The 'second parameter': a memory from the globular cluster formation epoch

We study the correlations between the distribution of stars on the horizontal branch (HB), the HB morphology, and some other properties of globular clusters (GCs) in a large sample of GCs. We strengthen previous results that a general correlation exists only between HB morphology and metallicity. Correlations with other properties, e.g. central density and core radius, exist only for GCs within a narrow metallicity range. We conjecture that the lack of correlations with present properties of GCs (besides metallicity) is because the variation of the HB morphologies between GCs having similar metallicities is caused by a process, or processes, the effect of which was determined at the formation time of GCs. This process (or processes) is historically termed the 'second parameter', metallicity being the 'first parameter'. We then argue that the 'planet second parameter' model, where the presence of planets and to a lesser degree brown dwarfs and low-mass main-sequence stars is the 'second parameter', fits this conjecture. This is because the processes that determine the presence of planets and their properties occur during the formation epoch of the star and its circumstellar disc.