Stars, Ozone, & Evolution of Complex Life

[Widdekind]

Earth first formed about 4.6 billion years ago, condensing out of the gases & dust in the proto-Sun's Planetary Disk. But, for about the 1^st billion years, the proto-planet was repeatedly pummeled by swarms of Impactors. They deposited gargantuan quantities of energy onto the Earth's surface, keeping it hot, molten, and inhospitable, even to primitive microbes. This period of "Heavy Bombardment" only ended about 3.5 billion years ago*. Around the same time (~3.5 billion years ago), the first Photo-Synthesizing microbes (eg. "Stromatolites") appeared, and began steadily producing Molecular Oxygen (O₂), for billions of years.

* TLC It Came from Space (VHS)
** Discovery Education Planet Earth (DVD) ; History Channel The Universe -- Astrobiology (DVD) ; James F. Luhr. Earth: the Definitive Visual Guide, pp. 26-29.​

Now, Earth Life eventually blossomed, into complicated forms, but only after an effective Ozone Layer had finally appeared, to protect the planet from DNA-damaging UV radiation. And, effective Ozone Layers (O₃) only arise when Oxygen (O₂) concentrations get sufficiently high. That happened, on Earth, about 550 million years ago*, as the end result of about 3 billion years of Oxygenic Photo-Synthesis by those primitive microbes (above). Geologists call this newly Oxygen-rich environment "Earth's Third Atmosphere", and it facilitated the famous "Cambrian Explosion" of Complex Lifeforms at that time**.

* History Channel How the Earth was Made (DVD)
** http://en.wikipedia.org/wiki/Earth's_atmosphere​

But, Ozone production also depends upon UV radiation reaching the planet's upper atmosphere. The exact equations are quite complicated*. However, if you assume that the "Fast" reactions** are always in equilibrium (mathematically "cancel out"), you obtain the simple yet (seemingly) solid approximation:

n(O₂) * F_hard ~ n(O₃) * F_soft​

On the left, the Photo-Dissociation Rate of Molecular Oxygen (O₂) by hard UV (< 240 nm) yields 2 Atomic Oxygens (2O). On the right, the Photo-Dissociation Rate of Ozone (O₃) by soft UV (240-310 nm) yields 1 Molecular Oxygen & 1 Atomic Oxygen (O₂ + O). The Molecular Oxygen from the right side replaces that lost on the left, and we are assuming that the 3 Atomic Oxgens remaining from both sides quickly recombine into Ozone, by "Fast" reactions***.

* See: http://en.wikipedia.org/wiki/Ozone
** See: http://en.wikipedia.org/wiki/Ozone-oxygen_cycle
*** I have omitted the Reaction Coefficients, which cancel out in the Normalized equations below.​

Thus, hotter Stars, which produce harder radiation (more F_hard relative to F_soft), will make more Ozone from less Molecular Oxygen. So, Life on world's in that Star's Habitable Zone need not make as much Molecular Oxygen before their Sun turns it into (sufficient) Ozone. Therefore, complex Life can appear earlier. These Flux Ratios (F_hard to F_soft) increase with the Star's surface temperature. Specific values can be calculated by appropriately integrating the Planck Function*, using the Incomplete Gamma Function**. For example, our Sun's Flux Ratio is roughly 1/4^th.

* http://en.wikipedia.org/wiki/Planck's_law
** http://en.wikipedia.org/wiki/Incomplete_gamma_function​

We assume that early Earth Life made Molecular Oxygen at a steady rate. We also assume that other Habitable Planets, by being in their parent Stars' Habitable Zones, receive comparable energy fluxes, for Photo-Synthesis. And, we further assume that those planets are comparably bombarded by impactors, for about 1 billion years, before Life can take root. Finally, we acknowledge those planets' Ozone Layers as having formed, once their Optical Depth of Ozone reaches "one", where "one" is what the Earth's was ~0.5 billion years ago. On Earth, this process took:

1 billion years (impactor bombardments) + 3 billion years (steady Oxygen production) = 4 billion years​

Then, any other Star's "Cambrian Explosion" would happen sooner, or later, depending upon whether its Flux Ratio was greater than, or less than, that of our Sun's. For example, a hotter star, having a Flux Ratio 4x higher, would produce 4x more Ozone from the same Molecular Oxygen concentration. Thus, its advanced Lifeforms could evolve after only 1/4th of the Oxygen production time, or:

1 billion years (impactor bombardments) + (1/4^th) x 3 billion years (steady Oxygen production) = 1.8 billion years​

Here, and below, we round all figures to the nearest 0.1 billion years, in acknowledgment of the approximate nature of our calculations.

However, while hotter Stars can create complex Lifeforms more quickly, those same Stars will also burn out sooner. Thus, the emergence of advanced Lifeforms rests on the relative rates of these 2 competing processes (birth of complex Life vs. Star death). The results are arranged in the table below. All units are in Solar ratios, save Temperatures (in Kelvins) & Times (in Giga years). We assume that the Sun (1.0 M_sun) lives 10 billion years*:

* Strictly speaking, this assumes that all Stars burn only Hydrogen, as in the Sun. Bigger Stars, by burning heavier elements, will live (somewhat) longer than listed.​

Star-Type   Mass   Temperature    Radius   Luminosity    Life-Span     Time-to-Advanced-Life
O           60.0        50,000     15.0     1,400,000        0.00043       1.015
B           18.0        28,000      7.0        20,000        0.009         1.1
A            3.2        10,000      2.5            40        0.8           1.9
F            1.7         7,400      1.3             6        2.8           2.7
G            1.1         6,000      1.1             1.2      9.2           4.0
K            0.8         4,900      0.9             0.4     20             6.4
M            0.3         3,000      0.4             0.04    75            34.6

See: http://zebu.uoregon.edu/~js/ast122/lectures/lec09.html ​

CONCLUSION:

Complex Lifeforms can only have evolved on Sun-like Stars (F/G/K-Class). For, Life around cool M-Class Stars has yet to make enough Ozone, the Universe itself being only about 15 billion years old. And, hot A/B/O-Class Stars burn out before their "Cambrian Explosions" can even happen. The best candidates are G/K-Class Stars, almost precisely the size of the Sun. Borderline F-Class Stars are an intriguing plausibility, but their "Cambrian Explosions" barely have the half-billion years needed (on Earth) to evolve from Trilobites through Tyrannosaurs to Intelligence.

 

[Widdekind]

APPENDIX 1 -- NECESSITY of OXYGEN for COMPLEX LIFE:

Current estimates put the age of the Earth at 4,600 million (i.e., 4.6 billion) years. The years from that date up until about 542 million years ago (mya) are grouped into one large division of Geological Time -- the Pre-Cambrian. This was the time when life first evolved... Fossil evidence of life is first seen in rocks dated at 3,800 million years old. The earliest life forms on Earth were simple cells & bacteria [Prokaryotes]. More complex cells [Eukaryotes] & algae first evolved about 1,000 mya. Multicelled plants & animals did not appear until near the end of the Pre-Cambrian -- about 550 mya.

The first living cells were microscopic organisms, possibly living in hot springs. By about 3,500 mya, photosynthesizing algae may have formed layered structures called Stromatolites. As Oxygen built up in the atmosphere, multicellular animals evolved.

Hazel Richardson. DK Smithsonian Handbooks -- Dinosaurs & Prehistoric Life, pp. 20-21.

Earth's history offers insights for a survey of extrasolar planets. Life arose very early and depended upon reduced volcanic emanations. Even after oxygenic photosynthesis arose [~2.4 Gya], perhaps 1 Gy or more passed before O₂ became a substantial atmospheric constituent [~1.4 Gya]. A dependable O₂ supply was essential for the development of complex (plants and animals) and intelligent (us?) life.

http://astrobiology.arc.nasa.gov/workshops/1996/palebluedot/abstracts/desmarais_01.html

 

[Widdekind]

APPENDIX 2 -- Steady Rate of Oxygen Production

Earth's early history was very violent. For nearly 800 million years from its formation (~4.6 billion years ago), the planet was bombarded by myriad impactors -- one, the size of Mars, making the Moon (~4.5 billion years ago). It was not until ~3.8 billion years ago that Earth's oceans appeared, & continents began being created. The earliest known Photo-Synthesizers (marine bacteria & Stromatolites) appeared between 3.8 to 3.5 billion years ago. They produced O₂, but "this oxygen was initially used up oxidizing iron in the oceans, and little entered the atmosphere"*.

* James F. Luhr. (DK Smithsonian) Earth: the Definitive Visual Guide, pp. 26-29.​

Thus began Earth's "Archaean Eon" (~3.8 to 2.5 billion years ago), when "the entire Earth was covered by ocean... the bulk of the continental masses, formed through volcanic outpourings, had yet to appear from beneath the waves"*. And, "3.5 billion years ago Earth's atmosphere contained nitrogen, carbon dioxide, and water vapor but little free oxygen... The Archean atmosphere and the sea surface in contact with that atmosphere had much less oxygen than today... it couldn't have been more than about 1 percent of present day levels and may have been much less"**.

* http://www.palaeos.com/Archean/Archean.htm . Geologists call these archaic Continental Cores "Shields".
** A.H. Knoll. Life on a Young Planet, pg. 68.​

By the end of the Archaean Eon (~2.5 billion years ago), 70% of Earth's Continental Land Masses had formed*. In turn, their growing Continental Shelves provided habitats where Cyanobacteria (Photo-Synthetic Blue-Green Algae) proliferated**. Thus, Molecular Oxygen (O₂) levels in the atmosphere started rising around 2.4 billion years ago***. Then, "atmospheric O₂ levels rose substantially between 2.2 and 2.07 billion years ago... by about 1.8 billion years ago, O₂ had finally permeated the deep oceans"#. So, while O₂ levels about 2.2 billion years ago were still only 1% of levels today, by ~1.9 billion years ago, O₂ levels had risen to 15% of today's levels##.

* http://www.palaeos.com/Archean/Archean.htm
** http://astrobiology.arc.nasa.gov/workshops/1996/palebluedot/abstracts/desmarais_01.html ; History Channel The Universe -- Astrobiology (DVD)
*** http://en.wikipedia.org/wiki/Evolutionary_history_of_life
# http://astrobiology.arc.nasa.gov/workshops/1996/palebluedot/abstracts/desmarais_01.html
## James F. Luhr. (DK Smithsonian) Earth, pp. 26-29. Banded Iron Formations (BIFs) stopped forming on the ocean floors at this time, indicating that O₂ had permeated the deep oceans.​

CONCLUSION: From ~2.2 to ~1.9 billion years ago, atmospheric O₂ levels rose from ~1% to ~15%. This represents a rate, of increase of atmospheric O₂ levels, of roughly 14% per 300 million years -- or 100% per 2,100 million years, which points to the present. Thus, with what data is readily available, a linear approximation accurately reflects the historical rise of O₂ in Earth's skies.

Accordingly, atmospheric Oxygen (O₂) concentrations had probably reached ~30-60% of present levels by the "Meso-Proterozoic Era" (Middle Early-Life Era) from ~1.6 to 1.0 billion years ago. During this period, early lifeforms evolved from simple single-celled Prokaryotes to more complex "double celled" (ie., nucleated) Eukaryotes (~1.5* to 1.0** billion years ago). Meanwhile, Sexual Reproduction also evolved (~1.2 to 1.0 billion years ago***).

* Discovery Education Planet Earth (DVD)
** Hazel Richardson. DK Smithsonian Handbooks -- Dinosaurs & Prehistoric Life, pp. 20-21.
*** http://en.wikipedia.org/wiki/Mesoproterozoic ; http://en.wikipedia.org/wiki/Sexual_reproduction​

This correlates with the rise of Oxygen (O₂) in Earth's skies, and further suggests its necessity for the evolution of Complex Life.

 

[Widdekind]

APPENDIX 3 -- DETAILED ANALYSIS of F/G/K/M-Class Stars:

O/B/A-Class stars do not form Planetary Systems*, so we limit our expanded analysis to F/G/K/M-Class stars.

* Carroll & Ostlie. Introduction to Modern Astrophysics, pg. 891.​

Same units as above. F5-Class stars are (probably) the largest capable of evolving complex life. M-Class stars (probably) have not evolved Complex Life, given the finite age of the Universe. The Sun (G2-Class) is amongst the most "precocious" of potentially habitable star systems, evolving Complex Life almost as quickly as G0- & F5-Class stars.

Type     Mass       Temp.    Radius   Lum.  Life-Span     Time-to-Advanced-Life
FO        1.6        7200     1.6     6.5        2.5        2.7
F5        1.4        6440     1.4     2.9        4.8        3.2
G0        1.05       6030     1.1     1.5        7.0        3.7
G5        0.92       5770     0.89    0.79      11.6        4.0
K0        0.79       5250     0.79    0.42      18.8        4.9
K5        0.67       4350     0.68    0.15      44.7        8.1
M0        0.51       3850     0.63    0.077     66.2       11.9
M2        0.40       3580     0.55    0.045     88.9       15.3
M5        0.21       3240     0.33    0.011    191         22.5
M8        0.06       2640     0.17    0.0012   500         57

Carroll & Ostlie. Introduction to Modern Astrophysics, pp. A-13 to A-14.​

 

[Widdekind]

APPENDIX 4 -- Total Planetary Angular Momentum (L_p)

O/B/A-Class stars do not produce Planetary Systems. For, less massive stars have significantly less Specific Angular Momentum (L/M_*) than their bigger & brighter counterparts. But, by adding in the planets' angular momentums, the Sun (at least) then has (essentially) the expected Specific Angular Momentum. Thus, the "angular momentum deficit" of F/G/K/M-Class stars suggests that the "missing momentum" has been deposited in Planetary Systems*.

* Carroll & Ostlie. Introduction to Modern Astrophysics, pg. 891.​

From the information provided, I calculated to Total Planetary Angular Momentum (L_p [cgs units]) as a function of star mass (M_*/M_sun). The result is plotted in the attached figure. Stars of ~1.5 M_sun (~F5-Class) are predicted to deposit the most Total Planetary Angular Momentum, ~1.5x that of the Solar System. Precisely these stars are the most "precocious" (see Appendix 3), most rapidly developing Complex Life, perhaps ~1 billion years more quickly than on Earth.

 

[Widdekind]

Alternative theory:
http://www.spaceref.com/news/viewpr.html?pid=11464

 

[Widdekind]

APPENDIX 5 -- Planetary Cooling Times (t_cool):

Terrestrial planetoids' Cooling Times (t_cool) are roughly g x 10 billion years*. And, it can be shown that, for rocky worlds which form in their parent star's Habitable Zone**, M ~ g³ / (0.536 + 0.464 x g)² ***.

* https://www.physicsforums.com/showthread.php?t=279445
** Defined by the presence of liquid water (~ 373 K > T > 273 K). See: Carrol & Ostlie. Introduction to Modern Astrophysics, pg. 893 ; National Geographic Naked Science -- Birth of the Solar System (TV)
*** https://www.physicsforums.com/showthread.php?t=278022​

Now, the presence of a protective Dynamo-Driven (?) central Magnetic Field is (evidently) as vital as an Ozone Layer* for Life. Thus, since we can estimate how long Complex Life needs to evolve on Habitable Exoplanets (above), we can infer how big those planets must be**. These estimates are tabulated below.

* National Geographic Naked Science -- Birth of the Solar System (TV)
** To remain warm, retain a molten core, and generate a protective central Magnetic Field.​

Type     Mass       Life-Span     Time-to-Advanced-Life    Minimum Planet Mass
FO        1.6            2.5            2.7                 0.05
F5        1.4            4.8            3.2                 0.07
G0        1.05           7.0            3.7                 0.10
G5        0.92          11.6            4.0                 0.12
K0        0.79          18.8            4.9                 0.20
K5        0.67          44.7            8.1                 0.64
M0        0.51          66.2           11.9                 1.4
M2        0.40          88.9           15.3                 2.3
M5        0.21         191             22.5                 4.6
M8        0.06         500             57                  18

Carroll & Ostlie. Introduction to Modern Astrophysics, pp. A-13 to A-14.​

CONCLUSION: M-Class stars' Habitable Exoplanets must be increasingly gargantuan, for their cores to remain molten, long enough for Complex Life to emerge. Such huge rocky planets, orbiting in their stars Habitable Zones, would be increasingly rare*. However, since planetesimals routinely reach ~0.1 M_earth**, this analysis does not substantially restrict the evolution of Complex Life around F/G/K-Class stars.

* Rocky planetismals max-out at about 0.1 M_earth. Further growth only happens when such planetesimals "collide & merge", see: http://www.sciam.com/article.cfm?id=the-genesis-of-planets&page=5 ; and, link below. Note that there is only ~2 M_earth of rocky material in the sun's Habitable Zone, far less than necessary for the immense worlds required for M-Class stars.
** http://www.sciam.com/article.cfm?id=the-genesis-of-planets&page=2​

 

[Widdekind]

Temperature may impact Ozone levels:
https://www.physicsforums.com/showthread.php?t=164885

 

[Widdekind]

W/in 1000 light years, there are:

• ~300,000 F-Class stars*
• ~500,000 G-Class stars**
• ~1,000,000 K-Class stars***

Thus, most Habitable star systems will probably "incubate" for billions more years, before they evolve Complex Life. At present, those worlds look like the early Earth, ~1 billion years ago, with primitive microbes, confined to the oceans, steadily producing Oxygen from under the protection of the water, as their (orange) suns blaze overhead. But, above the water-line, they are barren, desolate, and look like Tatooine (as it were).

* http://www.solstation.com/stars3/100-fs.htm
** http://www.solstation.com/stars3/100-gs.htm
*** http://www.solstation.com/stars3/100-ks.htm​