A GROWTH-RATE INDICATOR FOR COMPTON-THICK ACTIVE GALACTIC NUCLEI

Determining the growth rates of active galactic nuclei (AGNs) is important for understanding the build up of supermassive black holes. The key parameter to describe black hole growth is the Eddington ratio, λ_Edd. This is defined by the ratio of the bolometric luminosity of the AGN, L_Bol, to the Eddington luminosity, L_Edd (i.e., λ_Edd ≡ L_Bol/L_Edd). L_Bol is related to the mass accretion rate onto the black hole, $\dot{m}$, via the accretion efficiency, η, by ${L}_{{\rm{Bol}}}=\eta \dot{m}{c}^{2}$. L_Edd is the theoretical maximal luminosity (although observed to be exceeded in some sources e.g., Lanzuisi et al. (2016)) achieved via accretion when accounting for radiation pressure, and is dependent on the black hole mass (L_Edd = 4πGM_BH m_pc/σ_T ≃ 1.26 × 10³⁸(M_BH/M_⊙) erg s⁻¹).

For unobscured AGNs, λ_Edd is determined from the intrinsic disk emission observed in the optical/UV, from which L_Bol can be calculated, and M_BH that is estimated from measurements of the broad emission lines which trace the motions of gas close to the black hole (e.g., Shen 2013; Peterson 2014).

In obscured AGNs however, the intrinsic disk emission is completely extinguished by intervening material, and the broad line region is obscured from view, so λ_Edd is difficult to measure in these systems and must be estimated from indirect methods. For example, the observed relationship between the stellar velocity dispersion in the bulge of the galaxy and the black hole mass is often used to estimate M_BH. However, this relationship has a large intrinsic scatter in it, especially at low masses (e.g., Greene et al. 2010; Läsker et al. 2016). It is therefore important to have as many indirect methods as possible for estimating λ_Edd for both unobscured and obscured AGNs.

Studies of the X-ray emission of AGNs have found that λ_Edd is strongly correlated with the X-ray spectral index, Γ, in the range 0.01 ≲ λ_Edd ≲ 1 (e.g., Shemmer et al. 2006, 2008; Risaliti et al. 2009; Jin et al. 2012; Brightman et al. 2013). Γ depends on both the electron temperature and optical depth to Compton scattering in the hot corona (Rybicki & Lightman 1986; Haardt & Maraschi 1993; Fabian et al. 2015) that up-scatters the optical/UV emission from the accretion disk (e.g., Shakura & Sunyaev 1973). This relationship is thought to arise due to higher λ_Edd systems cooling their coronae more effectively than lower λ_Edd through enhanced optical/UV emission.

The observed relationship between Γ and λ_Edd suggests that a measurement of Γ could be used to estimate λ_Edd. This would be particularly useful for heavily obscured AGNs due to the fact that λ_Edd is, as mentioned, difficult to measure for such systems. However, this has its own challenges, since X-rays are also absorbed in these sources and at large column densities (N_H ∼ 10²⁴ cm⁻²) X-rays undergo Compton-scattering within the obscuring medium, which modifies their trajectory and energy. Nonetheless, up to N_H ∼ 10²⁵ cm⁻² and at high energy (E > 10 keV) absorption is negligible, and furthermore spectral models exist that take these effects into account, assuming a torus geometry of the obscuring medium, e.g., mytorus (Murphy & Yaqoob 2009) and torus (Brightman & Nandra 2011). In order to recover the intrinsic Γ using these models, broadband X-ray spectral measurements, especially above 10 keV where the scattering dominates, are required. NuSTAR (Harrison et al. 2013), with its sensitivity at these energies, is the ideal instrument with which to uncover the intrinsic X-ray emission from heavily obscured AGNs and since its launch in 2012 has amassed a large archive of data on these sources (e.g., Arévalo et al. 2014; Baloković et al. 2014; Gandhi et al. 2014; Puccetti et al. 2014; Annuar et al. 2015; Bauer et al. 2015; Brightman et al. 2015; Koss et al. 2015; Rivers et al. 2015; Marinucci et al. 2016; Ricci et al. 2016).

In this work our goal is to examine the relationship between Γ and λ_Edd for heavily obscured AGNs to test if it is consistent with the results from unobscured AGNs. This will reveal how well X-ray spectral modeling with the X-ray torus models recovers the intrinsic AGN parameters, or if orientation effects in the corona are present, related to AGN unification, and show if Γ can be used as a λ_Edd indicator for these heavily obscured systems.

This requires a sample of heavily obscured AGNs where the black hole mass has been measured reliably and broadband X-ray spectra are available. The most robust black hole mass measurements for obscured AGNs come from disk water megamasers (see Lo 2005, for a review), where the Keplerian motion of the masing material reveals the mass within (e.g., Greenhill et al. 1996). Due to the edge-on geometry of the medium required to produce masing emission, a high fraction of megamasers are heavily obscured AGNs (Zhang et al. 2006; Masini et al. 2016), making megamasers particularly well suited to our study.

Furthermore, megamasers are of interest since they are at the low-mass end of the supermassive black hole mass distribution, having a mass range of M_BH ≈ 10⁶–10⁷ M_⊙. Previous analyses of the Γ–λ_Edd relationship have concentrated on samples where the black hole mass has been measured from optical broad line fitting (e.g., Brightman et al. 2013) with M_BH ≈ 10⁷–10⁹ M_⊙. More recently, lower-mass black holes (M_BH ∼ 10⁶ M_⊙) have been investigated (e.g., selected via their rapid X-ray variability, Kamizasa et al. 2012), where it has been found that they are not fully consistent with the results from higher mass (Ai et al. 2011; Ho & Kim 2016). The megamaser AGNs thus give us the opportunity to further assess the validity of the relationship in this low-mass regime with a different sample selection.

We describe our sample and its selection in Section 2, give our results in Section 3 and discuss and conclude in Section 4.

There are ∼20 sources where megamaser emission has been used to measure black hole mass (e.g., Kuo et al. 2011). For our analysis, we require results from sensitive broadband X-ray spectral data, especially above 10 keV where Compton scattering effects dominate. For this reason we compile NuSTAR results on the megamaser AGNs. This was done recently by Masini et al. (2016) who compiled and analyzed X-ray spectral information of megamaser AGNs in order to study the connection between the masing disk and the torus. These AGNs include well-studied sources that have been the subject of detailed spectral analysis of NuSTAR data, such as Circinus (Arévalo et al. 2014), NGC 4945 (Puccetti et al. 2014), NGC 1068 (Bauer et al. 2015; Marinucci et al. 2016), and NGC 3393 (Koss et al. 2015), as well as samples of sources such as IC 2560, NGC 1368, and NGC 3079 (Baloković et al. 2014; Brightman et al. 2015).

In all of these studies, the mytorus and torus models were used to obtain the intrinsic Γ and 2–10 keV luminosities, L_X, correcting for columns of 10²³–10²⁶ cm⁻². In most studies of the megamaser AGNs listed above, both mytorus and torus models were fitted, with generally good agreement between spectral parameters (for a direct comparison see Brightman et al. 2015). For our study, we take the results on Γ and L_X from the model that the original authors found to be the best fitting one.

In order to test the Γ–λ_Edd relationship for the megamaser AGNs, we require good constraints on Γ, thus we exclude sources where the uncertainty on Γ is >0.25, which excludes NGC 1386 and NGC 2960 from our sample. Our final sample consists of nine AGNs. For NGC 4945, Puccetti et al. (2014) present a flux resolved analysis of the source, whereby they investigated the variation of Γ with the source luminosity (and hence λ_Edd), which is of particular interest here, so we include those individual results here, giving us 12 separate measurements of Γ for the sample. With the exception of NGC 4388 (N_H = 4 × 10²³ cm⁻², Masini et al. 2016), this sample consists wholly of CT (N_H ≥ 1.5 × 10²⁴ cm⁻²) AGNs.

With black hole masses from the megamasers and good measurements of Γ, the final ingredient required for our investigation is L_Bol, needed to calculate λ_Edd. Since the X-ray spectral modeling also yields intrinsic 2–10 keV luminosities, L_X, for our sample, the simplest approach is to apply a bolometric correction, κ_Bol, to L_X. Several works have presented results on κ_Bol, reporting that it is an increasing function of L_Bol (e.g., Marconi et al. 2004; Hopkins et al. 2007), or that it is a function of λ_Edd (Vasudevan & Fabian 2007). From a large X-ray selected sample in XMM-COSMOS, Lusso et al. (2012) confirm that κ_Bol is a function of both L_Bol and λ_Edd. Given the relatively low X-ray luminosities of our sample (L_X ∼ 10⁴²–10⁴³ erg s⁻¹) which correspond to bolometric luminosities of ∼10¹⁰–10¹¹ L_⊙, the results from Lusso et al. (2012) show that κ_Bol = 10 would be appropriate for these sources. Thus for our initial investigation we calculate λ_Edd in this way.

The uncertainty on λ_Edd is propagated from the uncertainty in M_BH and in L_X by adding them in quadrature. For M_BH the uncertainty is typically ∼5% or higher. For L_X we assume a systematic 25% uncertainty to account for uncertainties in the flux from spectral modeling and any uncertainty in the distance to the source, which for these nearby galaxies can be non-negligible. We explore the effect of calculating L_Bol from a bolometric correction on our results later in the paper, as well as the use of L_Bol estimated from multiwavelength data. The properties of our sample are summarized in Table 1.

Table 1.  Properties of the NuSTAR Megamaser Sample

AGN Name	Redshift	MBH/106 M⊙	log10(LX/erg s−1)	Γ	NH/1024 cm−2	λEdd	References
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
NGC 1068	0.0038	8.0 ± 0.3	43.34	2.10 ± 0.07	${5.0}_{-1.9}^{+4.2}$	0.210 ± 0.053	c, l
NGC 1194	0.0136	65.0 ± 3.0	42.78	1.59 ± 0.15	${1.4}_{-0.2}^{+0.3}$	0.007 ± 0.002	f, m
NGC 2273	0.0061	7.5 ± 0.4	43.11	2.10 ± 0.10	>7.3	0.132 ± 0.034	f, m
NGC 3079	0.0037	${2.4}_{-1.2}^{+2.4}$	41.53	1.86 ± 0.25	1.84 ± 0.32	0.011 ± 0.009	d, j
NGC 3393	0.0125	31.0 ± 2.0	43.40	1.82 ± 0.09	2.2 ± 0.4	0.062 ± 0.016	e, k
NGC 4388	0.0084	8.5 ± 0.2	42.59	1.65 ± 0.08	0.44 ± 0.06	0.035 ± 0.009	f, m
NGC 4945 (L)	0.0019	1.4 ± 0.7	42.09	1.77 ± 0.09	3.5 ± 0.2	0.068 ± 0.038	a, i
NGC 4945 (M)			42.39	1.88 ± 0.05	3.6 ± 0.1	0.135 ± 0.075
NGC 4945 (H)			42.62	1.95 ± 0.04	3.6 ± 0.1	0.229 ± 0.128
NGC 4945 (SH)			42.74	1.96 ± 0.07	3.5 ± 0.1	0.302 ± 0.169
IC 2560	0.0098	3.5 ± 0.5	42.90	2.50 ± 0.20	>13	0.175 ± 0.050	g, j
Circinus	0.0014	1.7 ± 0.3	42.50	2.27 ± 0.05	8.9 ± 1.2	0.143 ± 0.044	b, h

Note. Column (1) lists the name of the megamaser AGNs, where four different entries for NGC 4945 are given when it was observed at low (L), medium (M), high (H), and super-high (SH) flux levels (see Puccetti et al. 2014). Column (2) gives the redshift of the source, column (3) lists the black hole mass in units of 10⁶ M_⊙, column (4) gives the logarithm of the intrinsic 2–10 keV luminosity of the AGN determined through spectral modeling, column (5) gives Γ, column (6) gives the N_H in 10²⁴ cm⁻², and column (7) shows the Eddington ratio, λ_Edd given a bolometric correction of 10 to L_X. In column (8), we give the reference for the black hole mass—a. Greenhill et al. (1997), b. Greenhill et al. (2003), c. Lodato & Bertin (2003), d. Kondratko et al. (2005), e. Kondratko et al. (2008), f. Kuo et al. (2011), g. Yamauchi et al. (2012), and the X-ray spectral information—h. Arévalo et al. (2014), i. Puccetti et al. (2014), j. Brightman et al. (2015), k. Koss et al. (2015), l. Bauer et al. (2015), and m. Masini et al. (2016).

Download table as:  ASCIITypeset image

For our comparison of the Γ–λ_Edd relationship for megamaser AGNs with unobscured AGNs, we use the sample of Brightman et al. (2013) (B13), who studied a sample of 69 unobscured AGNs in the Cosmic Evolution Survey (COSMOS, Scoville et al. 2007) and Extended Chandra Deep Field-South (E-CDF-S, Lehmer et al. 2005) survey up to z ∼ 2 with black hole masses measured from optical broad line measurements. B13 fit the X-ray spectra of their sources in the 2–10 keV range with a simple power-law model. We plot the M_BH and L_X distributions of the megamaser sample in Figure 1 compared to the sample of B13. This shows that the megamaser sample extends the study of the Γ–λ_Edd relationship to lower black hole masses.

Zoom In Zoom Out Reset image size

We first test for the significance of a correlation between Γ and λ_Edd in the megamaser AGNs with a Spearman rank correlation test. This yields r_S = 0.73 and p = 0.007, where r_S is the Spearman rank correlation coefficient and p is the probability of obtaining the absolute value of r_S at least as high as observed, under the assumption of the null hypothesis of zero correlation. The small value of p indicates a significant correlation as observed in samples of unobscured AGNs.

We present a comparison of the distribution of Γ and λ_Edd for the megamaser AGNs to the unobscured AGNs in Figure 2. This shows that the two AGN samples occupy the same locus, given the measurement uncertainties, suggesting that they are drawn from the same underlying population. We test this quantitatively by fitting a linear regression to the megamaser AGN data, as done for the unobscured AGNs, and compare the results. So that a direct comparison can be made, we use the idl function linfit as done by B13, which fits the paired data {λ_Eddi, Γ_i} to the linear model, Γ = mlog₁₀λ_Edd + c, by minimizing the χ² error statistic. The measurement uncertainties on Γ are used to compute the χ² statistic (the uncertainty on λ_Edd is neglected).

Zoom In Zoom Out Reset image size

The result from the linear fitting yields Γ = (0.31 ± 0.07)log₁₀λ_Edd + (2.24 ± 0.06), where χ² = 59.9 for 10 degrees of freedom (dof). The same fit to the sample of B13 gave Γ = (0.32 ± 0.05)log₁₀λ_Edd + (2.27 ± 0.06). Both the slopes and offsets of the linear relationships are in very good agreement.

Other results on unobscured AGNs from Shemmer et al. (2008) (S08) and Risaliti et al. (2009) (R09) found similar values for the slope of the relationship, 0.31 ± 0.01 and 0.31 ± 0.06, respectively; thus, the results from the megamaser AGNs are also consistent with these results. As for the offsets, S08 measure 2.11 ± 0.01 and R09 measure 1.97 ± 0.02. However, R09 calculate their linear fit with log₁₀λ_Edd = −1 as their reference point, rather than 0 as we have done here, which corresponds to c = 2.28 with log₁₀λ_Edd = 0 as the reference point. Thus the offsets are consistent within ∼1–2σ.

Other authors have, however, found steeper slopes in the relationship. Jin et al. (2012) find a slope of 0.58 from a sample of unobscured nearby type 1 AGNs, while Keek & Ballantyne (2016) find that the slope is 0.54 when fitting for Γ versus λ_Edd in varying states of Mrk 335. These slopes are similar to that found by R09 for black hole masses based on the Hβ line only (0.58). Some of this disagreement appears to be due to the different statistical analyses used. Jin et al. (2012) suggest that χ² minimization may not be appropriate for quantifying this relation because it can be biased by small measurement errors in Γ for individual sources. The χ² normalization also does not take into account uncertainties in λ_Edd or any intrinsic scatter. Indeed the χ²/dof of 59.9/10 that we find from this indicates significant scatter is indeed present.

Kelly (2007) presented a Bayesian method to account for measurement errors in linear regression of astronomical data, linmix_err, which also takes into account uncertainties in the independent variable and allows for intrinsic dispersion in the regression. Applying this code to our data yields Γ = (0.41 ± 0.18)log₁₀λ_Edd + (2.38 ± 0.20) with an intrinsic scatter of 0.19 ± 0.19. While the slope is steeper compared to the χ² minimization result, the uncertainties are larger due to the inclusion of the λ_Edd uncertainties. The slopes of the χ² minimization and Bayesian methods are within 1σ of each other as well as with the slopes from the unobscured AGNs. This is likewise true of the offset, which is slightly higher with respect to the χ² minimization result, but the larger uncertainty makes it consistent within 2σ of all the results on the unobscured AGNs.

We plot the data with the result of the linear fit with the Bayesian method along with the upper and lower 1σ confidence bounds in Figure 3. The confidence bounds have been determined from a draw from the posterior distribution of the slope and offset parameters.

Zoom In Zoom Out Reset image size

3.1. How Does the Calculation of L_Bol Affect Our Results?

3.2. How Does the X-Ray Spectral Modeling Affect Our Results?

From the above analysis, albeit with a small sample, we conclude that the low-mass, heavily obscured megamaser AGNs are statistically consistent with the higher mass, unobscured AGNs through the Γ–λ_Edd relationship, where Γ = (0.41 ± 0.18)log₁₀λ_Edd + (2.38 ± 0.20). This result has the following implications.

First, the agreement indicates that the X-ray torus models effectively recover the intrinsic AGN parameters given sensitive broadband X-ray spectral data, despite the CT levels of absorption present in the megamaser systems. This has important value for results on heavily obscured AGNs from NuSTAR and future X-ray missions with hard X-ray sensitivity, and is particularly timely due to several new compilations of X-ray torus models (e.g., Liu & Li 2014; Furui et al. 2016).

Second, considering the low-M_BH nature of the megamasers (M_BH ≈ 10⁶–10⁷ M_⊙), our results imply that the connection between the accretion-disk emission, parameterized by λ_Edd, and the physical state of the X-ray emitting corona, parameterized by Γ, is constant over ∼3 orders of magnitude in black hole mass, M_BH ≈ 10⁶–10⁹ M_⊙ and ∼2 orders of magnitude in λ_Edd (≈0.01–1). A correlation between Γ and λ_Edd is also found in X-ray binaries, where M_BH ≈ 10 M_⊙, for the same λ_Edd regime (e.g., Yang et al. 2015), although the slope of the relationship, 0.58 ± 0.01, is different to what we find for our AGNs. Other results in the mass range we have investigated, selected on their small broadline widths (i.e., narrow-line Seyfert 1 s, Ai et al. 2011) or their X-ray variability (Kamizasa et al. 2012; Ho & Kim 2016) do not find a significant correlation between Γ and λ_Edd. However these results cover a smaller range in λ_Edd (∼1 order of magnitude) and with larger uncertainties on their black hole mass estimates, which may be the reason they did not detect the correlation.

Third, since the megamaser AGNs are edge-on systems, our results imply the lack of strong orientation effects when viewing the corona, which is assumed to be viewed more face-on in the unobscured AGNs. This gives broad support to the AGN unification scheme (Antonucci 1993; Urry & Padovani 1995) and theoretical modeling of the AGN disk-corona system that predicts that the spectral shape in the X-ray band is insensitive to the viewing angle (You et al. 2012; Xu 2015). One potential caveat to this, however, is that there are known misalignments between the outer edge of the accretion disk/inner edge of the torus, where the masing occurs, and the alignment of the inner disk/corona in some objects. See Lawrence & Elvis (2010) for a discussion. Furthermore, orientation dependence of spectral properties in X-ray binaries have been reported by Heil et al. (2015), where a difference of ΔΓ ≈ 0.17 between low and high inclination systems is reported. Such a difference would manifest itself in our results in the offset of the Γ–λ_Edd relationship. However, due to our small sample size, the statistical uncertainty in the offset is larger than 0.17, and furthermore we have shown there are systematic uncertainties in the offset due to estimation of L_Bol. Therefore differences at this level are currently undetectable.

Finally, although there is significant scatter in the relationship between λ_Edd and Γ for the heavily obscured AGNs, as there is for unobscured AGNs, there is potential for Γ to be used to give an indication of λ_Edd in heavily obscured AGNs where none would otherwise exist. For example, from the low Γ of 1.75 measured by Puccetti et al. (2016) in the NuSTAR spectrum of the highly absorbed system NGC 6240 supported the low accretion rate inferred in the source. However, this method should be restricted to large samples in order to reduce the effect of the intrinsic scatter. In the future, eROSITA (Merloni et al. 2012) will measure the 0.5–10 keV spectra of millions of AGNs over the whole sky and ATHENA (Nandra et al. 2013) will have the ability to carry out the measurements required for AGNs at high redshift in deep surveys, inferring λ_Edd distributions from large samples of AGNs over a wide redshift range.

This work was supported under NASA Contract No. NNG08FD60C, and made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. We thank the NuSTAR Operations, Software and Calibration teams for support with the execution and analysis of these observations. Furthermore, this research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. A.M. and A.C. acknowledge support from the ASI/INAF grant I/037/12/0-011/13. P.G. acknowledges funding from STFC (ST/J003697/2). M.B. acknowledges support from NASA Headquarters under the NASA Earth and Space Science Fellowship Program, grant NNX14AQ07H.

Facility: NuSTAR - The NuSTAR (Nuclear Spectroscopic Telescope Array) mission.