Modelling the luminosities and sizes of radio galaxies: radio luminosity
  function at z = 6
  We present a model to predict the luminosity function for radio galaxies and
their linear size distribution at any redshift. The model takes a black hole
mass function and Eddington ratio distribution as input and tracks the
evolution of radio sources, taking into account synchrotron, adiabatic and
inverse Compton energy losses. We first test the model at z = 2 where plenty of
radio data is available and show that the radio luminosity function (RLF) is
consistent with observations. We are able to reproduce the break in luminosity
function that separates locally the FRI and FRII radio sources. Our prediction
for linear size distribution at z = 2 matches the observed distribution too. We
then use our model to predict a RLF and linear size distribution at z = 6, as
this is the epoch when radio galaxies can be used as probes of reionisation. We
demonstrate that higher inverse Compton losses lead to shorter source lifetimes
and smaller sizes at high redshifts. The predicted sizes are consistent with
the generally observed trend with redshift. We evolve the z = 2 RLF based on
observed quasar space densities at high redshifts, and show that our RLF
prediction at z = 6 is consistent. Finally, we predict the detection of 0.63,
0.092 and 0.0025 z>=6 sources per sq. degree at flux density limits of 0.1, 0.5
and 3.5 mJy. We assess the trade-off between coverage area and depth and show
that LOFAR surveys with flux density limits of 0.1 and 0.5 mJy would are the
most efficient at detecting a large number of z>=6 radio sources.
