Abstract
Co-orbital planets have not yet been discovered, although they constitute a
frequent by-product of planetary formation and evolution models. This lack may
be due to observational biases, since the main detection methods are unable to
spot co-orbital companions when they are small or near the Lagrangian
equilibrium points. However, for a system with one known transiting planet
(with mass $m_1$), we can detect a co-orbital companion (with mass $m_2$) by
combining the time of mid-transit with the radial-velocity data of the star.
Here, we propose a simple method that allows the detection of co-orbital
companions, valid for eccentric orbits, that relies on a single parameter
$\alpha$, which is proportional to the mass ratio $m_2/m_1$. Therefore, when
$\alpha$ is statistically different from zero, we have a strong candidate to
harbour a co-orbital companion. We also discuss the relevance of false
positives generated by different planetary configurations.
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