YES, you've read that right - while for almost 2 years we've been chasing Earth-like conditions, there is about 10 or so months I've been willing to tackle this interesting subject - Superhabitable Planets, worlds that make Earth look like it's an universal impossibility, an oasis compared to how inadequate our planet is compared to the rest of the galaxy.
So why NOW? I mean, we could have made Project Paart in these parameters, it's little over 5 months in age by now - we could have done it in the most adequate way - but no, actually, while this would represent a perfect scenario, one of the things Paart has in special, is showing how resilient life actually is, being smaller, low oxygen / high carbon environment, around a cooler star, and still be habitable.
PRELIMINAR ASSUMPTIONS
The second reason for the WHY, is that yesterday I was playing around with Universe Sandbox² and stumbled around some updates - and one of the things was the Life Likelihood percentage, which calculates based on how similar is your orbit, composition, pressure, spin rate, and water content, and gives you a % of how likely it is to have life there. Manually, the highest you can get is 99,7% - to get 100%, you need to actually have the Earth object there.
The why and how the LL was calculated got me playing around with the options for a while, until I decided to look after, and well, it's made with the (ESI * Spin * Pressure * Water Content )^(1/4), each element has a weighting, but there isn't much information about how each element is calculated apart from Spin and ESI - the latter which is calculated a bit differently than IRL, so it doesn't exactly matter for us.
The point is, that I started to think I could actually come up with something interesting on the subject, given how much we've discussed and learned over the years now - and that's the part I get off bed at 2am, and spend the next hour scribbling this:
The top equation near the conscript is what we will focus for now.
Pv is just portuguese for Life Probability - it's calculated from the ESI, ie, on how much the planet already resembles Earth, but, you multiply it by how much the planet's temperature is close to the optimal temperature for Cyanobacteria (30~35°C), then by atmospheric pressure - with a lower boundary of 0,06atm and upper boundary of 10atm, then by spin rate between (initially 6h, but I then noticed how absurd it is) 12h and 20 days, then by water content which is between 0 and 4,35.
Now, apart from ESI, each one of these functions is a parabolic function, with a lower and upper limits resulting in 0 or negative values, which will either nullify or negate our chances here.
For example, if the planet attends every element but has no water, it's life probability is ZERO, if it has water, ESI, and temperature right, but has an atmospheric pressure that's 15x that of Earth, it's probability renders ZERO - I haven't weighted these, because I've considered every part of it as virtually essential.
Going for details, elements would be calculated as:
Cb ~ 1 - (TKelvin - 308)² × 0,0008163265
Ap ~ 1- (Patm - 5)² × 0,04
R ~1,727×0,977ʳᵒᵗᵃᵗᶦᵒⁿ ᶦⁿ ʰᵒᵘʳˢ
W ~ 1 - (woceans - 2,35)² × 0,182
If you put Earth parameters in the equation, Earth has a LP ~ 15,8%, which is interesting? Paart for perspective has a LP ~ 64,7%, which for my surprise was odd, but not so much, the planet has a greater atmospheric pressure, has more water, but not so much, and has a temperature around 30,8°C, it's as closer to "ideal" than Earth is.
The "Ideal" planet by these standards is one with 12h rotation, 35°C surface temperature, 5atm atmospheric pressure and 2,35x Earth's water content, and it's Earth-sized - which then renders a value between 1 and 1,26, depending on how similar the planet is to Earth in size and distance to it's star.
SUPERHABITABILITY
The Wikipedia article has a lot to say about it in depth, but in summary a superhabitable planet would be theorethically characterized by:
- Being ~2 MEARTH
- Having ~1,25 REARTH
- 1500m < oceans < 3700m
- scattered continents
- 600ppm < CO2 < 0,5% (5kppm)
- 20% < O2 < 30%
- Being at the center of habitable zone
- Average temperature of 25°C
- K type star (for it's longevity)
- 4,5~7 Gyr old (planet/star age)
- 12h < rotation < 500h
- Not have a large moon is somewhat desirable to encourage evolutionary pressure, as the wobbling of the planet would change global climates regularly over long periods of time.
- 0,01 < e < 0,03
Eccentricity, CO2, O2, Rotation and Ocean Depth is only implied to be between these values, oceans would be shallow but not too shallow, greater amounts of Oxygen and Carbon Dioxide but not too much to cause wildfires or turn the planet into a Moist Venus, a relatively more eccentric orbit for greater seasonal variation and thus more even global temperatures, a fast rotation rate would produce a magnetic field strong enough to protect the plane agains extraterrestrial radiation.
Atmospheric pressure is a quite of a loose factor, because some bacteria can even live under pressures of 400atm at the bottom of the ocean, given the adequate temperatures, the upper physical limit is ~4000atm.
In general, humans can survive pressures up to 4~8atm, with a tweaking of the air composition humans can survive pressures of 71atm, maybe up to 100atm, of course, for short periods of time.
So far, a limit of 0,06atm up to 10atm sounds reasonable for complex life.
Based off that, we could have a Superhabitability Index that looks like this:
where:
Mi ~ 1 - (MEarth - 2)² × 0,28
Ri ~ 1 - (REarth - 1,25)² × 1,39
Wd ~ 1 - (WDepth in meters - 3000)² × (0,111111 × 10⁻⁶)
Rr ~ 1 - (r in Hours - 40)² × 0,001
Ap ~ 1- (Patm - 5)² × 0,04
LCO₂ ~ (50 × 10³) × (CO₂ in ppm)^0,37
LO₂ ~ (8 - (O₂ % - 25)² × 0,0128) / 8
Ti ~ 1 - (TKelvin - 298)² × 0,0016
ei ~ 1 - (e - 0,045)² × (0,35×10³)
Rotational period was derived from the magnetic field strengh of Venus, Earth, Uranus and Neptune - Neptune and Uranus were chosen because their cores are slightly above the Super-Earth class, it's as close as you can get in the Solar System - as it presents an increase with a slower rotational speed, the increase becomes less significant the further it approaches 40h, it's assumed it begins to decrease above 40h - because Venus has a very weak field strenght of just about 50nT.
Multiplying Rr × 40 gives an approximation of the magnetic strenght in microtesla (µT), Earth-rotation in this approximation is about 29,76µT while in reality it is about 31,00µT - this can be tolerated as Earth has an abnormally larger metallic core compared to other terrestrial planets due to the Theia Impact.
The eccentricity is set to be more than Earth, but less than Mars, to avoid global freezings during the year.
I'm not including Age as regardless of star, the peak biodiversity would be reached at 4,5~6Gyr, we've dicussed that before.
In which case, this formula gives a 1 for as habitable as it can get, theoretically speaking.
Earth inputs gives us a SHI ~ 0,106. Mars inputs gives 0,0005 - and Paart's inputs turn out to give 0,121, which demonstrates it might work to an extent, by these standards, despite having less oxygen, Paart is warm and moist enough to compensate for that.
Extreme cases like Venus just break the equation, because, yes - it's not even worth doing it because it's so obvious it isn't habitable at the surface.
I need to admit this isn't as elegant as it could be, I'm not a matemathician - the equation is a big bodge on top of another, it's xtremely simplistic - and I can quite see the day I will look back at this and just go "ppffffftt..." at it, because I will then be able to have a firm grasp on the subject.
Arbitrarily speaking, we can say Earth-like planets occupy the spaces between 0,4 and 0,6 on the scale - while everything with a SHI >0,6 could be called superhabitable, everything bellow 0,4 through 0,2 is subhabitable, and bellow that, just outright inhospitable for complex life.
An example for that is the cyanobacteria world we saw in previous post, with a result of -0,001^(1/4), which just breaks the calculator right away.
LIFE LIKELIHOOD INDEX
One thing I haven't considered when first trying to tackle Life Likelihood is volcanic activity - see, even though planets might have all the necessary physical characteristics for supporting life, one could just be an inhospitable wet desert if it never had any significant volcanic activity, to change the planet's surface and leak minerals and nutrients into the it's oceans through hydrothermal vents.
And so we add Va as a factor in our LL index:
where:
ESIsf ~ Surface Flux ESI (considers greenhouse)
Cb ~ 1 - (TKelvin - 308)² × 0,0008163265
Ap ~ 1- (Patm - 5)² × 0,04
Rr ~ 1 - (r in Hours - 40)² × 0,001
w ~ APlanet × Wdepth / 1,887×10¹⁸
Wv ~ 1 - (w - 2,35)² × 0,182
Va ~ [ (Pstress / OCthickness) / Ctime ] / 0,022
ei ~ 1 - (e - 0,045)² × (0,35×10³)
It does pair the planet's size and stellar flux at the surface - so it does not dismiss planets in the outer habitable zone as frozen worlds, and then combine some of the important factors already presented - it does dismiss atmospheric composition, as microorganisms tend to be rather careless about it, it does consider water abundance based a controlable sea-depth times planet area though - Volcanic activity is inversely proportional to oceanic crust thickness and convection time, this way, it considers thicker crusts and slower mantles bad at delivering the chemicals, whereas thinner crusts and faster mantles do extremely well - and lastly the eccentricity.
By these standards, Mars still has a LL index of 0,129, Earth's is of 0,300, Paart's is of 0,302, for the same reasons as before, Paart being warm and wetter than Earth makes it slightly more habitable.
UPDATING THE DRAKE EQUATION
This does provide some interesting insights on the topic of search for extraterrestrial life - where this tells us that little less than 1/3rd of Earth-like planets actually develops life.
This post may still get an update in future posts, I made sure to include these calculations of the Star System Calculator LITE II, stay tuned - and good worldbuilding.
- M.O. Valent, 10/10/2020
