New Insights on the z-alpha Correlation from Complete Radio Samples
  The existence of a correlation between observed radio spectral index (alpha)
and redshift (z) has long been used as a method for locating high-z radio
galaxies. We use 9 highly spectroscopically complete radio samples, selected at
different frequencies and flux limits, to determine the efficiency of this
method, and compare consistently observed correlations between alpha,
luminosity, linear size, and redshift. We observe a weak correlation between z
and alpha which remains even when Malmquist bias is removed. The strength of
this correlation depends on both the k-correction and sample selection
frequency, in addition to the frequency at which alpha is measured, and
consistent results for both high and low frequency selected samples are only
seen if analysis is restricted to just extended radio galaxies. Many of the
highest redshift radio galaxies are very compact and often display a negatively
curved or peaked spectrum, and therefore the low-frequency radio spectrum as a
whole should be studied; this is something for which the LOFAR will be crucial.
We quantify both the efficiency and the completeness of various techniques used
to select high-z radio galaxies. A steep-spectrum cut applied to low-frequency
selected samples can more than double the fraction of high-z sources, but at a
cost of excluding over half of the high-z sources present in the original
sample. An angular size cut is an almost as equally effective method as a
steep-spectrum cut, and works for both high and low frequency selected samples.
In multi-wavelength data, selection first of infrared-faint radio sources
remains by far the most efficient method of selecting high-z sources. We
present a simple method for selecting high-z radio galaxies, based purely on
combining their radio properties of alpha and angular size, with the addition
of the K-band magnitude if available.[abridged]
