  The spectral properties of blazars seem to follow a phenomenological sequence
according to the source luminosity. By inferring the source physical parameters
through (necessarily) modeling the blazar spectra, we have previously proposed
that the sequence arises because the particles responsible for most of the
emission suffer increasing radiative losses as the luminosity increases. Here
we extend those results by considering the widest possible range of blazar
spectral properties. We find a new important ingredient for shaping the spectra
of the lowest power objects, namely the role of a finite timescale for the
injection of relativistic particles. Only high energy particles radiatively
cool in such timescale leading to a break in the particle distribution:
particles with this break energy are those emitting most of the power, and this
gives raise to a link between blazar spectra and total energy density inside
the source, which controls the cooling timescale. The emerging picture requires
two phases for the particle acceleration: a first pre-heating phase in which
particles reach a characteristic energy as the result of balancing heating and
radiative cooling, and a more rapid acceleration phase which further accelerate
these particles to form a power law distribution. While in agreement with
standard shock theory, this scenario also agrees with the idea that the
luminosity of blazars is produced through internal shocks, which naturally lead
to shocks lasting for a finite time.
