  (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.
