Class 11 - Interior models of the Giant Planets Part B
So, this brings us to real models of the giant planets (better approximations to the illusive truth....)
The thermal state of interiors we will discuss next time.
In the meantime, What are the observational contraints on models?
Wow! That's lots of new stuff..... dealing with these one at a time....
This is what the Legandre Functions look like:
The J2 function is b - the higher coefficients are not well measured (yet!) so the other functions are not used much.
Look at Table 8-1 of Hartmann for values - 0.4 for uniform sphere -> 0.0 for all the mass at the center.
So, that's all the observable contraints - R, M, J2, k=I/MR2, e - which are put into computer models of the interiors to generate models for realistic giant planets.
How do we know what the GPs are made of? WE GUESS. The first guess? Cosmic abundance... of course. BUT we need to concentrate more of the HYDROGEN COMPOUNDS - Water, Ammonia, Methane - WAM - in Uranus and Neptune - because they are MUCH smaller than the radius of a simple hydrogen gas blob that we calculated above (about 1/3 the size).
This is what you get:
What's this "Metallic Hydrogen" ? When hydrogen is compressed, the protons and electrons become separated and the electrons can move about freely - the hydrogen becomes like the metal mercury - like a liquid metal - electrically conducting.
Strictly speaking - you need to look at the PHASE DIAGRAM for hydrogen
At pressures of about 2-3 Mbars, hydrogen changes and becomes like a metal - this has been found experimentally in the lab, by taking hydrogen and "bashing" it very hard - in shock experiments - the pressure does not last for very long but long enough to measure high conductivity.
This is what the top models produce for interior conditions - different models produced by different people are slightly different - quite different in the very central regions where properties are less contrained.
This bottom plot happened to be on the same transparency - but it shows that
Saturn's density is so low that it would float - if you could find a big enough bathtub!
- We can build simple models of the interior just using the planet's self gravity-> high pressure, high temperature, high density
- Detailed models require careful treatment of the properties of matter, compositional variation inside the planet and from planet to planet
- A few observations of the exterior provide important contraints on interior models
- Combining these constraints and a little physics & chemistry, we can - quite remarkably - describe what is going on inside these giant planets.
