GAMMA-RAY LOUDNESS, SYNCHROTRON PEAK FREQUENCY, AND PARSEC-SCALE PROPERTIES OF BLAZARS DETECTED BY THE FERMI LARGE AREA TELESCOPE

We adopted the definition of Lister et al. (2011) for "γ-ray loudness" as the ratio of the γ-ray luminosity to the radio luminosity. Unlike Lister et al. (2011), we did not have multiple observations on our sources from which to determine a median radio luminosity. Instead, we only used a single observation to calculate a luminosity. Due to the variable nature of these blazars, this may not be the best representation of the sources' actual average luminosity. For the γ-ray luminosity, we used the average fluxes reported in the 1FGL and the 2FGL. The LAT measures γ-ray flux continuously from 20 MeV to over 300 GeV. For publication (e.g., in 1FGL and 2FGL) the measurements are later grouped into energy bands in order to provide spectral information. To obtain total γ-ray fluxes, we combined the fluxes from three bands where the LAT has the highest sensitivity: 100–300 MeV, 300 MeV–1 GeV, and 1–100 GeV. The fluxes were added and uncertainties were added in quadrature. However, some sources had only upper limits to their fluxes in certain bands. If a source's reported fluxes in one of the bands were upper limits, we use as the uncertainty half the reported flux in that band because the upper limits are given as 2σ results (Abdo et al. 2010a).

To calculate the γ-ray luminosities, we used the same process as Lister et al. (2011). We calculated the luminosities using data from both 1FGL/1LAC and 2FGL/2LAC, when available. We started with converting energy fluxes using the equation

$$\begin{equation} S_{0.1} = \frac{(\Gamma _{0}-1)C_{1}E_{1}F_{0.1}}{(\Gamma _{0}-2)}\left[1-\frac{E_{1}}{E_{2}}^{\Gamma _{0}-2}\right] \, {\rm erg\; cm^{-2}\; s^{-1},} \vspace*{4pt} \end{equation} \tag{ 1 }$$

where F_0.1 is the LAT flux from 100 MeV to 100 GeV in photons cm⁻² s⁻¹, E₁ = 0.1 GeV, E₂ = 100 GeV, C₁ = 1.602 × 10⁻³ erg GeV⁻¹, and Γ₀ is the γ-ray photon spectral index which is set to 2.1 for this calculation. Next, the luminosity was calculated using the equation

$$\begin{equation} L_{\gamma } = \frac{4 \pi D^{2}_{L} S_{0.1}}{(1+z)^{2-\Gamma }} \; {\rm erg\; s^{-1},} \end{equation} \tag{ 2 }$$

where D_L is the luminosity distance¹ in cm and Γ is the γ-ray photon spectral index from 1LAC and 2LAC.

We calculated the radio luminosities using the equation

$$\begin{equation} L_{R} = \frac{4 \pi D^{2}_{L} \nu S_{\nu }}{(1+z)} \; {\rm erg\; s^{-1},} \end{equation} \tag{ 3 }$$

where ν is 5 GHz and S_ν is the total VLBA flux density we measured at 5 GHz. We assumed a flat radio spectrum index (α = 0) for the purposes of the k-correction and luminosity calculations.

The γ-ray loudness is then simply

$$\begin{equation} G_{r,{\rm 1FGL}} = \frac{L_{\gamma,{\rm 1FGL}}}{L_{R}} \end{equation} \tag{ 4 }$$

for 1FGL measurements and

$$\begin{equation} G_{r,{\rm 2FGL}} = \frac{L_{\gamma,{\rm 2FGL}}}{L_{R}} \end{equation} \tag{ 5 }$$

for 2FGL measurements.

All of our sources were significantly γ-ray loud. For the 1FGL data, the minimum G_{r, 1FGL} was 545 and the maximum was 187,000, with an average value of 19,500. For the 2FGL data, the minimum G_{r, 2FGL} was 404 and the maximum was 95,100, with an average value of 13,000. There are two possible explanations for this large change in maximum G_r and the significant change in average G_r: (1) the 2FGL data were averaged over 2 years, so any sources in a high-activity/flaring state in the 11 months of 1FGL would naturally have lower γ-ray flux when averaged over a longer period of time and (2) the 1–100 GeV flux was calculated slightly differently for 2FGL than in 1FGL (Nolan et al. 2012). We plot the 1FGL γ-ray versus radio luminosities in Figure 1. The 2FGL luminosities were very similar to the 1FGL luminosities.

Zoom In Zoom Out Reset image size

Lister et al. (2011) reported a significant difference between the distributions of G_r for BL Lac objects and FSRQs. We did not find such a difference in our data. To examine the likelihood that the BL Lac objects and FSRQs were unrelated, we used the Kolmogorov–Smirnov (K-S) test² (e.g., Press et al. 1986). The K-S test returned an 8% probability that the 1FGL BL Lac objects and FSRQs were drawn from the same parent population. For the 2FGL data, the K-S test result was 18%. See Figure 2 for a plot of the G_r distributions.

Zoom In Zoom Out Reset image size

The frequency at which the synchrotron radiation is at a maximum (ν^S_peak) is typically found by making many measurements of the spectrum of a source and fitting a polynomial to these measurements (e.g., Nieppola et al. 2006). Ideally, one would like to have simultaneous multi-frequency measurements covering as much of the spectrum as possible. Unfortunately, such large simultaneous data are rarely available. When possible, we found estimates for ν^S_peak in the literature (see Table 1). It should also be noted that ν^S_peak is known to be variable (Rani et al. 2011). Therefore, we made an effort to use the most recent published data. We were able to find published ν^S_peak values for 102 of our sources, more than half of which came from Meyer et al. (2011).

If we could not find a published value of ν^S_peak, we employed the technique used in 2LAC. We used the average radio–optical (α_RO) and optical–X-ray (α_OX) spectral indices and the formula given in Abdo et al. (2010c):

$$\begin{equation} \hspace{-1pc}\log \big(\nu ^{S}_{{\rm peak}}\big) = \left\lbrace \begin{array}{@{}ll}13.85 + 2.30X & {\rm for\; X<0\; and\; Y<0.3}\\ \ms 13.15 + 6.58Y & {\rm otherwise}. \end{array} \right. \end{equation} \tag{ 6 }$$

Here, X = 0.565 − 1.433α_RO + 0.155α_OX and Y = 1.0 − 0.661α_RO − 0.339α_OX. As per Giommi et al. (2012a), the ν^S_peak for FSRQs was reduced by 0.5 in log  space. Also, all ν^S_peak determined using the 2LAC method were expressed in the source rest frame. For those BL Lac objects without a measured redshift, the median BL Lac object redshift of 0.27 from the 2LAC was used, but only for the purposes of estimating ν^S_peak (i.e., we did not use this redshift to compute the luminosities). We used the 2LAC estimation method to find ν^S_peak values for 76 of our sources.

If we could not find a published value and the α_RO and/or α_OX numbers were not in 2LAC, we used flux measurements from the NED and fitted a quadratic to the data in log(νF_ν) − log(ν) space. Again, we used the most recent measurements available. The ν^S_peak's found in this way are not as reliable as the 2LAC method, but they do tend to be reasonably close. To check the accuracy of the NED-fit method, we made fits for all of our sources. We threw out any fits that had less than eight points for fitting and any that were obviously suspicious (ν^S_{peak, fit} < 12 and ν^S_{peak, fit} > 19), and then compared the remaining values to the published and 2LAC estimated values. We calculated how close the ν^S_{peak, fit} was by using

$$\begin{equation} \Delta _{\%} = \frac{\left|\nu ^{S}_{{\rm peak}} - \nu ^{S}_{{\rm peak,fit}}\right|}{\nu ^{S}_{{\rm peak}}}\times 100\%. \end{equation} \tag{ 7 }$$

The mean for Δ_% was 6.3%. The median was 3.7%. While this is not ideal, we feel it shows that the ν^S_{peak, fit}'s are still acceptable estimates for those sources without a better alternative. We were able to obtain ν^S_{peak, fit} estimates for 28 of our sources: 18 FSRQs, 8 BL Lac objects, and 2 AGNs/other objects. This brings our total number of sources with ν^S_peak values to 206.

As per the 1LAC convention, our sources were divided into three types based on their ν^S_peak: high-synchrotron-peaked (HSP, ν^S_peak > 10¹⁵), intermediate-synchrotron-peaked (ISP, 10¹⁴ < ν^S_peak < 10¹⁵), and low-synchrotron-peaked (LSP, ν^S_peak < 10¹⁴). For brevity, we will refer to the HSP BL Lac objects as "HBLs," ISP BL Lac objects as "IBLs," and LSP BL Lac objects as "LBLs." We had 42 HBLs, 24 IBLs, and 29 LBLs in our sample. We could not get good estimates of ν^S_peak for the remaining 11 BL Lac objects. For the FSRQs, 99 were LSP type and 3 were ISP type. Note that we do not have any HSP FSRQs in our sample. We could not get reliable ν^S_peak estimates for 12 of our FSRQs.

We applied the Spearman test³ (e.g., Press et al. 1986) to look for correlations between G_r and ν^S_peak in our data. We found mostly weak or tentative correlations for our sample. For the 1FGL data, the BL Lac objects had the only significant correlation with a ρ_S of 0.46 and a p of 4 × 10⁻⁴. The FSRQs in the 1FGL data had a very tentative correlation with a ρ_S of 0.24 and a p of 0.02. We plot our 1FGL data in Figure 3. For the 2FGL data, both the BL Lac objects and the FSRQs showed low-significance correlations. The 2FGL BL Lac objects had a ρ_S of 0.40 and a p of 0.003 while the FSRQs had a ρ_S of 0.28 and a p of 0.006.

Zoom In Zoom Out Reset image size

The 1FGL result tentatively confirms the findings of Lister et al. (2011), who found a good correlation for the BL Lac objects and no correlation for the FSRQs. However, the low-significance results from the 2FGL data cast some doubt on the correlation for the BL Lac objects and also call into question whether or not there is a correlation for the FSRQs. Also, note that in Figure 3 we have a handful of sources with high ν^S_peak and relatively low G_r. With our large range in both, we do not suspect a selection effect here. However, Lister et al. (2011) had significantly fewer HBLs than we had in our sample (17 versus 30), so their result of a strong, positive correlation may have been caused by a selection effect. It does not seem to be caused by the fact that they were more biased toward high flux density objects. We limited our BL Lac object sample to those brighter than 200 mJy and again to those brighter than 100 mJy, and in both cases our correlations became weaker than when we used our full sample.

A strong correlation between G_r and ν^S_peak would indicate that the synchrotron self-Compton (SSC) model for γ-ray emission is more likely. That is, the seed photons for the inverse Compton scattering to γ-ray frequencies are internal to the source (i.e., provided by the synchrotron emission) and therefore both the synchrotron and inverse Compton emission have roughly the same Doppler factors. However, the fact that we see a lower-significance correlation in the 2FGL data indicates that such a model may not be as accurate as previously thought. The tentative correlation between G_{r, 2FGL} and ν^S_peak for the FSRQs could indicate that at least some fraction of their inverse Compton emission is SSC, but their seed photon population may be enriched by photons external to the synchrotron emitting region (i.e., external inverse Compton scattering) such as the dusty torus or broad line region (BLR). Again, the low-significance value for the correlation should make one cautious in drawing such a conclusion.

We found very strong correlations between the total VLBA flux density at 5 GHz and the synchrotron peak frequency for our BL Lac objects and FSRQs. The Spearman test result on the BL Lac objects was a ρ_S of −0.56 and a p of 5 × 10⁻⁹. The results for the FSRQs were a ρ_S of −0.33 and a p of 7 × 10⁻⁴. See Figure 4 for a plot of our flux density versus ν^S_peak. The S₅–ν^S_peak correlation is expected for the BL Lac objects and was also seen by Lister et al. (2011). The higher the ν^S_peak, the lower the radio flux density is going to be at 5 GHz which will contribute to a higher G_r. The FSRQs were not expected to show such a strong correlation. Lister et al. (2011) reported that their FSRQ sample showed no sign of correlation. It is possible that, because the MOJAVE program focuses on the brightest AGNs, their sample did not contain enough low flux density objects to show a correlation. In fact, if we limit our FSRQ sample to those with S₅ > 250 mJy (excluding the 22 dimmest FSRQs with valid ν^S_peak's), we no longer see a significant correlation (ρ_S = −0.04 and p = 0.74).

Zoom In Zoom Out Reset image size

Lister et al. (2011) reported a significant linear correlation between the γ-ray loudness and γ-ray photon spectral index for their BL Lac objects. We do not see a strong indication of this in our data. We used both 1FGL and 2FGL data, and only the 2FGL data showed any hint of this correlation. However, with a ρ_S of −0.25 and a p of 0.06, it is still too low a significance to claim a correlation in our sample. See Figure 5 for a plot of the 2FGL γ-ray loudness versus γ-ray photon spectral index. We should note that while our sample covers a very large range in G_r, we do not have the low G_r (G_r < 100) objects that Lister et al. (2011) had in their sample. It is possible that adding these low G_r sources would lead to a strong correlation.

Zoom In Zoom Out Reset image size

However, we do confirm the correlation between γ-ray luminosity and γ-ray photon spectral index reported by Ghisellini et al. (2009) and Chen & Bai (2011). For the 1FGL data, the Spearman test gives a ρ_S of 0.43 and a p of 2 × 10⁻⁹ for the full sample. The 2FGL data also showed a correlation with a ρ_S of 0.35 and a p of 4 × 10⁻⁶. Breaking the sources up by type, only the BL Lac objects show a correlation in either 1FGL (ρ_S = 0.54, p = 8 × 10⁻⁶) or 2FGL (ρ_S = 0.50, p = 10⁻⁴). See Figure 6 for a plot of the 1FGL γ-ray photon spectral index versus γ-ray luminosity (the 2FGL plot looks similar and is not shown). Ghisellini et al. (2009) and Chen & Bai (2011) argue that this correlation indicates that the low-luminosity–low-ν^S_peak sources have lower black hole masses than the high-luminosity–high-ν^S_peak sources. That is, the black hole mass, not beaming, may be responsible for the observed properties of low-luminosity LBLs. However, our results from investigating the core brightness temperature and variability (below) do not support this.

Zoom In Zoom Out Reset image size

We found a correlation between the core brightness temperature and the peak synchrotron frequency for our sources. When we applied the Spearman test to the entire sample, we found a ρ_S value of −0.40 and a p of 4 × 10⁻⁹. However, when we broke the sample up by optical type, only the BL Lac objects showed a significant correlation (ρ_S = −0.55, p = 10⁻⁸). See Figure 7 for a plot of the core brightness temperature versus ν^S_peak. High core brightness temperatures are generally associated with large Doppler factors (e.g., Tingay et al. 2001). Therefore, it would seem that the LBLs are more strongly beamed than the HBLs. Recall from Section 3.3 that the HBLs also tend to have larger G_r. Combining their high G_r and low core brightness temperatures indicates that the HBLs are probably more efficient at producing γ-rays. The LBLs, on the other hand, may be seen as γ-ray loud thanks to higher Doppler factors. Lister et al. (2011) did not report finding a correlation between core brightness temperature and ν^S_peak, but they did note that their HBLs tended to have lower core brightness temperatures than the IBLs and LBLs.

Zoom In Zoom Out Reset image size

We measured the mean apparent opening half angle for each source with core–jet morphology following the procedure described in Taylor et al. (2007). This method relies on averaging the apparent opening angles found for each jet component in a source. That is, the apparent opening angle is measured for several (more than two) jet components. The half-opening angle is calculated for each component to be

$$\begin{equation} \psi = {\rm arctan}[(|y^{\prime }|+dr)/|x^{\prime }|], \end{equation} \tag{ 8 }$$

where x' and y' are the positions of the component in a rotated coordinate system with the x'-axis aligned with the jet axis, and dr is the deconvolved Gaussian size perpendicular to the jet axis. The final mean opening angle for the source is the average of all of the opening angles for the individual jet components.

Lister et al. (2011) reported a nonlinear correlation between the opening angle and the γ-ray loudness. We found a tentative correlation, however, only when we used the 2FGL data. When we performed the Spearman test on all 33 sources with both a measured opening angle and a 2FGL γ-ray flux (including the radio galaxy NGC 6251), we found a ρ_S of 0.57 and a p of 5 × 10⁻⁴. When we break the sources up by type, we only see a tentative correlation for the FSRQs (ρ_S = 0.62, p = 0.004). However the sample sizes are very small: we only had 36 objects with opening angle and G_r measurements in 1FGL, and 33 in 2FGL. The sample in Lister et al. (2011), on the other hand, contained well over 100 sources. See Figure 8 for a plot of the 2FGL γ-ray loudness versus opening angle. We should also note that Lister et al. (2011) made their measurements of the apparent opening angle using mean sizes of jet components over several epochs, not the mean of multiple apparent opening angles from several components in a single observation as we did. The fact that MOJAVE is a monitoring program makes it much better suited to investigating the apparent (and intrinsic) opening angles than our sample.

Zoom In Zoom Out Reset image size

To measure the polarization properties of our sources, we used the Gaussian mask method described by Helmboldt et al. (2007). With this method, mask images were created using the Gaussian fit components in the Stokes I image to define the core and jet components. We then created mask images using the polarized intensity maps and mask out any pixels that do not have a signal to noise of at least five (compared to the noise image generated by the AIPS task COMB). The two mask types were then combined (multiplied) and applied to both the Stokes I and polarized intensity maps. Additionally, in order to be considered "polarized," a source had to have a polarized flux of at least 0.3% of the Stokes I peak value (to avoid leakage contamination). See Linford et al. (2012) for more discussion on the polarization properties of our sources.

Lister et al. (2011) reported that the HBLs in their sample tended to have lower core fractional polarization levels. We also see an indication of this in our sample. Our Spearman test returned only a very marginal correlation between core fractional polarization and ν^S_peak for the BL Lac objects, with a ρ_S value of −0.25 and a p of 0.04. However, we do note that the maximum HBL core fractional polarization is definitely less than the maximum for the IBLs or LBLs. We did not find any correlation between core fractional polarization and ν^S_peak for the FSRQs (see Figure 9 for a plot).

Zoom In Zoom Out Reset image size

It is well known that blazars tend to be highly variable sources. It is believed that this variability is related to Doppler beaming (e.g., Hovatta et al. 2009) because small changes in bulk material velocity and/or orientation angle can lead to large changes in the observed flux. It has also been shown that Doppler beaming can shorten the apparent timescales of flaring events (e.g., Lister 2001). We used the modulation index from the Owens Valley Radio Observatory (OVRO) blazar monitoring program (Richards et al. 2011) as a measure of our sources' variability. The modulation index is the standard deviation of the distribution of source flux densities in time divided by the mean flux density. Our sample and the OVRO sample had 120 sources in common. Richards et al. (2011) reported that the FSRQs in their sample tended to have larger variability than the BL Lac objects. We did not see strong evidence for this in our sample, but we should note that our sample is considerably smaller than Richards et al. (2011). However, we did find that the HBLs tend to have relatively low variability (see Figure 10). We also found a tentative correlation between the modulation index and ν^S_peak for the both the BL Lac objects and the FSRQs. The Spearman test results for the BL Lac objects were a ρ_S of −0.33 and a p of 0.02. This is another indication that the HBLs may not be as strongly beamed as the LBLs. Interestingly, the FSRQs showed tentative positive correlation with a ρ_S of 0.34 and a p of 0.007. However, it is hard to convince oneself that such a correlation exists for the FSRQs by examining Figure 10.

Zoom In Zoom Out Reset image size

As we mentioned in Section 3.2, we opted to use the most recent published values of ν^S_peak when available. However, it is likely that there were variations in how those values were determined in different studies. An alternative to using recent published values is to use the 2LAC estimation method for as many sources as possible, and fill in the blanks with published and NED-fit values. While the 2LAC method has been shown to be a reasonable estimate of ν^S_peak, it is still an empirical estimate and does not always agree well with values calculated from fitting the spectral energy distributions (SEDs).

We created a second data set favoring the 2LAC estimates of ν^S_peak and applied the Spearman test again to look for correlation. For this secondary data set, we used the 2LAC estimated ν^S_peak values for 165 of our sources. We also used 13 published values and 28 NED-fit values when the 2LAC estimation could not be calculated. In general, the correlations reported above were still present, but with slightly reduced ρ_S values (indicating weaker correlation) and increased p values (indicating less significant correlation). We did find a handful of significant differences when relying on the 2LAC values. First, the FSRQs do not show any significant correlation for G_R and ν^S_peak in either 1FGL or 2FGL. Second, we no longer see any significant correlation between ν^S_peak and core fractional polarization for the BL Lac objects. Finally, we no longer see any correlation between ν^S_peak and the modulation index (variability) for either BL Lac objects or FSRQs. It should be noted that all the correlations that disappeared when relying on the 2LAC ν^S_peak estimates were marginal or tentative correlations using the published ν^S_peak values.