  We present the optical and infrared properties of 39 extremely radio-loud
galaxies discovered by cross-matching the Subaru/Hyper Suprime-Cam (HSC) deep
optical imaging survey and VLA/FIRST 1.4 GHz radio survey. The recent
Subaru/HSC strategic survey revealed optically-faint radio galaxies (RG) down
to $g_\mathrm{AB} \sim 26$, opening a new parameter space of extremely
radio-loud galaxies (ERGs) with radio-loudness parameter of $\log
\mathcal{R}_\mathrm{rest} = \log (f_{1.4
\mathrm{GHz,rest}}/f_{g,\mathrm{rest}}) >4$. Because of their optical faintness
and small number density of $\sim1~$deg$^{-2}$, such ERGs were difficult to
find in the previous wide but shallow, or deep but small area optical surveys.
ERGs show intriguing properties that are different from the conventional RGs:
(1) most ERGs reside above or on the star-forming main-sequence, and some of
them might be low-mass galaxies with $\log (M_\star/M_\odot) < 10$. (2) ERGs
exhibit a high specific black hole accretion rate, reaching the order of the
Eddington limit. The intrinsic radio-loudness ($\mathcal{R}_\mathrm{int}$),
defined by the ratio of jet power over bolometric radiation luminosity, is one
order of magnitude higher than that of radio quasars. This suggests that ERGs
harbor a unique type of active galactic nuclei (AGN) that show both powerful
radiations and jets. Therefore, ERGs are prominent candidates of very rapidly
growing black holes reaching Eddington-limited accretion just before the onset
of intensive AGN feedback.
