Properties of a Mega-Earth

[Ar-cen-ciel]

Suppose that there's a planet roughly the size of Kepler-10c that could sustain life, what would be its distance from its sun?

Also, since it has a much stronger gravity than our Earth, is it possible to achieve spaceflight in such planet? And what's the minimum size for a meteor to penetrate its atmosphere and its impact velocity?

[Jonfliesgoats]

The more we explore, the more we learn our assumptions are wrong.  Tiny pluto has an atmosphere and tectonics!  A low gravity place like Titan has a thick atmosphere.

So we can't really know what sort of atmosphere would exist around a super-earth.  A lot depends on things which we can't predict by mass alone.  Large bodies should have enough of a magnetic field to protect an atmosphere from being blasted away by solar radiation, but there are so many variables at play that we simply don't know.

Would spaceflight be possible?  Yes.  It's just a matter of how much energy you need to pack into a given rocket. The engineering may be more challenging, but not impossible.

If you think that is challenging, imagine being a sea-creature from the inside of Europa that wants to fly in space!  Europa-squid could do it though.  They'd have to work their way to the surface first.

[kerbiloid]

After a rocky planet appears, a gravitaional differentiation starts inside. Iron sinks, silicates rise, Heat is being released,
Hydrates and carbonates decay, releasing water and carbon dioxide stored from the protoplanet times.
Water and CO₂ rise and release as volcanic gases. Volcano gas is mostly water steam and CO₂.
If it's enough cold, water condenses as an ocean, while carbon dioxide stays gaseous. So, atmosphere gets N₂ → N₂+CO₂+H₂O, as on early Earth,

Taking that total mass of released gases is proportional to decayed rocks mass, so to planet mass, we can presume that the ocean volume is proportional to the planet mass, i.e. V_ocean~R³.
Ocean surface is proportional to the planet surface: S_ocean ~ R².
So, ocean depth is ~R³/R²~R_planet
Earth ocean average depth ~3.7 km.

Surface detail height/depth is limited by gravity. The greater is gravity, the greater is pressure onto the mountain foot / trench wall.
Mountain mass ~size³, foot area ~size². So, pressure ~size³/size²~size.
Stress limit is a fixed value defined by atomic bounds energy. So, max.size ~pressure^-1.
As pressure ~gravity, max.detail height ~gravity^-1.
For example the Earth rocky details are limited with ~10 km. And we can see Everest 9 and Mariana -11.
Gravity = GM/r2 = G V density/r² ~r³/r²~r.
So, max.detail height ~r^-1.

Here we see that ocean depth is ~r, while mountain/trench height ~r^-1.
Increasing the Earth, we can estimate:
x * 3.8 = 10 / x;
x² = 10 / 3.8
x = sqrt(10 / 3.8) = 1.6

So, Earth will be covered with ocean if scale it up by 1.6 times.
M = 1.6³ = 4 M_earth

The greater is mass, the less is gas dissipation, but the dense is atmosphere, the greater is pressure.
Both are greenhouse gases. Greenhouse effect will heat up and additionally rise pressure.
Water absorbs CO₂ very well. Earth ocean contains 140 times more CO₂ than atmosphere.

So, a Superearth CO2 will be totally absorbed by the ocean, while the water steam pressure rise up to critical value.
The Superearth ocean becomes a hybride of atmosphere and hydrosphere at once.

Under huge pressure the inner layers of the ocean get solid making hot ice.
And we get a typical ice giant like Uranus or Neptune.

If it's too close to the star and gets heated up to 1000 K, it loses atmo and hydro, becoming a naked rocky core without any water.

So, there is no possible Superearth at all.
It's either under-Uranus, or super-Venus.

[Ar-cen-ciel]

@kerbiloid So a Kepler-10c sized superearth would be either an ocean planet or an ice giant at Earth's temperature?

[MaxL_1023]

Ice Giants in the traditional sense (Methane/Hydrogen atmospheres) wouldn't form at Earth's temperature, unless you consider a Nitrogen/Oxygen/Water Vapor Atmosphere which reaches water's critical point before the nominal sea level. Then, you would have the atmosphere gradually transitioning to high-pressure forms of ice, with no liquid water. You would need more mass to hold onto hydrogen, likely more than 4 Earth Masses. 

The key for a planet in the 2-5 Earth Mass range is how much volatile material gets incorporated at formation. A 5 earth mass planet would have 5 times the volatile material if it formed in exactly the same spot, assuming it still loses all hydrogen and helium but holds onto water (Methane would be photodissociated back into Carbon Dioxide, Water and some escaping hydrogen). In that situation, silicate weathering should deplete most of the primordial atmosphere through plate tectonics, locking away all but a few atmospheres worth of material as carbonate rocks after the planet cools from its formation. However, if it has too much volatile material it can get an atmosphere thick enough to prevent water from condensing and turn into the "hot ice" giant - I suspect anything above 4 or 5 earth masses is likely to run into this situation.

There are stable earth-like climate states for larger planets - I heard the limit somewhere near 5 earth masses before plate tectonics stops and you "forget" to weather down the atmosphere. A 2 or 3 earth mass planet might actually be better for life than earth, with a stronger magnetic field, more archipelago type landforms, shallow oceans and a longer geologically active lifetime. 

More study is needed though - until we get better observation data (why couldn't we have gotten the terrestrial planet finder Darn it) we are guessing.

Edit: Kepler-10C is way too big - that is a hot ice type planet. It would probably have a significant hydrogen envelope if it was far enough out to have liquid water (say 270K black body instead of 584K). In fact, I suspect it still has some hydrogen in its atmosphere, just not enough to budge its mass/radius relationship.  

Edited December 4, 2016 by MaxL_1023

[kerbiloid]

13 hours ago, Ar-cen-ciel said:

@kerbiloid So a Kepler-10c sized superearth would be either an ocean planet or an ice giant at Earth's temperature?

Imho, it can be or icy giant or burnt icy giant, or super-Venus wannabe icy giant.

[KerikBalm]

16 hours ago, MaxL_1023 said:

The key for a planet in the 2-5 Earth Mass range is how much volatile material gets incorporated at formation. A 5 earth mass planet would have 5 times the volatile material if it formed in exactly the same spot, assuming it still loses all hydrogen and helium but holds onto water (Methane would be photodissociated back into Carbon Dioxide, Water and some escaping hydrogen). In that situation, silicate weathering should deplete most of the primordial atmosphere through plate tectonics, locking away all but a few atmospheres worth of material as carbonate rocks after the planet cools from its formation. However, if it has too much volatile material it can get an atmosphere thick enough to prevent water from condensing and turn into the "hot ice" giant - I suspect anything above 4 or 5 earth masses is likely to run into this situation.

I seem to recall reading about a recent paper where the upper limit for a "super Earth" was well below 5 earth masses. Any larger and its more of a mini neptune. You mention hydrogen and helium escaping... but at 5 earth masses, it will hold on to that hydrogen and helium. Sure early in its formation, its not 5 earth masses, but atmosphere loss isn't instant either. Also it would be forming when the disk around the star is still rather dense, and before all that interplanetary gas is cleared out - so it can then accumulate these volatile a little later (still a short time frame in astronomical terms), no?

https://en.wikipedia.org/wiki/Super‐Earth#2016

Quote

The limit between rocky planets and planets with a thick gaseous envelope is calculated with theoretical models. Calculating the effect of the active XUV saturation phase of G-type stars over the loss of the primitive nebula-captured hydrogen envelopes in extrasolar planets, it's obtained that planets with a core mass of more than 1.5 Earth-mass (1.15 Earth-radius max.), most likely cannot get rid of their nebula captured hydrogen envelopes during their whole lifetime.^[66] Other calculations point out that the limit between envelope-free rocky super-Earths and sub-Neptunes is around 1.75 Earth-radii, as 2 Earth-radii would be the upper limit to be rocky (a planet with 2 Earth-radii and 5 Earth-masses with a mean Earth-like core composition would imply that 1/200 of its mass would be in a H/He envelope, with an atmospheric pressure near to 2.0 GPa or 20,000 bar).^[67] Whether or not the primitive nebula-captured H/He envelope of a super-Earth is entirely lost after formation also depends on the orbital distance. For example, formation and evolution calculations of the Kepler-11 planetary system show that the two innermost planets Kepler-11b and c, whose calculated mass is ≈2 M_⊕ and between ≈5 and 6 M_⊕ respectively (which are within measurement errors), are extremely vulnerable to envelope loss.^[68] In particular, the complete removal of the primordial H/He envelope by energetic stellar photons appears almost inevitable in the case of Kepler-11b, regardless of its formation hypothesis.

 

[MaxL_1023]

The issue with this is that it assumes that the planet cores form from the original protoplanetary disk before the gas dissipates. Earth and Potentially Super-Earth type planets can form from collisional accretion of smaller Moon-Mars size bodies after the gas dissipation. In fact, one theory of the solar system postulates that the current terrestrial planets formed from remnant material after an earlier generation of super-earths spiraled into the Sun after Jupiter and Saturn's migration disrupted the inner solar system.

I don't think many bodies will get to 5 earth masses when forming late, but if Earth and Venus did than it is not beyond possibility to have somewhat larger bodies. These would not have to worry about hydrogen capture at any rate. 

[MichaelPoole]

The problem with "theoretical models" is that they are often wrong. Don't get me wrong, they are useful tools, but nothing more. In this case, a planet is proven to have a mass, radius and density that mean it lacks a huge hydrogen envelope, yet is as massive as Uranus, so I am gonna believe the empirical evidence. There were plenty of models showing Pluto must be geologically dead too.

[78stonewobble]

On ‎04‎-‎12‎-‎2016 at 9:21 PM, MaxL_1023 said:

The issue with this is that it assumes that the planet cores form from the original protoplanetary disk before the gas dissipates. Earth and Potentially Super-Earth type planets can form from collisional accretion of smaller Moon-Mars size bodies after the gas dissipation. In fact, one theory of the solar system postulates that the current terrestrial planets formed from remnant material after an earlier generation of super-earths spiraled into the Sun after Jupiter and Saturn's migration disrupted the inner solar system.

I don't think many bodies will get to 5 earth masses when forming late, but if Earth and Venus did than it is not beyond possibility to have somewhat larger bodies. These would not have to worry about hydrogen capture at any rate. 

Or just that where the solar system formed was somewhat rare in gases, but rich in rocks?

So possibly unlikely, to very unlikely, but not completely impossible?

[MichaelPoole]

5 hours ago, 78stonewobble said:

Or just that where the solar system formed was somewhat rare in gases, but rich in rocks?

So possibly unlikely, to very unlikely, but not completely impossible?

I don't think it is very unlikely at all considering we already discovered such a planet. Way too much of this is theory, it reminds me of the oceans of oil theory of Venus or how Jovian moons were supposed to be barren cratered rocks before Voyager.

[78stonewobble]

16 hours ago, MichaelPoole said:

I don't think it is very unlikely at all considering we already discovered such a planet. Way too much of this is theory, it reminds me of the oceans of oil theory of Venus or how Jovian moons were supposed to be barren cratered rocks before Voyager.

Well I haven't really been keeping up on planet discoveries, so that might be the case.

I was just going by the arguments against.