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# Environmental and Clustering Properties of BL Lac and FSRQ Blazars

Abstract

We present results from a large-scale study of the megaparsec-scale environments of blazars, including BL Lac objects and flat-spectrum radio quasars. Using the catalog of galaxies from the Sloan Digital Sky Survey DR10 catalog, we compute spatial covariance amplitudes for a sample of 757 blazars. The covariance amplitudes are analyzed to compute the relative levels of clustering for various blazar types. We also compare the clustering of blazars to FR I and FR II radio galaxies to explore possibility of a parent population in the context of a blazar sequence. Finally, we present preliminary results on the morphologies of galaxies located within 1 Mpc of blazars, with classifications supplied by Galaxy Zoo data.

# Introduction

The standard model of blazars presumes that they are active galaxies with a jet closely aligned to the observer’s line of sight. Observationally, blazars can be distinguished from other active galaxies with a variety of diagnostics, including extreme luminosities and non-thermal spectra dominated by relativistic beaming.

The population of blazars displays significant observational diversity, however. The primary historical method of classification has been through the optical spectrum of the blazar, dividing them into two groups: (1) BL Lacs, characterized by weak or non-existent optical emission lines, and (2) flat-spectrum radio quasars (FSRQs), which have strong, broad emission lines in their optical spectrum. An enduring question for many years has been whether BL Lacs and FSRQs comprise physically distinct populations of galaxies, or whether a sequence exists between the two groups.

Since highly-beamed emission from the relativistic jet often dominates the light observed from the blazar, studies of the host galaxy itself are challenging. As an alternative approach, we study the clustering properties of blazars in an attempt to determine their parent populations. Clustering studies benefit from the fact that they are assumed to be independent of the blazar’s orientation to our line-of-sight. Differences in the clustering properties on scales of hundreds of kpc are already known to exist, for example, in the density-morphology relation (Dressler, 1980) and in the populations of powerful radio galaxies (Prestage et al., 1988).

Previous clustering studies of blazars have been limited by sample sizes of only a few tens. Wurtz et al. (1997) carried out a deep, largely subarcsec imaging survey of BL Lac objects conducted at the CFHT. Wurtz et al. (1993) described the results pertaining to the host galaxies of 50 BL Lac objects at $$z<0.65$$; Wurtz et al. (1997) report on the clustering environment of 45 of these 50 BL Lacs. The remaining five objects either have unknown or very uncertain redshifts or we were unable to obtain deep, photometrically calibrated images of them, which prohibited successful clustering analysis.

With this substantially larger (45 vs. 5) sample, Wurtz et al. (1997) confirmed the early result of Prestage et al. (1988) that BL Lac objects largely avoid rich clusters at low redshift and have distributions in $$B$$ richness measurements much more consistent with those of FR II radio galaxies than with FR I’s. The typical environment of a BL Lac object is a sub-Abell richness class 0 cluster with a CFHT sample mean of $$\langle$$$$B_{gB}$$$$\rangle=209$$ Mpc$$^{1.77}$$. Further, these results apply to all types of BL Lac objects regardless of selection method (e.g., radio or X-ray selection) or detailed property (e.g., high or low optical polarization percentage, presence/absence of emission lines etc.) because no BL Lac subtype has statistically distinct $$B_{gB}$$ values. The only exceptions to this statement are correlations between redshift and $$B_{gB}$$ and between host galaxy luminosity and $$B_{gB}$$, and a possible anticorrelation between $$B_{gB}$$ and radio core dominance.

Smith et al. (1995) computed $$B_{gB}$$ for 16 BL Lac galaxies and six FR I galaxies; their respective correlation amplitudes were statistically indistinguishable for the small sample sizes, consistent with an Abell richness class of 0.

Mention blazar envelope/sequence work, and possibility of how environment studies play into the larger scientific goal.

With the release of the Sloan Digital Sky Survey (SDSS), we have for the first time a large and deep catalog with nearly uniform photometry and coverage out to redshifts greater than 1. We combine the SDSS data with the latest identifications of blazars, for which counts are now in the thousands. The larger sample size allows for the first time robust classification of blazar clustering properties, which we compare to other data to explore the possible parent population(s).

# Measuring the clustering properties

\label{sec-methods}

There are a number of diagnostics used to quantify the local density of galactic environments, including two- and three-dimensional correlation functions, luminosity density fields, $$N^{{\rm th}}$$-nearest neighbors, and distance to the nearest cluster or group. We analyze blazars by measuring the spatial covariance amplitude $$B$$ (Longair et al., 1979). A significant advantage of this method is that it can be applied to projected neighbors without knowing the true three-dimensional distribution of neighboring galaxies, which would be required for density field or nearest neighbor techniques. Accurate redshifts are not available for most galaxies in the survey we use (SDSS), especially at redshifts $$z>0.2$$. The technique is well-established in the literature of active galaxy environments (e.g., Prestage et al., 1988; Yee et al., 1987; Ellingson et al., 1989; Wurtz et al., 1997) and so our results can be compared to other studies. Finally, the method has been shown to be robust independent of the magnitude limit of observations or the counting radius of neighbors. The major disadvantage of the method is that it is a statistical measurement, and so uncertainties on individial measurements are typically quite large. We mitigate this by computing $$B$$ for several hundred sources and analyzing the statistics of the group, rather than focusing on individual objects.

The technique for computing $$B$$ is briefly described here. For any population of objects as viewed on the sky in the far-field limit, its angular distribution can be approximated by:

$\label{eqn-angcov} n[\theta]d\Omega = N_g (1 + w[\theta]) d\Omega,$

where $$n[\theta]d\Omega$$ is the number of galaxies in a ring of solid angle $$d\Omega$$ at angular distance $$\theta$$ from the center of the ring. $$N_g$$ is the number of background galaxies in the ring, and the factor of $$(1+w[\theta])$$ expresses the probability of finding additional galaxies over the background level. $$w[\theta]=0$$ would correspond to a uniform angular distribution of galaxies in the universe (no clumping).

The standard assumption, confirmed with deep optical observations of field galaxies, is that the angular distribution of galaxies follows a power law such that:

$\label{eqn-wtheta} w[\theta] = A\theta^{1-\gamma},$

where $$A$$ is the angular covariance amplitude and $$\gamma$$ an index describing the slope of the power-law distribution. The amplitude of $$A$$ for a particular system, then, determines the degree of clustering with respect to other similarly-scaled structures in the universe.

Since this derivation has been completely general so far, we note that subscripts are used with computing the covariance amplitudes to indicate the type of object measured. For instance, $$A_{gg}$$ represents the galaxy-galaxy correlation amplitude, while $$A_{gB}$$ is the galaxy-BL Lac correlation amplitude.

Without a distance dependence, $$A$$ can be computed for any point on the sky by simply integrating Equation \ref{eqn-angcov} from 0 out to $$\theta$$. This gives:

$\label{eqn-angint1} \int^\theta_0 n[\theta^\prime]d\Omega = \int^\theta_0 N_g (1 + w[\theta^\prime]) d\Omega.$

The solid angle subtended by an angle of $$2\theta$$ is $$\Omega=2\pi(1-cos[\theta])$$; for $$\theta\ll1$$, this translates to a differential:

$d\Omega \simeq 2\pi \theta d\theta.$

Integrating Equation \ref{eqn-angint1} over the angle yields:

\begin{aligned} \int^\theta_0 n[\theta^\prime] 2 \pi \theta d\theta & = & \int^\theta_0 N_g (1 + w[\theta^\prime]) 2 \pi \theta d\theta \\ 2\pi \int^\theta_0 \theta^\prime n[\theta^\prime]d\theta & = & 2 \pi N_g \int^\theta_0 \theta^\prime (1 + A {\theta^\prime}^{1-\gamma}) d\theta \\ N_t \left(\frac{\theta^2}{2}\right) & = & N_g \left(\frac{\theta^2}{2} + \frac{A\theta^{3-\gamma}}{3-\gamma}\right),\end{aligned}

where $$N_t$$ is the integrated total number of galaxies within the circle. Solving for $$A$$, this gives:

\begin{aligned} A = \frac{N_t - N_g}{N_g} \left(\frac{3-\gamma}{2}\right) \theta^{\gamma-1}.\end{aligned}

Therefore, the angular covariance amplitude can be calculated for any galaxy as a function of the total number of galaxies in the field ($$N_t$$), the assumed background counts from a control field ($$N_g$$), the power-law index $$\gamma$$, and the field size $$\theta$$. We assume a canonical value of $$\gamma=1.77$$. The size of the field is determined by the scales used to derive the power-law dependence of $$w[\theta]$$; typical values are $$\theta\leq1.5^\circ$$.

For a three-dimensional distribution of galaxies around some point in space, its spatial distribution can be parameterized as:

$n[r]dV = \rho_g (1 + \xi[r]) dV,$

where $$n[r]dV$$ is the number of galaxies in a spherical shell at distance $$r$$ from the center. $$\rho_g$$ is the spatial density of background galaxies in the shell, and the factor of $$(1+\xi[r])$$ expresses the probability of finding additional galaxies over the background level.

If the de-projected angular distribution in Equation \ref{eqn-wtheta} is a power-law, then the spatial distribution will also follow a power-law with an index of $$-\gamma$$ (due to the increase in dimensions):

$\xi[r] = Br^{-\gamma}.$

Here, $$B$$ is the spatial covariance amplitude, with subscripts indicating the pairs of objects for which the correlation function is computed (similar to $$A$$).

Longair et al. (1979) project the spatial covariance function into angular space to establish a relationship between $$A$$ and $$B$$:

$\label{eqn-atob} B = \frac{A~N_{bg}[m]}{I_\gamma} \frac{D^{\gamma-3}}{\Psi[M(m,z)]}.$

Substituting for $$A$$, this gives the final form:

$\label{eqn-bgb} B = (N_t - N_{bg})\frac{(3-\gamma) D^{\gamma-3} \theta^{\gamma-1}}{2 A_\theta I_\gamma \Psi[M(m,z)]}$

Here, $$m$$ is the apparent magnitude completeness limit of the observation; depending on the redshift $$z$$, this is translated into an absolute magnitude limit $$M(m,z)$$. $$D$$ is the angular diameter distance1 to the source. $$\Psi[M]$$ is the normalized integral luminosity function of galaxies in the field down to brightnesses of $$M$$. $$n_{bg}[m]$$ is the surface density of background galaxies brighter than $$m$$, and $$I_\gamma$$ is an integration constant dependent on the index of the power-law. For the assumed value of $$\gamma$$, $$I_\gamma=3.87$$.

Since $$B$$ is impossible to measure directly without explicit data on the three-dimensional positions of all objects in the field (often not possible for fields of view with many faint objects), the standard technique is to measure $$A$$ from deep exposures and use Equation \ref{eqn-atob} to determine $$B$$. Therefore, measuring $$B$$ for any particular field requires:

• $$\theta$$ - angular size of the field

• $$m$$ - apparent magnitude limit of the observation

• $$z$$ - redshift of the target

• $$N_t$$ - total number of galaxies in the field

• $$N_g$$ - the expected background counts of galaxies down to $$m$$

• $$\Psi[m,z]$$ - luminosity function of galaxies down to $$m$$ at redshift $$z$$

The uncertainty in a value of $$B$$ can also be calculated as a function of the total number of background and galaxy counts:

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