The recent announcement of a Neptune-sized exomoon candidate around the transiting Jupiter-sized object Kepler-1625 b could indicate the presence of a hitherto unknown kind of gas giant moons, if confirmed. Three transits of Kepler-1625 b have been observed, allowing estimates of the radii of both objects. Mass estimates, however, have not been backed up by radial velocity measurements of the host star. Here we investigate possible mass regimes of the transiting system that could produce the observed signatures and study them in the context of moon formation in the solar system, i.e. via impacts, capture, or in-situ accretion. The radius of Kepler-1625 b suggests it could be anything from a gas giant planet somewhat more massive than Saturn (0.4 MJup) to a brown dwarf (BD) (up to 75 MJup) or even a very-low-mass star (VLMS) (112 MJup ≈ 0.11 M). The proposed companion would certainly have a planetary mass. Possible extreme scenarios range from a highly inflated Earth-mass gas satellite to an atmosphere-free water-rock companion of about 180 M⊕. Furthermore, the planet-moon dynamics during the transits suggest a total system mass of 17.6 +19.2 −12.6 MJup. A Neptunemass exomoon around a giant planet or low-mass BD would not be compatible with the common mass scaling relation of the solar system moons about gas giants. The case of a mini-Neptune around a high-mass BD or a VLMS, however, would be located in a similar region of the satellite-to-host mass ratio diagram as Proxima b, the TRAPPIST-1 system, and LHS 1140 b. The capture of a Neptune-mass object around a 10 MJup planet during a close binary encounter is possible in principle. The ejected object, however, would have had to be a super-Earth object, raising further questions of how such a system could have formed. In summary, this exomoon candidate is barely compatible with established moon formation theories. If it can be validated as orbiting a super-Jovian planet, then it would pose an exquisite riddle for formation theorists to solve.
We conclude that if the proposed companion around Kepler-1625 b is real, then the host is most likely a super-Jovian object. In fact, a BD would also be compatible with both the mass-radius relationship for substellar objects and with the dynamical transit signatures shown in the lightcurves by Teachey et al. (2017). If the satellite candidate can be confirmed, then dynamical modeling of the transits can deliver even better mass estimates of this transiting planet-moon system irrespective of stellar RVs.