The spectra of jet bases in FR I radio galaxies: implications for
  particle acceleration
  We present accurate, spatially resolved imaging of radio spectra at the bases
of jets in eleven low-luminosity (Fanaroff-Riley I) radio galaxies, derived
from Very Large Array (VLA) observations. We pay careful attention to
calibration and to the effects of random and systematic errors, and we base the
flux-density scale on recent measurements of VLA primary amplitude calibrators
by Perley & Butler (2013). We show images and profiles of spectral index over
the frequency range 1.4 - 8.5 GHz, together with values integrated over
fiducial regions defined by our relativistic models of the jets. We find that
the spectral index decreases (the spectrum flattens) with distance from the
nucleus in all of the jets. The mean spectral indices are 0.66 +/- 0.01 where
the jets first brighten abruptly and 0.59 +/- 0.01 after they recollimate. The
mean change in spectral index between these locations, which is independent of
calibration and flux-density scale errors and is therefore more accurately and
robustly measured, is -0.067 +/- 0.006. Our jet models associate the decrease
in spectral index with a bulk deceleration of the flow from 0.8c to <0.5c. We
suggest that the decrease is the result of a change in the characteristics of
ongoing particle acceleration. One possible acceleration mechanism is the
first-order Fermi process in mildly relativistic shocks: in the Bohm limit, the
index of the electron energy spectrum, p, is slightly larger than 2 and
decreases with velocity upstream of the shock. This possibility is consistent
with our measurements, but requires shocks throughout the jet volume rather
than at a few discrete locations. A second possibility is that two acceleration
mechanisms operate in these jets: one (with p = 2.32) dominant close to the
galactic nucleus and associated with high flow speeds, another (with p = 2.18)
taking over at larger distances and slower flow speeds.
