What Are the Minimum and Maximum Limits for Gas Giants and Terrestrial Worlds?

[natski]

Dear all,

Is anyone aware of any physicists who have worked/working on the theoretical limit to how small a gas giant can form? What is the minimum radius and mass that a gas giant can form at before it's simply evaporates too quickly to become a stable world? I'm guessing some fluid dynamics/planetary formation guys have worked out some kind of rough limit for this?

In contrast, has anyone done the upper limit for the mass of a terrestial world?

Thanks,
Natski

 

[mgb_phys]

The surface gravity compared to thermal velocity should be easy to work out (not having done it myself) how small a gas giant could be.

I don't know if there is a theoretical limit to the size of a rocky planet - it's more the shortage of rock in the inner solar system to form a planet. Again I don't think there are any theories that predict the relative sizes of rocky planets - it's just chance.

 

[Chronos]

Minimum size for a gas planet is about 3 Earth masses. Maximum size is about 10 Jupiter masses [any larger than that and they self ignite into brown stars]. That is a fairly large range of mass. Rocky planets are less certain. About 10 Earth masses is the practical limit.

 

[natski]

Chronos, can you provide a scientific refernce to the minimum size for gas giants value? I would be interested in seeing a detailed derivation.

I know 10 Earth masses is commonly quoted, but I don't believe there is any real work to substantiate this figure... I would love to read something on it though. I'm thinking of the planetary formation guys...

 

[Astronuc]

The size would depend on distance from the star, type of star (luminosity), and gas composition.

One can compute the escape velocity of hydrogen, since it is the lightest element, as a function of gravity and compared to the temperature distribution of the upper atmosphere. Do the same for ammonia and methane.

 

[natski]

Well yes I could go through the calculation btu I'm sure a much more sophisticated and detailed model ahs been already computed, do you know of a reference?

 

[Astronuc]

Not off-hand, but this is an interesting reference -

http://www.users.globalnet.co.uk/~mfogg/MSc Project.pdf

This might also be of interest -

http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/10038/1/02-2132.pdf (use 'save target as')

 

[FTL_Diesel]

Well yes I could go through the calculation btu I'm sure a much more sophisticated and detailed model ahs been already computed, do you know of a reference?

Pollack et al. (1996) is the basic paper for our present ideas about the core accretion model. If you buy core accretion (and not core collapse), you might set an (arbitrary) lower limit for what is a giant planet at something that has undergone runaway growth (which is generally considered to occur once a planetesimal hits 10 M_Earth, and is beyond the snow line). The end result will depend on how dense the proto-planetary disk is around your core (i.e. - Jupiter vs. Saturn vs. Neptune/Uranus).