Can Asteroid Belts Exist in the Luyten's System?

The extra-solar planetary system Luyten is relatively close (12.3 light years) to our Sun. The Luyten's red dwarf star is orbited by four planets, two of them Earth-like (in mass) and in 4:1 resonance. Extra-solar systems might contain asteroid belts such as ours. Therefore, it is important to investigate whether it is possible to have a stable population of minor bodies and compare them to those in our system. The study of extra-solar systems is crucial for understanding the evolution of planetary systems in general. Here, we investigate the stability of two possible asteroid populations in the Luyten's system: the main asteroid belt between the two inner and two outer planets, and an outer asteroid belt, situated beyond the planets. We also explore the likelihood of observing an asteroid or a dwarf planet in this system. Our study suggests that the existence of asteroid belts is possible, notably the main belt at 0.09-0.53 au from the star and an outer belt (with the inner boundary at 0.85 au and the outer boundary at similar to 66,000 au). The average Yarkovsky drift for the Luyten's main asteroid belt is similar to 0.5 x 10(-4) au/Myr for km-size objects. The Luyten's system might host extra-solar minor bodies, some of which could be capable of entering our own system. Presently, no asteroids can be detected in the Luyten's system, not even a Ceres-sized body, because the detection signal using the radial velocity method is at least two orders of magnitude less than that required for discerning such objects. The detection probability of an asteroid in the Luyten belt similar to Ceres is about 1.3%, which is less than the probability of finding Luyten B (similar to 3%).