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Dynamical mass and multiplicity constraints on co-orbital bodies around stars

Objects transiting near or within the disruption radius of both main sequence (e.g. KOI 1843) and white dwarf (WD 1145+017) stars are now known. Upon fragmentation or disintegration, these planets or asteroids may produce co-orbital configurations of nearly equal-mass objects. However, as evidenced by the co-orbital objects detected by transit photometry in the WD 1145+017 system, these bodies are largely unconstrained in size, mass, and total number (multiplicity). Motivated by potential future similar discoveries, we perform N-body simulations to demonstrate if and how debris masses and multiplicity may be bounded due to second-to-minute deviations and the resulting accumulated phase shifts in the osculating orbital period amongst multiple co-orbital equal point masses. We establish robust lower and upper mass bounds as a function of orbital period deviation, but find the constraints on multiplicity to be weak. We also quantify the fuzzy instability boundary, and show that mutual collisions occur in less than 5%, 10% and 20% of our simulations for masses of 10^{21}, 10^{22} and 10^{23} kg. Our results may provide useful initial rough constraints on other stellar systems with multiple co-orbital bodies.