In this scenario we have a brown dwarf with a powerful magnetic dynamo from metallic hydrogen. The magnetic field is modeled after Jupiter’s but just three orders of magnitude more powerful.
Orbiting the brown dwarf are two exact copies of Earth in a close horseshoe orbit. These planets are stripped of, and feed charged particles of atmosphere into a plasma torus, which is in all respects similar to Io’s.
Discounting the improbability of the setup, what are ways that the Atmosphere of these planets can be sustained with breathable compositions?
So far my research has led me to a few different processes that could help feed the atmosphere, but I’m doubtful of their ability to maintain breathability for humans. .
Erosion: Both Earth-like planets are tidally locked to the brown dwarf. If their sub-solar points have continental structures then the erosion from near constant precipitation could release large quantities of CO2. In addition, powerful tidal forces between horseshoe orbits will erode many coastal areas.
Volcanic Activity: Though the two planets have 0 eccentricity, they switch their orbits every 120 days. This change produces tides of 70m on the closer planet. My rough estimations based on period and tidal forces says that my planets should be two to three orders of magnitude less geologically active than Io. However, during “change events” volcanoes and Earthquakes should be common. These volcanoes will spit out water vapour, CO2, sulfur dioxide and other unpleasant vapours.
Plant life: Plants will do their thing and convert CO2 and H2O to oxygen. This could help keep our atmosphere breathable.
Are there any other ways that I’ve overlooked to plausibly sustain my atmosphere? The answers don’t have to be perfect, but I want some science base to them. No magic allowed. Natural processes are preferred, even if they are unlikely or rare effects. I will also accept “derelict/self sustaining technology” Perhaps in the form of abandoned terraforming equipment. Still:Natural processes are preferred