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Another possible bias, present in this as well as all other surveys which
use spectral indices based upon nonsimultaneous data in their selection
process, is due to variability. Existing X-ray surveys have
made variability-based allowances for this effect, which
likely decreases its impact greatly (see, e.g., Laurent-Muehleisen 1996;
Perlman et al. 1996a). The magnitude of this effect upon existing
samples which used radio-spectral index criteria has been addressed by
Drinkwater et al. (1997), who utilize the variability statistics compiled
by Stannard & Bentley (1977) to estimate that the number of sources which have
average values of that would not be included in a
survey based upon two radio fluxes measured at different frequencies at times
separated by
years, is
.
We have chosen to take a somewhat different approach to addressing this
issue. The basis for this approach is not only that variability affects the
measured spectral index when the data points in question are non-simultaneous,
but also that the physical meaningfulness of a cut at ,
as opposed to, say,
has never truly been tested.
A factor of two variability between nonsimultaneous observations
at 6 and 20 cm will change the observed radio spectral index by 0.58.
In order to minimize the effect of non-simultaneous radio survey data
upon our samples, we decided to expand the common definition of
flat-spectrum radio sources to extend to
(instead of
0.5). Selecting all sources with
(that is, 0.5 plus 0.6 to include a factor of two variability)
would considerably lower the efficiency of the technique, as the
large majority of such steep-spectrum sources are radio galaxies
(although some are radio-loud quasars, often called SSRQs, or
steep-spectrum radio-loud quasars, which are thought to be oriented at
intermediate angles between FR 2s and FSRQs). The compromise approach
we adopted
allows an intrinsically
source to vary by
between 20 cm and 6 cm survey observations. We believe the
incompleteness due to missing sources which varied by larger amounts is
small (
) given the distribution of instantaneous 3.6-6 cm spectral
indices among core-dominated radio sources from our ATCA radio
survey, and we will use the ATCA data to both estimate the contamination from
truly steep-spectrum sources (and try to eliminate it) and test the
significance and meaning of both our cutoff and the more traditional
one.
It is important to note that the selection of sources with as high as 0.7 makes our BL Lac sample virtually 100% complete. In fact,
of the 180 confirmed BL Lacs with radio spectral index information in the
multifrequency AGN database of Padovani et al. (1997b), only 5% have
and all of these have X-ray-to-radio flux ratios much
higher than those to which we are sensitive to. In other words, no BL Lac
object should have been missed because of the
cut.