The Fermi blazars divide
  Flat Spectrum Radio Quasars (FSRQs) and BL Lac objects detected in the first
three months of the Fermi survey neatly separate in the gamma-ray spectral
index vs gamma-ray luminosity plane. BL Lac objects are less luminous and have
harder spectra than broad line blazars. We suggest that this division has its
origin in the different accretion regimes of the two classes of objects. Using
the gamma-ray luminosity as a proxy for the observed bolometric one we show
that the boundary between the two subclasses of blazars can be associated with
the threshold between the regimes of optically thick accretion disks and of
radiatively inefficient accretion flows, which lies at an accretion rate of the
order of 0.01 the Eddington rate. The spectral separation in hard (BL Lacs) and
soft (FSRQs) objects can then result from the different radiative cooling
suffered by the relativistic electrons in jets propagating in different
ambients. We argue that the bulk of the most luminous blazars alread detected
by Fermi should be characterised by large black hole masses, around 10^9 solar
masses, and predict that lowering the gamma-ray flux threshold the region of
the alpha_gamma-L_gamma plane corresponding to steep spectral indices and lower
luminosities will be progressively populated by FSRQs with lower mass black
holes, while the region of hard spectra and large luminosities will remain
forbidden.
