Class 12 - Giant Planets - Heat and Formation

In Class 11 we covered the basic issues of giant planet interiors - how to build a gas giant. Here we will discuss some of the issues that we raised in Class 10 when we came up with a list of questions - these are the issues towards the bottom of the hierarchical list, issues that are less well understood.

- Measurement of current heat fluxes
- Thermal histories of giant planets
- Formation theories

HEAT FLUXES - and Equilibrium Temperatures

The giant planets receive, absorb and reflect sunlight - that's how we see them (left picture). But they also emit heat - infrared light (right)

Thus, the spectrum of the whole disk has a "double hump" - visible reflected sunlight at short wavelengths, and thermal IR at longer wavelengths.

Knowing the total output of sunlight and that light decreases as 1/distance2, we can calculate the amount of sunlight that should be hitting a square meter of each planet. The ALBEDO (A) of a planet is the reflectivity of a planet. Therefore, the total amount of sunlight absorbed the by the planet per square meter is (1-A)x Solar Flux@Earth / distance2 (where distance from the Sun is in AU). In equilibrium, we expect

ENERGY IN = ENERGY OUT

The energy emitted per square meter is described by the Stefan-Boltzmann law for thermal emission: Power/Area = sigma x T4 where T = Temperature of the radiating surface.

Allowing for the fact that objects receive an area 2piR2 of sunlight but emit from all 4piR2, and "normalizing" to the Earth (at 1 AU), we get

Tequilibrium = 285K [(1-A)/a2]1/4

 

(if you compare with Hartmann's page 297 you will see we are ignoring emissivity - a small correction generally, as it is inside the 4th root and the 4th root of a number close to 1 is very close to 1).

What happens when this equilibrium temperature is compared with the TRUE temperature (measured by looking at the IR spectrum and measuring the wavelength of maximum emission and using Wein's Law)?

This figure (from Hubbard's chapter in The New Solar System) shows that the giant planets tend to emit more energy than they receive - all except Uranus where the internal heat source (red arrow) is negligible. Hartmann quotes these ratios:

  Jupiter Saturn Uranus Neptune
Heat Emitted / Sunlight Absorbed 2.5 2.3 ~1.1 2.7

This table tells us that all of the giant planets except Uranus emits about 21/2 times the amount of solar energy absorbed. What's the story with Uranus? Why does it emit so much less energy? This is a MAJOR issue of planetary science.

So, putting the IR thermal emission of these planets in context, how bright do these giant planets glow? Is this really a lot of heat, like a star? If you compare JSN with the Earth, they are BRIGHT - but they are pretty dim compared with the Sun.

HEAT SOURCES

The main source of heat comes from formation - gravitational collapse and accretion of material

Gravitational Potential Energy -> Kinetic Energy (in-fall) -> Heat

This happens very quickly - during formation.

Then, slowly material begins to settle downwards - DIFFERENTIATION. This process is important for the Terrestrial Planets (more about that next week) but is also important for the giant planets.

First consider Jupiter and Saturn - The energy release by the formation of the small rock/iron cores is probably not very important for either Jupiter or Saturn (the cores are so small). So, most of the heat coming from Jupiter is thought to be primarily primordial - the heat generated in formation of the planet. For Saturn we have a different story - 2 pieces of evidence (i) a depletion of Helium in Saturn's atmosphere and (ii) lower internal temperatures on Saturn (derived via internal models as per Class 11) - suggest that there is HELIUM RAIN. That is, the PHASE DIAGRAM for H,He mixtures suggest that at high pressures liquid helium does not mix with liquid hydrogen - just like oil and water. The heavier liquid - helium - falls down through the hydrogen - the helium "rains out". The slightly warmer temperatures inside Jupiter probably prevent the helium from raining out much on Jupiter.

Second, what about Uranus and Neptune? These outer 2 giant planets are smaller and denser - consistent with much more denser materials than hydrogen and helium. We have discussed before that the prime candidates are the "hydrogen compounds" (often called "ices" even though they are not solid as ices inside the giant planets) which are made by combining the next most abundant elements - oxygen, carbon and nitrogen - with the abundant hydrogen. These are WAM - Water, Ammonia and Methane. These ices form the liquid layer outside the rock/metal core, below the outermost layer of hydrogen & helium. If Uranus and Neptune have similar interiors, why doesn't Uranus have a similar heat output? Was the heat dissipated (e.g. stirred up in a giant impact) or is there a stable layer of "opaque" material (a thermal blanket) preventing the heat from escaping - while Neptune was stirred up by an impact?.......???????

FORMATION

First, the Astro 101 story - as the solar nebula cooled, refractory materials condensed closer to the Sun while the more abundant, volatile "ices" condensed outside the "frost line" (along with the less abundant rock -> dirty snowballs).

The growing planet "embryos" were able to sweep up the surrounding gas to become giant planets. All this happened VERY QUICKLY - within 1-10 million years of the collapse of the original molecular cloud.

So - what about Uranus and Neptune? Farther out in the solar system the density of the solar nebula was less and the collision times between accreting materials is much slower. It is really difficult to make Uranus and Neptune where they are currently located. It would be MUCH easier if we could make them closer in and then allow them to migrate outwards. How can planets migrate? By interacting (gravitationally - not necessarily colliding) with other objects - specifically, Uranus and Neptune could migrate outwards by sending material inwards - where the objects get kicked out by Jupiter. This is the current theory for the formation of the Kuiper Belt - but wait a couple of months and there will probably be another theory around......