentrate life in the tropical areas, as it probably happened during the Varanger ice ages.
More, it is likely that most red dwarf planets are locked in rotation around their sun, creating a mandatory temperate zone. This expands the Goldilock zone much closer from their sun.
So this subchapter yields a sub-factor of 0.4, or even more if we account with the locked planets.
At this point, we still have a close range of estimated values, say 0.2 to 1. So that we do not really need to differentiate the minimum possible values (pessimistic) or maximum possible values (optimistic). This will unfortunately change further.
There is a lot of science literature explaining the size of our planets with common processes (thermal differentiation creating the giant gaseous planets and the small rocky planets, and Jupiter taking matter out of the asteroid belts). We are so infused with these theories that we often assume that other solar systems should follow the same patterns. This is however far from proven, and the observed regular planetary systems often show very different pictures, the most common being series of similar sized planets extending from burning hot temperatures to icy temperatures. This makes that the most likely content of the Goldilock zone is one or two rocky planet, of any mass between Mercury and Uranus. So let us discuss in this sub-chapter: which masses allow for life?
Unfortunately the range seems not very large. And in more, the few observation data we have does not allow us for any estimate.
-Too small planets lose their atmosphere in space, and especially water (by dissociation in hydrogen). Mars shows this, and even Venus seems to have lost a large amount of water. Even if it was cool as Earth, it would have only some shallow seas and narrow inhabitable coastal zones.
-Too large planets have a thick atmosphere. This will make them experience a very high greenhouse effect, making them uninhabitable, even in the Goldilock zone. We saw in the previous sub-chapter that such greenhouse planets may have suitable temperatures well beyond the Goldilock zone. But we discounted them, since they have little light reaching their ground, probably not allowing for photosynthesis.
And here we have a problem: Venus falls in the «too large» category, despite it is smaller than Earth! This tells us that the size range allowing for life is probably narrow, and even worse than being in the range does not necessarily make good conditions.
The only extrasolar observations available today (2015) are still heavily truncated: only large planets are detectable. Actually the database of exoplanets shows only one Earth sized planet, around Proxima centauri B, and too close from its star. This makes the observed value much too pessimistic: the real value is surely much larger, but we do not yet have any idea on how much.
So I do an intuitive guess for this contribution to ne: the most optimistic value may be 0.2, and the most pessimistic could be as low as 0.002. We may have more accurate values of the lower bound within some years. Hopefully higher.
The magnetic field of a planet is said to protect life from cosmic radiations. However it rather concentrates these radiations in auroras. And if these radiations do not reach the ground under the auroras, it is thanks to the atmosphere. The high energy radiations are not affected by the magnetic field, but here also it is the atmosphere which does most of the shielding.
In facts, the magnetic field mostly protects the atmosphere from the abrasion by the solar wind. It has been theorised that the lack of magnetic field around Venus and Mars may be the reasons why they lack water: solar wind erosion of the atmosphere expelled hydrogen from the water. On Mars, the remaining free oxygen went into oxidising iron in rocks, giving this planet its reddish colour. A common colour probably, which should be interpreted as a bad omen for life.
On Venus, the lack of water forbade erosion. However it is water weathering of rocks which dissolves light metals like calcium, magnesium and others. In turn, these metals allow to fix the carbon dioxide of the air, under the form of limestone. The sulphurous gasses are fixed under the form of sulphates. In the end, this process regulates the greenhouse effect, and keeps the temperature of the planet to something life can bear. So Venus and Earth are not so much different, after all. And indeed the mass of carbon dioxide in the Venus atmosphere is about the same than what is trapped in Earth's limestones and oceans. Also, the lack of water eliminates the deep circulations which on Earth cools the crust and make it plunge into the mantle. This drives the plates tectonics. So, on Venus we have no plates tectonics. And from here no currents in the metal core to produce a magnetic field.
Today there are still large unknowns about why a planet has a magnetic field or not. A molten core is not enough: all the rocky planets have one, even the Moon, but still only Earth has a permanent magnetic field.
What probably happens on a planet with favourable conditions, but without a magnetic field, is that life appears, but never reaches the level of a civilisation, since the water is lost well before the 4.5 billion years life needed to evolve on Earth. This likely happened on Mars, and perhaps on Venus. This later point makes that traces of bacterial life can validly be sought after on these two planets.
In fact, temperature, water and magnetic field are probably interlinked: if Venus has no plates tectonics, from lack of water, it may not have the core currents which produce the magnetic field. So it is hard to guess if it is lack of water which disallow the magnetic field, or lack of magnetic field which suppresses water. Perhaps Venus was ill fated with not enough water from the start.
We do not know which size makes a magnetic field sure. Most probably large planets always have one. Small planets never. But planets with a size suitable for life? The only observation case we have, Earth, tells that it is possible, but without giving any probability. Just that this probability rises sharply in a narrow range of sizes around Earth size.
Oh, since magnetic field, size and temperature are so interlinked, I think we can asses safely that the estimate of the contribution of magnetic field was already done in the temperature sub-chapter. So that the corresponding sub-factor is already counted.
It is generally assumed that all rocky planets have a similar composition: silicate rocks, with other alkaline elements in smaller proportions. So that this factor should count as one.
However we may have very different compositions: Carbon planets.
Since we commonly have carbon stars like Wolf Rayet stars ejecting soot (what a shame for a star!), it is only by chance that few or none contributed to the matter which was to form Earth. It is enough of 1% of carbon in mass to make a 100km thick layer of coal on the surface of a planet the size of Earth. Such a planet may still have oceans, but few trace elements and no surface volcanism. What most likely prevents these planets to form would be the presence of oxygen: the carbon becomes carbon dioxide. If we consider the quantity of limestone on Earth, we get a corresponding carbon layer of some hundred metres. Probably all this was oxidized in the furnace of the formation of Earth, before the free iron, until no more free oxygen was available. So that we get a carbon planet only if the starting nebula is very heavy in carbon.
Well, nothing forbids animals and plants to grow on coal mines on Earth. But what happens if photosynthesis appears on a planet which surface is entirely made of carbon? We may have the coal slowly oxidizing, or burning into inextinguishable fires. Coal fires are a common phenomenon on Earth, contributing 2% of carbon dioxide production. But on a carbon planet, there is enough carbon to consume all the oxygen of the air. So this would clamp the oxygen level in the air to a much lower level than the Earth's 20%, low enough to be unable to sustain fire. Such a level would still allow for intelligent life, though, with just larger lungs or Tibetan haemoglobin. But what is more problematic, is that the carbon dioxide would be unable to react with rocks to form limestone: the regulation of greenhouse effect which operates on Earth would not take place in a carbon planet. So the temperature would not be stable enough, or for no long enough for civilisations to appear.
We have only few carbon bodies in our system, and small. But other systems may pick more carbon, especially the ones formed near carbon stars explosions. In this case, we have a layer of carbon matter above the usual silicates mantle and iron core.
Into such an environment, with organic matter available everywhere from the ground, it is oxygen which would be the rare sought after food: plants performing photosynthesis would not release it into the atmosphere, but store it under the form of nitrates and other oxidizer compounds, instead of sugar or fat. And animals would eat plants for oxidizers, instead of fat. This situation however is not really symmetrical to the one on Earth: oxidizers, stored into structural hydrocarbons, would form unstable or explosive mixtures, limiting their quantity into the tissues. We imagine a single lightning on a tree, starting a chain of explosions over thousands of kilometres of forest... So clearly such a life form would have to develop different compositions for their structural materials, such as low flammability proteins, or even use the nitrate compounds themselves. Including for plants. But once this done, nothing forbids the appearance of brains, based on the same chemistry than ours. But these beings would not need to breath, if both oxygen and carbon are provided with the food.
Also, if intelligence appears on such a planet, fire as we know it cannot work: no heating, no cooking, no metal smelting, no engines. We can imagine organic or fossil sources of oxidizing compounds, which would then play the technical and economic roles oil or firewood play on Earth. But again the situation is not symmetrical: a deposit of nitrates in a coal mine would burn quickly, and even explode before being formed.
On a carbon planet, only explosive volcanoes would be able to send lava up to the surface. In other cases, lava would flow beneath the carbon layer, and gasses would remain trapped at this level. So that the planet heat would mostly escape through hydrothermal circulation of water through the carbon layer. In doing so, though, it would wash out and depose all kinds of soluble minerals from the rocks beneath, creating many small mines.
Similarly, plate tectonics would not operate in the carbon layer, so that there would be no large oceans or mountain ranges. At a pinch we would easily have a global ocean.
From a telescope search perspective, carbon planets with life would appear with a specific oxygen ratio, but lower than on Earth. My guess is 8-10%, about what usually quenches fires and stop engines on Earth.
What would define a carbon planet in facts would be when there would be not enough free oxygen during the formation, to burn all the available carbon. Such planets would have a larger iron core (since none is burned) and a thick carbon dioxide atmosphere, falling on the previous case of greenhouse planets.
From a total lack of knowledge of the composition of exoplanets, it is difficult to assess this sub-factor. So we can take an optimistic value of 1, where carbon planets are rare. From the proportion of carbon stars and supernovas, we can take a pessimistic value of 0.8, where these stars form carbon planets, assuming they are not supportive of life.
We have many water planets in our solar system, but cold, so that we call them ice planets. In the Goldilock zone, such a body appears as an ocean planet. If Earth had only three times more water, then no mountain would emerge, and there would be no place for human creatures, only for fishes. And fishes cannot develop intelligence, by lack of oxygen in water.
But especially, without forest fires to regulate it at 20% as on Earth, oxygen would accumulate to dangerous levels in the air.
If Earth had much less water, probably it would not have plate tectonics (water seems necessary to run the plate tectonics, as it cools the crust and force it to plunge into the mantle. Venus probably has no plate tectonics by lack of water).
But also, with few water, like on Mars, life would develop only into small oasis, and thus have little chances to evolve. The biomass on Earth would be much lower than today, and the production of oxygen too low to oxidise the iron (a necessary step before forming a breathable atmosphere). Such a planet may need tens of billions years to have an intelligent life... if its sun is a red dwarf able of lasting so long.
From a telescope search perspective, water planets with photosynthesis would appear with an oxygen ratio higher than on Earth, although with no defined value. Other planets may have non-biological oxygen too, so that this does not tell much.
Again, it is very hard to assess any value for this sub-factor. Water planets may not form at all in the Goldilock zone. Or on the contrary, they may be common, from oxygen-rich supernovas. After all Uranus and Neptune are formed mostly of water, which suggest that such bodies may be very common. So, as previously for carbon planets, let us guess an optimistic value of 1, and a pessimistic value of 0.2, where water planets are common but not supportive of life, or at least not of civilisation.
The discussions on the role of water and carbon dioxide were held above, and their contribution to ne assessed.
However we still have two important factors: the global pressure, and other gasses.
Life on Earth was able to adapt to a wide range of pressure, from 0.3bars (high mountain) to 1000 bars (deepest ocean troughs). And if life is poor in these milieus, it is from cold or from lack of resource, not from the pressure. The reason of this flexibility is that chemical reactions do not change much with pressure. There are still some minor changes, though, so that a given species adapts to a given pressure (even human races do: Tibetans and Quechuas have more haemoglobin). So that we can assess that life and brains can thrive anywhere where there is liquid water, and in a temperature range from at least 0°C to 42°C (observed values on Earth).
The minimum pressure for liquid water is 10 millibars, and Mars is not far from it. But such a thin atmosphere cannot support breathing easily: Martians would need huge lungs and nostrils 10 times larger than on Earth.
Very dense atmospheres would make flying easy, and legs useless. However lack of limbs would make technological civilizations difficult. But the contribution of thick atmospheres was already counted in previous sub-chapters. We concluded that they preclude life, well before limbs become unnecessary.
Combustible gasses like methane, ammonia, carbon monoxide, cyanogen, are excluded as soon as there is a production of oxygen. Other very reactive compounds like acids and sulfides would be quickly driven on the ground by rain, and neutralized. These processes are very efficient, and we owe them quite pure air and water on Earth.
Other gasses will usually be nitrogen. To be noted that, since the quantity of oxygen is clamped to a fixed proportion of the total pressure, it is finally the nitrogen pressure which determines the total atmospheric pressure. But it does so without impacting much the probability of life. This leads to a curious result: most inhabited planets will have an air directly breathable to Humans, just like in bad science-fiction.
At last, carbon dioxide can be the major constituent of the air, without impacting much the probability for life. This would be the case on Mars, if it had more carbon dioxide. It would then have enough greenhouse effect to harbour liquid water and life, but in a carbon dioxide atmosphere, instead of nitrogen. On Earth, carbon dioxide is asphyxiating, because large concentrations seldom happen and there was no evolutionary pressure to adapt. But there is no reason that such an adaptation cannot take place on planets with a large concentration of carbon dioxide. So that such planets can harbour life as well, just with a different proportion of oxygen (the minimum one which allows for fire).
Again, it is very hard to assess any value for this sub-factor. However unsuitable conditions are rather extreme ones (thin atmosphere) or their contribution was already counted (thick atmosphere making photosynthesis impossible).
From the previous discussion, we can assess the statistical repartition of oxygen levels in the exoplanets.
-A high peak at zero or weak oxygen levels from non-biological sources (say less than 3%, as observed on Mars and Venus). These are abiotic planets, or planets with bacterial life, but no massive photosynthesis. To be noted that Earth spent most of its life in this category, until about 1 billions years ago.
-A relatively constant background of planets with any proportion of oxygen. These would be abiotic planets which formed with an excess of oxygen, or where oxygen built up from dissociation of abundant water.
-An excess of the previous into the Goldilock zone will tell planets with massive photosynthesis but no emerged lands allowing for fires to regulate the oxygen content. Or at least that forests did not yet appeared, as it happened on Earth 280 millions years ago. Availability of more oxygen than today allowed for very big submarine animals (crustaceans in this time. Today we would have huge insects).
-A narrow peak of planets with a proportion of 20% tells planets with forests, allowing for both strong photosynthesis and forest fires to regulate the oxygen content. Such very Earth-like planets can quickly evolve toward civilisations, and it would be very likely that they already have one.
-Probably a second peak at 8-10% for carbon planets with photosynthesis, but not necessarily forests. Although this signal has some probability to also tell planets with carbon dioxide in the place of nitrogen. We saw that both are less conductive for life, and probably less common, although we cannot exclude them.
The evolution path of Earth (simplified) shows several steps. First, Earth remained from about -2,400 million years ago to -600 millions years ago with a weak photosynthesis slowly oxydising green ferrous iron Fe++ in red ferric iron Fe+++ (round dot). When all the ferrous iron was exhausted, oxygen proportion increased to the today values, with some overshooting (square dot) when there was a lack of plants able to burn in wildfires, making the Earth behave as an ocean planet.
Drawing this curve here has a precise purpose. This is because we may soon be able to measure the oxygen level on exoplanets (or at least of its derivative ozone). Maybe the James Webb space telescope will be able to do this, as soon as 2020, very likely others will do before 2030.
If we find the 20% peak, even for some close planets only, it will immediately give a global and accurate indication of the product of the first terms of the Drake equation, f>p , ne> and fl>, ending any discussion on the astronomical factors and even on the biological factors. So that this study on the Drake equation may be the last of its kind.
And we shall be very sure that planets in the 20% peak harbour a complex life, where civilisations can appear soon, or already appeared. Even the following arguments of cosmic hazards will no longer hold: such planets necessarily survived any extinction event.
Cosmic hazards are the most discussed, because of the large uncertainties, or with many noisy dogmatic statements retaining only one side of the problem to «demonstrate» the impossibility of extraterrestrial life.
Cosmic hazards are:
-Collision with another star. Evidence of them are seen in tightly packed globular clusters (the «blue stragglers»). This is an extreme case, though, and a close approach between two stars, without a frontal collision, is much more probable. But it will result into ejecting the planets out of their system, so that death is as much certain, just slower.
-Close supernovas may sterilize planets at several light years.
-Close gamma rays bursts. It has been theorized that they may sterilize planets as far as thousands light years, although this may be true only on the narrow path of the jet. Could such a thing happen on Earth, the night sky would suddenly appear of a blinding white. Normally the atmosphere is able to protect from a pretty massive amount of radiation, but pollution with nitrogen oxides may result of a massive gamma ray blast.
-Movement of massive galactic black holes, especially during a galaxy merger.
-Large meteorite or comet impacts.
None of these events are common at a given moment, but at the time scale of evolution of life, they may become the main limiting factor to the span of time available for evolution of life on a planet.
There are extensive discussions among astronomers, about these probabilities, but few or no actual numbers. I cannot bring such numbers by myself, but I shall however remark that any of these probabilities strongly depends on the place where the star resides in a galaxy:
-The core of galaxies are the deadliest places, with frequent catastrophic events.
-In packed globular clusters, with common encounters, most planets may wander in space... a wonderful starry sky, but deadly cold.
-Gamma ray bursts are all detected at very large distances, that is several billions years in the past. So clearly space is much quieter today. If this way, life would be rare, not because it is unlikely or «unique», but simply because we would be among the firsts to enjoy enough time to evolve.
-The outskirts (halo) of the galaxies are so quiet that we can consider that none of these events ever happened in the whole lives of these stars. Since most of these stars are up to ten billions years old, this gave twice more time for life to evolve, than with our own solar system.
-The disk of the Galaxies have intermediate probabilities: the zones of star formation are also the place of numerous supernovas. The Sun is here, passing regularly through such zones. Most likely, to assess a probability in these places needs to consider the timeline of merger events in our galaxy, or the passages through supernovas-prone zones, which both result in deadly events.
How to get figures out of this? Most optimistic value is close to 1 in the outskirts of our galaxy. Most pessimistic is practically zero in the heart of close globular clusters. In our neighbourhood, it is harder to assess any value, because we do not yet know the history of this place. So this contribution of the catastrophes to the ne factor would be 1 for the outskirts of our galaxy, giant galaxies or dwarf galaxies. For our close surrounding, that we are more likely to examine in the close future, we can assess 1 for the optimistic bound and 0.1 for the pessimistic bound.
We shall note that, due to their higher magnetic field, red dwarf stars are subjected to flares, which may end up stripping down the atmosphere of inhabitable planets. Happily the probability for a higher magnetic field increases with smaller sizes, so that this problem will mostly happen on stars with a reddish light, which are unable to sustain photosynthesis. For this reason, these stars were already discounted.
Last and probably most common source of hazard, are varied geological events bringing havoc on the surface of a planet. The most well known on Earth is the Chixculub asteroid impact, which caused the extinction of dinosaurs. However this was not the worse. 250 millions years ago, the Permian-Trias 10°C climate trip, probably caused by methane ices release, wiped out 95% of species in this time. The trigger was probably an extraordinary large volcanic eruption, the Siberian traps, which may itself be in relation with flips of magnetohydrodynamic phenomena into the metallic core of Earth, or the start of the crystallization of the seed. 600 millions years ago, several -50°C climate flips occurred from a runaway freezing of extra large polar oceans (formerly known as the Varanger ice age, now the Cryogenian era). It is the self-regulation of temperature which saved the world: formation of limestone cannot happen at such low temperatures, leading to the accumulation of carbon dioxide and greenhouse effect, until unfreezing. Other drastic mass extinction are known, but with no visible geological traces: hypernova radiation events are suspected. We even have a curious radiation event found in Japanese trees dating from the years 774 and 775, showing that these events may be numerous, but not so deadly as feared by astronomers.
However, since at least 3.9 billions years, life exists on Earth, and it survived all these dreadful events. It even managed to take advantage of them, like with the erasing of dinosaurs which favoured mammals. Even the -50°C climate flip is thought to have favoured the explosion of life which occurred just after, the Ediacara age. So it may happen that life flourishes better and evolves faster into dangerous places, unless of course a too large event destroys the whole biosphere.
This series of near extinction events however gives a feeling that civilization on Earth exists only because it won 20 times in a row to the roulette in the casino: in mathematical terms, we would be extremely lucky.
Really? An event such as the Chixculub impact, or the Permian-Trias extinction, would certainly wipe out our today civilization. But would it really wipe out mankind? Each time a dreadful event happened on Earth, some protective oasis existed, allowing the survivors to start with another step. Even the 1000kms wide impact which happened during the Late Heavy meteorite bombardment did not erased the microbial life which already existed in this time. So that life seems very resilient to geological catastrophes, after all. As long as the biosphere itself is not destroyed.
How to estimate the probability of life to disappear from some geological catastrophe? From observation: on the five rocky bodies which we can observe today (Earth, Moon, Mercury, Venus, Mars), two undergone massive climate changes: Mars and Venus. But they were discussed above, in relation with size and atmosphere, so that this was already counted. After, the largest known events are huge lava flow on Venus (the longest known), the Moon (formation of the mares) and Earth (Siberian trapps causing the Permian-Trias extinction). And still, planetologists think that the huge Venusian events are a consequence of its lack of plate tectonics, which would produce periodic upheavals in the mantle. That is, something which cannot happen on Earth.
That makes life relatively calm, after all. Anyway far from winning 20 times in a row to the roulette.
For this reason I assign a relatively narrow range of values for this part: from 1 to 0.1.
Assessing a global value for ne, or more exactly the optimistic and pessimistic bounds, just needs to multiply all of the partial values found above. We find 0.1 for the optimistic bound of ne, and 0.0000032 for the pessimistic one. In more, we have a statistical advantage: values forbidding life cannot be all together optimistic or pessimistic, since they are independent phenomena (we took care of not counting the same several times). So that we can bring a geometric averaging of each bound with the geometric average of both. This makes that the actual limits are most likely between 0.0075 and and 0.0002.
These values are true in the halo of our galaxy. They are lower in our vicinity, due to the supplementary contribution of cosmic hazards, that we estimated between 1 and 0.1 in our vicinity. This makes ne varying between between 0.0075 and 0.00002 in our vicinity.
Multiplied with the latest results of the previous chapter on fp, this makes a product of 0.003 for the optimistic bound, and for the pessimistic bound values between 0.00008 for our neighbouring and 0.0008 for the galaxy halo.
Translated in terms of closeness, that makes, assuming an uniform density of stars:
-30 light years for the optimistic bound
-100 light years for the pessimistic bound in our vicinity
-For the halo, the stars are much farther anyway, in both optimistic and pessimistic cases. Although some may cross our place at times, so that we still have some chances to find them.
These are prudent figures, not the easiest to observe, but soon within range of SETI and telescopes.
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