What does and doesn't work with this planetary system around a red dwarf?

Question

So I have the following scenario for a story, and I want to know if it runs into any ridiculous no-nos from a scientific point of view:

There is an earth-like world orbiting a red dwarf (similar to AD Leonis, though it is not tidally locked. It doesn't have to be hospitable but does have to be habitable (there will be other factors drawing humans to this world). It's much colder than earth, maybe only habitable in a narrow band around the equator, and with a lower gravity (say 0.8 g, somewhere in that neighbourhood).

Smaller worlds are more likely to be in tight orbits around a red dwarf from what I understand so it'll be the third planet in the system with an orbital period of ~190 (earth) days (close enough to half an Earth year to make it easy to count). Days would be a bit longer, maybe 29 hours or so.

The most important parts are that it is possible to survive, if not exactly comfortably, outdoors, and that reaching orbit is at worst as much work as it is here on Earth. A smaller planet with lower gravity (assuming close to as dense an atmosphere as Earth) should make it a little easier to get things into space.

Here is the rest of the system (briefly), from star and going outwards:

• 1 hot molten (lava) world
• 1 cold rocky world
• 1 Earth-like world (described above)
• 1 gas giant
• 1 gas giant
• 1 cold gas world (Neptune-like)
• 1 tiny rock-world (Pluto analog)
• Cometary halo and asteroid belt

Answer 1

I can see four key problems with the system as you've described it:

• Giant planets. The major thing that concerns me about the system is the presence of at least two gas giants. It's long been thought that low-mass stars like red dwarfs are unable to form giant planets, because the stars' protoplanetary disks are generally low-mass, and there's simply not enough material to form as many giant planets as in other systems. There are some counterexamples, like GJ 3512 (Morales et al. 2019), but these are general few and far between.
• A lack of tidal locking. Planets around red dwarfs are likely to be tidally locked, for two reasons. The timescale for tidal locking scales as $\tau\propto a^6/M^2$, where $a$ is the planet's semi-major axis and $M$ is the mass of the star. If you have a planet with a tight orbit around a low-mass star, as we do here, the planet will be tidally locked quite quickly, possibly long before life has a chance to arrive.
• High-multiplicity systems are problematic. You have seven planets orbiting this red dwarf, presumably in tight orbits. The closest analog I can draw to this is TRAPPIST-1, which hosts seven planets, much like this system. The orbits are stable only because the planets lie in orbital resonances with one another (i.e. the ratios of their periods are ratios of integers). The problem is, even a system with such resonances may develop instabilities on timescales of tens of millions of years (Gillon et al. 2017). The presence of massive planets in particular makes me a little nervous. Keep in mind that the masses of the TRAPPIST-1 planets are comparable to Earth or lower (Grimm et al. 2018).
• The Earth-like planet may not be habitable. Given the 190-day period, I derive a semi-major axis for your planet of 0.48 astronomical units. Calculating the planet's effective temperature tells me that it should be about 157 Kelvin, give or take, given the luminosity of AD Leonis. This means that the planet would have to be closer to the star for the surface temperature to be right without a massive runaway greenhouse effect.

To mitigate this, you might consider placing the giant planets in orbits far from the star, away from the other planets, to prevent instabilities. Similarly, the Earth-like planet could also have a large semi-major axis, to increase the tidal locking timescale (even doubling $a$ increases the timescale by a factor of 64); unfortunately, this would then make the planet colder and uninhabitable. I don't have a great solution to the issue of gas giant formation, but perhaps some external source of matter could be responsible.