  With the aim of exploring the properties of the class of FR0 radio galaxies,
we selected a sample of 108 compact radio sources, called FR0CAT, by combining
observations from the NVSS, FIRST, and SDSS surveys. The catalog includes
sources with z$\leq 0.05$, with a radio size $\lesssim$ 5 kpc, and with an
optical spectrum characteristic of low-excitation galaxies. Their 1.4-GHz radio
luminosities range $10^{38} \lesssim \nu L_{1.4} \lesssim 10^{40}$ erg/s. The
FR0CAT hosts are mostly (86%) luminous ($-21 \gtrsim M_r \gtrsim -23$) red
early-type galaxies with black hole masses $10^8 \lesssim M_{\rm BH} \lesssim
10^9 M_\odot$: similar to the hosts of FRI radio galaxies, but they are on
average a factor $\sim$1.6 less massive. The number density of FR0CAT sources
is $\sim$5 times higher than that of FRIs, and thus they represent the dominant
population of radio sources in the local Universe. Different scenarios are
considered to account for the smaller sizes and larger abundance of FR0s with
respect to FRIs. An age-size scenario that considers FR0s as young radio
galaxies that will all eventually evolve into extended radio sources cannot be
reconciled with the large space density of FR0s. However, the radio activity
recurrence, with the duration of the active phase covering a wide range of
values and with short active periods strongly favored with respect to longer
ones, might account for their large density number. Alternatively, the jet
properties of FR0s might be intrinsically different from those of the FRIs, the
former class having lower bulk Lorentz factors, possibly due to lower black
hole spins. Our study indicates that FR0s and FRI/IIs can be interpreted as two
extremes of a continuous population of radio sources that is characterized by a
broad distribution of sizes and luminosities of their extended radio emission,
but shares a single class of host galaxies.
