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View Full Version : Is there a maximum mass/ radius for a rocky planet?



orochi
2007-Nov-13, 04:50 AM
With all the extrasolar planets being discovered, I have been thinking about what kinds of worlds might be out there. I was wondering if astronomers today have any idea whether or not there is a kind of "dividing line" between the sizes of terrestrial planets and gas giants. If so, what do they think is the maximum radius of a terrestrial type planet? In other words, at what point in size do rocky planets stop being rocky planets and become something else? Thanks.

George
2007-Nov-13, 05:01 AM
You might want to check out this very recent post (http://www.bautforum.com/astronomy/58157-interesting-extrasolar-planet-discoveries-6.html#post1110080) by eburacum45, regarding the exoplanet classifications.

neilzero
2007-Nov-17, 03:31 AM
If a solar system had lots of elements, but not much hydrogen and helium except in it's sun, then I suppose rocky planets with 100 Earth mass would be possible. They would likely be only about 3 times the diameter of Earth as the pressure near the center would crush many of the molecules to a denser form. The surface gravity would be unbarable to humans. It is possible that a million Earth mass rocky planet would be possible, but much more and it would collapse into a white dwarf, without ever being even a proto star. So it seems to me. Neil

eburacum45
2007-Nov-17, 09:46 AM
There is a very good paper about the properties of large Earth-like (that is to say rocky) planets here (note: this is a .pdf file)
http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.3454v2.pdf
Summarised, Valencia, Sasselov and O'Connell look at the three main components of a terrestrial planet, which are the metallic core, the rocky mantle and the water, or icy, hydrosphere.

They include a nice series of triangular diagrams which show how planets might be composed of different ratios of these three materials,and how it affects the density. A planet which is almost entirely metallic core, for instance, will be very dense, so will have a high gravity.

Planets with small metal cores, but with big crusts, will be less dense, and have lower gravities, while planets which are mostly ice, will be the least dense, and have the lowest gravities. There might be planets with metal cores and ice, but minimal crust, which fall in the middle range as well.

What does this mean for the atmospheres of such worlds? Well, the dense, more metallic worlds will have such high gravities that they will probably have dense, hydrogen rich atmospheres. Hydrogen is light, and tries to escape, but the gravity of these dense worlds prevents it.
So a dense, giant planet with a high metalic core will almost certainly have a dense atmosphere to go with it.

If a rocky world is large enough, its core will become highly compressed and the gravity will go way up, and so a large rocky planet will also probably have a dense atmosphere. But waterworlds are quite a bit less dense, so their atmospheres will be quite a bit thinner.

Looking from the outside, a large rocky or metallic world would probably resemble a gas giant in many ways- although the dense atmosphere might be noticably compressed by the higher gravity.

There are a few known extrasolar planets with high densities:
Mu Arae d for instance.
http://en.wikipedia.org/wiki/Mu_Arae_d
From that entry:

14 Earth masses is theoretically the maximum size for a terrestrial planet. A rocky planet this size could certainly have formed, since Mu Arae has a higher metallicity than our Sun. I don't know if this is true, as the entry doesn't give any references to back up that assertion. It may be that larger rocky/metallic planets can form, but their atmospheres would probably be so large that they would be essentially gas giants.

eburacum45
2007-Nov-17, 09:49 AM
This paper may also be of help; they say that a planet with "more than several Earth masses" will go on to become a gas giant, but that is a little vague, as lots of other factors enter into the equations.

http://arxiv.org/PS_cache/astro-ph/pdf/0606/0606117v1.pdf

filrabat
2007-Nov-17, 03:34 PM
Something just struck me that the issue here is more the planet's H2 escape velocity than it is size per se.

Gas giants can only form if a body has the right solar radiation/intrinsic temperature/mass combination to trap H2 in its atmosphere - IF sufficient H2 is present in its neighborhood.

I could be wrong, but it seems to me that, were our planet X times more massive than it actually is, it could have been a gas giant.

neilzero
2007-Nov-17, 04:52 PM
If the planet forms ten million kilometers from a class g star (proto star mode),with a circular orbit; it will have few volitiles, but could have enormous mass, as its intrinsic temperature could be a million degrees k, due to compression of the infalling materials. The intense solar wind would rarely let the planet capture any hydrogen or helium. Perhaps many of the "hot Jupiters" have little hydrogen or helium? Neil

eburacum45
2007-Nov-18, 05:36 PM
Several of the 'Hot Jupiters' are also observable in transit; none of them have the radius expected of a planet with only rock as its main constituent. All of them have at least some atmosphere.

So it looks like even hot jupiters start off with plenty of hydrogen and helium; one reason for that seems to be that they have formed in the middle-to-outer regions of the star's protplanetary disc, and migrated inwards.

Maybe one day we'll find a hot, dry, massive, rocky/iron planet with no atmosphere to speak of; such a planet may have formed in the innermost part of the early system, or perhaps lost its atmosphere over time.

But as far as I know we haven't found one yet.

Spaceman Spiff
2007-Nov-19, 03:51 AM
This paper (http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.2895v1.pdf) is addresses a related but fundamental question of how the equation of state (and composition) affect the mass-radius relationship.
See especially the discussion surrounding Figure 4.