\label{sec-survey_results}
Figure \ref{fig-bgb_hist} shows the distribution of the blazar clustering amplitudes (all spatial correlation amplitudes are reported in units of Mpc\(^{1.77}\)). The mean value for all blazars is \(121\), confirming the basic conclusion that blazars tend to lie in moderately overdense regions of the universe. The spread of \(B_{gB}\) values for the blazars is large, ranging from \(-2652\) to \(5801\). Negative values of \(B_{gB}\) indicate that some blazars do lie in apparent voids; however, 71% have clustering amplitudes greater than zero. According to the Abell richness class calibration of \citet{yee99}, this places xx% of blazars in clusters with Abell classes of 0.
Splitting the sample by blazar type, the clustering amplitudes for BL Lacs and FSRQs are remarkably similar. BL Lacs have a mean \(B_{gB}\) of \(148\pm312\), while FSRQs have \(144\pm268\). A Kolmogorov-Smirnov test confirms that the distributions are not inconsistent with being drawn from the same population at a probability of \(0.274~(1.0\sigma)\). Therefore, there is no evidence based on the clustering statistics that BL Lacs and FSRQs inhabit different environments at redshifts \(z<0.75\).
Among the objects studied are 131 objects whose blazar type is defined by BZCAT as “uncertain”. Discuss possibility of matching these to BL Lac/FSRQ, information available on selection method, and whether the environmental technique might be used as a diagnostic for blazar type. Probably due to optical lines?
Results from our study can be compared to earlier results; however, differences in the parameters used in Equation \ref{eqn-bgb} will cause systematic differences. The most immediate are the parameters used for the galaxy luminosity function \(\Psi[M]\) and the cosmology used to compute the distance. For example, applying the cosmology assumed by \citet{wur97} (\(q_0=0.02, \Omega_\Lambda=0, H_0=50~\mbox{km s}^{-1}\mbox{Mpc}^{-1}\)) to our blazar sample raises the mean \(B_{gB}\) value from \(121\pm436\) to \(167\pm558\). Their luminosity function parameters are very similar to our own, with a slightly shallower slope (\(\alpha=-1.0\)), a \(M_r^*\) value of \(-20.9\), and a luminosity function evolution where \(M\) evolves as \(E(z)\sim z\). Adjusting only for the cosmology, our mean value for the BL Lacs of \(161\pm367\) is close to the \citet{wur97} value of \(209\pm386\).
The blazar \(B_{gB}\) values are relatively flat as a function of redshift for \(z<0.5\). Between \(z=0.5\) and 0.75, however, there is a significant increase in the average \(B_{gB}\), increasing by a factor of \(\sim2-3\). The same effect is seen for both BL Lacs and FSRQs (Figure \ref{fig-bgb_redshift}). Similar results were found for BL Lacs by \citet{wur97}, who found that the median \(B_{gB}\) increased by a factor of four at \(z>0.35\), and for which the trend is the same for both radio- and X-ray-selected BL Lacs. Our results, which have \(\sim10\) times as many objects, suggest that richer clusters begin to occur at a higher redshift; the medians of the samples when split at \(z=0.35\) are almost identical.