## Gas Giants!

I’m currently working on a series of tutorials on the use of Wilbur. It isn’t going all that quickly. In the meantime, I thought I’d put up a post with some information on gas giant planets.

First off, there’s an interesting thread by Constantine Thomas(Evil Doctor Ganymede) on the Sci-Fi RPG Forum about the size-limits of satellites of gas giant planets here. The paper he references is apparently not available online, but here is a useful reference with some numerical values.

The latter reference, by Abel Mendez Torres, gives a mass relation ship of,

mm = 0.318 mp,

Where:
mm is the mass of the moon in Earth masses, and
mp is the mass of the gas giant planet in Jupiter masses.

rm = 0.444 mp0.302

Where,

Referring to the somewhat impenetrable, Albedo and Reflection Spectra of Extrasolar Giant Planets(Sudarsky et al, 2000), the Extrasolar Visions page gives us some really useful information on the likely colors of various gas giants.

Class I Jovians with effective temperatures of less than or about 150 Kelvins(equivalent to Jupiter or Saturn) will have their color determined by ammonia clouds in their tropospheric layers and condensed carbon and sulfur compounds. At the warm end they’d look like Jupiter due to the condensates. As the planets get cooler the white ammonia haze would thicken, muting the bright colors and making them look more like Saturn. For a sunlike star of spectral class G2 V, the Bond albedo would tend toward 0.57 as the ammonia haze becomes predominant. Toward the warmer end, the colors of the condensates would predominate, reducing the Bond albedo to about 0.47. The Bond albedo of Jupiter is about 0.343 so there is in practice a bit of play around the theoretical predictions. My assumption based on this was that Saturn would have a Bond albedo closer to 0.57 than that of Jupiter, but the value for Staurn’s albedo is actually 0.342 so maybe my understanding of this is a bit off. Still, this gives us a good start for believable values I guess…

Image of Class II planet from Extrasolar Visions(http://www.extrasolar.net/speculations.html)

The color of warmer Class II Jovians begins to be determined by the presence of water clouds in their tropospheres. These exist between an equilibrium temperature of 150 K and 350 K. Habitable moons would probably orbit these bright, nearly white worlds. Albedo estimates on these planets range from about 0.81 in the fiducial model to as little as 0.37 with 1% condensation. This is actually less than the estimate for Class I Jovians, so these guys could plausibly actually be darker than outer system planets. Perhaps those darker planets would be largely blue like the Class III clear atmosphere planets found further in but with bright cloud systems. Presumably, with the fast rotation that we would expect from the very large gas giants that would be orbited by Earthlike moons, these would have the same sort of narrow stripes as Jupiter. Only in blue and white. Cool!

Image of Class III planet from Extrasolar Visions(http://www.extrasolar.net/speculations.html)

When the planets effective temperature is between 350 K and 900 K, the troposphere is too hot for water-ice to condense in the clouds, so these, “clarified,” planets will be blue for the same reason that a clear atmosphere on Earth is blue. These Class III planets will be very dark with a theoretical Bond albedo of about 0.12 to 0.09. As clear as they are, you are probably seeing hazy, shadowy depths of the planet.

Image of Class IV planet from Extrasolar Visions(http://www.extrasolar.net/speculations.html)

Above 900 K, heavy absorption by sodium and potassium vapor makes Class IV planets even darker, with albedo around 0.03 to 0.16.

Image of Class V planet from Extrasolar Visions(http://www.extrasolar.net/speculations.html), a Class IV planet would be darker without the brighter silicate cloud bands.

Class V planets are found where effective temperatures exceed about 1500 K. Reflective clouds of silicates forming above the sodium and potassium layers makes these planets more reflective with Bond albedos of about 0.55.

Based on these numbers, I devised a quick-and-dirty way of determining the orbital radius of extrasolar gas giants similar to the 2300AD method of determining a star’s habitable region. This is only technically valid for G2V stars like the Sun, and it’s based off of blackbody temperature rather than effective temperature which would take albedo into consideration. A more sophisticated model than what I’m doing here would have a lot more overlap of the zones with the actual classification of planets within the overlap being very dependent on the detailed composition and thermal history of the planet.

Class I: r > 2.874 √L,
Class II: 2.874 √L > r > 0.528 √L,
Class III: 0.528 √L > r > 0.0798 √L,
Class IV: 0.0798 √L > r > 0.029 √L,
Class V: r <= 0.029 √L,

Where:
r is radius of planet’s orbit in a.u.’s, and
L is the luminosity of the star in Solar luminosities.

For those who would appreciate a more detailed and nuanced model, I present a couple of tables from Sudarski(2000).

Table 1: EGP(Extrasolar Giant Planets) albedo estimates from Sudarski(2000) based on full condensation models using modified(fiducial) profiles and “isolated” profiles, and models with 1% and 10% condensation.

Table 2: Same as Table 1, but for G7V through M4V stars, rather than A8V through G2V stars. Other charts with information for specific extrasolar planets and their stars can be found in the referenced paper.

Hopefully, this has been as enjoyable and useful to you as it has been for me. Hopefully, I’ll be back soon with more posts.