UNDER THE BRIGHTEST SHADE, INTO THE DARKEST LIGHT
There is a limit to how much or how little light can a plant feed on before dying on either end of the spectrum - people who have houseplants know well that matter to some extent - too little light and it won't trigger photosynthetic reactions, too much and it will overheat and dehydrate - eventually dying.
The point at with the photosynthetic reaction balances the plant's own respiration is called a balance point, bellow that point, the plant starts consuming it's own reserves in order to breathe, in nature this happens at night so it's a great concern, but plants can't stay bellow that level for extended periods of time, or else they die - that's why having an illuminated house is good for indoor plants.
Our eyes don't work with a linear light sensitivity, it works on logarithmic scale, so an object or ambient that looks slightly darker than its surroundings can actually be dozens to hundreds of times darker - or brighter if on the other end.
For an idea on the subject, a dark overcast day is over 100x brighter than the full moon at night, and direct sunlight is over 250x brighter than the sunrise lighting (wow I would have never guessed that the atmosphere filtered that much light).
It' safe to say - that despite all plants having evolved for Earth conditions, which is already a wide range of environments and energy levels - biochemistry has it's limit - no matter what planet you came from, you're astronomically more likely to be: Carbon-based, using RNA&DNA and need some kind of fluid medium - or posses your own stock of fluid.
This way, photosynthesis can only happen with so little and so much light, because of the weakness of it's reagents and pigments, and metabolic processes for animals can only happen above the freezing point of whatever fluid it's based on (could be more commonly water) and the boiling point of that liquid.
LIFE'S BIOCHEMISTRY BOUNDARIES
On Earth, the temperatures range from -89°C recorded in Antarctica to ~350°C in the deep sea hydrothermal vents - while some extremophiles can be found on the borderlines of -20°C and 120~122°C (highest temperatures for life-cycle completion belongs to Archea), these often are what we consider simple organisms such as bacteria and even as such, require specific conditions to thrive - more complex and active organisms live in the temperature range of 0°C to ~60°C.
An example on how these limits act - we have a temperature range x cyanobacteria richness by species, we see that little to now cyanobacteria will be found to grow on temperatures of 70°C or above (It's also reasonable to assume that it's null bellow the freezing point of water) - because that's how biochemistry works.
Some chemists out there reading these might point out that if would really be the case - then most life wouldn't be possible at all - for the values of such weak interactions such as the Van der Walls and Hydrogen bond forces are on the same energetic level as ambient temperature in most of the world.
The paper points the following:
These values are of the same order of magnitude as the mean thermal energy of molecules at 25 °C, and hence are likely to break more frequently at higher temperatures. The most common adaptations to allow macromolecules to function at high temperatures include changes in the number of residues influencing overall hydrophobicity, and an increase in the number of weak interactions to increase stability.
So - apart from establishing how little and how much lighting are we giving plant-life, we are also taking a step into determining sort of a temperature-based habitable zone.
Life possible at temperatures up to:
Archea - 122°C
Bacteria - 100°C
Terrestrial Invertebrates - from 60°C to 70°C
Angiosperms - 65°C
Unicellular algae and Yeasts - 60°C
Mosses - around 50°C
Freshwater Invertebrates and Ectothermic Vertebrates - around 46°C
Lichens and Macroalgae - around 45°C
Marine Invertebrates - from 42°C to 90°C
Endothermic Vertebrates - cells work between 30°C and 45°C
Plants (in direct sunlight) - up to 65°C of internal temperature
And with temperatures as low as:
Freshwater Invertebrates - 0°C
Marine Invertebrates and Ectothermic Vertebrates - minus 2°C
Lichens - minus 10°C
Archea - minus 16,5°C
Bacteria and Yeast - minus 20°C, but some were found to engage in respiration at minus 196°C
Mosses - minus 30°C
Angiosperms - minus 70°C
Terrestrial Invertebrates (particularly the Tardigrade) - minus 196°C
INSOLATION IN PLANTS
Lower Boundary - about 0,16 W/m² or 0,00012x Earth's TOI
House plants which live in low light from 107 to 161 W/m² indoors, could live with as little as 0,16 W/m² of artificial lighting.
0,16 W/m² is the same lighting as a comet far into the Kuiper Belt receives - ie, sunlight at ~92AU.
Upper Boundary - about 4.110 W/m² or 3x Earth's TOI
Although the researchers found limits and records of ~65°C for a plant's leaf temperature, I'm backing it up for +5°C, to account for other strategies for heat dispersion or materials in cell make-up we might explore in the future, still not so far from reality, so we will be figuring out the limiting temperature for plants similar to that of cyanobacteria and invertebrates - around 70°C.
There is two ways we can do that:
1 - IMAGINE A SPHERICAL PLANT IN A VACUUM...
We use the planet equilibrium temperature equation to see at what insolation does our plant reach 70°C, that gives us 3,27x Earth's top of atmosphere insolation, or 4.480 W/m².
2 - PHYSICS
We figure out how much light we have to shine on a plant given it's physical properties to heat it up that much.
Most of plant products are 80~94% water by mass, the heat capacity of a plant that's 85% water and 15% wood would be around 3.900 J/kg*K, so we get that to push our model plant, that have a mass of 10kg, from 0°C to 70°C, we would need 2,73MJ, or over 2,73kW of power, of course, we are forgetting to take into account the time the plant takes to heat up to that point, and how much surface area the plant has for the intake of light.
So we will assume our little model plant - Steve, has a total leaf area of 1m², with a 0,7cm thickness, it's density of 0,6g/cm³, giving us 4,2kg of leaf material, we only need to deplete it's water content of the course of this one model-day, or about 3,57kg of water - which has a latent heat capacity of 2,5MJ per kg.
It's native planet has a rotation period of 24h, and it's average surface temperature is around 0°C, but it gets a bit hotter during day time, we will assume that it takes little over 3/4 of daytime for it to heat up, so our heating time will be little over 9h, or 32.400s.
An ideal plant would waste only 28,34% of the sun energy as heat, so whatever energy we get from our calculation, that much heat equates to those 28,34% of the spectrum, but we can work out the rest from that, dividing it by 0,2834.
Steve would need to exposed to 972 W/m² of sunlight to heat up that much. Which is 70,9% of Earth's top of atmosphere insolation - that may seem out of place but remember, the atmosphere does filter out a lot of radiation, so much that the actual lighting on Earth's surface is little over 340W/m², so this value is about 2,86x Earth's TOI.
Now, considering plant strategies to mitigate evaporation such as stomata behavior, wax layers or hairs for increased heat dispersal, and even wind heat transfer, which can even account for a 33K decrease in leaf temperature, we get between 1.004 W/m² to 1020 W/m², or 2,95x to 3,00x Earth's TOI.
A PRACTICAL STELLAR PHOTOSYNTHETIC ZONE
Using Earth and the Sun as a parameter, photosynthesis could occur as close as 0,57~0,6 AU from the Sun, under an Earth-like atmospheric filtering - of course, an Earth-like atmosphere at such distance from the Sun - would actually make the surface temperature over 104°C, and is more likely to be a Moist Venusian instead.
However, having the atmospheric mass down to 1/5th that of Earth's put's the average temperature just about 71°C, implying that temperatures on the tropics and poles may just lie bellow that point.
Speaking of atmospheric mass, plants are shown able to survive to pressures as low as 5~10Pa (about 0,000074 atm), WHICH DOESN'T BY ANY WAY means that you could have a tinfoil thin atmosphere on your planet that has a vulcanoid orbit - because plants descend from algae, and algae descend from cyanobacteria, and those need liquid water to appear in the first place.
Too little pressure and ice will start sublimating like on Mars, so keep your atmospheric pressure above the required for the Triple Point of water, or more than 0,006 atm.
That said, an Earth-sized planet with an atmospheric pressure of 0,006 atm - would need to orbit at least 0,54AU to have an average temperature of ~70°C, but at this pressure and temperature the water boils at -4,7°C, so the planet is actually a Steam-World - that's losing a lot of water to space also....
Having cyanobacteria in mind, the lowest pressure you could have is about 0,32atm - when water boils at 70°C.
This paper notes how different rotation rates even out the global heat.
An approximation to the model's pole-to-equator difference is:
ΔTₖ ~ 75 × r^(-0,175)
with r = planet rotation period in hours
With a rotational period of 24h, our pole to equator difference is about 43K, so we want to keep our Equator water temperature just bellow 70°C, so the oceans don't boil away and we don't end up with a Moist Venusian or Steam-World, so lets go back to that 65°C record for plant-life.
43 K bellow 65°C is about 22°C, so we're aiming for a planet which average temperature is 318 K, or about 43 ~ 44°C.
Which is not unreasonably hot, given Earth's average temperature back in the Archean Eon.
So, under those conditions, the closest your planet could ever be to it's star is ~0,7x it's mean Habitable Zone, with little over 1,4x Earth's surface insolation in it's surface (about 480 W/m²) - that's it.
POSSIBILITY OF LIFE ON VENUSIAN PLANETS
Is rather inevitable that after this, that we note Venus lying on the bordeline of the so called Stellar Photosynthetic Zone we just calculated, at about 0,723 AU, as discussed before, at an altitude of 50km above Venus' surface, the pressures and temperatures are just right so simple life-forms could appear and thrive, if such a gaseous medium could really support a life-bearing event is still in doubt to this day - as one argument in favour of liquid water is that it has just the right density for biochemistry, "ice is too still, vapor is just too disperse for biochemistry to arise" thing.
LIFE ON COLD VENUSIANS
On the other side of the spectrum, where planets are further away from the star, but apart from Earth or Mars, have considerably thicker atmospheres, we have worlds like Aliens', Acheron.
In worlds far away from their stars, bordering the habitable zone, having a thick atmosphere may help - but in some cases, the atmosphere may be so thick it actually makes days hot and dark like the full-moon, and nights freezing cold and pitch-black.
Let's use a model planet that has a 75% cloud cover, a surface albedo of 0,20 and a cloud layer with albedo 0,70 - the planet's overall albedo is then about ~0,575.
Using 4x Earth's atmospheric mass, at Earth atmosphere composition, at the edge of he habitable zone, at 1,3AU, the planet has an average surface temperature of -2,7°C.
Spin it at a rate of 30h, and we would get a pole temperature of -43°C, and an equatorial temperature of 39°C.
However, we are ignoring the part that the clouds block light over the planet - thick clouds have a transmittance on the order of 0,18, within variance, our minimum value based of that is 0,15 transmittance.
The planet's TOI is ~810 W/m², so with cloud reflection we get only 42,5% of the TOI lighting into the clouds (344,25 W/m²), with a cloud 0,18 transmittance we get a surface insolation of ~62 W/m², with an atmospheric radiative power of 159 W/m² - the day on this planet is similar as a dense overcast day on Earth.
The average temperature is then -22°C, it makes 20°C in the equator, and -63°C in the poles - actually not too bad for plants.
Pushing the planet into Mars' orbit at 1,52 AU puts the mean global temperature around -42°C, -1°C in the equator and -85°C on the poles, the planet's polar circles are cold enough to have CO² snow, and daytime illumination is around 45,9W/m².
Planet 1 we've described in this part has an ESI between 0,806* and 0,819 - while Planet 2 has an ESI between 0,709* and 0,720.
*Values considering the planet's atmospheric greenhouse flux
Planet 1 is borderline Earth-like as the standards require indexes greater than 0,8 to be classified as such.
We see that even though having a thick atmosphere, Planet 2 is too cold for most Earth life, it's rather unlikely to have liquid water on it's surface besides from nearby hydrothermal hotspots - what in theory is a good sign, but it would then be limited to these regions, unable to migrate outwards, and unable to grow much more complex than a microbial paste, if it even does so.
It does require a bit of a stretch to make atmospheric conditions suitable for life to even arise in martian-analogue orbits, and the ESI for Earth-like conditions is at it's lowest around our usual 1,3~1,37x the star's mean habitable zone. Unless by some reason the illumination conditions of a planet lower over the course of it's history, is unlikely plants or life would appear much further than that distance from the star, even if the illumination conditions are tolerable for plant-life.
- M.O. Valent, 25/09/2020
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