A TALE OF TWO POPULATIONS: THE CONTRIBUTION OF MERGER AND SECULAR PROCESSES TO THE EVOLUTION OF ACTIVE GALACTIC NUCLEI

In order to determine the space density of AGNs triggered at each redshift, the space density of gas-rich massive galaxies at redshift z must be calculated. First, the minimum stellar mass of a massive galaxy, M^min_*, at z is derived by parameterizing the median mass of ultra-luminous infrared galaxies (ULIRGs) as a function of redshift (Treister et al. 2010a), which gives

$$\begin{equation} M_*^{{\rm min}}(z) = 5 \times 10^{11} (1.0+z)^{-1.5} M_{\odot }. \end{equation} \tag{ 1 }$$

The space density of massive galaxies at z, N_gal(M_* > M^min_*(z)), in Mpc⁻³, can then be calculated by integrating the stellar mass function (SMF) from M^min_*(z) to M^max_* = 10^12.5 M_☉, such that

$$\begin{equation} N_{{\rm gal}}(M_*>M_*^{{\rm min}}(z)) = \int _{M_*^{{\rm min}}(z)}^{M_*^{{\rm max}}} \frac{d\Phi _{{\rm gal}}(M_*,z)}{d\log M_*}d \log M_*, \end{equation} \tag{ 2 }$$

where dΦ_gal/dlog M_* is the SMF of Pérez-González et al. (2008) for z ≲ 4. The dependence of the results on the SMF is considered in Sections 4.1 and 4.2. To determine the space density of gas-rich massive galaxies, the fraction of gas-rich galaxies at z, f_g(z), must be determined. Considering observations of the GOODS fields (Dahlen et al. 2007), Treister et al. (2010a) find that f_g(z) can be parameterized as

$$\begin{equation} f_g(z) = \left\lbrace \begin{array}{@{}ll}0.11(1+z)^{2.0} & z\le 2 \\ \ms 1 & z>2 \end{array}\right.\!\!. \end{equation} \tag{ 3 }$$

Thus, the space density, in Mpc⁻³, of potential AGN host galaxies at redshift z is f_g(z)N_gal(M_* > M^min_*(z)).

The space density of AGNs triggered by a merger at redshift z is then calculated by multiplying the space density of potential AGN host galaxies at z by the fraction of massive galaxies that will undergo a merger at z. Following Hopkins et al. (2010a), who derive the major merger rate per galaxy per Gyr, d²Ψ/dt dN, from simulations and observational constraints, we parameterize d²Ψ/dt dN as

$$\begin{equation} \frac{d^2 \Psi }{dt\,dN} = A \big(M_*^{{\rm min}} \big)(1.0+z)^{\beta (M_*^{{\rm min}})}, \end{equation} \tag{ 4 }$$

where

$$\begin{equation} A(M_*) = 0.02\left[1+\left(\frac{M_*}{2\times 10^{10} M_{\odot }}\right)^{1/2}\right] \textnormal {Gyr}^{-1} \end{equation} \tag{ 5 }$$

and

$$\begin{equation} \beta (M_*) = 1.65\hbox{--}0.15\log \left(\frac{M_*}{2\times 10^{10} M_{\odot }}\right). \end{equation} \tag{ 6 }$$

Here, the major merger is said to occur upon the coalescence of the two similarly massive galaxies (Hopkins et al. 2010b). By assuming that every major merger leads to an AGN event, with a negligible time delay between the merger and the triggering of the AGN activity, the space density of AGNs triggered by major mergers, dN_merg, at redshift z is

$$\begin{equation} {\it dN}_{{\rm merg}} (z) = \frac{d^2 \Psi }{{\it dN}\, {\it dt}} \,N_{{\rm gal}}\big(M_* > M_*^{{\rm min}}(z)\big) \,f_{g}(z)\, dt \, \textnormal {Mpc}^{-3}. \end{equation} \tag{ 7 }$$

The rate at which AGNs are triggered through secular processes, such as galaxy interactions, cold gas accretion, and internal disk instabilities, is calculated in a similar manner. For AGNs triggered by secular processes, M^min_*(z) = 5 × 10⁹ M_☉, in agreement with the findings of Schawinski et al. (2010b). The fractional rate of massive gas-rich galaxies that are triggered through secular processes every Gyr, f_sec, is assumed to be constant with redshift. Yamada et al. (2009) found that the fraction of galaxies with M_* > 10¹¹ M_☉ hosting AGNs, which are triggered through both secular processes and mergers, is ∼0.3. As the fraction of AGNs triggered by secular processes is poorly constrained observationally, and we are considering galaxies with M_* > 5 × 10⁹ M_☉, the constraint f_sec ≪ 0.3 Gyr⁻¹ is used. The specific value of f_sec is set by calculating the predicted AGN HXLF and minimizing a χ² test that compares against the observed HXLF. The space density of AGNs triggered by secular mechanisms, dN_sec, at redshift z is then

$$\begin{equation} {\it dN}_{{\rm sec}} (z) = f_{{\rm sec}} \,N_{{\rm gal}}\big(M_* > M_*^{{\rm min}}(z)\big) \,f_{g}(z)\, dt \, \textnormal {Mpc}^{-3}. \end{equation} \tag{ 8 }$$

Once the AGN has been triggered, its Eddington ratio is used to parameterize the accretion as a function of time since the AGN was triggered. While there is evidence that AGNs are an intermittent phenomenon, Treister et al. (2010a) show that quasars can grow most of their black hole mass in a single, merger-triggered event. Therefore, a single-peaked light curve is assumed.

Based on hydrodynamical simulations, Hopkins & Hernquist (2009) suggest

$$\begin{equation} \lambda (t) = \left[1+(\vert t\vert /t_Q)^{1/2}\right]^{-2/\beta }, \end{equation} \tag{ 9 }$$

where t = t_on − t_Q, where t_on is the time since the AGN was triggered, t_Q = t₀η^β/(2βln 10), and t₀, η, and β are fitting parameters that describe the quasar lifetime, maximum Eddington ratio, and light-curve slope, respectively.¹

By combining the triggering rate and light curve, the space density of AGNs with Eddington ratio λ can be calculated at any redshift z ≲ 4. However, to compute model predictions that can be compared to observational constraints, the black hole mass must be used to convert Eddington ratios into bolometric luminosities. Once the bolometric luminosity is computed, the Marconi et al. (2004) bolometric correction is used to determine L_X. The distribution of black hole masses is determined by the fractional ABHMF at z, which describes the fraction of active black holes at redshift z with black hole mass M_•.

Two ABHMFs are considered. The first ABHMF is a Gaussian fit to the combined type 1 and type 2 AGN ABHMF at z ∼ 0.15 observed by Netzer (2009). The second ABHMF considered is a Schechter function with the same slope and critical mass, M_crit, as the black hole mass function described by Merloni & Heinz (2008). Both ABHMFs are considered over the range log (M^min_•/M_☉) = 5.95 and log (M^max_•/M_☉) = 10.55. A black hole with M_• < M^min_• would need to accrete at Eddington ratio λ ≳ 0.1 to achieve log L_X ≳ 41.5. According to the light curve used here, the vast majority of the AGN lifetime is spent at λ < 0.1. Therefore, black holes with M_• < M^min_• are expected to only make a very small contribution to the observed AGN population (Marconi et al. 2004; Merloni & Heinz 2008). Black holes with M_• > M^max_• correspond to ≪ 0.1% of all active black holes according to both the Merloni & Heinz (2008) and Netzer (2009) ABHMFs, in agreement with the maximum black hole mass derived by Natarajan & Treister (2009).

Both the Merloni & Heinz (2008) and Netzer (2009) ABHMFs are derived using scaling relationships to determine black hole masses. These scaling relationships have an intrinsic scatter of ∼0.3 dex (Peterson & Bentz 2006; Merloni & Heinz 2008; Netzer 2009). This leads to an uncertainty in the calculated L_X of a factor ∼2 × λ. For the majority of sources, λ < 0.1; thus, the uncertainty introduced by the ABHMF is a smaller part of the error budget than the uncertainty in the major merger rate, which is a factor ∼2.

For both ABHMFs two redshift evolutions are investigated. The first ABHMF evolution uses the continuity equation (Small & Blandford 1992; Merloni & Heinz 2008)

$$\begin{equation} \frac{\partial n_M(M_{\bullet },t)}{\partial t}+\frac{\partial [n_M(M_{\bullet },t)\langle \dot{M}(M_{\bullet },t)\rangle ]}{\partial M}=0, \end{equation} \tag{ 10 }$$

where n_M is the ABHMF and $\langle \dot{M}(M_{\bullet },t)\rangle$ is the average accretion rate of black holes with mass M_• at time t. By integrating this conservation equation forward and backward in time, using the observed ABHMF as the boundary condition, the ABHMF can be evolved to any redshift z. This evolution assumes that black hole growth occurs through accretion and that binary mergers are not the primary mechanism of black hole growth (e.g., Volonteri et al. 2003). The second ABHMF evolution considered is based on the observations of Labita et al. (2009), who found that the maximum black hole mass of the quasar population increases with redshift. Thus, M^crit_•(z) = M^crit_•(0)(1.0 + z)^1.64. In order to compare the two considered evolutions, a power law is fit to M^crit_•(z) of the Merloni & Heinz (2008) ABHMF evolved with the continuity equation, and it is found that M^crit_•(z) ≈ M^crit_•(0)(1.0 + z)^0.5. For both ABHMFs, the ABHMF is re-normalized at each redshift so that integrating over all black hole masses gives 1.

With the observationally determined AGN triggering rate, theoretical Eddington ratio evolution, and the ABHMF in place, the AGN population at z < 4 can be fully modeled.² To determine the light-curve fitting parameters, t₀, β, and η, the AGN population model must be compared to observational constraints.

The HXLF, dΦ_X(L_X, z)/dlog L_X, is computed at five different redshifts, z = 2.3, 1.2, 0.6, 0.3, and 0.1. The HXLFs observed by Ueda et al. (2003), La Franca et al. (2005), Silverman et al. (2008), Aird et al. (2010), and Ueda et al. (2011) are each presented in different redshift bins. Therefore, we compute the predicted HXLF at the central redshift of each of the Ueda et al. (2003) redshift bins.

The bolometric AGN luminosity function at redshift z, dΦ(L_bol, z)/dlog L, is computed by integrating over the space density of AGNs triggered at redshift z_t and that, at redshift z, have black hole mass M_• and Eddington ratio λ such that the bolometric luminosity is L_bol. Thus,

$$\begin{equation} \frac{d\Phi (L_{{\rm bol}}, z)}{d\log L} = \int _{M_{\bullet }^{{\rm min}}}^{M_{\bullet }^{{\rm max}}} n_{M}(M_{\bullet },z) d\log M_{\bullet } \int ^4_z \Phi _{\lambda }(M_{\bullet },z) dz_t, \end{equation} \tag{ 11 }$$

where log (M^min_•/M_☉) = 5.95, log (M^max_•/M_☉) = 10.55, z_t is the triggering redshift, and

$$\begin{equation} \Phi _{\lambda }(M_{\bullet },z) = \left\lbrace \begin{array}{@{}ll}\frac{dN(z_t)}{d\log L} & \lambda (z,z_t) L_{{\rm Edd}}(M_{\bullet }) = L_{{\rm bol}} \\ \ms 0 & \textnormal {otherwise} \end{array}\right., \end{equation} \tag{ 12 }$$

where dN is either dN_merg or dN_sec. The Marconi et al. (2004) luminosity-dependent bolometric correction is then used to convert L_bol to L_X.

As the observed HXLF only includes Compton-thin AGNs, the Compton-thick AGNs are removed from the calculated HXLF by assuming that one-third of all obscured AGNs are Compton thick in agreement with the fraction of Compton-thick AGNs necessary for the Ueda et al. (2003) observed HXLF to be in agreement with the peak of the XRB at ∼30 keV (Draper & Ballantyne 2009, 2010; Ballantyne et al. 2011). The fraction of Compton-thin obscured sources, f₂, is assumed to be a function of luminosity and redshift such that f₂∝(1 + z)^a(log L_X)^−b, where a = 0.4 (Ballantyne et al. 2006; Treister & Urry 2006) and b = 4.7. The normalization factor is determined by assuming that the type 2 to type 1 AGN ratio is 4:1 at z = 0 and log L_X = 41.5. Thus, the space density of Compton-thick AGNs also depends on L_X and, in Mpc⁻³ dex⁻¹, is (f₂/2) dΦ_X/dlog L_X.

According to both the Marconi et al. (2004) and Vasudevan et al. (2009) bolometric corrections, to achieve L_X = 10^46.5 erg s⁻¹, it is necessary to have a black hole with mass ≈10^10.7–10^10.9 M_☉ accreting at its Eddington rate. The Gaussian fit to both the Netzer (2009) and the Merloni & Heinz (2008) ABHMF predict that the fraction of active black holes with mass ∼10¹¹ M_☉ is ∼0, in agreement with the black hole mass upper limit derived by Natarajan & Treister (2009). This strongly suggests that AGNs with L_X ≳ 10⁴⁶ erg s⁻¹ are accreting at super-Eddington rates. The light-curve model used allows for 0 ≲ λ ≲ 1. Therefore, super-Eddington accretion cannot be taken into account. Thus, the models presented here will necessarily underpredict the L_X > 10⁴⁶ erg s⁻¹ observed HXLF data points. For completeness, the HXLF data points at L_X > 10⁴⁶ erg s⁻¹ are still taken into account when performing the χ² fitting.³

To calculate the black hole mass density, the Sołtan (1982) argument is used. Thus, the black hole mass density at redshift z, ρ_•(z), is calculated as

$$\begin{equation} \rho _{\bullet } (z) = \int _z^{\infty }\frac{dt}{dz}dz\int _0^{\infty }\frac{1-\epsilon }{\epsilon c^2}L_{{\rm bol}}\frac{d\Phi (L,z)}{d\log L}d\log L, \end{equation} \tag{ 13 }$$

where = 0.1 is the radiative efficiency, c is the speed of light, and dΦ(L, z)/dlog L is the AGN luminosity function (Yu & Tremaine 2002; Marconi et al. 2004; Treister et al. 2011).⁴ The contribution of Compton-thick AGNs to the black hole mass density is included. The predicted black hole mass density is compared to the local black hole mass density observed by Shankar et al. (2009) and the z ∼ 2 black hole mass density observed by Treister et al. (2010b).

The XRB spectrum model closely follows that described by Draper & Ballantyne (2009). Instead of inputting the observed luminosity function, the HXLF calculated as described in Section 3.1 is used. Also, a torus reflection component (Gilli et al. 2007) is included that is computed using "reflion" (Ross & Fabian 2005). The type 2 fraction, f₂, is determined as in Section 3.1. The Compton-thick fraction, f_CT, is defined as the ratio of the number of Compton-thick AGNs to the number of Compton-thin type 2 AGNs and is set to f_CT = 0.5, in agreement with the f_CT necessary for the Ueda et al. (2003) HXLF to be in agreement with the XRB spectrum and the local Compton-thick AGN space density (Draper & Ballantyne 2009, 2010; Ballantyne et al. 2011). The unabsorbed type 1 sources are evenly distributed over column densities log N_H = 20.0, 20.5, 21.0, and 21.5. The Compton-thin type 2 sources are distributed equally over log N_H = 22.0, 22.5, 23.0, and 23.5. The contribution of Compton-thick AGNs to the XRB is included. To do so, it is assumed that Compton-thick sources evolve similarly to less obscured AGNs and are evenly distributed over log N_H = 24.0, 24.5, and 25.0.

The AGN number counts in the 2–10 keV and 15–55 keV bands are also calculated. This is done by using the same AGN spectra, f₂, and f_CT as in the XRB model described above, including the contribution of Compton-thick AGNs, and by using the HXLF calculated as in Section 3.1.

The light-curve fitting parameters—t₀, which is related to the AGN lifetime, η, which is related to the peak Eddington ratio, and β, which determines the slope of the light curve—are determined by comparing the resulting models against the observed HXLF, evolving black hole space density, XRB spectrum, and AGN number counts. The fractional rate of massive galaxies that are triggered by secular processes each Gyr, f_sec, is also determined by comparing against observational constraints.

The focus of this study is not to fit the AGN light-curve parameters, but to investigate the contribution to the AGN population of AGNs triggered by major mergers and AGNs triggered by secular processes. Therefore, a minimization algorithm is not used. Instead, the best-fit parameters for the AGN light curve are determined by considering models with t₀ = 1.0 × 10⁷, 5.0 × 10⁷, 1.0 × 10⁸, 2.5 × 10⁸, 5.0 × 10⁸, 7.5 × 10⁸, and 1.0 × 10⁹ yr. Hopkins & Hernquist (2006) found that their model results were not very dependent on η, so the values η = 0.2, 0.4, 1.0, 2.5, and 3.0 are considered. Steps of 0.05 in the range from 0.05 to 1.0 are used to determine β. For f_sec, the values 0.0, 0.005, 0.01, 0.02, and 0.05 Gyr⁻¹ are investigated. The best-fit parameters for each model are determined by minimizing a χ² test that takes into account the 127 HXLF data points for z = 2.3, 1.2, 0.6, 0.3, and 0.1 presented by Ueda et al. (2003), La Franca et al. (2005), Silverman et al. (2008), Aird et al. (2010), and Ueda et al. (2011). By comparing against the observed AGN HXLF, black hole mass density, XRB spectrum, and AGN number counts, the model is fully constrained, allowing for some conclusions to be reached about the AGN light-curve parameters. The model sensitivity to the light-curve parameters is discussed in Section 6.1.

First, it is assumed that all AGNs are triggered by major mergers; thus, f_sec = 0.0. The best fit to the HXLF is found using the Merloni & Heinz (2008) ABHMF with the Labita et al. (2009) evolution, t₀ = 2.5 × 10⁸ yr, β = 0.7, and η = 2.5, similar to that found by Cao (2010). When compared to the 127 data points from the Ueda et al. (2003), La Franca et al. (2005), Silverman et al. (2008), Aird et al. (2010), and Ueda et al. (2011) observed HXLFs in the five redshift ranges considered, this model has a reduced χ², χ²_red = 2.4. If t₀ is changed by 0.5 × 10⁸ yr, β is changed by 0.05, or η is changed by 0.5, the resulting χ²_red will increase by ∼0.1–0.2. The light-curve fitting parameters are summarized in Table 1. As shown by the dot-dashed red lines in Figure 1, this model provides a relatively good fit to the observed HXLF at z ≳ 1; however, at z < 1, this model has χ²_red = 2.6 for 85 data points. The space density of major mergers at z < 1 is too low to explain the space density of observed AGNs in this redshift range. This model is in agreement with the observed local black hole mass density (Shankar et al. 2009) and the z ∼ 2 observed black hole mass density (Treister et al. 2010b). However, this model significantly underpredicts the XRB spectrum, as well as the 2–10 keV and 15–55 keV AGN number counts. Thus, despite major-merger-triggered AGNs being able to account for the integrated black hole growth, merger-triggered AGNs cannot account for the space density of the entire AGN population. Specifically, major mergers cannot account for the z ≲ 1 AGN population.

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The finding that major mergers are not capable of accounting for the z ≲ 1 AGN population is robust against several assumptions. To test the dependence of the merger-triggered-AGN-only model on the SMF, the z = 1.3–3 SMF presented by Marchesini et al. (2009) and the z = 0.1 SMF presented by Cole et al. (2001) are used to define an evolving SMF. When using the combined Cole et al. (2001) and Marchesini et al. (2009) SMF, the merger-triggered-AGN-only model is not able to account for the space density of AGNs at z ≲ 1, with minimum χ²_red = 3.6. Similarly, if the minimum mass of a potential AGN host galaxy (M^min_*) is reduced, the merger-only model cannot supply a decent fit to the observational constraints.

Next, we consider the scenario where all AGNs are triggered by secular processes. For this model, the best fit to the HXLF is found when using the Netzer (2009) ABHMF with the continuity equation evolution, t₀ = 2.5 × 10⁸ yr, β = 0.8, η = 0.4, and f_sec = 0.02 Gyr⁻¹. This model has χ²_red = 2.1 for 127 data points. If t₀ is changed by ∼0.5 × 10⁸ yr, β is changed by 0.05, or f_sec is changed by 0.01 Gyr⁻¹, the resulting χ²_red will change by ∼0.2. If η is changed by ∼0.5, the resulting χ²_red will increase by ∼0.1. As shown by the blue dashed lines in Figure 1, this model underpredicts the space density of low L_X AGNs at z ≲ 1 and underpredicts high L_X sources at z ≳ 1. Furthermore, this model significantly underpredicts the local black hole mass density, the XRB, and the 2–10 keV number counts. This model slightly overpredicts the Swift/BAT 15–55 keV number count and is inconsistent with the findings of Koss et al. (2010) that ∼20% of Swift/BAT AGN host galaxies have disturbed morphology indicative of a recent major merger. Thus, secular processes alone are not sufficient to account for the entire AGN population. Specifically, secular processes are not able to account for the AGN population at z ≳ 0.5. When the minimum mass of a potential AGN host galaxy is reduced or the evolving SMF defined by combining the Cole et al. (2001) and Marchesini et al. (2009) SMFs is used, the secular-evolution-only model still cannot account for the z ≳ 0.5 AGN population, with minimum χ²_red = 2.0. It is found that AGNs triggered by secular mechanisms alone cannot explain the observed AGN population.

Neither merger-triggered AGNs nor secularly triggered AGNs alone are able to account for the entire AGN population. Reducing the minimum mass of potential AGN host galaxies and using the combined Cole et al. (2001) and Moretti et al. (2009) SMF does not change this result. The space density of major mergers at z < 1 is too low to account for the low-redshift AGN population but can account for the local space density of black holes. In contrast, AGNs triggered by secular mechanisms are not able to account for the buildup of the black hole mass density over cosmic time. Thus, we consider the possibility that AGNs are triggered by both major mergers and secular processes.

The AGN light-curve model used has three parameters, t₀, β, and η. The η parameter is related to the peak Eddington ratio of the light curve. The AGN population model is least sensitive to η; however, it is found that η ≳ 1.0 provides the best fit to the observational constraints, suggesting that short periods of super-Eddington accretion are likely in a significant fraction of the AGN population. The AGN population model is moderately dependent on the timescale parameter, t₀. If this timescale is too short, the AGNs fade too quickly, and the space density of low-luminosity AGNs is severely underpredicted. Thus, t₀ is most important for the normalization of the AGN HXLF. The shape of the HXLF is primarily controlled by the slope of the light curve, which is controlled by the β parameter. The AGN population model is most sensitive to β. Changing β by 0.1 can cause the resulting HXLF shape to change substantially. The primary goal of this study is to investigate whether it is necessary that AGNs be triggered by both mergers and secular processes or a single mechanism can account for the entire AGN population, not to determine the best-fit AGN light-curve parameters. However, the observational constraints used in this study do provide interesting restrictions on the AGN light-curve parameters.

Hopkins & Hernquist (2009) point out that different models of the AGN light curve predict different light-curve slopes, β. Therefore, the AGN light-curve fit provides information about the physical conditions in the vicinity of the accretion disk. For example, self-regulated models, where the black hole accretion is feedback limited, predict β = 0.3–0.8. Meanwhile, if AGNs are fueled by mass loss from a nuclear star cluster, β = 0.9–1.0. Models in which the fuel supply of a Shakura & Sunyaev (1973) accretion disk is suddenly cut off predict β = 0.80–0.84. In all of the best-fit merger-triggered AGN models presented here, β = 0.7, suggesting that for merger-triggered AGNs, the accretion is feedback limited. Also, for the best-fit model presented here, η, the parameter related to light-curve peak Eddington ratio, is much smaller for AGNs triggered by secular mechanisms than for AGNs triggered by major mergers.

Here, it is assumed that every major merger triggers an AGN and major mergers can account for the AGN population at z = 2.3; thus, this analysis is an upper limit for the contribution of major-merger-triggered AGNs. Still, it is found that at z ≲ 2, a significant fraction of all AGNs are triggered through secular mechanisms. Figure 7 shows the space and luminosity density of AGNs with log L_X > 42, 43, and 44, which are triggered by mergers and secular processes as a function of redshift for the mixed ABHMF model. At all three luminosity ranges, the luminosity density and space density of AGNs are dominated by major-merger-triggered AGNs at z ≳ 1.5 and secularly triggered AGNs at z ≲ 1.5. By varying model parameters, we find that the minimum redshift at which major mergers can dominate AGN trigger is z ∼ 1. This finding is in agreement with Georgakakis et al. (2009), who found that ∼30% of the AGN space density and ∼25% of the AGN luminosity density at z ∼ 1 is due to AGNs hosted by disk-dominated hosts, implying that secular processes are responsible for at least one-quarter of the AGN luminosity density at z ∼ 1. It is found that merger-triggered AGNs account for ∼20% of the space density of log L_X > 43 AGNs at z < 0.05, consistent with findings of Koss et al. (2010). Thus, AGNs hosted by disk-dominated galaxies are a significant fraction of the AGN population by z ∼ 1, indicating that secular evolution is an important mode of galaxy evolution at this redshift.

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Similarly, Draper & Ballantyne (2011) found that for AGNs at z ≲ 1 the host galaxies of obscured and unobscured AGNs are, on average, the same, suggesting that at z ≲ 1 AGN and galaxy evolution is controlled by secular processes. However, at z ≳ 1, the host galaxies of unobscured AGNs are intrinsically less dusty than the host galaxies of obscured AGNs at similar redshifts, suggesting a fundamental change in the mechanisms that control AGN activity at z ∼ 1 (Draper & Ballantyne 2011). Indeed, Figure 2 shows that, at z ≲ 1, AGNs triggered through secular processes dominate even the high L_X end of the HXLF, while fading major-merger-triggered AGNs dominate the low L_X end of the HXLF. These findings are also in agreement with the conclusions of a variety of recent observational studies that found that secular processes are an important form, and possibly the dominate form, of galaxy evolution at z ≲ 2 (Georgakakis et al. 2009; Allevato et al. 2011; Cisternas et al. 2011; Schawinski et al. 2011; Williams et al. 2011). Indeed, according to the HXLF, we find that AGNs triggered by secular processes can account for the entire AGN population with log L_X > 43 at z ≲ 0.5. Hopkins & Hernquist (2006) suggest that secularly triggered AGNs are not cosmologically important; however, the findings of this study illustrate that AGNs triggered by secular mechanisms are necessary to describe the AGN population and dominate the space density of AGNs with log L_X > 43 at z ≲ 1.5.

The findings of Schawinski et al. (2010b) suggest that this fundamental change in AGN activity at z ∼ 1.5 is due to cosmic downsizing. By studying AGN black hole masses as a function of host galaxy morphology for AGNs observed by the Sloan Digital Sky Survey (SDSS), Schawinski et al. (2010b) find that it is preferentially the least massive black holes in less massive early-type galaxies (stellar mass M_* ∼ 10¹⁰ M_☉) that are currently active. In contrast, the black holes that are currently active in late-type galaxies are preferentially the most massive black holes hosted by more massive late-type host galaxies (M_* ∼ 10¹¹ M_☉). A stellar disk generally indicates that a galaxy has not undergone a major merger or that the last major merger experienced by the galaxy was long enough ago that a disk had time to reform, ≳500 Myr (Hota et al. 2011). We can therefore assume that, for AGNs hosted by late-type galaxies, the current episode of AGN activity was triggered by secular processes. Schawinski et al. (2010b) suggest that the early-type galaxy hosts in their sample may be smaller versions of the mode of galaxy evolution experienced by massive ellipticals at high redshift. Thus, the early-type host galaxies in the sample of Schawinski et al. (2010b) may host downsized versions of major-merger-triggered AGNs. Thus, it appears that the dominance of major mergers in galaxy evolution began to decline by z ∼ 2 and is continuing to decline, in agreement with the theory of cosmic downsizing. Meanwhile, the importance of secular evolution increased as the importance of major mergers decreased, until secular evolution became the dominate form of galaxy evolution at z ∼ 1.5. Since we are still early in the era of secularly dominated galaxy evolution, it is the more massive systems that are currently undergoing secularly triggered AGN activity. Cosmic downsizing would therefore predict that as the era of secular dominance continues, AGNs triggered through secular processes will become more common in lower mass systems.

It is found that AGNs triggered by major mergers at z < 4 have, on average, more massive central black holes than AGNs triggered by secular processes, at least at high redshift. Locally, it appears that merger-triggered AGNs and secularly triggered AGNs have similar black holes masses (Schawinski et al. 2010b), necessitating that the ABHMF of merger-triggered AGNs evolves differently than the ABHMF of secularly triggered AGNs. The ABHMF of AGNs triggered by secular mechanisms appears to evolve in a manner consistent with the continuity equation (Equation (10)), which describes the evolution of the combined active and quiescent black hole mass function (e.g., Small & Blandford 1992; Merloni & Heinz 2008). However, if the ABHMF of merger-triggered AGNs evolves following the continuity equation, then at z ≳ 1 the average active black hole mass is too small to account for the high L_X end of the HXLF. In contrast, if the Labita et al. (2009) ABHMF evolution is used to evolve the ABHMF of secularly triggered AGNs, then the low L_X end of the z ≲ 1 HXLF is significantly underpredicted. Thus, it appears that not only are both secular processes and major mergers important mechanisms for triggering the z < 2 AGN population, but these two mechanisms trigger different populations of black holes and these two populations have different redshift evolution.

It is not surprising that the ABHMF of merger-triggered AGNs evolves differently from the secularly triggered ABHMF and the quiescent black hole mass function. The major merger rate evolves strongly with redshift and galaxy mass (Hopkins et al. 2010a). Thus, it is expected that the ABHMF of AGNs triggered by major mergers would also evolve strongly with redshift (e.g., Treister et al. 2011). In contrast, the rate of AGNs being triggered by secular evolution, f_sec, is assumed to be constant with redshift. Therefore, it is expected that the ABHMF for AGNs triggered by secular processes will be less redshift dependent than the ABHMF for merger-triggered AGNs. Also, as the majority of supermassive black holes at any redshift are quiescent, the combined quiescent and ABHMF evolves more slowly with redshift than the merger-triggered ABHMF. Thus, it is expected that the merger-triggered ABHMF will evolve more strongly with redshift than the ABHMF of secularly triggered AGNs or of the combined active and quiescent black hole mass function.

Observational and theoretical evidence suggests that Compton-thick AGNs are AGNs that were recently triggered by a mechanism that has caused a large amount of gas and dust to be funneled into the nuclear regions of the host galaxy (e.g., Fabian 1999; Page et al. 2004; Fabian et al. 2008, 2009; Draper & Ballantyne 2010; Treister et al. 2010a; Draper & Ballantyne 2011). Due to the large amount of gas and dust required for the rapid AGN fueling and high column density necessary for an AGN to be Compton thick, the most likely triggering process is a wet major merger (Sanders et al. 1988; Hopkins et al. 2006a), though Weinzirl et al. (2011) argue that Compton-thick levels of obscuration are also possible in instances of clumpy cold-flow accretion onto the host galaxy. Here, we set f_CT = 0.0 for the secularly triggered AGN and calculate f_CT for the merger-triggered AGN as described in Section 3.1. If it is assumed that Compton thickness is an evolutionary phase that only merger-triggered AGNs experience, the χ²_red of the mixed ABHMF increases by 0.1 and the model is still in agreement with the observed black hole space density, XRB spectrum, and the 2–10 keV and 15–55 keV number counts. Therefore, the hypothesis that Compton-thick AGNs are an evolutionary stage of merger-triggered AGNs is fully consistent with the model presented here.