The Villafranca catalog of Galactic OB groups: I. Systems with O2-O3.5 stars.

CONTEXT. The GOSSS spectral classifications and Gaia data have significantly improved our ability to measure distances and determine memberships of stellar groups with OB stars. AIMS. We have started a program to identify, measure distances, and determine the membership of Galactic stellar groups with OB stars. We start with the identification and distance determinations of groups with O stars. In this paper we concentrate on groups that contain stars with the earliest spectral subtypes. METHODS. We use GOSSS to select Galactic stellar groups with O2-O3.5 stars and a method that combines Gaia DR2 photometry, positions, proper motions, and parallaxes to assign robust memberships and measure distances. We also include the two clusters in that paper to generate our first list of 16 O-type Galactic stellar groups. RESULTS. We derive distances, determine the membership, and analyze the structure of sixteen Galactic stellar groups with O stars, Villafranca O-001 to O-016, including the 14 groups with the earliest-O-type optically-accessible stars known in the Milky Way. We compare our distance with previous results and establish that the best consistency is with VLBI parallaxes and the worst is with kinematic distances. Our results indicate that massive stars can form in relatively low-mass clusters or even in near-isolation, as is the case for the Bajamar star in the North America nebula. This lends support to the hierarchical scenario of star formation, where some stars are born in well-defined bound clusters but others are born in associations that are unbound from the beginning: groups of newborn stars come in many shapes and sizes. We propose that HD 64 568 and HD 64 315 AB could have been ejected simultaneously from Villafranca O-012 S. Our results are consistent with a difference of approx. 20 microas in the Gaia DR2 parallax zero point between bright and faint stars. (ABRIDGED)