Radical (chemistry)

From Wikipedia, the free encyclopedia

The hydroxyl radical, Lewis structure shown, contains one unpaired electron

In chemistry, a radical (more precisely, a free radical) is an atom, molecule, or ion that has an unpaired valence electron.^[1][2] With some exceptions, these unpaired electrons make free radicals highly chemically reactive. Many free radicals spontaneously dimerize. Most organic radicals have short lifetimes.

A notable example of a free radical is the hydroxyl radical (HO•), a molecule that has one unpaired electron on the oxygen atom. Two other examples are triplet oxygen and triplet carbene (:CH
₂) which have two unpaired electrons.

Free radicals may be generated in a number of ways, but typical methods involve redox reactions. Ionizing radiation, heat, electrical discharges, electrolysis, are known to produce radicals. Radicals are intermediates in many chemical reactions, more so than is apparent from the balanced equations.

Free radicals are important in combustion, atmospheric chemistry, polymerization, plasma chemistry, biochemistry, and many other chemical processes. A large fraction of natural products are generated by radical-generating enzymes. In living organisms, the free radicals superoxide and nitric oxide and their reaction products regulate many processes, such as control of vascular tone and thus blood pressure. They also play a key role in the intermediary metabolism of various biological compounds. Such radicals can even be messengers in a process dubbed redox signaling. A radical may be trapped within a solvent cage or be otherwise bound.

Depiction in chemical reactions

In chemical equations, free radicals are frequently denoted by a dot placed immediately to the right of the atomic symbol or molecular formula as follows:

${\displaystyle \mathrm {Cl} _{2}\;{\xrightarrow {UV}}\;{\mathrm {Cl} \cdot }+{\mathrm {Cl} \cdot }}$

Chlorine gas can be broken down by ultraviolet light to form atomic chlorine radicals.

Radical reaction mechanisms use single-headed arrows to depict the movement of single electrons:

The homolytic cleavage of the breaking bond is drawn with a 'fish-hook' arrow to distinguish from the usual movement of two electrons depicted by a standard curly arrow. The second electron of the breaking bond also moves to pair up with the attacking radical electron; this is not explicitly indicated in this case.

Free radicals also take part in radical addition and radical substitution as reactive intermediates. Chain reactions involving free radicals can usually be divided into three distinct processes. These are initiation, propagation, and termination.

• Initiation reactions are those that result in a net increase in the number of free radicals. They may involve the formation of free radicals from stable species as in Reaction 1 above or they may involve reactions of free radicals with stable species to form more free radicals.
• Propagation reactions are those reactions involving free radicals in which the total number of free radicals remains the same.
• Termination reactions are those reactions resulting in a net decrease in the number of free radicals. Typically two free radicals combine to form a more stable species, for example: 2Cl·→ Cl₂

Formation

The formation of radicals may involve the breaking of covalent bonds by homolysis, a process that requires significant amounts of energy. Such energies are known as homolytic bond dissociation energies, usually abbreviated as "ΔH °". Splitting H₂ into 2H•, for example, requires a ΔH ° of +435 kJ·mol^-1, while splitting Cl₂ into 2Cl• requires a ΔH ° of +243 kJ·mol^-1.

The energy needed to break a specific bond (generally covalent) between two atoms known as bond energy is a result of all the relative attractions and repulsions between the atoms of the molecule, however the most relevant are the bond's atoms and the immediate neighbors. As an approximation the most important parameters that influence the bonding between two atoms in a molecule are the mutual energy match and overlap of covalent orbitals and the repulsion between nonbonding orbitals. Likewise, radicals requiring more energy to form are less stable than those requiring less energy. An additional barrier can be the selection rule. Propagation, however, is very exothermic.

Radical formation through homolytic bond cleavage most often happens between two atoms of similar electronegativity; in organic chemistry, this is often between the O–O bond in peroxide species or between O–N bonds. Radicals may also be formed by single-electron oxidation or reduction of an atom or molecule: an example is the production of superoxide by the electron transport chain. Early studies in organometallic chemistry – especially F. A. Paneth and K. Hahnfeld's studies of tetra-alkyl lead species during the 1930s – supported the heterolytic fission of bonds and a radical-based mechanism. Although radical ions do exist, most species are electrically neutral.

Persistence and stability

The radical derived from α-tocopherol

Although radicals are generally short-lived due to their reactivity, there are long-lived radicals. These are categorized as follows:

Stable radicals

The prime example of a stable radical is molecular dioxygen (O₂). Another common example is nitric oxide (NO). Organic radicals can be long lived if they occur in a conjugated π system, such as the radical derived from α-tocopherol (vitamin E). There are also hundreds of examples of thiazyl radicals, which show low reactivity and remarkable thermodynamic stability with only a very limited extent of π resonance stabilization.^[3][4]

Persistent radicals

Persistent radical compounds are those whose longevity is due to steric crowding around the radical center, which makes it physically difficult for the radical to react with another molecule.^[5] Examples of these include Gomberg's triphenylmethyl radical, Fremy's salt (Potassium nitrosodisulfonate, (KSO₃)₂NO·), aminoxyls, (general formula R₂NO·) such as TEMPO, TEMPOL, nitronyl nitroxides, and azephenylenyls and radicals derived from PTM (perchlorophenylmethyl radical) and TTM (tris(2,4,6-trichlorophenyl)methyl radical). Persistent radicals are generated in great quantity during combustion, and "may be responsible for the oxidative stress resulting in cardiopulmonary disease and probably cancer that has been attributed to exposure to airborne fine particles."^[6]

Diradicals

Diradicals are molecules containing two radical centers. Multiple radical centers can exist in a molecule. Atmospheric oxygen naturally exists as a diradical in its ground state as triplet oxygen. The low reactivity of atmospheric oxygen is due to its diradical state. Non-radical states of dioxygen are actually less stable than the diradical. The relative stability of the oxygen diradical is primarily due to the spin-forbidden nature of the triplet-singlet transition required for it to grab electrons, i.e., "oxidize". The diradical state of oxygen also results in its paramagnetic character, which is demonstrated by its attraction to an external magnet.^[7] Diradicals can also occur in metal-oxo complexes, lending themselves for studies of spin forbidden reactions in transition metal chemistry.^[8]

Reactivity

Radical alkyl intermediates are stabilized by similar physical processes to carbocations: as a general rule, the more substituted the radical center is, the more stable it is. This directs their reactions. Thus, formation of a tertiary radical (R₃C·) is favored over secondary (R₂HC·), which is favored over primary (RH₂C·). Likewise, radicals next to functional groups such as carbonyl, nitrile, and ether are more stable than tertiary alkyl radicals.

Radicals attack double bonds. However, unlike similar ions, such radical reactions are not as much directed by electrostatic interactions. For example, the reactivity of nucleophilic ions with α,β-unsaturated compounds (C=C–C=O) is directed by the electron-withdrawing effect of the oxygen, resulting in a partial positive charge on the carbonyl carbon. There are two reactions that are observed in the ionic case: the carbonyl is attacked in a direct addition to carbonyl, or the vinyl is attacked in conjugate addition, and in either case, the charge on the nucleophile is taken by the oxygen. Radicals add rapidly to the double bond, and the resulting α-radical carbonyl is relatively stable; it can couple with another molecule or be oxidized. Nonetheless, the electrophilic/neutrophilic character of radicals has been shown in a variety of instances. One example is the alternating tendency of the copolymerization of maleic anhydride (electrophilic) and styrene (slightly nucleophilic).

In intramolecular reactions, precise control can be achieved despite the extreme reactivity of radicals. In general, radicals attack the closest reactive site the most readily. Therefore, when there is a choice, a preference for five-membered rings is observed: four-membered rings are too strained, and collisions with carbons six or more atoms away in the chain are infrequent.

Triplet carbenes and nitrenes, which are diradicals, have distinctive chemistry.

Combustion

Spectrum of the blue flame from a butane torch showing excited molecular radical band emission and Swan bands

A familiar free-radical reaction is combustion. The oxygen molecule is a stable diradical, best represented by ·O-O·. Because spins of the electrons are parallel, this molecule is stable. While the ground state of oxygen is this unreactive spin-unpaired (triplet) diradical, an extremely reactive spin-paired (singlet) state is available. For combustion to occur, the energy barrier between these must be overcome. This barrier can be overcome by heat, requiring high temperatures. The triplet-singlet transition is also "forbidden". This presents an additional barrier to the reaction. It also means molecular oxygen is relatively unreactive at room temperature except in the presence of a catalytic heavy atom such as iron or copper.

Combustion consists of various radical chain reactions that the singlet radical can initiate. The flammability of a given material strongly depends on the concentration of free radicals that must be obtained before initiation and propagation reactions dominate leading to combustion of the material. Once the combustible material has been consumed, termination reactions again dominate and the flame dies out. As indicated, promotion of propagation or termination reactions alters flammability. For example, because lead itself deactivates free radicals in the gasoline-air mixture, tetraethyl lead was once commonly added to gasoline. This prevents the combustion from initiating in an uncontrolled manner or in unburnt residues (engine knocking) or premature ignition (preignition).

When a hydrocarbon is burned, a large number of different oxygen radicals are involved. Initially, hydroperoxyl radical (HOO·) are formed. These then react further to give organic hydroperoxides that break up into hydroxyl radicals (HO·).

Polymerization

In addition to combustion, many polymerization reactions involve free radicals. As a result, many plastics, enamels, and other polymers are formed through radical polymerization. For instance, drying oils and alkyd paints harden due to radical crosslinking by oxygen from the atmosphere.

Recent advances in radical polymerization methods, known as living radical polymerization, include:

• Reversible addition-fragmentation chain transfer (RAFT)
• Atom transfer radical polymerization (ATRP)
• Nitroxide mediated polymerization (NMP)

These methods produce polymers with a much narrower distribution of molecular weights.

Atmospheric radicals

The most common radical in the lower atmosphere is molecular dioxygen. Photodissociation of source molecules produces other free radicals. In the lower atmosphere, important free radical are produced by the photodissociation of nitrogen dioxide to an oxygen atom and nitric oxide (see eq. 1. 1 below), which plays a key role in smog formation—and the photodissociation of ozone to give the excited oxygen atom O(1D) (see eq. 1. 2 below). The net and return reactions are also shown (eq. 1. 3 and eq. 1. 4, respectively).

${\displaystyle {\ce {{NO2}->[h \nu] {NO}+ {O}}}}$

(eq. 1. 1)

${\displaystyle {\ce {{O}+ {O2}-> {O3}}}}$

(eq. 1. 2)

${\displaystyle {\ce {{NO2}+ {O2}->[h \nu] {NO}+ {O3}}}}$

(eq. 1. 3)

${\displaystyle {\ce {{NO}+ {O3}-> {NO2}+ {O2}}}}$

(eq. 1. 4)

In the upper atmosphere, the photodissociation of normally unreactive chlorofluorocarbons (CFCs) by solar ultraviolet radiation is an important source of radicals (see eq. 1 below). These reactions give the chlorine radical, Cl•, which catalyzes the conversion of ozone to O₂, i.e., Ozone depletion (eq. 2. 2–eq. 2. 4 below).

${\displaystyle {\ce {{CFCS}->[h \nu] {Cl.}}}}$

(eq. 2. 1)

${\displaystyle {\ce {{Cl.}+ {O3}-> {ClO.}+ {O2}}}}$

(eq. 2. 2)

${\displaystyle {\ce {{O3}->[h \nu] {O}+ {O2}}}}$

(eq. 2. 3)

${\displaystyle {\ce {{O}+ {ClO.}-> {Cl.}+ {O2}}}}$

(eq. 2. 4)

${\displaystyle {\ce {{2O3}->[h \nu] 3O2}}}$

(eq. 2. 5)

Such reactions cause the depletion of the ozone layer, especially since the chlorine radical is free to engage in another reaction chain; consequently, the use of chlorofluorocarbons as refrigerants has been restricted.

In biology

Free radicals play important roles in biology. Many of these are necessary for life, such as the intracellular killing of bacteria by phagocytic cells such as granulocytes and macrophages. Free radicals are involved in cell signalling processes,^[9] known as redox signaling. For example, free radical attack of linoleic acid produces a series of 13-Hydroxyoctadecadienoic acids and 9-Hydroxyoctadecadienoic acids, which may act to regulate localized tissue inflammatory and/or healing responses, pain perception, and the proliferation of malignant cells. Free radical attacks on arachidonic acid and docosahexaenoic acid produce a similar but broader array of signaling products.^[10]
 

Structure of the deoxyadenosyl radical, a common biosynthetic intermediate.^[11]

Free radicals may also be involved in Parkinson's disease, senile and drug-induced deafness, schizophrenia, and Alzheimer's.^[12] The classic free-radical syndrome, the iron-storage disease hemochromatosis, is typically associated with a constellation of free-radical-related symptoms including movement disorder, psychosis, skin pigmentary melanin abnormalities, deafness, arthritis, and diabetes mellitus. The free-radical theory of aging proposes that free radicals underlie the aging process itself. Similarly, the process of mitohormesis suggests that repeated exposure to free radicals may extend life span.

Because free radicals are necessary for life, the body has a number of mechanisms to minimize free-radical-induced damage and to repair damage that occurs, such as the enzymes superoxide dismutase, catalase, glutathione peroxidase and glutathione reductase. In addition, antioxidants play a key role in these defense mechanisms. These are often the three vitamins, vitamin A, vitamin C and vitamin E and polyphenol antioxidants. Furthermore, there is good evidence indicating that bilirubin and uric acid can act as antioxidants to help neutralize certain free radicals. Bilirubin comes from the breakdown of red blood cells' contents, while uric acid is a breakdown product of purines. Too much bilirubin, though, can lead to jaundice, which could eventually damage the central nervous system, while too much uric acid causes gout.^[13]

Reactive oxygen species

Reactive oxygen species or ROS are species such as superoxide, hydrogen peroxide, and hydroxyl radical, commonly associated with cell damage. ROS form as a natural by-product of the normal metabolism of oxygen and have important roles in cell signaling. Two important oxygen-centered free radicals are superoxide and hydroxyl radical. They derive from molecular oxygen under reducing conditions. However, because of their reactivity, these same free radicals can participate in unwanted side reactions resulting in cell damage. Excessive amounts of these free radicals can lead to cell injury and death, which may contribute to many diseases such as cancer, stroke, myocardial infarction, diabetes and major disorders.^[14] Many forms of cancer are thought to be the result of reactions between free radicals and DNA, potentially resulting in mutations that can adversely affect the cell cycle and potentially lead to malignancy.^[15] Some of the symptoms of aging such as atherosclerosis are also attributed to free-radical induced oxidation of cholesterol to 7-ketocholesterol.^[16] In addition free radicals contribute to alcohol-induced liver damage, perhaps more than alcohol itself. Free radicals produced by cigarette smoke are implicated in inactivation of alpha 1-antitrypsin in the lung. This process promotes the development of emphysema.

Oxybenzone has been found to form free radicals in sunlight, and therefore may be associated with cell damage as well. This only occurred when it was combined with other ingredients commonly found in sunscreens, like titanium oxide and octyl methoxycinnamate.^[17]

ROS attack the polyunsaturated fatty acid, linoleic acid, to form a series of 13-Hydroxyoctadecadienoic acid and 9-Hydroxyoctadecadienoic acid products that serve as signaling molecules that may trigger responses that counter the tissue injury which caused their formation. ROS attacks other polyunsaturated fatty acids, e.g. arachidonic acid and docosahexaenoic acid, to produce a similar series of signaling products.^[18]

History and nomenclature

Moses Gomberg (1866–1947), the founder of radical chemistry

Until late in the 20th century the word "radical" was used in chemistry to indicate any connected group of atoms, such as a methyl group or a carboxyl, whether it was part of a larger molecule or a molecule on its own. The qualifier "free" was then needed to specify the unbound case. Following recent nomenclature revisions, a part of a larger molecule is now called a functional group or substituent, and "radical" now implies "free". However, the old nomenclature may still appear in some books.

The term radical was already in use when the now obsolete radical theory was developed. Louis-Bernard Guyton de Morveau introduced the phrase "radical" in 1785 and the phrase was employed by Antoine Lavoisier in 1789 in his Traité Élémentaire de Chimie. A radical was then identified as the root base of certain acids (the Latin word "radix" meaning "root"). Historically, the term radical in radical theory was also used for bound parts of the molecule, especially when they remain unchanged in reactions. These are now called functional groups. For example, methyl alcohol was described as consisting of a methyl "radical" and a hydroxyl "radical". Neither are radicals in the modern chemical sense, as they are permanently bound to each other, and have no unpaired, reactive electrons; however, they can be observed as radicals in mass spectrometry when broken apart by irradiation with energetic electrons.

In a modern context the first organic (carbon–containing) free radical identified was triphenylmethyl radical, (C₆H₅)₃C•. This species was discovered by Moses Gomberg in 1900. In 1933 Morris Kharash and Frank Mayo proposed that free radicals were responsible for anti-Markovnikov addition of hydrogen bromide to allyl bromide.^[19][20]

In most fields of chemistry, the historical definition of radicals contends that the molecules have nonzero electron spin. However, in fields including spectroscopy, chemical reaction, and astrochemistry, the definition is slightly different. Gerhard Herzberg, who won the Nobel prize for his research into the electron structure and geometry of radicals, suggested a looser definition of free radicals: "any transient (chemically unstable) species (atom, molecule, or ion)".^[21] The main point of his suggestion is that there are many chemically unstable molecules that have zero spin, such as C₂, C₃, CH₂ and so on. This definition is more convenient for discussions of transient chemical processes and astrochemistry; therefore researchers in these fields prefer to use this loose definition.^[22]

Diagnostics

Radicals typically exhibit paramagnetism, but the bulk magnetic properties of a ion or molecule are often not conveniently measured. Electron spin resonance is instead the definitive and most widely used technique for characterizing free radicals. The nature of the atom bearing the unpaired electron and its neighboring atoms can often be deduced by the EPR spectrum.^[23]

The presence of free radicals can also be detected or inferred by chemical reagents that trap (i.e. combine with) radicals. Often these traps are themselves radicals, such as TEMPO.

Rare Earth hypothesis

From Wikipedia, the free encyclopedia

The Rare Earth Hypothesis argues that planets with complex life, like Earth, are exceptionally rare

In planetary astronomy and astrobiology, the Rare Earth Hypothesis argues that the origin of life and the evolution of biological complexity such as sexually reproducing, multicellular organisms on Earth (and, subsequently, human intelligence) required an improbable combination of astrophysical and geological events and circumstances. According to the hypothesis, complex extraterrestrial life is a very improbable phenomenon and likely to be extremely rare. The term "Rare Earth" originates from Rare Earth: Why Complex Life Is Uncommon in the Universe (2000), a book by Peter Ward, a geologist and paleontologist, and Donald E. Brownlee, an astronomer and astrobiologist, both faculty members at the University of Washington.

A contrary view was argued in the 1970s and 1980s by Carl Sagan and Frank Drake, among others. It holds that Earth is a typical rocky planet in a typical planetary system, located in a non-exceptional region of a common barred-spiral galaxy. Given the principle of mediocrity (in the same vein as the Copernican principle), it is probable that we are typical, and the universe teems with complex life. However, Ward and Brownlee argue that planets, planetary systems, and galactic regions that are as friendly to complex life as the Earth, the Solar System, and our galactic region are very rare.

Requirements for complex life

The Rare Earth hypothesis argues that the evolution of biological complexity requires a host of fortuitous circumstances, such as a galactic habitable zone, a central star and planetary system having the requisite character, the circumstellar habitable zone, a right-sized terrestrial planet, the advantage of a gas giant guardian like Jupiter and a large natural satellite, conditions needed to ensure the planet has a magnetosphere and plate tectonics, the chemistry of the lithosphere, atmosphere, and oceans, the role of "evolutionary pumps" such as massive glaciation and rare bolide impacts, and whatever led to the appearance of the eukaryote cell, sexual reproduction and the Cambrian explosion of animal, plant, and fungi phyla. The evolution of human intelligence may have required yet further events, which are extremely unlikely to have happened were it not for the Cretaceous–Paleogene extinction event 66 million years ago removing dinosaurs as the dominant terrestrial vertebrates.

In order for a small rocky planet to support complex life, Ward and Brownlee argue, the values of several variables must fall within narrow ranges. The universe is so vast that it could contain many Earth-like planets. But if such planets exist, they are likely to be separated from each other by many thousands of light years. Such distances may preclude communication among any intelligent species evolving on such planets, which would solve the Fermi paradox: "If extraterrestrial aliens are common, why aren't they obvious?"^[1]

The right location in the right kind of galaxy

Rare Earth suggests that much of the known universe, including large parts of our galaxy, are "dead zones" unable to support complex life. Those parts of a galaxy where complex life is possible make up the galactic habitable zone, primarily characterized by distance from the Galactic Center. As that distance increases:

1. Star metallicity declines. Metals (which in astronomy means all elements other than hydrogen and helium) are necessary to the formation of terrestrial planets.
2. The X-ray and gamma ray radiation from the black hole at the galactic center, and from nearby neutron stars, becomes less intense. Thus the early universe, and present-day galactic regions where stellar density is high and supernovae are common, will be dead zones.^[2]
3. Gravitational perturbation of planets and planetesimals by nearby stars becomes less likely as the density of stars decreases. Hence the further a planet lies from the Galactic Center or a spiral arm, the less likely it is to be struck by a large bolide which could extinguish all complex life on a planet.

Dense center of galaxies such as NGC 7331 (often referred to as a "twin" of the Milky Way^[3]) have high radiation levels toxic to complex life.

According to Rare Earth, globular clusters are unlikely to support life.

Item #1 rules out the outer reaches of a galaxy; #2 and #3 rule out galactic inner regions. Hence a galaxy's habitable zone may be a ring sandwiched between its uninhabitable center and outer reaches.

Also, a habitable planetary system must maintain its favorable location long enough for complex life to evolve. A star with an eccentric (elliptic or hyperbolic) galactic orbit will pass through some spiral arms, unfavorable regions of high star density; thus a life-bearing star must have a galactic orbit that is nearly circular, with a close synchronization between the orbital velocity of the star and of the spiral arms. This further restricts the galactic habitable zone within a fairly narrow range of distances from the Galactic Center. Lineweaver et al.^[4] calculate this zone to be a ring 7 to 9 kiloparsecs in radius, including no more than 10% of the stars in the Milky Way,^[5] about 20 to 40 billion stars. Gonzalez, et al.^[6] would halve these numbers; they estimate that at most 5% of stars in the Milky Way fall in the galactic habitable zone.

Approximately 77% of observed galaxies are spiral,^[7] two-thirds of all spiral galaxies are barred, and more than half, like the Milky Way, exhibit multiple arms.^[8] According to Rare Earth, our own galaxy is unusually quiet and dim (see below), representing just 7% of its kind.^[9] Even so, this would still represent more than 200 billion galaxies in the known universe.

Our galaxy also appears unusually favorable in suffering fewer collisions with other galaxies over the last 10 billion years, which can cause more supernovae and other disturbances.^[10] Also, the Milky Way's central black hole seems to have neither too much nor too little activity.^[11]

The orbit of the Sun around the center of the Milky Way is indeed almost perfectly circular, with a period of 226 Ma (million years), closely matching the rotational period of the galaxy. However, the majority of stars in barred spiral galaxies populate the spiral arms rather than the halo and tend to move in gravitationally aligned orbits, so there is little that is unusual about the Sun's orbit. While the Rare Earth hypothesis predicts that the Sun should rarely, if ever, have passed through a spiral arm since its formation, astronomer Karen Masters has calculated that the orbit of the Sun takes it through a major spiral arm approximately every 100 million years.^[12] Some researchers have suggested that several mass extinctions do correspond with previous crossings of the spiral arms.^[13]

Orbiting at the right distance from the right type of star

According to the hypothesis, Earth has an improbable orbit in the very narrow habitable zone (dark green) around the Sun.

The terrestrial example suggests that complex life requires liquid water, requiring an orbital distance neither too close nor too far from the central star, another scale of habitable zone or Goldilocks Principle:^[14] The habitable zone varies with the star's type and age.

For advanced life, the star must also be highly stable, which is typical of middle star life, about 4.6 billion years old. Proper metallicity and size are also very important to stability. The Sun has a low 0.1% luminosity variation. To date no solar twin star twin, with an exact match of the sun's luminosity variation, has been found, though some come close. The star must have no stellar companions, as in binary systems, which would disrupt the orbits of planets. Estimates suggest 50% or more of all star systems are binary.^{[15][16][17][18]} The habitable zone for a main sequence star very gradually moves out over its lifespan until it becomes a white dwarf and the habitable zone vanishes.

The liquid water and other gases available in the habitable zone bring the benefit of greenhouse warming. Even though the Earth's atmosphere contains a water vapor concentration from 0% (in arid regions) to 4% (in rain forest and ocean regions) and – as of February 2018 – only 408.05^{[citation needed]} parts per million of CO₂, these small amounts suffice to raise the average surface temperature by about 40 °C,^[19] with the dominant contribution being due to water vapor, which together with clouds makes up between 66% and 85% of Earth's greenhouse effect, with CO₂ contributing between 9% and 26% of the effect.^[20]

Rocky planets must orbit within the habitable zone for life to form. Although the habitable zone of such hot stars as Sirius or Vega is wide, hot stars also emit much more ultraviolet radiation that ionizes any planetary atmosphere. They may become red giants before advanced life evolves on their planets. These considerations rule out the massive and powerful stars of type F6 to O (see stellar classification) as homes to evolved metazoan life.

Small red dwarf stars conversely have small habitable zones wherein planets are in tidal lock, with one very hot side always facing the star and another very cold side; and they are also at increased risk of solar flares (see Aurelia). Life therefore cannot arise in such systems. Rare Earth proponents claim that only stars from F7 to K1 types are hospitable. Such stars are rare: G type stars such as the Sun (between the hotter F and cooler K) comprise only 9%^[21] of the hydrogen-burning stars in the Milky Way.

Such aged stars as red giants and white dwarfs are also unlikely to support life. Red giants are common in globular clusters and elliptical galaxies. White dwarfs are mostly dying stars that have already completed their red giant phase. Stars that become red giants expand into or overheat the habitable zones of their youth and middle age (though theoretically planets at a much greater distance may become habitable).

An energy output that varies with the lifetime of the star will very likely prevent life (e.g., as Cepheid variables). A sudden decrease, even if brief, may freeze the water of orbiting planets, and a significant increase may evaporate it and cause a greenhouse effect that prevents the oceans from reforming.

All known life requires the complex chemistry of metallic elements. The absorption spectrum of a star reveals the presence of metals within, and studies of stellar spectra reveal that many, perhaps most, stars are poor in metals. Because heavy metals originate in supernova explosions, metallicity increases in the universe over time. Low metallicity characterizes the early universe: globular clusters and other stars that formed when the universe was young, stars in most galaxies other than large spirals, and stars in the outer regions of all galaxies. Metal-rich central stars capable of supporting complex life are therefore believed to be most common in the quiet suburbs^[vague] of the larger spiral galaxies—where radiation also happens to be weak.^[22]

With the right arrangement of planets

Depiction of the Sun and planets of the Solar System and the sequence of planets. Rare Earth argues that without such an arrangement, in particular the presence of the massive gas giant Jupiter (fifth planet from the Sun and the largest), complex life on Earth would not have arisen.

Rare Earth proponents argue that a planetary system capable of sustaining complex life must be structured more or less like the Solar System, with small and rocky inner planets and outer gas giants.^[23] Without the protection of 'celestial vacuum cleaner' planets with strong gravitational pull, a planet would be subject to more catastrophic asteroid collisions.

Observations of exo-planets have shown that arrangements of planets similar to our Solar System are rare. Most planetary systems have super Earths, several times larger than Earth, close to their star, whereas our Solar System's inner region has only a few small rocky planets and none inside Mercury's orbit. Only 10% of stars have giant planets similar to Jupiter and Saturn, and those few rarely have stable nearly circular orbits distant from their star. Konstantin Batygin and colleagues argue that these features can be explained if, early in the history of the Solar System, Jupiter and Saturn drifted towards the Sun, sending showers of planetesimals towards the super-Earths which sent them spiralling into the Sun, and ferrying icy building blocks into the terrestrial region of the Solar System which provided the building blocks for the rocky planets. The two giant planets then drifted out again to their present position. However, in the view of Batygin and his colleagues: "The concatenation of chance events required for this delicate choreography suggest that small, Earth-like rocky planets – and perhaps life itself – could be rare throughout the cosmos."^[24]

A continuously stable orbit

Rare Earth argues that a gas giant must not be too close to a body where life is developing. Close placement of gas giant(s) could disrupt the orbit of a potential life-bearing planet, either directly or by drifting into the habitable zone.

Newtonian dynamics can produce chaotic planetary orbits, especially in a system having large planets at high orbital eccentricity.^[25]

The need for stable orbits rules out stars with systems of planets that contain large planets with orbits close to the host star (called "hot Jupiters"). It is believed that hot Jupiters have migrated inwards to their current orbits. In the process, they would have catastrophically disrupted the orbits of any planets in the habitable zone.^[26] To exacerbate matters, hot Jupiters are much more common orbiting F and G class stars.^[27]

A terrestrial planet of the right size

Planets of the Solar System to scale. Rare Earth argues that complex life cannot exist on large gaseous planets like Jupiter and Saturn (top row) or Uranus and Neptune (top middle) or smaller planets such as Mars and Mercury

It is argued that life requires terrestrial planets like Earth and as gas giants lack such a surface, that complex life cannot arise there.^[28]

A planet that is too small cannot hold much atmosphere, making surface temperature low and variable and oceans impossible. A small planet will also tend to have a rough surface, with large mountains and deep canyons. The core will cool faster, and plate tectonics may be brief or entirely absent. A planet that is too large will retain too dense atmosphere like Venus. Although Venus is similar in size and mass to Earth, its surface atmospheric pressure is 92 times that of Earth, and surface temperature of 735 K (462 °C; 863 °F). Earth had a similar early atmosphere to Venus, but may have lost it in the giant impact event.^[29]

With plate tectonics

The Great American Interchange on Earth, around ~ 3.5 to 3 Ma, an example of species competition, resulting from continental plate interaction.

An artist's rendering of the structure of Earth's magnetic field-magnetosphere that protects Earth's life from solar radiation. 1) Bow shock. 2) Magnetosheath. 3) Magnetopause. 4) Magnetosphere. 5) Northern tail lobe. 6) Southern tail lobe. 7) Plasmasphere.

Rare Earth proponents argue that plate tectonics and a strong magnetic field are essential for biodiversity, global temperature regulation, and the carbon cycle.^[30] The lack of mountain chains elsewhere in the Solar System is direct evidence that Earth is the only body with plate tectonics, and thus the only nearby body capable of supporting life.^[31]

Plate tectonics depend on the right chemical composition and a long-lasting source of heat from radioactive decay. Continents must be made of less dense felsic rocks that "float" on underlying denser mafic rock. Taylor^[32] emphasizes that tectonic subduction zones require the lubrication of oceans of water. Plate tectonics also provides a means of biochemical cycling.^[33]

Plate tectonics and as a result continental drift and the creation of separate land masses would create diversified ecosystems and biodiversity, one of the strongest defences against extinction.^[34] An example of species diversification and later competition on Earth's continents is the Great American Interchange. North and Middle America drifted into South America at around 3.5 to 3 Ma. The fauna of South America evolved separately for about 30 million years, since Antarctica separated. Many species were subsequently wiped out in mainly South America by competing Northern American animals.

A large moon

Tide pools resulting from tidal interaction of the Moon are said to have promoted the evolution of complex life.

The Moon is unusual because the other rocky planets in the Solar System either have no satellites (Mercury and Venus), or only tiny satellites which are probably captured asteroids (Mars).

The Giant-impact theory hypothesizes that the Moon resulted from the impact of a Mars-sized body, dubbed Theia, with the very young Earth. This giant impact also gave the Earth its axial tilt (inclination) and velocity of rotation.^[32] Rapid rotation reduces the daily variation in temperature and makes photosynthesis viable.^[35] The Rare Earth hypothesis further argues that the axial tilt cannot be too large or too small (relative to the orbital plane). A planet with a large tilt will experience extreme seasonal variations in climate. A planet with little or no tilt will lack the stimulus to evolution that climate variation provides.^{[citation needed]} In this view, the Earth's tilt is "just right". The gravity of a large satellite also stabilizes the planet's tilt; without this effect the variation in tilt would be chaotic, probably making complex life forms on land impossible.^[36]

If the Earth had no Moon, the ocean tides resulting solely from the Sun's gravity would be only half that of the lunar tides. A large satellite gives rise to tidal pools, which may be essential for the formation of complex life, though this is far from certain.^[37]

A large satellite also increases the likelihood of plate tectonics through the effect of tidal forces on the planet's crust.^{[citation needed]} The impact that formed the Moon may also have initiated plate tectonics, without which the continental crust would cover the entire planet, leaving no room for oceanic crust.^{[citation needed]} It is possible that the large scale mantle convection needed to drive plate tectonics could not have emerged in the absence of crustal inhomogeneity.

Earth's atmosphere

Atmosphere

A terrestrial planet of the right size is needed to retain an atmosphere, like Earth and Venus. On Earth, once the giant impact of Theia thinned Earth's atmosphere, other events were needed to make the atmosphere capable of sustaining life. The Late Heavy Bombardment reseeded Earth with water lost after the impact of Theia.^[38] The development of an ozone layer formed protection from ultraviolet (UV) sunlight.^[39][40] Nitrogen and carbon dioxide are needed in a correct ratio for life to form.^[41] Lightning is needed for nitrogen fixation.^[42][42] The carbon dioxide gas needed for life comes from sources such as volcanoes and geysers. Carbon dioxide is only needed at low levels^{[citation needed]} (currently at 400 ppm); at high levels it is poisonous.^[43][44] Precipitation is needed to have a stable water cycle.^[45] A proper atmosphere must reduce diurnal temperature variation.^[46][47]

One or more evolutionary triggers for complex life

This diagram illustrates the twofold cost of sex. If each individual were to contribute to the same number of offspring (two), (a) the sexual population remains the same size each generation, where the (b) asexual population doubles in size each generation

Regardless of whether planets with similar physical attributes to the Earth are rare or not, some argue that life usually remains simple bacteria. Biochemist Nick Lane argues that simple cells (prokaryotes) emerged soon after Earth's formation, but since almost half the planet's life had passed before they evolved into complex ones (eukaryotes) all of whom share a common ancestor, this event can only have happened once. In some views, prokaryotes lack the cellular architecture to evolve into eukaryotes because a bacterium expanded up to eukaryotic proportions would have tens of thousands of times less energy available; two billion years ago, one simple cell incorporated itself into another, multiplied, and evolved into mitochondria that supplied the vast increase in available energy that enabled the evolution of complex life. If this incorporation occurred only once in four billion years or is otherwise unlikely, then life on most planets remains simple.^[48] An alternative view is that mitochondria evolution was environmentally triggered, and that mitochondria-containing organisms appeared very soon after the first traces of atmospheric oxygen.^[49]

The evolution and persistence of sexual reproduction is another mystery in biology. The purpose of sexual reproduction is unclear, as in many organisms it has a 50% cost (fitness disadvantage) in relation to asexual reproduction.^[50] Mating types (types of gametes, according to their compatibility) may have arisen as a result of anisogamy (gamete dimorphism), or the male and female genders may have evolved before anisogamy.^[51][52] It is also unknown why most sexual organisms use a binary mating system,^[53] and why some organisms have gamete dimorphism. Charles Darwin was the first to suggest that sexual selection drives speciation; without it, complex life would probably not have evolved.

The right time in evolution

Timeline of evolution; human writings exists for only 0.000218% of Earth's history.

While life on Earth is regarded to have spawned relatively early in the planet's history, the evolution from multicellular to intelligent organisms took around 800 million years.^[54] Civilizations on Earth have existed for about 12,000 years and radio communication reaching space has existed for less than 100 years. Relative to the age of the Solar System (~4.57 Ga) this is a short time, in which extreme climatic variations, super volcanoes, and large meteorite impacts were absent. These events would severely harm intelligent life, as well as life in general. For example, the Permian-Triassic mass extinction, caused by widespread and continuous volcanic eruptions in an area the size of Western Europe, led to the extinction of 95% of known species around 251.2 Ma ago. About 65 million years ago, the Chicxulub impact at the Cretaceous–Paleogene boundary (~65.5 Ma) on the Yucatán peninsula in Mexico led to a mass extinction of the most advanced species at that time.

If there were intelligent extraterrestrial civilizations able to make contact with distant Earth, they would have to live in the same 12Ka period of the 800Ma evolution of life.

Rare Earth equation

The following discussion is adapted from Cramer.^[55] The Rare Earth equation is Ward and Brownlee's riposte to the Drake equation. It calculates ${\displaystyle N}$, the number of Earth-like planets in the Milky Way having complex life forms, as:

According to Rare Earth, the Cambrian explosion that saw extreme diversification of chordata from simple forms like Pikaia (pictured) was an improbable event

${\displaystyle N=N^{*}\cdot n_{e}\cdot f_{g}\cdot f_{p}\cdot f_{pm}\cdot f_{i}\cdot f_{c}\cdot f_{l}\cdot f_{m}\cdot f_{j}\cdot f_{me}}$^[56]

where:

• N* is the number of stars in the Milky Way. This number is not well-estimated, because the Milky Way's mass is not well estimated, with little information about the number of very small stars. N* is at least 100 billion, and may be as high as 500 billion, if there are many low visibility stars.
• ${\displaystyle n_{e}}$ is the average number of planets in a star's habitable zone. This zone is fairly narrow, because constrained by the requirement that the average planetary temperature be consistent with water remaining liquid throughout the time required for complex life to evolve. Thus ${\displaystyle n_{e}}$=1 is a likely upper bound.

We assume ${\displaystyle N^{*}\cdot n_{e}=5\cdot 10^{11}}$. The Rare Earth hypothesis can then be viewed as asserting that the product of the other nine Rare Earth equation factors listed below, which are all fractions, is no greater than 10⁻¹⁰ and could plausibly be as small as 10⁻¹². In the latter case, ${\displaystyle N}$ could be as small as 0 or 1. Ward and Brownlee do not actually calculate the value of ${\displaystyle N}$, because the numerical values of quite a few of the factors below can only be conjectured. They cannot be estimated simply because we have but one data point: the Earth, a rocky planet orbiting a G2 star in a quiet suburb of a large barred spiral galaxy, and the home of the only intelligent species we know, namely ourselves.

• ${\displaystyle f_{g}}$ is the fraction of stars in the galactic habitable zone (Ward, Brownlee, and Gonzalez estimate this factor as 0.1^[6]).
• ${\displaystyle f_{p}}$ is the fraction of stars in the Milky Way with planets.
• ${\displaystyle f_{pm}}$ is the fraction of planets that are rocky ("metallic") rather than gaseous.
• ${\displaystyle f_{i}}$ is the fraction of habitable planets where microbial life arises. Ward and Brownlee believe this fraction is unlikely to be small.
• ${\displaystyle f_{c}}$ is the fraction of planets where complex life evolves. For 80% of the time since microbial life first appeared on the Earth, there was only bacterial life. Hence Ward and Brownlee argue that this fraction may be very small.
• ${\displaystyle f_{l}}$ is the fraction of the total lifespan of a planet during which complex life is present. Complex life cannot endure indefinitely, because the energy put out by the sort of star that allows complex life to emerge gradually rises, and the central star eventually becomes a red giant, engulfing all planets in the planetary habitable zone. Also, given enough time, a catastrophic extinction of all complex life becomes ever more likely.
• ${\displaystyle f_{m}}$ is the fraction of habitable planets with a large moon. If the giant impact theory of the Moon's origin is correct, this fraction is small.
• ${\displaystyle f_{j}}$ is the fraction of planetary systems with large Jovian planets. This fraction could be large.
• ${\displaystyle f_{me}}$ is the fraction of planets with a sufficiently low number of extinction events. Ward and Brownlee argue that the low number of such events the Earth has experienced since the Cambrian explosion may be unusual, in which case this fraction would be small.

The Rare Earth equation, unlike the Drake equation, does not factor the probability that complex life evolves into intelligent life that discovers technology (Ward and Brownlee are not evolutionary biologists). Barrow and Tipler^[57] review the consensus among such biologists that the evolutionary path from primitive Cambrian chordates, e.g., Pikaia to Homo sapiens, was a highly improbable event. For example, the large brains of humans have marked adaptive disadvantages, requiring as they do an expensive metabolism, a long gestation period, and a childhood lasting more than 25% of the average total life span. Other improbable features of humans include:

• Being one of a handful of extant bipedal land (non-avian) vertebrate. Combined with an unusual eye–hand coordination, this permits dextrous manipulations of the physical environment with the hands;
• A vocal apparatus far more expressive^{[citation needed]} than that of any other mammal, enabling speech. Speech makes it possible for humans to interact cooperatively, to share knowledge, and to acquire a culture;
• The capability of formulating abstractions to a degree permitting the invention of mathematics, and the discovery of science and technology. Only recently did humans acquire anything like their current scientific and technological sophistication.

Advocates

Writers who support the Rare Earth hypothesis:

• Stuart Ross Taylor,^[32] a specialist on the Solar System, firmly believes in the hypothesis. Taylor concludes that the Solar System is probably very unusual, because it resulted from so many chance factors and events.
• Stephen Webb,^[1] a physicist, mainly presents and rejects candidate solutions for the Fermi paradox. The Rare Earth hypothesis emerges as one of the few solutions left standing by the end of the book.
• Simon Conway Morris, a paleontologist, endorses the Rare Earth hypothesis in chapter 5 of his Life's Solution: Inevitable Humans in a Lonely Universe,^[58] and cites Ward and Brownlee's book with approval.^[59]
• John D. Barrow and Frank J. Tipler (1986. 3.2, 8.7, 9), cosmologists, vigorously defend the hypothesis that humans are likely to be the only intelligent life in the Milky Way, and perhaps the entire universe. But this hypothesis is not central to their book The Anthropic Cosmological Principle, a thorough study of the anthropic principle and of how the laws of physics are peculiarly suited to enable the emergence of complexity in nature.
• Ray Kurzweil, a computer pioneer and self-proclaimed Singularitarian, argues in The Singularity Is Near that the coming Singularity requires that Earth be the first planet on which sentient, technology-using life evolved. Although other Earth-like planets could exist, Earth must be the most evolutionarily advanced, because otherwise we would have seen evidence that another culture had experienced the Singularity and expanded to harness the full computational capacity of the physical universe.
• John Gribbin, a prolific science writer, defends the hypothesis in Alone in the Universe: Why our planet is unique.^[60]
• Guillermo Gonzalez, astrophysicist who coined the term galactic habitable zone uses the hypothesis in his book The Privileged Planet to promote the concept of intelligent design.^[61]
• Michael H. Hart, astrophysicist who proposed a very narrow habitable zone based on climate studies, edited the influential book "Extraterrestrials: Where are They" and authored one of its chapters "Atmospheric Evolution, the Drake Equation and DNA: Sparse Life in an Infinite Universe".^[62]
• Howard Alan Smith, astrophysicist and author of 'Let there be light: modern cosmology and Kabbalah: a new conversation between science and religion'.^[63]
• Marc J. Defant, professor of geochemistry and volcanology, elaborated on several aspects of the rare earth hypothesis in his TEDx talk entitled: Why We are Alone in the Galaxy.^[64]

Criticism

Cases against the Rare Earth Hypothesis take various forms.

Anthropic reasoning

The hypothesis concludes, more or less, that complex life is rare because it can evolve only on the surface of an Earth-like planet or on a suitable satellite of a planet. Some biologists, such as Jack Cohen, believe this assumption too restrictive and unimaginative; they see it as a form of circular reasoning.

According to David Darling, the Rare Earth hypothesis is neither hypothesis nor prediction, but merely a description of how life arose on Earth.^[65] In his view Ward and Brownlee have done nothing more than select the factors that best suit their case.

What matters is not whether there's anything unusual about the Earth; there's going to be something idiosyncratic about every planet in space. What matters is whether any of Earth's circumstances are not only unusual but also essential for complex life. So far we've seen nothing to suggest there is.^[66]

Critics also argue that there is a link between the Rare Earth Hypothesis and the creationist ideas of intelligent design.^[67]

Exoplanets around main sequence stars are being discovered in large numbers

An increasing number of extrasolar planet discoveries are being made with 3,786 planets in 2,834 planetary systems known as of 2 June 2018.^[68] Rare Earth proponents argue life cannot arise outside Sun-like systems. However, some exobiologists have suggested that stars outside this range may give rise to life under the right circumstances; this possibility is a central point of contention to the theory because these late-K and M category stars make up about 82% of all hydrogen-burning stars.^[21]

Current technology limits the testing of important Rare Earth criteria: surface water, tectonic plates, a large moon and biosignatures are currently undetectable. Though planets the size of Earth are difficult to detect and classify, scientists now think that rocky planets are common around Sun-like stars.^[69] The Earth Similarity Index (ESI) of mass, radius and temperature provides a means of measurement, but falls short of the full Rare Earth criteria.^[70][71]

Rocky planets orbiting within habitable zones may not be rare

Planets similar to Earth in size are being found in relatively large number in the habitable zones of similar stars. The 2015 infographic depicts Kepler-62e, Kepler-62f, Kepler-186f, Kepler-296e, Kepler-296f, Kepler-438b, Kepler-440b, Kepler-442b, Kepler-452b.^[72]

Some argue that Rare Earth's estimates of rocky planets in habitable zones (${\displaystyle n_{e}}$ in the Rare Earth equation) are too restrictive. James Kasting cites the Titius-Bode law to contend that it is a misnomer to describe habitable zones as narrow when there is a 50% chance of at least one planet orbiting within one.^[73] In 2013 a study that was published in the journal Proceedings of the National Academy of Sciences calculated that about "one in five" of all sun-like stars are expected to have earthlike planets "within the habitable zones of their stars"; 8.8 billion of them therefore exist in the Milky Way galaxy alone.^[74] On 4 November 2013, astronomers reported, based on Kepler space mission data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy.^[75][76] 11 billion of these estimated planets may be orbiting sun-like stars.^[77]

Uncertainty over Jupiter's role

The requirement for a system to have a Jovian planet as protector (Rare Earth equation factor ${\displaystyle f_{j}}$) has been challenged, affecting the number of proposed extinction events (Rare Earth equation factor ${\displaystyle f_{me}}$). Kasting's 2001 review of Rare Earth questions whether a Jupiter protector has any bearing on the incidence of complex life.^[78] Computer modelling including the 2005 Nice model and 2007 Nice 2 model yield inconclusive results in relation to Jupiter's gravitational influence and impacts on the inner planets.^[79] A study by Horner and Jones (2008) using computer simulation found that while the total effect on all orbital bodies within the Solar System is unclear, Jupiter has caused more impacts on Earth than it has prevented.^[80] Lexell's Comet, a 1770 near miss that passed closer to Earth than any other comet in recorded history, was known to be caused by the gravitational influence of Jupiter.^[81] Grazier (2017) claims that the idea of Jupiter as a shield is a misinterpretation of a 1996 study by George Wetherill, and using computer models Grazier was able to demonstrate that Saturn protects Earth from more asteroids and comets than does Jupiter.^[82]

Plate tectonics may not be unique to Earth or a requirement for complex life

Geological discoveries like the active features of Pluto's Tombaugh Regio appear to contradict the argument that geologically active worlds like Earth are rare.^[83]

Ward and Brownlee argue that tectonics is necessary to support biogeochemical cycles required for complex life, and predicted that such geological features would not be found outside of Earth, pointing to a lack of observable mountain ranges and subduction.^[84] There is, however, no scientific consensus on the evolution of plate tectonics on Earth. Though it is believed that tectonic motion first began around three billion years ago,^[85] by this time photosynthesis and oxygenation had already begun. Furthermore, recent studies point to plate tectonics as an episodic planetary phenomenon, and that life may evolve during periods of "stagnant-lid" rather than plate tectonic states.^[86]

Recent evidence also points to similar activity either having occurred or continuing to occur elsewhere. The geology of Pluto, for example, described by Ward and Brownlee as "without mountains or volcanoes ... devoid of volcanic activity",^[22] has since been found to be quite the contrary, with a geologically active surface possessing organic molecules^[87] and mountain ranges^[88] like Tenzing Montes and Hillary Montes comparable in relative size to those of Earth, and observations suggest the involvement of endogenic processes.^[89] Plate tectonics has been suggested as a hypothesis for the Martian dichotomy, and in 2012 geologist An Yin put forward evidence for active plate tectonics on Mars.^[90] Europa has long been suspected to have plate tectonics^[91] and in 2014 NASA announced evidence of active subduction.^[92] In 2017, scientists studying the Geology of Charon confirmed that icy plate tectonics also operated on Pluto's largest moon.^[93]

Kasting suggests that there is nothing unusual about the occurrence of plate tectonics in large rocky planets and liquid water on the surface as most should generate internal heat even without the assistance of radioactive elements.^[78] Studies by Valencia^[94] and Cowan^[95] suggest that plate tectonics may be inevitable for terrestrial planets Earth sized or larger, that is, Super-Earths, which are now known to be more common in planetary systems.^[96]

Free oxygen may neither be rare nor a prerequisite for multicellular life

Animals like Spinoloricus nov. sp. appear to defy the premise that animal life would not exist without oxygen

The hypothesis that molecular oxygen, necessary for animal life, is rare and that a Great Oxygenation Event (Rare Earth equation factor ${\displaystyle f_{c}}$) could only have been triggered and sustained by tectonics, appears to have been invalidated by more recent discoveries.

Ward and Brownlee ask "whether oxygenation, and hence the rise of animals, would ever have occurred on a world where there were no continents to erode".^[97] Extraterrestrial free oxygen has recently been detected around other solid objects, including Mercury,^[98] Venus,^[99] Mars^[100] Jupiter's four Galilean moons,^[101] Saturn's moons Enceladus,^[102] Dione^[103][104] and Rhea^[105] and even the atmosphere of a comet.^[106] This has led scientists to speculate whether processes other than photosynthesis could be capable of generating an environment rich in free oxygen. Wordsworth (2014) concludes that oxygen generated other than through photodissociation may be likely on Earth-like exoplanets, and could actually lead to false positive detections of life.^[107] Narita (2015) suggests photocatalysis by titanium dioxide as a geochemical mechanism for producing oxygen atmospheres.^[108]

Since Ward & Brownlee's assertion that "there is irrefutable evidence that oxygen is a necessary ingredient for animal life",^[97] anaerobic metazoa have been found that indeed do metabolise without oxygen. Spinoloricus nov. sp., for example, a species discovered in the hypersaline anoxic L'Atalante basin at the bottom of the Mediterranean Sea in 2010, appears to metabolise with hydrogen, lacking mitochondria and instead using hydrogenosomes.^[109][110] Stevenson (2015) has proposed other membrane alternatives for complex life in worlds without oxygen.^[111] In 2017, scientists from the NASA Astrobiology Institute discovered the necessary chemical preconditions for the formation of azotosomes on Saturn's moon Titan, a world that lacks atmospheric oxygen.^[112] Independent studies by Schirrmeister and by Mills concluded that Earth's multicellular life existed prior to the Great Oxygenation Event, not as a consequence of it.^[113][114]

NASA scientists Hartman and McKay argue that plate tectonics may in fact slow the rise of oxygenation (and thus stymie complex life rather than promote it).^[115] Computer modelling by Tilman Spohn in 2014 found that plate tectonics on Earth may have arisen from the effects of complex life's emergence, rather than the other way around as the Rare Earth might suggest. The action of lichens on rock may have contributed to the formation of subduction zones in the presence of water.^[116] Kasting argues that if oxygenation caused the Cambrian explosion then any planet with oxygen producing photosynthesis should have complex life.^[117]

A magnetic field may not be a requirement

The importance of Earth's magnetic field to the development of complex life has been disputed. Kasting argues that the atmosphere provides sufficient protection against cosmic rays even during times of magnetic pole reversal and atmosphere loss by sputtering.^[78] Kasting also dismisses the role of the magnetic field in the evolution of eukaryotes, citing the age of the oldest known magnetofossils.^[118]

A large moon may neither be rare nor necessary

The requirement of a large moon (Rare Earth equation factor ${\displaystyle f_{m}}$) has also been challenged. Even if it were required, such an occurrence may not be as unique as predicted by the Rare Earth Hypothesis. Recent work by Edward Belbruno and J. Richard Gott of Princeton University suggests that giant impacts such as those that may have formed the Moon can indeed form in planetary trojan points (L₄ or L₅ Lagrangian point) which means that similar circumstances may occur in other planetary systems.^[119]

Collision between two planetary bodies (artist concept).

Rare Earth's assertion that the Moon's stabilization of Earth's obliquity and spin is a requirement for complex life has been questioned. Kasting argues that a moonless Earth would still possess habitats with climates suitable for complex life and questions whether the spin rate of a moonless Earth can be predicted.^[78] Although the giant impact theory posits that the impact forming the Moon increased Earth's rotational speed to make a day about 5 hours long, the Moon has slowly "stolen" much of this speed to reduce Earth's solar day since then to about 24 hours and continues to do so: in 100 million years Earth's solar day will be roughly 24 hours 38 minutes (the same as Mars's solar day); in 1 billion years, 30 hours 23 minutes. Larger secondary bodies would exert proportionally larger tidal forces that would in turn decelerate their primaries faster and potentially increase the solar day of a planet in all other respects like earth to over 120 hours within a few billion years. This long solar day would make effective heat dissipation for organisms in the tropics and subtropics extremely difficult in a similar manner to tidal locking to a red dwarf star. Short days (high rotation speed) causes high wind speeds at ground level. Long days (slow rotation speed) cause the day and night temperatures to be too extreme.^[120]

Many Rare Earth proponents argue that the Earth's plate tectonics would probably not exist if not for the tidal forces of the Moon.^[121][122] The hypothesis that the Moon's tidal influence initiated or sustained Earth's plate tectonics remains unproven, though at least one study implies a temporal correlation to the formation of the Moon.^[123] Evidence for the past existence of plate tectonics on planets like Mars^[124] which may never have had a large moon would counter this argument. Kasting argues that a large moon is not required to initiate plate tectonics.^[78]

Complex life may arise in alternative habitats

Complex life may exist in environments similar to black smokers on Earth.

Rare Earth proponents argue that simple life may be common, though complex life requires specific environmental conditions to arise. Critics consider life could arise on a moon of a gas giant, though this is less likely if life requires volcanicity. The moon must have stresses to induce tidal heating, but not so dramatic as seen on Jupiter's Io. However, the moon is within the gas giant's intense radiation belts, sterilizing any biodiversity before it can get established. Dirk Schulze-Makuch disputes this, hypothesizing alternative biochemistries for alien life.^[125] While Rare Earth proponents argue that only microbial extremophiles could exist in subsurface habitats beyond Earth, some argue that complex life can also arise in these environments. Examples of extremophile animals such as the Hesiocaeca methanicola, an animal that inhabits ocean floor methane clathrates substances more commonly found in the outer Solar System, the tardigrades which can survive in the vacuum of space^[126] or Halicephalobus mephisto which exists in crushing pressure, scorching temperatures and extremely low oxygen levels 3.6 kilometres deep in the Earth's crust,^[127] are sometimes cited by critics as complex life capable of thriving in "alien" environments. Jill Tarter counters the classic counterargument that these species adapted to these environments rather than arose in them, by suggesting that we cannot assume conditions for life to emerge which are not actually known.^[128] There are suggestions that complex life could arise in sub-surface conditions which may be similar to those where life may have arisen on Earth, such as the tidally heated subsurfaces of Europa or Enceladus.^[129][130] Ancient circumvental ecosystems such as these support complex life on Earth such as Riftia pachyptila that exist completely independent of the surface biosphere.^[131]