Orange Suns and Blue Jupiters

Question

I am developing a fictional planetary system in which a large gas giant planet (slightly less than the mass of Saturn), has migrated into the habitable zone during the formational years of the system, and hosts habitable moons.

The star in question is a K0V Orange Dwarf, which is reasonably quiet (i.e. doesn't flare often or at all anymore)

In trying to determine what colour my gas giant should be, it became clear to me that photochemical reactions in the atmospheres of these planets are a major factor in determining what compounds are present, and thus their colouration.

Most importantly, in our own solar system, Jupiter and Saturn receive more UV radiation (which breaks down methane into other compounds), than Uranus and Neptune (which are able to retain methane, and are thus bluer.)

Since my fictional gas giant is orbiting its star very closely to be within its habitable zone, my initial thought was that the planet would not be able to retain methane, and would therefore lack blue colouration. However, I then remembered that K-type and M-type stars are cooler, and therefore emit less UV radiation in the first place (except for flares).

What I am trying to determine is this; Does a quiet K-type star emit a sufficiently low fraction of its output in the UV spectrum, that a Jovian/Saturnian type planet would be blue or blue-white even at a habitable distance?

System parameters:

Star (K0V)

• 0.85 Sol masses
• 0.75 Sol radii
• 0.40 Sol Luminosity
• ~5,250K surface temperature
• Age: ~8 gya

Planet (Gas Giant)

• 82 Earth masses
• ~50,000km radius
• Semi-Major Axis: 0.85 AU

Answer 1

You have two questions to consider here: Can compounds required for blue atmospheres form in significant amounts on this planet, and are the temperatures right for them to condense and form clouds?

I talked about atmospheric composition and color in an answer to a related question. Essentially, the question of whether or not compounds like ammonia and methane (known as volatiles) - can exist in a giant planet's atmosphere depends on the orbit of the planet in relation to the star's frost line. The frost line is the point at which, in the protostellar nebula, these compounds could condense. This critical temperature is thought to be around 145 Kelvin. For a solar-type star, the frost line would have been around 2.7 - 2.8 AU. I suspect your star would have a frost line slightly lower than this, perhaps 2.5 AU. This would seem to indicate that your setup is impossible.

However, giant planets have been found quite far inside the frost line; notable are the gas of exoplanets known as hot Jupiters. These planets migrated inwards through interactions with the protoplanetary disk or planetesimals early in the system's history, allowing giant planets to orbit quite close to their parent stars. You can easily place your planet inside the frost line if you allow migration to occur.

Now we get to our second issue: condensation. In general, different gases condense and are dominant at different temperatures, and so the color of the atmosphere depends on the planet's temperature. The effective temperature of a planet scales as $T_{eff}\propto L_*^{1/4}$, where $L_*$ is the parent star's luminosity. Plugging in the numbers, this means that your planet should have an atmospheric temperature (neglecting greenhouse effects) suitable for water vapor but too hot for methane or ammonia. Water vapor clouds could lend a blue color to the atmosphere, but unfortunately it would not be aided by the presence of atmospheric methane or ammonia.