The faint source population at 15.7 GHz - I. The radio properties
  We have studied a sample of 296 faint (> 0.5 mJy) radio sources selected from
an area of the Tenth Cambridge (10C) survey at 15.7 GHz in the Lockman Hole. By
matching this catalogue to several lower frequency surveys (e.g. including a
deep GMRT survey at 610 MHz, a WSRT survey at 1.4 GHz, NVSS, FIRST and WENSS)
we have investigated the radio spectral properties of the sources in this
sample; all but 30 of the 10C sources are matched to one or more of these
surveys. We have found a significant increase in the proportion of flat
spectrum sources at flux densities below approximately 1 mJy - the median
spectral index between 15.7 GHz and 610 MHz changes from 0.75 for flux
densities greater than 1.5 mJy to 0.08 for flux densities less than 0.8 mJy.
This suggests that a population of faint, flat spectrum sources is emerging at
flux densities below 1 mJy.
  The spectral index distribution of this sample of sources selected at 15.7
GHz is compared to those of two samples selected at 1.4 GHz from FIRST and
NVSS. We find that there is a significant flat spectrum population present in
the 10C sample which is missing from the samples selected at 1.4 GHz. The 10C
sample is compared to a sample of sources selected from the SKADS Simulated Sky
by Wilman et al. and we find that this simulation fails to reproduce the
observed spectral index distribution and significantly underpredicts the number
of sources in the faintest flux density bin. It is likely that the observed
faint, flat spectrum sources are a result of the cores of FRI sources becoming
dominant at high frequencies. These results highlight the importance of
studying this faint, high frequency population.
