05 July, 2019

OTHER CONCEPTS | THE VENUS ZONE


THE VENUS ZONE

You read that right, the Venus Zone, as the name suggests, it is a zone where a planet similar to Earth in mass and size may actually turn into a Venus relative rather than a tropical paradise world.

For a little bit of context, we suppose the Habitable Zone for our solar system may be between 0,5AU and 1,5AU, which is from roughly 4x times more sunlight down to 40% the sunlight we have here on Earth, any place on those extremes may be habitable with some degree of gear and terraforming, however a more conservative measurement puts the HZ between 0,7AU and 1,25AU, which is from twice as much sunlight down to 64% sunlight Earth receives if we consider we may not have that much of Geo-engineering at reach.

As a consequence of the space, light from our sun spreads over the inverse square distance, Venus is 25% closer to the Sun relative to Earth, but receives almost double the sunlight, and that is where the Venus Zone problem begin.
After the invention of telescopes, many astronomers found clouds revolving around Venus, they already expected them to be pretty bright and the presence of those dynamic clouds could only say one thing, "there is water vapour in the atmosphere", and many early 20th century astronomers, as well astrophysicists and sci-fi writers often were lead to believe that was clear evidence that Venus had water in the triple point, ie, ice, liquid water and vapour could exist there as they do on Earth, but due to the extra heat from the sun, there would be a thick layer of rainclouds and immense tropical storms everywhere, some even firmly believed Venus were a swampy world covered in a dense fog or haze of water vapour, whose soil where filled with petroleum from early living beings now sedimented, or even carbonated water, and Venus' similarity to Earth in size and mass even suggested it to be a considerable Earth Twin.

Truth is, that when Radar measurements went on Venus, they revealed some sad facts, the planet's rotation were messed up, a retrograde motion made the local day 243 days long, a abnormal microwave spectrum of the planet suggested something there on the atmosphere was pretty hot, and in 1962 the American probe Mariner 2 made a flyby past Venus, registering the atmosphere temperature to be around ~500ºC, and no magnetic field.
Something indeed was pretty wrong about our estimates, Venus was in our boundaries of what Earth-like planets can exist, and newer observations like the Kepler Mission shows that exo-Venuses are not that rare in that proportional orbits to their habitable zones, what leads us to believe in a more contained habitable zone after what we now call, the Venus Zone.
"Overall, the team estimates based on Kepler data that approximately 32% of small low-mass stars have terrestrial planets that are potentially like Venus, while for G-class stars like the Sun, the figure reaches 45%."
Kane, Kopparapu and Domagal-Goldman, “On the frequency of potential Venus analogs from Kepler data,” accepted for publication in 'The Astrophysical Journal Letters'.
The Inner Boundary
Before dipping really into what the Venus Zone really represents, let's think about how close a planet can be to it's star and still have air, I mean, not have it's atmosphere evaporated by the solar wind?

We could call this the end of the Mercury Zone by the way, but sounds too cheesy already, where in those 44 million km separating Mercury and Venus is that atmosphere zone?
As far as I could research, the planets around the red-dwarf YZ Ceti are the ones closest to their parent star, YZ Ceti b, which orbits YZ Ceti at a distance of 0,01557AU is calculated to receive around 3,26x more radiation than Earth, yet, it's temperature estimates range from 74~218 °C, while the yet to be confirmed YZ Ceti e, would receive 7,64x more radiation, 1,1x that received by Mercury, or about 389,4ºC if it has no atmosphere like Mercury.

Venus presents an albedo of 0,67 (geometric), ie, it reflects 67% the light that reaches it, for comparison, the Moon reflects about 12% of light. If we recall the Planetary Energy Budget, we find out that ~842,18 W/m² are being absorbed by the planet's atmosphere, despite the double albedo compared to Earth, by being closer to the Sun it is absorbing nearly as much energy as our planet does.

Planet Gliese 3470 b is constantly having it's atmosphere evaporated due solar wind, and it orbits at one tenth the distance from Sun to Mercury, using it as our meter-stick we can set some standards, Gliese 3470 is red-dwarf ~2 billion years old, in 2Gyr the planet is yet to lost all of it's atmosphere, having ~14 Earth masses and being 4,3x as large than Earth we find out that the planet has a 'surface' gravity of 0,75 G, so, if such a low density planet can yet maintain it's Hydrogen atmosphere (which evaporates very quickly compared to heavier gas mixtures like N²/O²) for roughly 2Gyr, it's atmosphere mass could be any between 5% and 20% the planet's total mass, going with 20%, it is expected for it to loss it's atmosphere in the next billion years at least, so, such a low density planet this close to it's star can't maintain an atmosphere for more than 3 billion years, which is roughly how much time it took for multicellular life to occur on Earth after the Hadean.

Balancing the math a bit, this is losing about 2,8 Earth's worth of [H] in 3 billion years, 0,93x Earth's of atmosphere every billion years.

Earth's atmosphere is just 1 tenth of a thousandth of the Earth's mass, and have 1,33x as much gravity, our N²/O² atmosphere is 28.9x denser than H², which means that if we swap GJ3470 b by Earth, our atmosphere is evaporated in ~2.316,8 years (80 years with a [H]/[He] atmosphere), at a rate of -0,043% every year, since Earth-sized planets take 500Myr to form, we need to find a distance to the Sun where Earth would have lost it's atmospheric material in that time at least.

Admitting the solar wind as the only significant actor of this effect, if we double the radius of the orbit, we get 1/4th the rate as a consequence of the inverse square law, hence, it takes 4x more time for the atmosphere to evaporate completely.
At Mercury's orbit, Earth would take ~231.680 years, at 0,5 AU it would take ~401.053 years, at Venus' orbit it would take ~831.968 years, at our current distance 1,6 million years, what doesn't seem right at the start.

But, we are considering the Sun has the same windblown of a turbulent red-dwarf such as GJ3470, those stars can produce as much as 10.000x more radiation than the Sun in flares, if we consider that our Sun is really 10.000x more quiet and constant, then we got a 16Gyr lifespan for our atmosphere at 1AU, 8Gyr at Venus' orbit, 4Gyr at 0,5 AU, 2Gyr at Mercury's orbit, and finally 500 million years at ~0,19 AU, BINGO.
In case you are curious, it would take 23,1 million years for Earth's atmosphere to be stripped away if close to the Sun as GJ3470 b.
We can suppose that any Earth-sized planet with an Earth-like atmosphere of N²/O² will completely lose it's atmospheric material within it's formation period if as close as 1/5th of the Habitable Zone Radius for it's star in AU.

MZ ~ 0.2*sqrt(L)

Then for the Solar System, the Mercury Zone is between 0,1AU and ~0,65AU, the distance where a Earth-like planet with an Earth-like atmosphere will no longer have an atmosphere at 4,5 billion years old...

BUT WAIT...
Although the line of thinking used above is on the correct path, we need some real numbers for us to really work out the Inner boundary of the Venus Zone.
For Earth, this number is about ~3kg of [H] per second, and ~50g of [He] per second. A simple derivation like above for how long it would take for all of Earth's atmosphere to be blow away, gives us 96,18 billion kg a year, if it was made of [H]/[He],~53,52 million years.

Multiplying by the 28,9x harder to push N²/O² atmosphere, and it outputs ~1,54 billion years.
Which still absurdly high - what are we missing?
The rate at which the atmosphere is escaping, is rather unclear, but we can deduce that from a study about Venus' atmospheric escape.
We found from our study that solar wind pick up of H+ and O+ ions yields loss rates of about 1 × 1025 s −1 and 1.6 × 10^25 s −1 , respectively. [...]
Which is ~26,56 moles of Oxygen per second, or ~424,9g [O⁺] per second.
Now, Venus is very similar to Earth down in it's base physical aspects, we are interested in it's gravity, which is 0,905 that of Earth.
As Earth pushes 10,49% harder, we go down to ~24,04 moles a second, or ~384,6 grams per second.
Again, as Earth is further away than Venus, the effect is less dramatic to the inverse square law,  giving us, a loss of about. 12,57 moles a second, or all the way down to 201,1g per second. As Nitrogen is 0,875% the mass of Oxygen, we could say such a gas would escape at a rate according to it's mass, giving off ~13,37 moles or 187,18 grams per second.
Taking the proportions of N² and O², Earth's atmosphere would have an average loss rate of ~188,3g/s, 5,938 million kg/yr, and gone in 252,6 million years...

Considering we're looking for stars that are as old as the Sun, Mercury falls inside this zone clearly, and we see that also Venus has a pretty good atmospheric lifespan too, since the believed minimal atmospheric pressure 'for life to exist in a comfy way' is around 15mbar (Vladilo et al. 2013) or 0,01atm, we can point the region where the atmosphere can still exist close to this pressure after the planet formation (~500Myr) as X AU (we don't know that yet), yet not enough of course for multicellular life to emerge or be even habitable at our time. 

At 45km high, pressure is about ~143Pa (0,95% of said minimum pressure) or 0,0143atm and the air density is ~0,0018kg/m³, or about 0,14% that of sea-level air at -8,15°C.
And between 90~99% of the atmosphere is contained bellow 45km.

For the next step, Mars can help us out.
Gravity is 0,37 Earth's.
Atmospheric pressure is about 600Pa, or ~0,4x the minimum pressure.
Atmosphere is also 50% heavier than Earth's, about 43,3 g/mol.
Atmospheric mass is about ~0,485% that of Earth's.

In order to be inside the 15mbar range, Mars atmospheric pressure would have to be 2,5x greater. And in order to increase pressure, it would need to have more mass, and achieve a minimum air density of ~0,024kg/m³ (at -63°C), or 2,42x the current density.
Doubling the mass of the atmosphere as the numbers suggest gives us an atmosphere mass that is 1,21% that of Earth's.

If we assume that the atmosphere is squished more by Earth-like gravity, that is 2,7x more pressure, taking it up to 37,5mbar (assuming the planet still the same size of Mars).

Which means, that our planet is technically safe for life even with ~1/100th of atmosphere mass.

Now we work out the evaporation of 1% of Earth's atmospheric mass, now increasing the rate with the inverse square law.

((5.1480×10^18)/100) / 89073.4
577,95 billion years at 1AU.

((5.1480×10^18)/100) / 23752915.2
2,1 billion years at 0,5AU.

((5.1480×10^18)/100) / 95011660.8
541,8 million years at 0,25AU.

((5.1480×10^18)/100) / 102807360
500,7 million years at 0,24AU. 

The minimum distance a planet with minimum life-supporting atmosphere pressure can exist beyond it's cooling time is about ~0,24 AU.
And the minimum distance that such a planet can still hold it's atmosphere for about 4,5 billion years is about ~0,721AU. And denser atmospheres will take much longer to be blown away.

Also, according to David Catling's paper, Mercury sized bodies can hold on atmospheric water, if the temperatures are near the ones at the top of the Martian atmosphere.
If the paper illustration I'm referring to isn't to scale, Earth's temperature value is 2.700K (on the thermosphere), similarly to the Gas Giants, probably to their dense magnetic field interactions than the sunlight itself. Mercury's mean temperature is about 625K, and it's just bellow Earth, the Moon's temperature wander around 300K, Mars is in between both Mercury and the Moon, therefore it's temperature should be over 460K and less than 500K, the upper atmosphere of Venus has a temperature close to 300K as well, and on Titan about 98K.
Using that as an approximate model, a body with ~5% the mass of Earth, could in theory hold an atmosphere if it's thermosphere temperature dropped from 352°C all the way down to less than 170°C, which given Mercury's orbit, it would have to be between 0,44~0,5AU.
What do checks out, since Titan's mass is ~2,2% that of Earth, and it does hold a dense atmosphere - being very far away from the Sun, of course.
Unfortunately, I can't see or find any more data, in a way I could properly establish a graph relating temperature, mass, and atmospheres.
For now, we have this blurry line, 0,1~0,25AU bellow which, Earth-sized planets will definitely be airless worlds past 500Myr.

For all effects, Mz ~ 0,2*sqrt(L) still pretty accurate though.

THE OUTER BOUNDARY
How close to it's star a planet have to be to turn into a Venusian world?
If we assume that it is true, or a least very likely most of times a planet that receives close to twice as much sunlight as Earth will turn into a Venusian world, we must find where in the that 55 million km is this line if there is one, or if somewhere there is a region we could find a wide range of midterm planets, "Carbonic Earths" for lack of a better expression at moment, planets with a CO² rich atmosphere but yet not a Venus neither Earth-like, maybe like Paart on the most earthly side.

It is already a good thing that we managed to pin the inner boundary of the Venus zone as ~0,65AU, the weird thing is that it between it and the outer boundary, there is an huge tendency to start a runaway greenhouse effect before "Earth's island of stability" at 1AU, the point where the distance from the Sun plays a smaller role in regulating the planet's climate, and volcanism and civilization are the real dealers of it.

Thinking linearly, ie, being pretty arbitrary and assuming that there is a ramp where you slip into runaway greenhouse, I would kick ~0,95+-0,045 AU, see, we are already in this ramp, humans have the potential to really frick this world up, but nothing compared to extra 10% sunlight, extra water evaporation means that the oceans cannot retain carbon dioxide enough to balance the carbon-cycle, and thus fill the atmosphere up with carbon and spiral into a Venusian climate, and that based that when the Sun becoming Red Giant, is expected that to happen as far we expect extra 10% more sunlight.

A team in 1993 (Kasting et al) proposed a similar situation where the most optimistic models secured the inner habitable zone as 0,97AU, and the more pessimistic realistic model suggested 0,99AU (according to Wiki, original paper cites 0,93~1,37AU), ie, Earth as we know it, is a MIRACLE, being so close to the edge of this doomed pit.

If we combine the estimates of maintaining at least 3/4 of the atmosphere for as long as 4,5 billion years, and the a low moisture mix of air, considering water and carbon are major players in greenhouse effect, we could maybe still find Earth-like planets at 0,90AU with average temperatures of 10º C, what to some point seems to make sense, extra 25% lighting would easily wipe a great portion of water molecules away during it's early age, but yet some other factor may contribute to not trigger the runaway greenhouse effect, like a higher albedo of surface due to a whiter rock type, or a faster rotation rate to help distribute the extra heat across the atmosphere, or even being a super-earth would help irradiate any extra heat, for instance, a planet that have 1,5x Earth radii have 2,25x more surface area to irradiate heat.

I would risk even 0,85AU if we take into account that many planets may have large arrays of moons that always eclipse parts of the sun, or rings that cast a shadow over a whole hemisphere during most of the year, making only ~1/4 of planet surface actually lit by the star.

So while there is a pretty wide array of ways to prevent a planet from heating too much, let's stick with this blurry line around 0,875AU.
The closer to the sqrt(L) it gets, the less likely it is to become a Venusian world in around 1% per 0,00125 AU towards it (value proportional to star Habitable Zone).

The more likely to become a Venusian world in 1% per 0,00025 AU the closer it gets to 0,85*sqrt(L) from that 0,875*sqrt(L) mark, which bellow it will be certainly a Venus or Hot Neptune.

While being closer to this zone of 0,875AU may signify the planet is either a recent Venus, ie, on it's way into a Venusian climate on the inner approach, or either in a rather state of equilibrium at warm climate like the south African or Amazon climate, either way, if given enough time and the right pushes along the way, such worlds in the outer edge of the Venus Zone would have more biodiversity to be explored ever due high counts of energy available for life, and the right landmarks may also allow a wide range of climates and biomes to exist all around.

Don't forget to also consider the rate of subduction of tectonic plates and how they may contribute or worsen the carbon and water cycles in such planets.

VZ ~ 0.85*sqrt(L)

BY THE WAY...
Admitting we could sustain living at 1000ppm (0.1%) of CO² in the atmosphere with the help of O² saturation gear and stuff, the habitable zone expands way up to 3AU.
I have made an adaptation to the Keplerian Distribution Graph so it shows all the zones a single-star system given the system's distribution and the host-star's mass.


-M.O. Valent, 05/07/2019
-M.O. Valent, Updated in 15/01/2020

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