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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