The Effect of Continuum Variability on Spectral Indices

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 $\alpha_{\rm r} < 0.5$ that would not be included in a survey based upon two radio fluxes measured at different frequencies at times separated by $\sim 2$ years, is $\sim 10\%$.

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 $\alpha_{\rm r} = 0.5$, as opposed to, say, $\alpha_{\rm r} = 0.7$ 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 $\alpha_{\rm r} = 0.7$ (instead of 0.5). Selecting all sources with $\alpha_{\rm r} \leq 1.1$ (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 $\alpha_{\rm r} = 0.5$ source to vary by $\sim 20\%$between 20 cm and 6 cm survey observations. We believe the incompleteness due to missing sources which varied by larger amounts is small ($<5\%$) 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 $\alpha_{\rm r} = 0.5$ one.

It is important to note that the selection of sources with $\alpha_{\rm r}$ 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 $\alpha_{\rm r} \gt 0.7$ 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 $\alpha_{\rm r}$ cut.