The Classifications and Some Correlations for Fermi Blazars

In a recent paper, we constructed the spectral energy distributions (SEDs) for 1425 Fermi blazars. We classify them as low synchrotron peak sources (LSPs) if log νp(Hz) ≤ 14.0, intermediate synchrotron peak sources (ISPs) if 14.0 < log νp(Hz) ≤ 15.3, and high synchrotron peak sources (HSPs) if log νp(Hz) > 15.3. We obtain an empirical relation to estimate the synchrotron peak frequency, ν p from effective spectral indexes αox and αro as log ν Eq. p = 16 + 4.238X if X < 0, and log ν p = 16 + 4.005Y if X > 0, where X = 1.0− 1.262αro − 0.623αox and Y = 1.0 + 0.034αro − 0.978αox. In the present work, we investigate the correlation between the peak frequency and the radio-to-X-ray spectral index, between peak luminosity (bolometric luminosity) and γ-ray/optical luminosity, and between peak luminosity and bolometric luminosity. Some discussion is presented.


Introduction
Blazars show rapid variability, high and variable polarization, superluminal motions, core-dominated non-thermal continuum, and strong γ-ray emission, .Blazars consist of two subclasses, namely BL Lacertae objects (BL Lacs) and flat spectrum radio quasars (FSRQs).Both subclasses have common continuum properties, while their emission line features are quite different.Namely, FSRQs have strong emission lines, while BL Lacs have no or very weak emission lines.The spectral energy distributions of blazars consist of two bumps; the first one, for which synchrotron radiation is responsible, peaks at infrared/optical or UV/X-ray or even higher energy bands; the second one, peaking in the GeV or TeV bands, is often attributed to the inverse Compton process.
In 2010, [25] calculated the SEDs for 48 Fermi blazars, and proposed the subclasses of blazars using the acronyms LSP (low synchrotron peak source), ISP (intermediate synchrotron peak source), and HSP (high synchrotron peak source) as: LSPs if log ν p (Hz) ≤ 14, ISPs if 14.0 < log ν p (Hz) ≤ 15, and HSPs if log ν p (Hz) > 15.An empirical function is suggested for the estimation of peak frequency using the effective spectral indexes.Quite recently, we calculated the spectral energy distributions (SEDs) for 1425 Fermi blazars and successfully obtained SEDs for 1392 sources [26].Based on that paper, we will investigate some correlations statistically.
The spectral index α is defined as F ν ∝ ν −α , and all luminosities νL ν are denoted simply by L ν .

Sample and Classifications
In our previous paper [26], SEDs were calculated for a sample of 1425 Fermi detected blazars selected from the Fermi LAT third source catalog (3FGL) [1] by fitting the following relation with a least square fitting method: log(νF ν ) = P 1 (logν − P 2 ) 2 + P 3 , where P 1 , P 2 , and P 3 are constants, with P 1 being the spectral curvature, P 2 the peak frequency (log ν p ), and P 3 peak flux (log (ν p F ν p )).However, SEDs were obtained for only 1392 sources, among which 999 have known redshift.When the Bayesian Information Criterion (BIC) is adopted to the logarithmic of frequency in the comoving frame for 999 sources, the following criteria were proposed for the classifications: log ν p (Hz) ≤ 14.0 for LSPs, 14.0 < log ν p (Hz) ≤ 15.3 for ISPs, and log ν p (Hz) > 15.3 for HSPs.
When the averaged redshifts are adopted to the redshift unknown sources, and based on the criteria, we have that 34.77% of the whole sample are LSPs, 40.09% are ISPs, and 25.14% are HSPs for 1392 blazars.
In 2010, Abdo et al. [25] presented an empirical relation to estimate the synchrotron peak frequency ν p from effective spectral indexes α ox and α ro .Following their work, we obtain an empirical relation to estimate the synchrotron peak frequency, ν Eq.
p from effective spectral indexes α ox and α ro as log ν Eq.

Discussion and Conclusions
When the Bayesian Information Criterion (BIC) was adopted to the comoving peak frequencies, we found that three components are enough to fit the peak frequency distribution, and proposed the boundaries for subclasses as log ν p (Hz) ≤ 14.0 for LSPs, 14.0 < log ν p (Hz) ≤ 15.3 for ISPs, and log ν p (Hz) > 15.3 for HSPs.This classification is quite similar to that of [25].There is no extreme high peak frequency component.We also proposed a function to estimate the peak frequency by using effective spectral indexes.From the comparison shown in Figure 1, we can see that the empirical function can estimate the peak frequency well when peak frequency is lower than log ν p < 17, but the estimated peak frequency is under-estimated when log ν p > 17.
Figure 2 shows that there is an anti-correlation between the effective spectral index α rx and the peak frequency log ν p for the whole sample.However, we can see that there is a tendency for α rx to increase with log ν p for lower peak frequency sources.When the peak frequency moves to the lower side, then the X-ray emission will increase, since they are the sum of the synchrotron emission tail and the inverse Compton emission.Therefore, α rx will decrease, resulting in the positive tendency.
We also investigate the correlation between the peak luminosity/bolometric luminosity and γ-ray luminosity.We have found a very strong correlation.Similar results are also found between the peak luminosity/bolometric luminosity and optical luminosity.This means that we can use γ-ray (or optical) luminosity to estimate the peak luminosity/bolometric luminosity and γ-ray luminosity.
In this work, we introduce the classification of subclasses of blazars and an empirical function of peak frequency estimation using effective spectral indexes, investigate the correlation between effective radio-to-X-ray spectral index and peak frequency, as well as the correlation between peak/bolometric luminosity and γ-ray/optical luminosity.Conclusions are: (1) There are only three subclasses of Fermi blazars (LSPs, ISPs, and HSPs), and there is no extreme high peak frequency component for blazars.On the contrary, there are extreme blazars not detected by Fermi but detected by Cherenkov telescope; (2) There is an anti-correlation between broad band spectral index (α rx ) and peak frequency; (3) Peak frequency can be estimated using the broad band spectral indexes; (4) The peak/bolometric luminosity can be estimated using γ/optical luminosity; (5) There is a very significant correlation between peak and bolometric luminosity.

Figure 1 .
Figure 1.Correlations between estimated peak frequency using the empirical function and the fitted peak frequency for different classes of blazars.The solid line stands for the best-fit result.BL: BL Lacertae object; FSRQ: flat spectrum radio quasars.

Figure 4 .
Figure 4.The correlations between optical luminosity (log L o ) and peak luminosity (log L p ) (a); and bolometric luminosity (log L bol ) (b).

Figure 5 .
Figure 5.The correlations between bolometric luminosity (log L bol ) and peak luminosity (log L p ).

Table 1 .
Some correlation results for Fermi blazars.