I Plausibility of high density rocky planets

[SammiEmN]

I was having a discussion with a friend as to whether or not a planet of rocky composition could exist with an extremely high density. We were thinking something approximately Earth sized, but weighing 4.35 × 10^27 Kg. He says it's impossible, whereas I think it is. Any help anyone can provide on this subject would be greatly appreciated.

 

[rootone]

It turns out that Earth is the densest planet in the solar system.
(I had thought Mercury was more dense but seems I'm wrong on that.)
In the end it depends on the content of the original material in the nebula from which the planet formed.
It's quite possible I would think that a planet could form in a region where there was an abundance of heavy elements due to nearby supernovae at some point in the past.

 

[Hornbein]

I was having a discussion with a friend as to whether or not a planet of rocky composition could exist with an extremely high density. We were thinking something approximately Earth sized, but weighing 4.35 × 10^27 Kg. He says it's impossible, whereas I think it is. Any help anyone can provide on this subject would be greatly appreciated.

You can have a white dwarf that is about 2 x 10^28 Kg with four times the Earth's radius. (I haven't done the math, just looked at a graph.) If you want Earth radius it is about 2 x 10^29 Kg.

I couldn't find out easily whether it is possible, but I think not. I found a badly labeled graph that seemed to indicate radius always increases with mass. That makes sense: most of the planet's mass is close to the surface, so the highly compressed center is relatively small.

 

[phyzguy]

Look at the attached graph, from a presentation by Sara Seager at MIT. It shows calculated masses and radii for planets of different compositions, overlaid with actual observed planets. So you are asking whether a planet with ~1000 Earth masses and 1 Earth radius could exist. This is in the lower right corner of the diagram, and it looks like the answer is no.

 

[Sei]

With the mass of 4.35 × 10^27 km, you got a planet the mass of 728.37602286598383507557529147599 Earth masses, 2.32 times the mass of Jupiter. To say, it is impossible for a terrestrial planet to have such high mass. However, white dwarves usually have much more mass than that, at about 0.5 Solar masses, or about 150,000 Earth masses.

The result is: It's not possible by our current understanding.

 

[|Glitch|]

Based upon Most 1.6 Earth-Radius Planets are not Rocky (arXiv 1407.4457) and according to The Mass-Radius Relation for 65 Exoplanets Smaller than 4 Earth Radii (arXiv 1312.0936v4) the highest density a rocky planet may have is 7.6 g/cm³ at 1.4 R_⊕. Which would result in a mass of 2.259 × 10¹³ kg, or ≈3.78 M_⊕.

 

[Sei]

Based upon Most 1.6 Earth-Radius Planets are not Rocky (arXiv 1407.4457) and according to The Mass-Radius Relation for 65 Exoplanets Smaller than 4 Earth Radii (arXiv 1312.0936v4) the highest density a rocky planet may have is 7.6 g/cm³ at 1.4 R_⊕. Which would result in a mass of 2.259 × 10¹³ kg, or ≈3.78 M_⊕.

And do the Mega-Earth!

 

[|Glitch|]

And do the Mega-Earth!

1.4 R_⊕ is the "mega-Earth." As I sourced above, exoplanets ≥ 1.6 R_⊕ are not likely to be rocky. Even at 1.6 R_⊕ the density would be 7.854 ± 1.24 g/cm³ based upon equation #1 in the other above source I cited. Where: ρ_P = 2.43 + 3.39( R_P / R_⊕) g/cm³, including a 20% margin for error in mass and 10% margin for error in radii. However, they concluded that the weighted mean density peaks at ≈1.4 R_⊕ and 7.6 ± 1.2 g/cm³. Exoplanets with a radius ≥ 1.6 R_⊕ the density decreases. They cease to be rocky and become more like Neptune. It would appear that to be considered a rocky planet it must have a radii < 1.6 R_⊕.

 

[Sei]

1.4 R_⊕ is the "mega-Earth." As I sourced above, exoplanets ≥ 1.6 R_⊕ are not likely to be rocky. Even at 1.6 R_⊕ the density would be 7.854 ± 1.24 g/cm³ based upon equation #1 in the other above source I cited. Where: ρ_P = 2.43 + 3.39( R_P / R_⊕) g/cm³, including a 20% margin for error in mass and 10% margin for error in radii. However, they concluded that the weighted mean density peaks at ≈1.4 R_⊕ and 7.6 ± 1.2 g/cm³. Exoplanets with a radius ≥ 1.6 R_⊕ the density decreases. They cease to be rocky and become more like Neptune. It would appear that to be considered a rocky planet it must have a radii < 1.6 R_⊕.

Wrong!
Mega-Earths are planets with mass comparable to Neptune (+10 Earth masses), while having density higher than Earth!

Backup claims:
https://en.wikipedia.org/wiki/Mega-Earth
http://exoplanetarchive.ipac.caltec...Overview?objname=K2-3+d&type=CONFIRMED_PLANET

 

[|Glitch|]

Wrong!
Mega-Earths are planets with mass comparable to Neptune (+10 Earth masses), while having density higher than Earth!

Backup claims:
https://en.wikipedia.org/wiki/Mega-Earth
http://exoplanetarchive.ipac.caltec...Overview?objname=K2-3+d&type=CONFIRMED_PLANET

If they have a mass ≥ 1.6 R_⊕ then they are likely to have a density < 7.6 ± 1.2 g/cm³. According to the Almenara et al. 2015 paper:

We have low confidence in the mass and density of planets c and d (Sec. 4).

4. Results
...
We conclude that our data robustly measure the mass of Planet b, 8.4 ± 2.1 M_⊕, but not those of c and d. Many more observations and very careful analysis will be needed to disentangle signatures of Planets c and d from the activity signal.

So while planets c and d may exist, their mass is highly speculative. Since they used the mass of the planets c and d to approximate the radius, and then used the radius and mass ratio to calculate density, it makes the density of both c and d also very questionable.

The one planet (b) where they did obtain accurate information has a mass 8.4 ± 2.1 M_⊕ and a density less than Earth at 4.32 (+2.0, -0.76) g/cm³.