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In my setting, there's a gas giant orbiting in the habitable zone of a red dwarf (for specificity, its radius is about half Jupiter's, and it's 0.35 AU from 61 Cygni B. Ignore the effect of the other star in the binary, it's too far away to matter). All I want to know is, what does the planet look like?

Even more specifically, I'd like to know what it would look like in the sky of a nearby planet (orbiting at 0.5 AU). At closest approach, the gas planet would appear to be 1/3 the size of the sun/moon seen from Earth, so it definitely looks like more than just another point of light.

Here's what I have so far:

  1. It's too hot for methane or ammonia in the atmosphere, which would prevent it from having Neptune's blue coloring, and anyway, there isn't a lot of blue light coming from the star. I'd like it to stand out in the (yellow-orange) sky of the planet, so I'm hoping it's possible for it to be pale, like Saturn. But I don't know enough about gas planet atmospheres to narrow down the possibilities.
  2. It's tidally locked. I imagine that means that there will be continuous convection currents between the hot side and the cold side. Could these be visible in the sky?
  3. Auroras. This planet orbits a flare star, meaning lots of solar wind, meaning bright auroras at the poles (assuming that tidally-locked planets, with their slow rotations, can still have strong magnetic fields). Would these be visible, and if so, on which side? Could they be bright enough to be seen above the dark (cold) side of the gas giant, or even against the brighter (hot) side that faces the star?
  4. Rings? Apparently, rocky rings around warm gas planets could be a thing. If so, I'd love that, because as is pretty obvious by this point, the main role of this planet is to look awesome. Any ideas what color the rings would be?

Sorry if this is too many questions at once. I could split this up into different posts, but since they all relate to the appearance of this single example planet, I thought that would be overkill.

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I'm not an astronomer (yet!) but after seeing this question's inactivity I thought I'd pitch in.

1) Atmosphere

You may be interested in Sudarsky's gas giant classification, which predicts the appearance of gas giants based on their temperatures. It's not exactly clear what temperature your gas giant is, but I used this calculator to get some rough estimates. Entering Jupiter's bond albedo of ~50.00 and 0.00 greenhouse effect assuming the Sudarsky classification cares about the temperature of the very upper atmosphere, I got a surface temperature of 15 degrees Celsius. If this is in the right ballpark, your gas giant is a Class II or III. This means you are correct that it's too hot for ammonia, but water or methane might still exist, giving you something whitish or blue. Or perhaps this calculator is better suited toward terrestrial planets. Either way, the Sudarsky classification should give you some plausible options.

2) Convection currents

If the planet is a Class II, it may have visible clouds that follow its convection currents. If the planet is a Class III, it won't have distinguishable clouds, so its convection might not show on the surface. Notably, tidally locked worlds still experience the Coriolis Effect because they are still rotating - just in sync with their orbits. You would see some equatorial clouds moving on a Class II planet independent of its dayside-nightside convection.

3) Auroras

Lucky for you, this is a gas giant! While terrestrial planets may need to rotate to maintain active cores, gas giants produce magnetic fields in their mantles. Jupiter's hydrogen mantle is so dense that hydrogen acts like a metal, producing a magnetic field larger than anything in our solar system (except for the heliosphere itself!).

As a result, Jupiter has some huge auroras. It is not just conceivable but likely that your planet's strong magnetic field will interact with your star's strong solar wind, producing auroras visible from space. I suspect they'll still occur at the planet's poles, as defined by its axis of rotation, but don't quote me on that.

4) Rings

Rings definitely seem plausible, as outlined in your article, although I wonder if the planet is too close to your star to hold a stable ring system for long. I'm reminded of how Mercury and Venus are the only moonless planets because they orbit too close to the Sun - and without moons to tear apart, your planet may not form stable rings. Still, for all intents and purposes, your gas giant may capture and shred some asteroids to produce rings stable enough to exist for the duration of your story. Or maybe I'm wrong, and stellar gravity is a non-issue.

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