ACTIVE GALACTIC NUCLEI CLUSTERING IN THE LOCAL UNIVERSE: AN UNBIASED PICTURE FROM SWIFT-BAT

It is now commonly believed that almost all galaxies host a central supermassive black hole (SMBH). Dynamical evidence show that the mass of the central BHs are closely linked to the mass as well as the stellar velocity dispersion of the bulge component of the host galaxy (Kormendy & Richstone 1995; Magorrian et al. 1998). This suggests that the formation and evolution of the spheroidal component of galaxies and their SMBHs are closely connected. It is of utmost importance to understand the mechanism of funneling interstellar gas into the vicinities of the SMBH, triggering the accretion. Galaxy mergers or tidal interaction between close pairs may have played a major role (Hopkins et al. 2007); furthermore, some mechanism internal to the galaxy, like galaxy disk instability may be important. Clustering properties of active galactic nuclei (AGNs) in various redshifts give an important clue to understanding which of these mechanisms trigger AGN activities in what stage of the evolution of the universe, through, e.g., the mass of the dark matter halos (DMH) in which they reside, which is linked to BH mass lifetime and Eddington rate. Measurements of the AGN clustering show that AGNs are typically hosted by DMH with a mass of the order of log(M) ∼ 12.0–13.5 M/M_☉ (Yang et al. 2006; Miyaji et al. 2007; Gilli et al. 2009; Coil et al. 2009; Hickox et al. 2009; Krumpe et al. 2010). However, these measurements have been produced by using AGN samples obtained by optical and soft X-ray (i.e., 0.5–10 keV) surveys. Optical and soft X-ray selections miss a major part of the SMBH accretion. In the optical band, the selection of AGNs is biased by galaxy starlight dilution and by dust absorption. Although luminous soft X-ray emission is a signature of the presence of an AGN, absorbed sources can be missed with a soft X-ray selection, either because they are intrinsically less luminous (Hasinger 2008) or because of the high column density. However, X-ray emission from these sources leaks out at higher energies (i.e., >5–10 keV) where the efficiency of instruments mounting X-ray focusing optics is low. For this reason, hard X-ray selected samples could provide clean and unbiased samples of AGNs. The Swift-BAT all-sky survey provides a spectroscopically complete (100%) sample of local AGNs detected in the 15–55 keV energy band, with an unprecedented depth and characterization of the source properties, from redshifts to column densities. In this Letter, we present the first study of clustering of hard X-ray selected AGNs in the local universe. Throughout this Letter, we will assume a Λ-CDM cosmology with Ω_m = 0.3, Ω_Λ = 0.7, H₀ = 100h⁻¹ km s⁻¹ Mpc, and σ₈ = 0.8. Unless otherwise stated, errors are quoted at the 1σ level.

The Burst Alert Telescope (BAT; Barthelmy et al. 2005) on board the Swift satellite (Gehrels et al. 2004) represents a major improvement in sensitivity for imaging the hard X-ray sky. BAT is a coded mask telescope with a wide field of view (FOV, 120°×90° partially coded) aperture sensitive in the 15–200 keV domain. Thanks to its wide FOV and its pointing strategy, BAT continuously monitors up to 80% of the sky every day achieving, after several years of survey, deep exposure in the entire sky. Results of the BAT survey (Markwardt et al. 2005; Ajello et al. 2008; Tueller et al. 2010) show that BAT reaches a sensitivity of ∼1 mCrab⁸ in 1 Ms of exposure.

The sample used in this work consists of 199 non-blazar AGNs detected by BAT during the first three years and precisely between 2005 March and 2008 March. This sample is part of the one used in Ajello et al. (2009) which comprises all sources detected by BAT at high (|b|>15°) Galactic latitude and with a signal-to-noise ratio (S/N) exceeding 5σ. The reader is referred to Ajello et al. (2009) for more details about the sample and the detection procedure. The flux limit at each direction in the sky has been computed, following Ajello et al. (2008), analyzing the local background around that position. For each source, we use the redshift already provided in Ajello et al. (2009) and the measurement of the absorbing column density as determined from joint XMM-Newton/XRT–BAT fits (D. Burlon et al. 2010, in preparation). The redshift distribution of the sample is shown in Figures 1 together with the redshift cone diagram of the survey up to 20,000 km s⁻¹ (z ∼ 0.07).

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The two-point autocorrelation function (ACF, ξ(r)) describes the excess probability over random of finding a pair with an object in the volume dV₁ and another in the volume dV₂, separated by a distance r so that dP = n²[1 + ξ(r)]dV₁dV₂, where n is the mean space density. A known effect when measuring pairs separations is that the peculiar velocities combined with the Hubble flow may cause a biased estimate of the distance when using the spectroscopic redshift. To avoid this effect, we computed the projected ACF (Davis & Peebles 1983): $w(r_p)=2\int _{0}^{\pi _{\rm max}}\xi (r_p,\pi)d\pi$, where r_p is the distance component perpendicular to the line of sight and π parallel to the line of sight (Fisher et al. 1994). It can be demonstrated that, if the ACF is expressed as ξ(r) = (r/r₀)^−γ, then

$$\begin{equation} w(r_{p})=A(\gamma)r_{0}^{\gamma }r_{p}^{1-\gamma }, \end{equation} \tag{ 1 }$$

where A(γ) = Γ(1/2)Γ[(γ − 1)/2]/Γ(γ/2) (Peebles 1980).

The ACF has been estimated by using the minimum variance estimator described by Landy & Szalay (1993):

$$\begin{equation} \xi (r_p,\pi)=\frac{\rm DD-2DR+RR}{\rm RR}, \end{equation} \tag{ 2 }$$

where DD, DR, and RR are the normalized number of data–data, data–random, and random–random source pairs, respectively. Equation (2) indicates that an accurate estimate of the distribution function of the random samples is crucial in order to obtain a reliable estimate of ξ(r_p, π). Several observational biases must be taken into account when generating a random sample of objects in a flux limited survey. In particular, in order to reproduce the selection function of the survey, one has to carefully reproduce the space and flux distributions of the sources, since the sensitivity of the survey in not homogeneous on the sky. Simulated AGNs were randomly placed on the survey area. In order to reproduce the flux distribution of the real sample, we followed the method described in Mullis et al. (2004). The cumulative AGN logN–logS source count distribution, in the 15–55 keV band, can be described by a power law, S = kS^−α, with α ∼ 1.55 (Ajello et al. 2008). Therefore, the differential probability scales as S^−(α+1). Using a transformation method, the random flux above a certain X-ray flux S_lim is distributed as $S=S_{\rm lim}(1-p)^{\frac{-1}{\alpha }}$, where p is a random number uniformly distributed between 0 and 1 and S_lim = 7.6 ×10⁻¹² erg cm⁻² s⁻¹. All random AGNs with a flux lower than the flux limit map at the source position were excluded. Redshifts were randomly drawn from the smoothing of the real redshift distribution with a Gaussian kernel with σ_z = 0.3. An important choice for obtaining a reliable estimate of w(r_p) is to set π_max in the calculation of the integral above. One should avoid values of π_max too large since they would add noise to the estimate of w(r_p). If, instead, π_max is too small one could not recover all the signal. We have calculated w(r_p) by varying π_max and found that the result converges at π_max∼60 Mpc h⁻¹.

Errors on w(r_p) were computed with a bootstrap resampling technique with 100 realizations. It is worth noting that in the literature, several methods are adopted for error estimates in two-point statistics, and no one has been proved to be the most precise. However, it is known that Poisson estimators generally underestimate the variance because they do consider that points in ACF are not statistically independent. Jackknife resampling method, where one divides the survey area in many sub-fields and iteratively re-computes correlation functions by excluding one sub-field at a time, generally gives a good estimates of errors. But it requires that sufficient number of almost statistically independent sub-fields. This is not the case for our small sample. For these reasons, we used the bootstrap resampling for the error estimates which, in our case, are comparable with the Poisson errors.

We show in Figures 2 the projected ACF measured on the whole AGN sample of the survey. The ACF has been evaluated in the projected separation range ∼0.2 Mpc h⁻¹ <r_p< 200 Mpc h⁻¹ and has been plotted in form of w(r_p)/r_p in order to reproduce the slope of ξ(r) (see above). The bin size for computing w(r_p) has been set to Δlog(r_p, π) = 0.15. We obtained an estimate of w(r_p)/r_p with a significance of the order 4σ–5σ. In order to evaluate the power of the clustering signal, we fitted w(r_p) with χ² minimization technique by using Equation (1) as a model with r₀ and γ as free parameters. The correction due to the integral constraint (Peebles 1980) is estimated to be much smaller than the statistical uncertainties in our sample, and thus has not been made. As a result, we obtained r₀ = 5.56^+0.49_−0.43 Mpc h⁻¹ and γ = 1.64^+0.07_0.08. The confidence contours of the fit are presented in Figures 2. We also measured the ACF for different data subsamples. We first divided the sample according to the column density: we defined as Type II AGN (or absorbed) sources with log(N_H)⩾ 22 cm ⁻² and as Type I AGN (or unabsorbed) sources if log(N_H)< 22 cm ⁻². As a result, we constructed a sample of 96 Type I AGNs and one of 103 Type II AGNs. For both samples, we computed the ACF with the technique described above. We also split the sample into high- and low-luminosity subsamples. All the sources with L_15–55 > 43.2 erg s⁻¹ (i.e., the median luminosity of the whole sample, HL sources) were classified as high luminous, while the sources with L_15–55< 43.2 erg s⁻¹ (LL sources) as low-luminosity sources. The results of the measurement of the ACF as a function of the source type and luminosity class are presented in Figures 2 together with the fit confidence contours. Note that for the HL sample, the fit parameters are poorly constrained because of the lack of close pairs in the sample. We also repeated the fit by freezing γ to 1.7, and obtained consistent results (Table 1). A summary of the fit results of all the samples used here is given in Table 1. Type I AGNs show a larger correlation with respect to that of type II AGNs, the significance of this difference is of the order ∼2.7σ–3.3σ. HL AGNs show a 1.7σ–4.6σ higher correlation length with respect to LL AGNs. We also checked the correlation between r₀ and <L_X > of all the subsamples and found a linear correlation coefficient R = 0.95, which corresponds to a ∼2σ significant correlation. We can use the weighted mean dispersion of the results on the measurement of r₀ in our subsamples to estimate the impact of sample variance on our results under the assumption that this is the main reason of the fluctuations. Our estimates suggest that overall our results are affected by this effect at ∼10% level. It is worth to note that our results are more significant than those obtained by, e.g., Mullis et al. (2004), with a similar number of sources. This is because our sources are distributed in a much smaller volume than that sampled by the NEP survey and, by being on average less luminous, have an intrinsic higher space density resulting in a larger number of close source pairs.

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Table 1. Summary of the Results

Sample	Na	<z>	<log(LX)>	r0	γ	$r_{0_{\gamma \,=\,1.7}}$b
			(erg s−1)	(Mpc h−1)		(Mpc h−1)
All	199	0.045	43.2	5.56+0.49−0.43	1.64+0.07−0.08	5.54+0.1−0.1
Type I	96	0.046	43.37	7.93+1.14−0.79	2.1+0.20−0.25	8.12+1.57−1.00
Type II	103	0.024	42.87	4.72+0.60−0.70	1.78+0.24−0.17	4.90−0.70+0.20
HL	99	0.054	43.67	13.92+5.48−6.69	1.41+0.15−0.19	15.63+1.57−2.57
LL	100	0.023	42.55	3.37+0.51−0.68	1.86+0.25−0.17	3.56+0.15−0.66

Notes. ^aNumber of sources in the Sample. ^br₀ obtained by freezing γ = 1.7 in the fit.

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In the linear theory of structure formation, the bias factor defines the relation between the ACF of large-scale structure tracers and the underlying overall matter distribution. In the case of X-ray selected AGNs, we can define the following relation: ξ_X(r, z) = b_X(r, z)²ξ_m(r, z), where ξ_X, ξ_m, and b_X are the ACF of AGNs, DM, and the AGN bias factor, respectively. In order to compute the b_X, we estimated the amplitude of the fluctuations of the AGN distribution in a sphere of 8 Mpc h⁻¹ (also know as σ₈), by using Equations (12) and (13) of Miyaji et al. (2007) and all the combinations of r₀ and γ are reported in Table 1. In order to derive the bias factor of the AGNs in our samples, we used b_AGN = σ_8,AGN(z)/σ₈D(z), where D(z) is the growth factor. This quantity allows us to compare the observed AGN clustering to the underlying mass distribution from linear growth theory (Hamilton 2001). As a result, we obtain for the whole sample b_AGN(z ∼ 0.04) = 1.21^+0.06_−0.07. We have repeated this calculation for all the samples listed in Table 1, and we report the corresponding values of the bias factor in Table 2 for all the possible best-fit results.

Table 2. Bias Factor and Mass of the Dark Matter Halos Hosts of the AGNs in the Samples

Sample	baX	MbDM	τcAGN	log(MBH)d	log()e	Mf
		log(M/h−1M☉)	(Gyr)	log(M/M☉)		(1010/M☉)
All	1.21+0.06−0.07	13.15+0.09−0.13	0.68	8.51	−1.96	18.2
Type I	2.01+0.15−0.13	13.94+0.15−0.21	4.99	8.79	−2.02	31.6
Type II	1.08+0.26−0.29	12.92+0.11−0.38	1.32	7.96	−1.85	6.38
HL	2.28+0.95−0.90	14.08+0.37−0.70	3.91	9.28	−2.12	80.5
LL	0.80+0.06−0.16	11.89+0.34−∞	0.24	7.43	−1.68	2.28

Notes. ^aAGN bias factor. ^bMass of the typical dark matter halo hosting an AGN. ^cAGN duty cycle in Gyr. ^dBlack hole mass. ^eEddington ratio. ^fStellar mass of the bulge.

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It is widely accepted that the clustering amplitude of DMH depends primarily on their mass (see, e.g., Sheth et al. 2001). In this way, we can estimate the typical mass of the DMH in which the population of AGNs reside, under the assumption that the typical mass of the host halo is the only variable that causes AGN biasing. We have then computed the expected large-scale bias factor for different dark matter halo masses by using the prescription of Tinker et al. (2005). The required ratio of the critical overdensity to the rms fluctuation on a given size and mass is calculated by ν = δ_cr/σ(M, z), for our purposes we assumed δ_cr ≈ 1.69 and compute σ₈(M, z) and therefore b(M, z) using Equations (A8)–(A10) in van den Bosch (2002). The typical DMH mass that hosts an AGN has been estimated to be log(M_DMH) = 13.15^+0.09_−0.13 h⁻¹M/M_☉. This is consistent with similar measurements in the local universe of Krumpe et al. (2010), Grazian et al. (2004), and Akylas et al. (2000). We have computed the typical mass of the DMH for all the subsamples listed in Table 1 and reported for simplicity in Table 2. Following Martini & Weinberg (2001), by knowing the AGN and DMH halo space density at a given luminosity and mass (n_AGN, n_DMH), one can estimate the duty cycle of the AGN, $\tau _{\rm AGN}(z)=\frac{n_{\rm AGN}(L,z)}{n_{\rm DMH}(M,z)}\tau _H(z)$, where τ_H(z) is the Hubble time at a given redshift.⁹ For the whole sample at z ∼ 0, n_DMH∼ 6.7 × 10⁻⁴ Mpc⁻³ (Hamana et al. 2002) and n_AGN∼ 3.4 × 10⁻⁵ Mpc⁻³ (Sazonov et al. 2007) which leads to an estimate of τ_AGN(z = 0)∼0.68 Gyr. To fully characterize our sample, we derived the average properties of the active BHs and their host galaxies. By using the bolometric correction prescribed by Hopkins et al. (2007), we estimated from <L_X >, <L_Bol >, and <L_B > (B-band luminosity). L_B is related to the black holes mass and the stellar mass of the host galaxy via scaling relations (Marconi & Hunt 2003). From <M_BH >, we derived <L_Edd > and the Eddington rate =<L_Bol>/<L_Edd > (see Table 2 for a summary). We point out that the estimates obtained above have several limitations which mostly arise from the uncertainties on scaling relations and from the broad range of luminosities sampled here. We therefore consider these values as estimate for the "average" local AGN population.

In this Letter, we report on the measurement of clustering of 199 AGNs in the local universe using the Swift-BAT all-sky survey sample. This result gives, for the first time, an unbiased picture of the z = 0 DMH–galaxy–AGN coexistence/evolution. We obtained a correlation length r₀ = 5.56^+0.49_−0.43 Mpc h⁻¹ and γ = 1.64^+0.07_−0.08. We measured the ACF for Type I and Type II AGNs and found a significant difference in their correlation lengths. We have measured a marginally significant higher r₀ for high-luminosity AGNs than for the low-luminosity ones. We propose that the observed difference in Type I versus Type II clustering is driven by the intrinsic higher <L_X > of Type I AGNs, as we show a marginal evidence of a correlation between r₀ and L_X. We estimated the typical mass of the DMH hosting an AGN of the order log(M_MDH) ∼ 13.15 h⁻¹M/M_☉. In Figures 3, we show the bias-redshift plane results from AGN and galaxy surveys (references in the figure). In the same plot, we show the expected evolution of different DMH masses. We compared only bias values of studies that rely on the real space correlation function ξ(r) (values of σ_8,AGN/GAL from Krumpe et al. 2010). This approach allows us to compare all different clustering studies on a common basis.

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The majority of the X-ray surveys agree with a picture where AGNs are typically hosted in DM halos with mass of the order of 12.5 h⁻¹M/M_☉< log(M_MDH) < 13.5 h⁻¹M/M_☉ which is the mass of moderately poor group. Optically selected AGNs instead reside in lower density environment and of the order of the log(M_MDH) ∼ 12.5 h⁻¹M/M_☉. Another interesting aspect is that X-ray selected AGN samples (including ours) cluster similarly to red galaxies and that LL AGNs or type II AGNs are found typically in less-massive environments. On the contrary, HL AGNs and Type I AGNs are hosted in massive galaxies in massive DM halos (clusters).

We estimated that Swift-BAT AGNs are powered by black holes with a typical mass log(M_BH/M_☉) ∼ 8.5, accreting at very low Eddington ratio (i.e., ∼0.01 L_Edd) and that they are hosted by massive galaxies with mass of the order ∼2 × 10¹¹ M/M_☉. These properties, except , scale with <L_X > and Type (HL and Type I are hosted in higher mass DMH in more massive galaxies with bigger black holes). The upper limits on the duty cycle suggest that these AGNs are shining since at least for 0.2–1.2 Gyr.¹⁰

We then tested the AGN merger-driven triggering paradigm by comparing the theoretical predictions for AGN clustering of the model of Marulli et al. (2008) and Bonoli et al. (2009) with our results on the whole sample. The theoretical model is based on the assumption that AGN activity is triggered by galaxy mergers and the light curve associated to each accretion event is described by an Eddington-limited phase followed by a quiescent phase modeled after Hopkins et al. (2005). Applied to the Millennium Simulation (Springel et al. 2005), such model has been shown to be successful in reproducing the main properties of the black hole and AGN populations (Marulli et al. 2008) and the clustering of optical quasars (Bonoli et al. 2009). Using this model, we computed the expected correlation length of a sample of simulated AGNs at z∼0 with intrinsic L_bol luminosities similar to the ones of our observed AGNs. The model predicts a clustering length r₀ = 5.68 ± 0.08 which is in agreement within 1σ with our measurement.

By merging the observational evidences and the model predictions, a plausible scenario for the history of local AGNs is the following.

• 1.  
  Swift-BAT AGN switched on about 0.7 Gyr ago after a galaxy merger event.
• 2.  
  They shine in an Eddington-limited regime for the first part of their lives where they gain most of their mass.
• 3.  
  In the second phase of their lives (i.e., after 0.2–0.5 Gyr), they start to accrete with lower and lower efficiency. Their luminosity drops because of the decreased gas reservoirs.
• 4.  
  At z∼ 0, they have grown to ∼10⁸–10⁹ M/M_☉ SMBHs, shining as moderately low-luminosity AGNs at low accretion rates.

We thank Gigi Guzzo, Roberto Gilli, Angela Bongiorno, and Simon White for the useful comments. Support from NASA NNX07AT02G, CONACyT 83564, PAPIIT IN110209 is acknowledged.