The Classifications and Some Correlations for Fermi Blazars

In a recent paper, we calculate spectral energy distributions (SEDs) for 1425 Fermi blazars, classifications of low synchrotron peak sources (LSPs) if log $\nu_{\rm p} (\rm Hz) \leq $ 14.0, intermediate synchrotron peak sources (ISPs) if $14.0 < \,\log\, \nu_{\rm p} (\rm Hz) \leq 15.3 $, and high synchrotron peak sources (HSPs) if $ \log\, \nu_{\rm p} (\rm Hz) > 15.3$ are made based on 999 logarithms of synchrotron peak frequencies with known redshift, and we obtain an empirical relation to estimate the synchrotron peak frequency, $\nu_{\rm p}^{\rm Eq.}$ from effective spectral indexes $\alpha_{ox}\, {\rm and}\, \alpha_{ro}$ as $\log \nu_{\rm p}^{\rm Eq.} = 16+4.238X $ if $X < 0$, and $\log \nu_{\rm p}^{\rm Eq.} = 16+4.005Y $ if $X > 0$, where $X = 1.0 - 1.262 \alpha_{ro} - 0.623 \alpha_{ox}$, and $Y = 1.0 + 0.034 \alpha_{ro} - 0.978 \alpha_{ox}$ \cite{Fan16}. In the present work, we investigate the correlation between the peak frequency and the radio to X-ray spectral index, that between peak luminosity (integrated luminosity) and $\gamma$-ray/optical luminosity, and that between peak luminosity and integrated luminosity. Some discussions are presented.