Long duration radio transients lacking optical counterparts are possibly Galactic Neutron Stars

(abridged) Recently, a new class of radio transients in the 5-GHz band was detected by Bower et al. We present new deep near-Infrared (IR) observations of the field containing these transients, and find no counterparts down to a limiting magnitude of K=20.4 mag. We argue that the bright (>1 Jy) radio transients recently reported by Kida et al. are consistent with being additional examples of the Bower et al. transients. We refer to these groups of events as "long-duration radio transients". The main characteristics of this population are: time scales longer than 30 minute but shorter than several days; rate, ~10^3 deg^-2 yr^-1; progenitors sky surface density of >60 deg^-2 (95% C.L.) at Galactic latitude ~40 deg; 1.4-5 GHz spectral slopes, f_\nu ~ \nu^alpha, with alpha>0; and most notably the lack of any counterparts in quiescence in any wavelength. We rule out an association with many types of objects. Galactic brown-dwarfs or some sort of exotic explosions remain plausible options. We argue that an attractive progenitor candidate for these radio transients is the class of Galactic isolated old neutron stars (NS). We confront this hypothesis with Monte-Carlo simulations of the space distribution of old NSs, and find satisfactory agreement for the large areal density. Furthermore, the lack of quiescent counterparts is explained quite naturally. In this framework we find: the mean distance to events in the Bower et al. sample is of order kpc; the typical distance to the Kida et al. transients are constrained to be between 30 pc and 900 pc (95% C.L.); these events should repeat with a time scale of order several months; and sub-mJy level bursts should exhibit Galactic latitude dependence. We discuss possible mechanisms giving rise to the observed radio emission.