Expected planets in globular clusters

We argue that all transient searches for planets in globular clusters have a very low detection probability. Planets of low-metallicity stars typically do not reside at small orbital separations. The dependence of planetary system properties on metallicity is clearly seen when the quantity I_e ≡ M_p[a(1 - e)]² is considered; M_p, a and e are the planet mass, semimajor axis and eccentricity, respectively. In high-metallicity systems, there is a concentration of systems at high and low values of I_e, with a low-populated gap near I_e ∼ 0.3M_J au², where M_J is Jupiter's mass. In low-metallicity systems, the concentration is only at the higher range of I _e, with a tail to low values of I_e. Therefore, it is still possible that planets exist around main-sequence stars in globular clusters, although at small numbers because of the low metallicity, and at orbital periods of ≳10 d. We discuss the implications of our conclusions on the role that companions can play in the evolution of their parent stars in globular clusters, for example, influencing the distribution of horizontal branch stars on the Hertzsprung-Russell diagram of some globular clusters, and in forming low-mass white dwarfs.