Bolometric luminosity of Seyfert galaxies

# Contribution of the accretion disk, hot corona, and obscuring torus to the luminosity of Seyfert galaxies: Integral and Spitzer observations

S. Sazonov11affiliation: Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow 117997, Russia 22affiliation: Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Garching 85741, Germany S.P. Willner33affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 A.D. Goulding33affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 R.C. Hickox44affiliation: Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755 V. Gorjian55affiliation: MS 169-327, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109 M.W. Werner55affiliation: MS 169-327, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109 E. Churazov22affiliation: Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Garching 85741, Germany 11affiliation: Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow 117997, Russia R. Krivonos22affiliation: Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Garching 85741, Germany 11affiliation: Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow 117997, Russia M. Revnivtsev11affiliation: Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow 117997, Russia R. Sunyaev22affiliation: Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Garching 85741, Germany 11affiliation: Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow 117997, Russia C. Jones33affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 S.S. Murray33affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 66affiliation: Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 A. Vikhlinin33affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 11affiliation: Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow 117997, Russia A.C. Fabian77affiliation: Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United Kingdom W.R. Forman22affiliation: Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Garching 85741, Germany
###### Abstract

We estimate the relative contributions of the supermassive black hole (SMBH) accretion disk, corona, and obscuring torus to the bolometric luminosity of Seyfert galaxies, using Spitzer mid-infrared (MIR) observations of a complete sample of 68 nearby active galactic nuclei (AGNs) from the INTEGRAL all-sky hard X-ray (HX) survey. This is the first HX-selected (above 15 keV) sample of AGNs with complementary high angular resolution, high signal to noise, MIR data. Correcting for the host galaxy contribution, we find a correlation between HX and MIR luminosities: . Assuming that the observed MIR emission is radiation from an accretion disk reprocessed in a surrounding dusty torus that subtends a solid angle decreasing with increasing luminosity (as inferred from the declining fraction of obscured AGNs), the intrinsic disk luminosity, , is approximately proportional to the luminosity of the corona in the 2–300 keV energy band, , with the ratio varying by a factor of 2.1 around a mean value of 1.6. This ratio is a factor of smaller than for typical quasars producing the cosmic X-ray background (CXB). Therefore, over three orders of magnitude in luminosity, HX radiation carries a large, and roughly comparable, fraction of the bolometric output of AGNs. We estimate the cumulative bolometric luminosity density of local AGNs at  erg s Mpc. Finally, the Compton temperature ranges between and  keV for nearby AGNs, compared to  keV for typical quasars, confirming that radiative heating of interstellar gas can play an important role in regulating SMBH growth.

galaxies: active – galaxies: Seyfert – infrared: galaxies – X-rays: galaxies

## 1. Introduction

Active galactic nuclei (AGNs) are extremely powerful sources of electromagnetic radiation over many decades in frequency from radiowaves to gamma-rays. According to the commonly accepted scenario, an AGN shines due to accretion of gas onto a supermassive black hole (SMBH) residing in a galactic nucleus.

In Seyfert galaxies and quasars, most of the luminosity is emitted in the form of ultraviolet (UV) radiation generated in a geometrically thin, optically thick accretion disk (Shakura & Sunyaev, 1973), giving rise to a “big blue bump” (BBB) in the spectral energy distribution (SED, e.g., Malkan & Sargent 1982). Additional, higher energy radiation is generated in a hot corona of the accretion disk (e.g., Haardt & Maraschi 1993) and possibly also in collimated outflows (jets) of relativistic plasma, producing a hard X-ray (HX) peak in the SED. The integrated (and redshifted) HX emission of all AGNs in the observable Universe makes up the bulk of the cosmic X-ray background. There is also a third, mid-infrared (MIR) peak in AGN SEDs (e.g., Barvainis 1987), which arises from reprocessing of a significant fraction of the disk’s and some of the coronal radiation in a torus of molecular gas and dust surrounding the inner accretion flow. In fact, only in unobscured or “type 1” AGNs can all three spectral components, the HX bump, the BBB, and the MIR bump, be observed. According to the unified model (Antonucci, 1993), these are objects viewed through the funnel of the dusty torus. In contrast, only the HX and MIR components are visible in the SEDs of obscured or “type 2” AGNs, because the torus is opaque to UV emission from the accretion disk but transparent to coronal radiation at energies above 15 keV (except in Compton-thick sources) and to its own infrared emission (at least at wavelengths  m). All other emission components, including broad- and narrow-line emission and non-thermal radio and gamma-ray radiation are usually not significant as regards their contribution to the angular-integrated bolometric luminosity of AGNs; these components will therefore not be discussed below.

To understand how electromagentic radiation is emitted and reprocessed during accretion of matter onto SMBHs, it is crucial to explore i) in what proportion the AGN luminosity is shared between the accretion disk and its corona, ii) what fraction of the bolometric luminosity is reprocessed in the torus, and iii) how these properties depend on black hole mass and accretion rate. One also needs such information to study the role of AGN feedback in regulating SMBH growth and galactic evolution. One of the proposed feedback mechanisms is photoionization and Compton heating of interstellar gas by AGN radiation (e.g., Ciotti & Ostriker 2001; Proga et al. 2008), whose efficiency critically depends on the AGN SED (Sazonov et al., 2004, 2005). Finally, information on AGN SEDs can be used to derive bolometric corrections required to reconstruct the cosmic history of SMBH accretion growth based on AGN statistics provided by extragalactic surveys (e.g., Marconi et al. 2004; Merloni & Heinz 2008).

Among all types of AGNs, the SEDs of unobscured high-luminosity quasars have been studied most extensively (see, e.g., Elvis et al. 1994; Richards et al. 2006; Shang et al. 2011). Their obscured counterparts – type 2 quasars – have been explored to a much lesser degree, although recent surveys have begun to find such objects in significant numbers (e.g., Polletta et al. 2006; Hickox et al. 2007; Lanzuisi et al. 2009). There is also much uncertainty with respect to the SEDs of Seyfert galaxies, which are typically less luminous than more distant quasars. The difficulty is that even in Seyfert 1s, the accretion disk emission is usually contaminated by host galaxy stellar emission in visible bands and the BBB peaks in the observationally difficult far-UV band (see, however, Scott et al. 2004; Vasudevan & Fabian 2007, 2009).

The goal of the present study is to systematically assess the relative contributions of the accretion disk, hot corona, and obscuring torus to the bolometric luminosity of local Seyfert galaxies. To this end, we i) cross-correlate the HX luminosities of nearby AGNs detected during the all-sky survey of the International Gamma-Ray Laboratory (INTEGRAL, Winkler et al. 2003) with the MIR luminosities of these objects measured by the Spitzer Space Telescope (Werner et al., 2004), and ii) use the proportion of obscured to unobscured AGNs to estimate the opening angle of dusty tori as a function of luminosity. We then put our findings for nearby AGNs into the broader context of cosmic SMBH growth by making a comparison with distant quasars.

Most previous relevant studies were based on AGN samples compiled in a fairly arbitrary manner from optical and/or soft X-ray (below 10 keV) catalogs (e.g., Lutz et al. 2004; Horst et al. 2006; Hönig et al. 2010). In these energy bands, AGNs can easily be missed due to absorption, as powerful sources can become invisible when obscured by large amounts of dust and cold gas in the torus and/or host galaxy. Furthermore, as already noted above, optical emission from relatively low-luminosity AGNs can be diluted against the background of a luminous galaxy (see Mushotzky 2004 for a detailed discussion of AGN selection at different wavelengths).

The hard X-ray band, above  keV, provides a census of AGNs that is far less biased with respect to the viewing orientation of the torus and is unbiased with respect to host galaxy properties. There have been a few previous attempts (Vasudevan et al., 2010; Mullaney et al., 2011) of systematically studying the MIR properties of HX selected AGNs using the Swift all-sky hard X-ray survey (Tueller et al., 2010). However, these studies either used data from the IRAS all-sky photometric infrared survey, so that it was impossible to reliably subtract the host galaxy contribution from the AGN emission, or used high angular resolution Spitzer data but only for statistically incomplete subsamples of Swift AGNs. Our INTEGRAL sample is the first statistically complete, HX selected sample of AGNs with complementary high angular resolution, high signal to noise, MIR data. The extensive Spitzer coverage (3.6–38 m) available for the entire INTEGRAL sample makes this a unique data set for studying SEDs of AGNs in the local Universe.

## 2. Integral AGN sample

Our study is based on the complete sample of AGNs (Krivonos et al., 2007; Sazonov et al., 2007) detected in the 17–60 keV energy band by the IBIS/ISGRI detector (Ubertini et al., 2003) aboard INTEGRAL during the first three and a half years of the mission, from 2002 October until 2006 June. These observations compose a serendipitous all-sky HX survey with the flux limit varying by a factor of a few over the sky. We have excluded from the present analysis blazars (flat spectrum radio quasars and BL Lac objects), a relatively rare subclass of AGNs whose observed emission is believed to be dominated by a narrow, strongly collimated component. We have also excluded AGNs located in the “zone of avoidance” near the Galactic plane () because there remain unidentified INTEGRAL sources in this region of the sky while we wish our sample to be nearly 100% complete to minimize selection effects.

The resulting set comprises 68 AGNs (Table 1). In the first seven columns of Table 1 we have collected information on optical/radio AGN types, distances, HX fluxes and luminosities, and X-ray absorption column densities (). These data are mostly adopted from the original INTEGRAL catalog (Krivonos et al., 2007; Sazonov et al., 2007) although some updates take into account follow-up observations carried out since publication of the catalog. In particular, thanks to recent X-ray observations by Chandra, Swift, and XMM-Newton, all of the previously missing values have now been estimated. All the reported absorption columns may be considered reliable because they are based on high signal-to-noise X-ray spectroscopic data. We do not quote the uncertainties associated with the values, because the information on absorption columns has been compiled from various sources and in most cases the actual uncertainty is likely dominated by systematic effects associated with the particular spectral modeling procedure used. In fact, multiple measurements taken for some AGNs at different times and/or by different instruments sometimes yield values that differ from each other by more than their reported uncertainties. We estimate that the total uncertainties associated with columns for our sources are typically smaller than 30% and do not affect the present study in any significant way.

All but one of our AGNs are located at low redshift (, the most distant one, IGR J094462636, being at ). For 18 nearby (closer than  Mpc) Seyfert galaxies we have adopted distance estimates from either Tully et al. (2009) or Tully (1988); otherwise luminosity distances have been calculated from the spectroscopic redshifts assuming a cosmology with , , and  km s Mpc.

The INTEGRAL AGN sample has HX (17–60 keV) luminosities ranging over almost five orders of magnitude, from (NGC 4395) to (IGR J094462636) erg s. Therefore, this is a representative, hard X-ray selected sample of nearby AGNs, mostly Seyfert galaxies, although our most luminous objects may be better referred to as nearby quasars, because their HX luminosities exceed  erg s.

One special object in the sample is the Seyfert 1.8 galaxy NGC 4395, a famous low-luminosity AGN (LLAGN) sometimes referred to as a “dwarf Seyfert nucleus”. It appears to be a quite atypical Seyfert galaxy in terms of its black hole mass, luminosity, and variability properties (see, e.g., Moran et al. 1999; Peterson et al. 2005; Vaughan et al. 2005). It is therefore possible that the properties of its dusty torus (if there is any) are also different from typical Seyfert galaxies and quasars. We thus treat this object separately from the rest of the sample in performing the HX–MIR cross-correlation analysis (§5).

As noted above, the HX selection (17–60 keV) implies that there is almost no bias from absorption. Our AGN sample is not sensitive to photoabsorption (and we have thus not corrected the measured HX fluxes for line-of-sight absorption) as long as the column density of the gas is less than a few or equivalently the Thomson optical depth is less than a few; at even larger column densities, the flux from a source drops considerably at all X-ray energies. The Seyfert 2 galaxy NGC 1068 distinguishes itself from the rest of the sample because it is the only significantly Compton-thick AGN (having  cm, Matt et al. 2000). We therefore exclude NGC 1068 from our baseline HX–MIR cross-correlation analysis but discuss its properties in comparison with Compton-thin sources (§5, §6).

## 3. Spitzer observations and data reduction

More than half of the INTEGRAL sample consists of well-known Seyfert galaxies, many of which have been targets of observational campaigns with Spitzer. For the remaining part, largely represented by AGNs discovered by INTEGRAL, we carried out short Spitzer observations (Program ID 50763) consisting of 3.6–8 m imaging with IRAC and low-resolution MIR spectroscopy with IRS; in addition, far-infrared photometry was performed with MIPS for a subset of objects. Our proprietary and publicly available archival data together provide complete coverage of the INTEGRAL sample with Spitzer at 3.6–38 m.

All of the sources in our hard X-ray selected sample would have been robustly detected by Spitzer even if they had been 1–3 orders of magnitude fainter. Hence, our sample is not limited by MIR flux and any correlations derived between the HX and MIR luminosities can be considered representative of the local AGN population without significant bias.

### 3.1. Irs

We used the InfraRed Spectrograph (IRS, Houck et al. 2004) on Spitzer to obtain low-resolution spectra of our objects. Our program’s observations, for a total of 30 AGNs, were done in spectral mapping mode using the Short-Low (SL) and Long-Low (LL) IRS modules. Each of these modules has first- and second-order sub-slits (SL1, SL2, LL1, and LL2) with widths of 3.7, 3.6, 10.7, and 10.5 arcsec, respectively. We used SL1, LL1, and LL2 for the entire sample and SL2 for a subset of objects. The resulting spectra thus cover a range from either 5.2 or 7.5 m up to 38 m. Observations with SL1 and SL2 consisted of one cycle of 6 pointings with a ramp duration of 6 s with two 19 steps in the slit direction and three 1.8 steps in the dispersion direction. For LL1 and LL2, one cycle of 3 pointings with a ramp duration of 6 s and a step size of 42 in the slit direction was implemented.

For those sources that were not covered by our Spitzer program, we used archival low-resolution IRS data: mapping mode observations for 14 AGNs and staring mode observations for another 23 AGNs. Almost all of the archival mapping mode observations have the following setup: one cycle of 13 pointings with a step size of 1.8 in the dispersion direction for SL1 and SL2 and 5 pointings with a step size of 4.85 in the dispersion direction for LL1 and LL2, the ramp duration being 6 s. For the archival staring mode observations, the ramp times and numbers of cycles vary from one object to another.

In the analysis of mapping mode observations, we used basic calibrated data (BCD), extracted from the Spitzer Science Center pipeline (versions S18.0.1 and newer for our program’s observations and versions S15.3.0 and newer for the archival observations). For each order of a given IRS module and for each position of a given source within the slit, we first produced a background image. For our program’s observations, this was done by averaging over 2D spectra obtained in significantly ( for SL and for LL) off-source positions, whereas for the archival observations, a similar averaging was done over 2D spectra obtained in the other order of a given IRS module. The background image was then subtracted from the on-source 2D spectrum. Then, a 1D spectum of the source was obtained using the Spitzer IRS Custom Extraction software (SPICE) by applying the regular extraction algorithm, which uses an aperture that gradually increases with wavelength in accordance with the telescope’s point spread function (e.g., the aperture width is 7.2 at 6 m and 36.6 at 27 m). Finally, an averaging over a set of 1D spectra extracted in different source positions within the slit was done. The staring mode spectra were obtained simply by averaging over nod-subtracted post-BCD spectra. These were derived with the same regular extraction algorithm as was used in our analysis of mapping mode observations.

Although the data reduction procedure described above is fairly simplistic and does not fully exploit the potential of mapping mode observations (which are available for nearly two thirds of our sample), it is adequate for the purposes of our HX–MIR cross-correlation study, as confirmed by a comparison with an alternative, more detailed analysis of IRS data for a subset of INTEGRAL sources (see §4.4).

The Compton-thick Seyfert 2 galaxy NGC 1068 is an extremely bright ( Jy at 15 m) infrared source, which caused saturation of IRS. We therefore quote in Table 1 its MIR flux estimate based on a compilation of high angular resolution, infrared observations (Mason et al., 2006).

### 3.2. Irac

We used images obtained by the InfraRed Array Camera (IRAC, Fazio et al. 2004) to determine source flux densities at 3.6, 4.5, 5.8, and 8.0 m. This wavelength range partially overlaps with that covered by IRS spectroscopy, enabling direct comparison between the spectroscopic and photometric results and providing an extension of spectra to shorter wavelengths.

Our IRAC program included 35 INTEGRAL sources. Observations were done in high dynamic range (HDR) mode. Specifically, a combination of a 0.6 s frame and a 12 s frame was repeated in 9 random dithers for each source. For the rest of the sample, we made use of archival observations, for which the number and duration of frames varied from source to source. Since most of our objects are bright infrared sources, our analysis was in most cases based on stacking the 0.6 s frames. For the 5 weakest sources ( mJy at 3.6–8.0 m), including LEDA 138501, IGR J094462636, ESO 263-G013, IGR J103864947, and NGC 4395, to improve the accuracy, we determined the fluxes by stacking the long (2, 12, or 30 s) frames. This was also done for 3C 111 and Mrk 3 despite their relative brightness because the observations were not done in HDR mode. We verified that none of the sources was saturated.

We analyzed post-BCD data using the standard point source extraction package APEX, part of the MOPEX software. Post-BCD images are adequate for this work because their main deficiency, poor artifact correction, is unimportant for 0.6-s frames. We estimated source fluxes by integrating the surface brightness in different apertures with radii between 2.4 to 12 and correcting for flux leakage outside the aperture under the assumption of a point-like source. Although this procedure is inaccurate for measuring fluxes of spatially extended sources, it is good enough to indicate the presence of extended host galaxy emission as a significant difference between fluxes measured in large and small apertures (see Appendix A).

The existing IRAC photometric measurements for the Compton-thick Seyfert 2 galaxy NGC 1068 proved to be saturated and hence were not used.

## 4. Infrared spectra: AGN MIR emission

Infrared emission from dust associated with star formation in the host galaxy can provide a significant contribution to AGN MIR spectra. Therefore, to study torus emission, we need to estimate and subtract the star formation contribution from the Spitzer data. We observe clear signatures of star formation in many of our IRS spectra. These include polycyclic aromatic hydrocarbon (PAH) emission features and the continuum rising toward the far-infrared. We therefore modelled the measured spectra by a sum of starburst and AGN components, similarly to a number of previous studies (e.g., Netzer et al. 2007; Mullaney et al. 2011).

Figure 1 shows examples of IRS spectra with negligible, significant, and strong star formation contribution as deduced using the fitting procedure described below. At short wavelengths, we also show IRAC photometric fluxes measured in 2.4 and 12 apertures.

### 4.1. Spectral decomposition using a starburst template

We adopted the starburst template from Brandl et al. (2006)111brandl/SB_template.html, which is an average over low-resolution IRS spectra of a dozen nearby ( Mpc) starburst galaxies. This template is well suited for our analysis because it was obtained by low-resolution IRS spectroscopy, similarly to the spectra studied here.

We normalized starburst components in our objects based on the observed strength of PAH lines, which are believed to be a generic signature of star formation (Roche et al., 1991). The presence of an AGN in a star forming galaxy may lead to a weakening of the PAH spectral features because PAH molecules can be destroyed by hard AGN radiation (Voit, 1992). However, the importance of this effect is controversial (see, e.g., Smith et al. 2007b; O’Dowd et al. 2009; Sales et al. 2010), and we have assumed that the shape of the starburst spectral component is not affected by the presence of a central AGN.

Our analysis consisted of the following steps. First, we fitted the spectra around (typically within  m of) the 6.2 m and 11.3 m PAH lines by a sum of a linear continuum and a Gaussian. We then compared the derived PAH line fluxes with the corresponding values for the starburst template, which yielded two independent estimates of the amplitude of the star-formation component. The average of these two values was then adopted as the normalization of the starburst template. On average, the coefficients implied by the 6.2 m and 11.3 m features proved to be consistent with each other, although there is % scatter around the 1:1 ratio of the two coefficients. This indicates that there are % systematic uncertainties in the derived amplitudes of starburst components for our objects (this issue is further discussed in §4.4 below). If there were no IRS data for the 6.2 m feature (i.e., only first-order SL data at  m were available), we used the flux of the 11.3 m line to normalize the starburst component. If the observed PAH features proved to be strong enough (depending on the source brightness, we required the PAH equivalent widths, EW, to be larger than 0.01–0.02 m, as compared to EW=0.45 and 0.55 m for the 6.2 m and 11.3 m bands, respectively, in the starburst template), we subtracted the estimated starburst contribution from the total spectrum to derive the AGN component. Otherwise, we considered star formation contamination insignificant and did not perform any subtraction.

We applied an additional correction to 13 spectra that contained detectable PAH features and exhibited a significant (10–20%, depending on the source brightness) discontinuity near 14 m, where the short-wavelength segment measured in the 3.7-wide SL1 slit connects to the long-wavelength segment measured in the 10.5-wide LL2 slit. Such a “jump” is mostly likely caused by an extended source, i.e., it cannot be due to the AGN. In these objects, the long-wavelength ( m) part of the starburst component was rescaled to make the AGN component smooth across the SL–LL boundary. We did not make such a correction for NGC 4395, by far the weakest infrared source in our sample (with an estimated flux density of 13 mJy at 15 m), despite the apparent presence of a significant SL–LL discontinuity in its spectrum, because of its low statistical quality (see Fig. 1). Furthermore, our comparison with available high-resolution spectroscopy for this object (see §4.2 below) indicates that the SL slit was not positioned sufficiently accurately on the nucleus of NGC 4395, which might have caused an artificial discontinuity at 14 m in the low-resolution IRS spectrum.

In principle, we could also use another known strong PAH feature, at 7.7 m, for estimating the contribution of star formation. However, this band overlaps with the high-ionization [NeVI] 7.65 m line, which can be bright in AGNs (Sturm et al., 2002) and is impossible to separate from the PAH feature in low-resolution IRS spectra. Moreover, the 7.7 m feature might be significantly affected by AGN radiation (Smith et al., 2007b; O’Dowd et al., 2009).

### 4.2. AGN dominated (clean sample) vs. starburst dominated sources

In agreement with previous studies (e.g., Weedman et al. 2005; Buchanan et al. 2006; Shi et al. 2006; Deo et al. 2009; Wu et al. 2009), we observe a large variety of infrared spectral shapes among Seyfert galaxies. However, those spectra dominated by dust reprocessed emission generated by black hole accretion (see examples in the left column of Fig. 1), rather than by star formation, almost invariably peak (when plotted in units) at 15–20 m, in good agreement with models of dusty tori heated by a central source of UV radiation (e.g., Dullemond & van Bemmel 2005; Hönig et al. 2006; Nenkova et al. 2008; Alonso-Herrero et al. 2011). Furthermore, the AGN components of those IRS spectra with inferred significant starburst contamination (see the middle column of Fig. 1) prove to be similar to the spectra of “pure” AGNs. In particular, most of the former also peak at 15–20 m. However, since our procedure of estimating the star formation contribution based on the strength of PAH features becomes progressively less reliable with increasing wavelength, there is much uncertainty in the deduced AGN spectral contributions at  m. All these findings are similar to the results of previous attempts to decompose Spitzer spectra of quasars and Seyfert galaxies into AGN and starburst components (e.g., Netzer et al. 2007; Mullaney et al. 2011).

The IRS spectra of six objects, NGC 1142, ESO 005-G004, IGR J075634137, NGC 4945, IGR J145613738, and MCG+04-48-002 (see the right column of panels in Fig. 1) closely resemble the starburst template. We found it practically impossible to distinguish AGN and host galaxy components in these starburst dominated sources and therefore excluded them (see Table 1) from most of the subsequent analysis. Interestingly, most of our starburst dominated objects are strongly X-ray absorbed AGNs ( cm). One may speculate that i) large supplies of cold gas and dust associated with starburst activity in a galactic nucleus facilitate the formation of a dense central obscuring torus, and/or ii) part of the X-ray absorption is caused by cold gas tracing star formation in the galaxy and located outside a parsec-scale AGN torus.

The remaining 61 objects (with NGC 1068 excluded for being a Compton-thick source) compose a “clean” sample for our subsequent analysis. As concerns the LLAGN NGC 4395, since its (low signal to noise) low-resolution IRS spectrum leaves doubts as to the presence of a significant starburst contribution (we estimate it at % at 15 m), we have also analyzed available high-resolution IRS data, following the methods described aby Goulding & Alexander (2009). While the derivation of an accurate continuum shape, using only high-resolution IRS, is complicated by the tip-tilt effects of the individual echelle orders, the high-resolution MIR spectrum of NGC 4395 is characterized almost entirely by an AGN-produced broken power law with little or no evidence ( m) for superposed PAH features. Hence, NGC 4395 is clearly AGN dominated and thus should be part of our clean sample. Nevertheless, as noted before, we still distinguish this “dwarf Seyfert” from the rest of the sample during our HX–MIR cross-correlation analysis because it might represent a physically different class of AGNs.

### 4.3. 15 μm flux and luminosity

We have just seen (Fig. 1 and §4.2) that after subtraction of the star formation contribution, AGN MIR continua have an approximately constant shape. This suggests that it should be possible to estimate bolometric luminosities of AGN obscuring tori using their flux densities measured at a single MIR wavelength. We have chosen to use for this purpose the rest-frame  m. Specifically,  (15 m) was determined by averaging a given spectrum over the wavelength range 14.7–15.2 m. There are several reasons behind this choice. First,  m is approximately where AGN torus emission peaks. Second, since IRS SL2 data are not available for some of our sources, we can only use wavelengths  m for the whole sample. Third, wavelengths  m are disfavored because cool dust emission associated with star formation becomes more important with increasing wavelength and frequently dominates far-infrared and even mid-infared spectra of Seyferts. Finally, there are no strong emission lines or absorption features within  m on either side of 15 m.

The last three columns of Table 1 present the total measured flux densities () and corresponding luminosities () at 15 m as well as estimated fractions of AGN emission in the total flux at 15 m, . Statistical uncertainties for the infrared fluxes and luminosities are negligibly small. For the six starburst dominated objects, we assume that %. In the subsequent analysis, the starburst subtracted MIR flux of AGNs is defined as

 f15μm=FAGNνfν (15 μm). (1)

The corresponding AGN luminosity is defined as

 L15μm=FAGNνLν (15 μm). (2)

### 4.4. Uncertainty in AGN MIR flux estimates

The main potential source of systematic uncertainty in our estimation of AGN fluxes at 15 m is the use of a fixed starburst spectral template from Brandl et al. (2006). In reality, the spectral properties of infrared emission from dust heated by starbursts may vary from one galaxy to another, and some authors (e.g., Mullaney et al. 2011) have attempted to take this diversity into account in separating AGN and host galaxy components for Seyfert galaxies.

A crude estimate of the systematic uncertainty associated with our use of a fixed spectral template was already made in §4.1 using the difference in the normalizations of starburst spectral components determined using the 6.2 and 11.3 m PAH features. Namely, starburst component amplitudes could be estimated by our fitting procedure to within %. This implies that for AGN dominated sources, i.e., those objects with %, the AGN fluxes at 15 m are also estimated to within %, i.e., to better than 0.1 dex in log space.

To better understand the uncertainties associated with our estimates of , we performed an alternative spectral analysis based on a set of starburst spectral templates for a subsample of our objects. Specifically, we selected a representative subset (16 objects) of AGN-dominated, mixed, and starburst-dominated sources. This comparison sample is equally divided between sources with IRS-staring and mapping data. In §4.1, we assumed that the SL—LL discontinuity observed in the MIR spectra of some of these AGNs arises due to extended host galaxy emission which provides an additional contribution to the larger aperture LL spectrum. However, it has also been suggested in previous studies that this discontinuity between the spectral orders derives from an IRS detector effect; for the purposes of comparison, we imposed this assumption for our sub-sample. Furthermore, for those sources with IRS mapping data, we combined the rogue-pixel cleaned BCD images and extracted nuclear spectra using the 3D spectral reduction program CUBISM (Smith et al., 2007a), which is used widely in recent MIR AGN literature (e.g., Dale et al. 2009; Goulding & Alexander 2009; Diamond-Stanic & Rieke 2010; Petric et al. 2011; Alonso-Herrero et al. 2012). We used DecompIR (Mullaney et al., 2010) to deconvolve the MIR spectra for our comparison sample using a set of empirical and theoretical starburst templates (e.g., Goulding et al. 2011) and assumed an absorbed broken power law to model the AGN component. The derived AGN fractions and fluxes prove to be entirely consistent with the values established by our baseline analysis (§3.1, §4.1) for those sources with (the average scatter in the derived is %). However, for those sources with (i.e., the spectra appear starburst dominated), the spectral fits become strongly dependent on the imposed starburst templates, and the scatter in the measured AGN flux increases to a factor of .

As an additional check of our IRS spectral measurements, we can use the IRAC imaging data available for all of our AGNs. For the vast majority of the sources, the absolute values of flux densities measured by IRAC and IRS in the overlapping spectral region below 8 m are in good mutual agreement (see Fig. 1), especially when the smallest (2.4) IRAC aperture is used (recall that the IRS SL slits have similar widths, 3.6–3.7). However, there are a few sources for which there is a significant discrepancy between the spectroscopic and photometric fluxes at  m. Since the corresponding IRAC and IRS observations were separated by several years in time, these flux differences probably indicate significant intrinsic variability of AGN torus emission, especially at shorter wavelengths (Suganuma et al., 2006; Kishimoto et al., 2009; Tristram et al., 2009; Kozłowski et al., 2010). Also, as shown in Appendix A, the detection of significant extended emission at 8 m by IRAC in many sources is fully consistent with our conclusions about the host-galaxy contamination of IRS spectra.

Finally, we compared our results for 16 AGNs with higher angular resolution observations from Gandhi et al. (2009). We find excellent agreement (see Fig. 5 and discussion in §5.2) between the fluxes derived from the very different observational data sets, which suggests that host galaxy contamination of our measured values of AGN MIR fluxes is minimal.

We conclude that the combined statistical and systematic uncertainty in our AGN 15 m-flux estimates for the clean sample (i.e., AGN dominated sources) is probably less than 0.1 dex. This uncertainty proves to be small in comparison with the intrinsic scatter in the HX–MIR flux and luminosity correlations (see §5 below). We further discuss the potential influence of starburst contamination on our derived correlations in §5.1.

## 5. HX–MIR luminosity relation

Before comparing the luminosities of AGN structural components (accretion disk, corona, and obscuring torus), which will be the subject of the next section (§6), we first perform a cross-correlation analysis of AGN luminosities measured in the HX and MIR bands by INTEGRAL and Spitzer, respectively. The results of this analysis may also be interesting in its own right for any studies addressing links between X-ray and infrared emission in AGNs.

Figure 2 shows the scatter plot of vs. , where is the luminosity in the 17–60 keV energy band and was defined in eq. (2). In computing luminosities from fluxes, we neglected uncertainties associated with source distances.

Considering the clean AGN sample without NGC 4395 and fitting as a function of (computing the linear regression in log-log space), we find a strong, non-linear correlation between MIR and HX luminosities (see Table 2):

 L15μm,43=(1.7±0.2)L0.74±0.06HX,43, (3)

where the luminosities are measured in units of  erg s. The rms scatter of values around the mean trend is 0.34 dex.

As can be seen in Fig. 2, NGC 4395 is a clear outlier from the luminosity correlation, with its MIR luminosity being almost 2 orders of magnitude below the trend described by eq. (3). If we consider this LLAGN together with the rest of the clean sample, the slope of the correlation increases from 0.74 to 0.85 (see Table 2), although formally the change is not significant.

Fig. 2 also shows the six starburst dominated sources, assuming that their AGN fractions %. Surprisingly, the upper limits to the 15 m fluxes of AGN components for all these objects lie below the best-fitting relation for AGN dominated sources (eq. [3]). At least in some cases, this behavior is likely caused by attenuation of the intrinsic MIR emission from the nucleus in the obscuring torus and in the surrounding galaxy (see Goulding et al. 2012). In particular, the IRS spectrum of NGC 4945 (Fig. 1) exhibits a very deep silicate absorption trough at 10 m, which, assuming the standard composition of interstellar dust (Draine, 2003) and the simplest scenario of an infrared source surrounded by a shell of dust, suggests that the neighboring continuum emission at  m should be attenuated by a factor of –5. In reality, depending on the actual distribution of dust in the nucleus and body of the galaxy, the AGN MIR emission can be absorbed even more strongly than suggested by the depth of the 10 m trough.

Finally, Fig. 2 shows the Compton-thick Seyfert 2 galaxy NGC 1068, which is a clear outlier from the correlation between and described by eq. (3). This result is expected because intrinsic hard X-ray emission is strongly absorbed in this object, and it is only the infrared signal that reveals the true power of this AGN. In fact, the discrepancy between the general trend and the position of NGC 1068 on the diagram suggests that its true X-ray luminosity is two orders of magnitude higher than measured by INTEGRAL, i.e.,  erg s. This estimate is consistent with values reported in the literature (e.g., Matt et al. 2000).

The mean trend described by eq. (3) suggests that the MIR/HX luminosity ratio decreases with increasing . This can be better seen in Fig. 3, which shows the ratio as a function of . Grouping our clean sample into 0.5 dex-wide bins in shows that the ratio decreases from –3 at  erg s to –1 at  erg s, although the “dwarf Seyfert” NGC 4395 is a clear outlier from this trend.

### 5.1. Robustness of the correlation

The derived relation, eq. (3), makes it possible to predict the HX luminosity for a given MIR luminosity. The combination of three facts, i) that our AGN sample is hard X-ray selected, ii) that this sample is not limited by sensitivity in the MIR band, and iii) that the correlation has been derived by fitting as a function of , ensures that this relation reproduces the intrinsic correlation between and for the local AGN population without any bias.

To further test the robustness of the derived trend, we repeated our cross-correlation analysis for various subsamples of AGNs. First, one may ask whether our procedure of separating AGN and starburst spectral components significantly affects the results. To address this issue, we computed the correlation for 46 strongly AGN dominated sources – those objects in which the AGN component accounts for at least 90% of the total emission at 15 m (i.e., ). The result (see Table 2) is very close to the correlation found for the total clean sample from which NGC 4395 is excluded (eq. [3]). In addition, we repeated the analysis for the clean sample (without NGC 4395) using total measured 15 m fluxes instead of AGN fluxes (i.e., setting ). The amplitude of the correlation increased by %, obviously due to the unsubtracted contribution of starburst emission, but the slope changed by less than from 0.74 to 0.68. These tests demonstrate that the correlation between and is not significantly affected by the details of our spectral analysis of IRS data.

We next repeated the analysis separately for nearby (, 35 objects, excluding NGC 4395) and distant (, 25 objects) sources from the clean sample. The correlation, in particular the slope of , derived for the distant subsample (see Table 2) is fully consistent with the correlation found for the total sample (eq. [3]). Since the set, owing to the INTEGRAL detection limit, is represented by luminous AGNs only, with  erg s, this result also implies that the slope of the high-luminosity part of the HR–MIR correlation is not significantly different from the trend found over a broader range of luminosities. However, the slope, , determined for the nearby () subsample, mainly consisting of lower luminosity AGNs with  erg s, is somewhat different from the general trend, but this difference is less than significant.

Finally, we repeated our analysis for different types of AGNs, namely Seyfert 1s (Sy1, including the intermediate types 1.2 and 1.5) and Seyfert 2s (Sy2, including the intermediate types 1.8 and 1.9). The derived relations (Table 2) are consistent with each other and with eq. (3). As can be seen from Fig. 4, Sy1s and Sy2s do not distinguish themselves on the diagram, nor do narrow-line Seyfert 1 galaxies occupy a distinct region of this diagram. Finally, there is no significant dependence of the ratio on the X-ray absorption column density except for the clear separation of the extremely Compton-thick source NGC 1068 from the rest of the sample.

We conclude that the correlation between HX and MIR luminosities described by eq. (3) is robust, although there is a weak indication that the slope of the correlation is not constant and decreases with increasing AGN luminosity.

For some applications, one may also be interested in knowing the distribution of for a given , rather than as a function of . We have therefore also computed (Appendix B) the inverse linear regression, i.e., as a function of , for our clean sample excluding NGC 4395. As can be seen in Fig. 2, this relation is different from the dependence of on .

### 5.2. Comparison with previous work

Mullaney et al. (2011) have studied infrared properties of nearby AGNs detected in the 14–195 keV energy band by Swift/BAT. This sample, although not statistically complete, is similar to our INTEGRAL sample in that it is hard X-ray selected. Using a subsample of AGNs having both Spitzer/IRS spectroscopic and IRAS photometric data, Mullaney et al. (2011) developed and tested a procedure, based on a set of starburst spectral templates, that make it possible to separate AGN and starburst contributions to the infrared flux using IRAS four-band photometry only. They then applied this procedure to a sample of 44 BAT AGNs and found that . This result is in excellent agreement with our eq. (3).

On the other hand, Gandhi et al. (2009) have reported a near proportionality between 2–10 keV () and 12 m luminosities for Seyfert galaxies using high angular resolution infrared observations: their best estimate is . This result seems to contradict our conclusion that the ratio decreases with increasing luminosity.

A number of factors might contribute to this discrepancy, but the most important one appears to be the difference in sample luminosities. A difference in galaxy weighting makes at most a minor difference. In their preferred regression procedure, Gandhi et al. (2009) took into account individual uncertainties in X-ray and infrared luminosities. However, the X-ray uncertainties were estimated in a rather arbitrary way, taking into account long-term variability for some sources but not for others. This led to significantly different weights ascribed to different sources in fitting. In our view, for the problem at hand, it is preferable to use a standard linear regression procedure in log–log space giving equal weights to all the sources in a sample. In fact, Gandhi et al. (2009) did perform such an analysis and obtained a somewhat flatter dependence , which is, however, still significantly steeper than the relation found here.

Another potentially important factor is the use of 2–10 keV X-ray luminosities by Gandhi et al. (2009) vs. our use of HX luminosities. Due to our hard X-ray selection and the resulting insensitivity to absorption effects, we are able to determine HX luminosities directly from 17–60 keV fluxes measured by INTEGRAL. In comparison, the Gandhi et al. (2009) sample contains a large number of significantly absorbed ( cm) sources whose intrinsic 2–10 keV luminosities were estimated through model-dependent analysis of X-ray spectra or, in some cases, even using [OIII] optical line fluxes. We have compared the HX and X-ray luminosities for 16 Seyfert galaxies (excluding the Compton thick Seyfert NGC 1068) which are present in both the INTEGRAL and Gandhi et al. (2009) samples. The data, spanning the range from  erg s (Cen A) to  erg s (Mrk 509), prove to be consistent with being proportional to . The small scatter (0.23 dex) associated with this correlation can be fully attributed to the uncertainties in the values as estimated by Gandhi et al. (2009), whereas the mean ratio may be considered typical for AGNs and is only slightly larger than the ratio (1.2) corresponding to a fiducial AGN spectrum used in our analysis below (§6.1). Furtheremore, systematic studies based on AGNs from the INTEGRAL (de Rosa et al., 2012) and Swift/BAT (Winter et al., 2009) hard X-ray surveys have not revealed a significant dependence of the HX/X-ray flux ratio on luminosity. We thus conclude that the use of by Gandhi et al. (2009) vs. our use of is unlikely to lead to a significant difference between the results of the corresponding X-ray–infrared cross-correlation analyses.

Differences in the infrared data analysis might also play a role. Our study is based on Spitzer/IRS spectroscopy and uses a template based separation of AGN and starburst spectral components. Gandhi et al. (2009) use narrow-filter photometry near rest-frame 12 m with the VISIR instrument on VLT, which provides a significantly better angular resolution compared to Spitzer/IRS and hence presumably minimizes host galaxy contamination. We have again used the overlapping sample of 16 Seyferts to check if there are any systematic differences associated with these two approaches. Specifically, we used our IRS spectra and derived fluxes within the VISIR filters that were used by Gandhi et al. (2009), which differ from object to object. As shown in Fig. 5, although the total fluxes measured by IRS spectra are somewhat higher than those measured by VISIR, our standard correction for the host galaxy contamination brings both data sets to nearly perfect agreement. A significant difference (a factor of ) is only observed for NGC 3081, but it seems natural to expect some deviations in a sample of 16 objects, given that Spitzer/IRS and VLT/VISIR observations were not simultaneous (for the same reason, the 8 m fluxes measured by IRAC and IRS differ significantly for some of our AGNs, see §4.4). Furthermore, there is no trend with either distance or luminosity, although the comparison sample spans distances from 3.6 Mpc (Cen A) to 174 Mpc (ESO 209-G012). We conclude that the differences in the infrared data analysis do not significantly bias our results with respect to those of Gandhi et al. (2009).

Perhaps most importantly, Gandhi et al. (2009) used a heterogeneous sample of 42 Seyfert galaxies, whereas we use a statistically complete and somewhat larger sample. As a result, the Gandhi et al. (2009) sample is significantly shifted to lower luminosities relative to ours (Fig. 6): e.g., the corresponding fractions of AGNs with  erg s are 12% and 38%. As was dicusssed in §5.1, dividing our sample into two subsets, and , represented by relatively low and high luminosity AGNs, respectively ( vs.  erg s), tentatively suggests that the slope of the X-ray–infrared correlation changes from to as the AGN luminosity increases. The Gandhi et al. (2009) sample effectively probes the luminosity range  erg s, similar to our subsample, and the slopes inferred for these two data sets are in satisfactory agreement with one another. This suggests that the results of Gandhi et al. (2009) and the present work are actually consistent with each other.

We conclude that further studies using larger, well-defined samples of AGNs are required to clarify if the slope of the X-ray–infrared correlation depends on luminosity, as tentatively suggested by the existing data.

## 6. Torus vs. disk and corona

The unified model posits that a torus of molecular gas and dust subtending a solid angle (if viewed from the SMBH) intercepts optical, UV, and soft X-ray radiation from the central accretion flow and converts it into thermal infrared emission. Therefore, assuming that the central source of radiation is isotropic, the total luminosity of the torus is expected to be

 LTorus≈ΩTorus4πLDisk, (4)

where is the luminosity of the accretion disk, presumably emitted between  m (NIR) and  keV (soft X-rays). These boundaries usually separate the MIR, BBB, and HX components (see §1) in the SEDs of type 1 AGNs (see, e.g., Elvis et al. 1994; Sazonov et al. 2004). Physically, the 1 m boundary marks the onset of thermal emission from hot dust at sublimation temperature ( K), whereas accretion disk emission is expected to peak in the near- or far-UV bands in quasars and Seyfert galaxies (e.g., Shakura & Sunyaev 1973; Hubeny et al. 2001). Therefore, the chosen energy boundaries for ensure that virtually all of the accretion disk luminosity is accounted for.

Depending on the column density through the torus, it can also reprocess a fraction of the higher energy (2–10 keV) luminosity emitted by a hot corona of the accretion disk. We have neglected this contribution in eq. (4), first because the torus’s optical depth may be significantly smaller than unity for 5–10 keV X-rays, in contrast to the softer emission from the accretion disk, and also because we expect the X-ray (below 10 keV) luminosity of the corona to be much lower than the bolometric luminosity of the accretion disk. This last assumption will be verified below upon completion of our cross-correlation analysis. Finally, it is assumed that none of the hard X-ray emission (above 10 keV) is absorbed within the AGN, which is a reasonable assumption expect for very Compton-thick objects such as NGC 1068.

As demonstrated below, Spitzer and INTEGRAL data together make it possible to estimate the luminosity () and the solid angle () of the torus as well as the luminosity of the corona (at energies 2–300 keV), . We can therefore use eq. (4) to study the relationship between and , i.e., between emission properties of the accretion disk and corona.

### 6.1. Bolometric corrections

We proceed by determining coefficients for conversion of the measured quantities and to the AGN intrinsic quantities and , respectively. Hard X-ray spectral shapes do not vary much from one Seyfert galaxy to another, apart from the photoabsorption rollover in type 2 objects below 10 keV. Typically, absorption corrected AGN spectra can be described above 2 keV as a power law with a photon index (e.g., Reeves & Turner 2000) and a rollover above  keV (e.g., Molina et al. 2009). We adopt that

 LHX≈0.3LCorona. (5)

This relation corresponds to a power-law spectrum with and an exponential cutoff at  keV and is consistent with an average 3–300 keV spectrum of local AGNs detected during INTEGRAL and RXTE surveys of the sky (Sazonov et al., 2008, 2010). Assuming that the values of the power-law index and cutoff energy vary from to 1.9 and from to  keV from one Seyfert galaxy to another (as indicated by numerous studies, e.g., Zdziarski et al. 1995; Molina et al. 2009), we can estimate that the conversion described by eq. (5) can introduce a scatter in values for a given of %, i.e.,  dex.

We next introduce a similar correction factor for the reprocessed emission from the torus:

 L15μm≈0.5LTorus. (6)

To obtain the above coefficient, we compared the 15 m luminosity with that integrated over the rest-frame 6–32 m band, , for those Spitzer/IRS spectra (21 in total) that span this whole wavelength range (i.e., there are available data from the IRS second-order SL module) and do not suffer from significant contamination by MIR emission from dust associated with star formation. For the majority of these objects, the ratio is bounded in the narrow range of 0.65–0.85, only slightly depending on whether AGN emission lines (such as [OIV] 25.9 m) are taken into account or not. We therefore adopted the relation for AGN tori and additionally lowered this ratio by one third in eq. (6) to account for non-negligible (%) additional torus emission both shortward of 6 m and longward of 32 m (see, e.g., Nenkova et al. 2008). While the resulting ratio (eq. [6]) is determined less strictly than the ratio above, the associated scatter in individual values around the mean trend given by eq. (6) is probably less than 20%, as suggested by the comparison of IRS spectra for “pure” objects, described above.

### 6.2. Solid angle of the torus

The next step in our analysis is to derive the torus solid angle . To this end, we assume that, for a given hard X-ray luminosity, is determined by the relative number of obscured (type 2) AGNs of that luminosity, i.e.,

 ΩTorus4π(LHX)=Ntype 2(LHX)Ntotal(LHX). (7)

We consider an AGN obscured if its X-ray absorption column density  cm. In this connection, recall (see §2) that the values for our objects are not based on INTEGRAL hard X-ray measurements but have been determined through analysis of high-quality X-ray spectra obtained by various X-ray telescopes.

Dividing our AGN sample into several bins in , Fig. 7 shows the fraction of absorbed AGNs as a function of . A strong trend of decreasing ratio with increasing luminosity is evident. We can estimate the statistical significance of this trend using a maximum-likelihood estimator,

 L=−2∑ilnP1,2(LHX,i). (8)

Here, the summation is over our sample of AGNs and is the probability for a given object with luminosity to be either obscured () or unobscured (). We restrict our consideration to the luminosity range , because there are only two objects in the sample which fall outside this range (one on either side, see Fig. 7). Suppose now that the fraction of obscured AGNs has a power-law dependence on luminosity:

 P2=p+α(logLHX−41.5). (9)

Obviously,

 P1=1−P2. (10)

Requiring that over the range yields constraints on the slope and intercept of the trend:

 0

and

 −p3.5<α<1−p3.5. (12)

With these definitions, the maximum of the likelihood function proves to be at and . By integrating over (, ) parameter space with the priors given by eqs. (11) and (12), i.e., using a Bayesian approach, we find that the probability that is 0.999. Hence, the declining luminosity trend of the obscured fraction is ascertained with more than 3 significance.

Sazonov et al. (2010) have recently confirmed this luminosity dependence (see their Fig. 3) using a nearly doubled sample of AGNs detected during 7 years of INTEGRAL observations (compared to the 3.5-year all-sky survey used in the present work). Furthermore, the existence of this trend has been reliably established in the past decade using various X-ray selected samples of AGNs (Ueda et al. 2003; Steffen et al. 2003; Sazonov & Revnivtsev 2004; La Franca et al. 2005; Sazonov et al. 2007; Hasinger 2008; Burlon et al. 2011; see in particular Fig. 8 in Hasinger 2008 and Fig. 13 in Burlon et al. 2011). Therefore, in accordance with eq. (7) we adopt the expression

 ΩTorus4π = ⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩1,logLHX≤41.51−0.25(logLHX−41.5),\omit41.5

We thus assume that the phenomenon of decreasing fraction of absorbed AGNs with increasing luminosity reflects an underlying trend of increasing opening angle of the obscuring torus. This is one of the crucial points in our analysis. According to eq. (13), the slope of the () dependence is approximately equal to 0.25 for ranging between and  erg s with the associated uncertainty being small, % as determined from the dispersion of data points in Fig. 7 and from the Bayesian analysis described above. However, the () dependence holds true in a statistical sense only, and there might be variations in the torus opening angle among AGNs of a given luminosity. Unfortunately, observations do not yet provide reliable information on the distribution of values for a given , and hence we cannot predict to what degree this scatter could affect our results below. Furthermore, the exact parameters of the () dependence adopted in eq. (13) should be applied only to the local () population of AGNs, in particular because the fraction of obscured sources among high-luminosity AGNs appears to be larger in the distant () Universe (e.g., Hickox et al. 2007; Hasinger 2008; Treister et al. 2008).

### 6.3. Disc vs. Corona

We are now ready to estimate the accretion disk luminosities for our AGNs using eq. (4):

 LDisk≈4πΩTorus(LHX)LTorus. (14)

Specifically, we first determine and using eqs. (5) and (6), respectively and then use eq. (14) to find . The resulting scatter plot of vs. for the clean sample excluding NGC 4395 is shown in Fig. 8.

Fitting the vs. data in Fig. 8 with a power law yields the correlation

 LDisk,44=(1.59±0.16)L0.97±0.06Corona,44, (15)

where the luminosities are measured in units of  erg s. The rms scatter around the mean trend is 0.33 and 0.34 dex along the and coordinates, respectively.

The derived relation, eq. (15), allows one to predict the disk luminosity for a given coronal luminosity. Hence, if the coronal luminosity of an AGN is known, one can expect its accretion disk luminosity to be equal within a factor of (at the 1 confidence level) to . The ratio does not significantly depend on luminosity in the effective range of from to  erg s.

The 2–10 keV energy band contains % of the total coronal luminosity. If all of this X-ray emission were converted in the torus into infrared radiation as efficiently as accretion disk emission, it would increase by only %. This justifies the approximation adopted in eq. (4).

For some applications, one may also be interested in knowing the distribution of for a given , rather than as a function of . We have therefore also computed (Appendix B) the inverse linear regression, i.e., as a function of , for our clean sample excluding NGC 4395. As can be seen in Fig. 8, this relation is different from the dependence of on .

### 6.4. Scatter around the mean trend

Fig. 9 shows the distribution of residuals for the correlation. Although it is plotted in terms of deviations, the distribution of residuals is quite similar. The distribution can be well-described by a log-normal function, ], where is the measured rms scatter of the correlation.

Although the observed scatter in the correlation is fairly small, the intrinsic correlation between the corona and disk luminosities in Seyfert galaxies is probably even tighter. Indeed, the 15 m fluxes measured by Spitzer, from which the values were derived, presumably represent reprocessed accretion disk emission averaged over a number of years. Interferometric observations of Seyfert galaxies have established that the size of the MIR-emitting dust region is of the order of several light years or more (Tristram et al., 2009). Specifically, the characteristic size of the 12 m source was found to scale approximately as the square root of the AGN luminosity222This is consistent with the simple argument based on considering dust heating by a central source of UV emission (Barvainis, 1987). and to vary from  pc for  erg s to  pc for  erg s. For example, Tristram et al. (2009) and Tristram & Schartmann (2011) found –3 pc for NGC 1068, NGC 1365, MCG 5-23-16, and NGC 4151 and  pc for NGC 7469. Therefore, the values used in our cross-correlation analysis should represent accretion disk luminosities averaged over the -long period immediately preceding the Spitzer observation of a given AGN, which is expected to range from a few years for the least luminous sources to a few tens of years for the most luminous ones. As demonstrated in Appendix C, variability of the HX coronal emission, detected by INTEGRAL on time scales shorter than the characteristic time scale of MIR variations, is expected to induce a scatter of –0.25 dex around the mean trend.

Additional contributions to the observed scatter around the mean trend can be provided by systematic uncertainties associated with: i) measurement of and , each  0.1 dex (see Table 1 and §4.4), ii) conversion from to and from to , also  dex each (§6.1), and iii) determination of the mean torus solid angle () for a given AGN luminosity and consequently conversion from to (via eq. [14]),  dex (§6.2). Hence, each of the above effects can contribute of the order of, or less than, 0.1 dex to the observed scatter in the correlation. Adding these contributions in quadrature to that expected from varibility implies that the total induced scatter is  dex. After subtraction of this contribution from the measured scatter of the correlation, with rms  dex, there remains a scatter –0.25 dex, i.e., a factor of 1.5–2.

Therefore, the intrinsic correlation between accretion disk and coronal emission in Seyfert galaxies is fairly tight. Furthermore, neither the relation nor the relation, from which it originates, shows a significant dependence on either optical AGN type or X-ray absorption column density, although there are exceptions, which are discussed below. Assuming that the torus is co-aligned with the accretion disk and is a quasi-isotropic MIR emitter, this suggests that the coronal hard X-ray emission is at most modestly (less than a factor of ) anisotropic. This conclusion also holds true if the obscuring torus is oriented quasi-randomly with respect to the accretion disk/corona axis because for given there is little scatter in . By the same argument, the hard X-ray luminosity of AGNs cannot be dominated by collimated emission from relativistic jets.

As to the origin of the remaining (unaccounted for) scatter, at least two effects are likely to contribute to it. First, our analysis was based on the assumption that the characteristic solid angle subtended by the obscuring torus, , is the same for all AGNs of a given luminosity. In reality, it is possible that varies from one object to another (e.g., Elitzur 2012). This would directly affect our estimates of from and introduce scatter in the resulting correlation between and . Similarly, the amplitude of the Compton reflection component, ignored in our analysis, may vary from one AGN to another, which would introduce additional scatter. Therefore, the scatter in the intrinsic ratio of powers generated in the accretion disk and corona is likely even smaller than 0.2 dex.

### 6.5. Comparison with typical quasars

The results of this work pertain to nearby Seyfert galaxies, and it is interesting to put them into the broader context of the cosmic history of SMBH growth. To this end, we compare our findings with the properties of the SED of the “average quasar” from Sazonov et al. (2004). This template essentially rests on the assumption that the cosmic X-ray background (CXB) represents the integrated hard X-ray emission of all AGNs in the Universe and on the argument of Soltan (1982) that the cumulative bolometric luminosity of AGNs is determined by the mean radiative efficiency with which the integrated mass of local SMBHs has been accumulated over the cosmic time. Adopting , Sazonov et al. (2004) found that % of the bolometric luminosity (below 300 keV) of the average quasar, is emitted at energies above 2 keV. Attributing this emission to the corona of the accretion disk and making a small correction for absorption in the 2–10 keV energy band (because here we are interested in intrinsic rather than observed properties of accretion disks and coronae), we find that for the average quasar. If we instead assume that , which corresponds to the standard Shakura–Sunyaev disk around a Schwarzschild black hole, then . By construction, this ratio primarily characterizes quasars with  erg s, which produce the bulk of the CXB (e.g., Ueda et al. 2003).

We can now determine the corresponding average ratio for the local AGN population, using a completely different method. The mean trend given by eq. (15) and the associated scatter (0.34 dex) imply that the ratio varies between and (the 1 range) around the mean value of . Averaging over the log-normal distribution of yields , independently of . This ratio characterizes the summed radiation of the local AGN population. Therefore, the ratio appears to be larger, but only by a factor of , for typical quasars making up the CXB relative to typical AGNs in the local Universe. This implies that the ratio of the disk and coronal luminosities is approximately constant in all actively accreting, radiatively efficient SMBHs.

### 6.6. Possible effect of anisotropic accretion disk emission

Our treatment so far has been based on the assumption that the accretion disk is an isotropic source, i.e., its observed luminosity is independent from the viewing angle. This implies that the primary (UV) and reprocessed (infrared) luminosities of AGNs are related through eq. (4). However, the actual angular distribution of radiation emergent from the accretion disk around a SMBH might be close to Lambert’s law, in which case the luminosity per solid angle , where is the viewing angle with respect to the axis of the disk. If, in addition, an obscuring torus is not randomly oriented but its equator lies in the plane of the accretion disk, then there will be a different relation between and :

 LTorus≈(ΩTorus4π)2LDisk. (16)

Considering this possibility a feasible alternative to our baseline scenario, we repeated our calculations using eq. (16) instead of eq. (4). The resulting correlation between the corona and disk luminosities is shown in Fig. 10 and the corresponding best-fitting relation is given by:

 LDisk,44=(3.4±0.3)L1.21±0.06Corona,44, (17)

with the rms scatter in .

The anisotropic scenario predicts significantly larger / ratios at high luminosities (a factor of at  erg s) compared to the isotropic case. However, at these luminosities there is large uncertainty in the inferred values for the anisotropic case, which is not fully reflected in the formal uncertainties quoted in eq. (17). Specifically, the uncertainty associated with our adopted dependence of the torus solid angle on luminosity, eq. (13), is not taken into account. As is clear from Fig. 7, this additional uncertainty is large at high luminosities,  erg s, which was relatively unimportant when we considered the isotropic scenario but is the dominant source of uncertainty for the anisotropic scenario due to the quadratic dependence on in eq. (16).

The above consideration ignores two potentially important effects. First, radiative transfer in the accretion disk may lead to a limb-darkening effect, making the emission even more collimated in the polar direction than (e.g., Sunyaev & Titarchuk 1985; Laor & Netzer 1989). On the other hand, strong gravity in the vicinity of a black hole tends to harden the spectrum and increase the luminosity for observers viewing the accretion disk at grazing angles, with this effect being especially pronounced for rapidly rotating black holes (Cunningham, 1975; Malkan, 1983).

Taking these various factors into account, it is likely that the correlations obtained in our isotropic (Fig. 8) and anisotropic (Fig. 10) scenarios bracket the true relationship between the corona and disk emission in AGNs. Furthermore, orientation effects and object-to-object variations in the black hole spin can contribute to the scatter in the relation between and .

## 7. Discussion and conclusions

The main result of this work is that the luminosities of the accretion disk and corona are nearly proportional for nearby AGNs: . To reveal this correlation, we derived intrinsic (presumably emitted between  m and  keV) accretion disk luminosities from observed torus luminosities, , using eq. (14), which assumes that radiation from the accretion disk is reprocessed in a dusty torus whose effective solid angle decreases with increasing luminosity from almost at  erg s to at  erg s, as suggested by the observed falling fraction of obscured AGNs (eqs. [7] and [13]). This effect of decreasing obscuration fraction is responsible for the MIR/HX luminosity ratio decreasing with increasing AGN luminosity: .

The observed relation implies a mean ratio for nearby AGNs. For comparison, for typical quasars producing the cosmic X-ray background, –6 (see §6.5). Hence, hard X-ray radiation from accretion disk coronae (with a possible contribution from jets) carries a significant and roughly constant fraction, –35%, of the bolometric luminosity of SMBHs accreting in radiatively efficient mode (with a possible exception of black holes accreting near the critical Eddington rate, see §7.5 below).

### 7.1. Intrinsic ratio of disk and corona luminosities

The measured ratio likely overestimates the ratio of the intrinsic UV and hard X-ray luminosities produced by the accretion disk and corona, respectively, because roughly half of the luminosity emitted by the corona is intercepted by the disk (and a small additional amount by the obscuring torus) and only –20% of this radiation (e.g., Haardt & Maraschi 1993) is reflected, while the rest is reprocessed into thermal, softer emission and thus contributes to the disk luminosity. In contrast, it is well-known that the corona in Seyfert galaxies intercepts only a small fraction of the disk’s radiation, probably because the corona is patchy (e.g., Zdziarski et al. 1997). Indeed, the measured shapes of the hard X-ray spectra of Seyferts imply that the hot corona is characterized by an amplification factor –10 (Gilfanov et al., 2000), i.e., the luminosity of the Comptonized hard X-ray radiation emergent from the corona is several times the luminosity of the incident soft photons. This would imply that if the disk were embedded in a homogeneous corona. Since in reality , as suggested by the results of the present study, the presence of a strong big blue bump in the spectra of type 1 AGNs, and theoretical arguments (e.g., Zdziarski et al. 1997), the solid angle subtended by the corona with respect to the accretion disk must be small, i.e., to a first approximation the corona does not shield the disk from the observer.

On the other hand, the Compton reflection hump is located approximately in our working INTEGRAL energy band (17–60 keV) and may significantly contribute to the measured hard X-ray flux (see examples of tentatively detected reflection components in INTEGRAL spectra of AGNs in de Rosa et al. 2012), so that we likely overestimate the flux of HX radiation coming directly from the corona in our simplistic analysis.

Considering these counteracting effects together, the intrinsic ratio of the disk and coronal luminosities could be a factor of smaller than the measured ratio. This implies that in Seyfert galaxies, approximately equal powers are generated in the accretion disk and hot corona.

### 7.2. AGN bolometric corrections. Current rate of SMBH growth

Our results suggest that hard X-ray luminosity is a good proxy for bolometric AGN luminosity (), except for extremely Compton-thick sources like NGC 1068. Using eqs. (15) and (5), we can estimate the bolometric correction for the 17–60 keV energy band and the associated range (due to the scatter in the correlation):

 LbolLHX≈9(6−15) (18)

in the range –10 erg s.

The cumulative hard X-ray (17-60 keV) luminosity density of nearby AGNs found by integrating their luminosity function measured by INTEGRAL at  erg s is  erg s Mpc (Sazonov et al., 2007, 2010). Low-luminosity ( erg s) AGNs may add up to % to this volume emissivity, as follows from cross-correlating the cosmic X-ray background intensity with the local galaxy distribution (e.g., Revnivtsev et al. 2008; Miyaji et al. 1994; Carrera et al. 1995). Using the ratio from eq. (18), the bolometric luminosity density of local AGNs is thus  erg s Mpc. This implies that the integrated present-day growth rate of SMBHs is  yr Mpc, where is the average radiative efficiency of accretion. Comparing with the total mass density of local SMBHs,  Mpc (Yu & Tremaine, 2002; Marconi et al., 2004), the total SMBH mass is currently growing on a time scale  times the age of the Universe.

This estimate of the SMBH growth rate does not fully account for the contribution of obscured accretion taking place in Compton-thick ( cm) AGNs. Moreover, it is valid only for accretion that is occurring in a radiatively efficient mode. In reality, a substantial fraction of SMBH growth at the present epoch may be taking place through a radiatively inefficient mode of accretion, dominated by mechanical rather than radiative energy output (e.g., Churazov et al. 2005; Merloni & Heinz 2008). Therefore, the total SMBH accretion rate may be higher.

We can re-calculate the bolometric correction given by eq. (18) to the standard X-ray band, 2–10 keV. Assuming, as in §6.1, a power-law spectrum with and an exponential cutoff with  keV, the 2–10 keV/17–60 keV luminosity ratio and therefore

 LbolLX≈11(7−18). (19)

This formula predicts the bolometric luminosity of an AGN from its intrinsic (i.e., unabsorbed) luminosity in the 2–10 keV energy band in the range –10 erg s.

Finally, we can estimate the bolometric correction for the MIR band (m), using eqs. (18) and (3):

 LbolL15μm≈5. (20)

This formula should be accurate to within a factor of for AGNs with –10 erg s. We have not tried to take into accout the non-linear dependence of on , because it should only be used to predict for a given but not for a given . A more reliable bolometric correction for the MIR band could be obtained by using a MIR selected sample of AGNs. Interestingly, eq. (20) is in good agreement with an early estimate by Spinoglio & Malkan (1989), , based on direct integration of the IR-to-UV (–100 m) spectra of bright Seyfert galaxies. In reality, as we have shown in this paper, the decreasing trend of the MIR/bolometric luminosity ratio with increasing largely arises owing to the decreasing torus angular size, , whereas the fraction remains nearly constant.

### 7.3. Comparison with the UV–X-ray luminosity relation

A number of studies have found that the ratio of near-UV () to soft X-ray ( keV) luminosities in type 1 AGNs increases with luminosity (e.g., Vignali et al. 2003; Strateva et al. 2005; Steffen et al. 2006; Young et al. 2010; see, however, Yuan et al. 1998; Gaskell et al. 2004; Tang et al. 2007). This suggests that the disk/corona luminosity ratio increases with luminosity, in apparent contradiction to our finding that this ratio is approximately constant over about two decades in luminosity.

Part of the explanation may be that, although the near-UV flux might be a good proxy of the bolometric luminosity of the accretion disk in luminous quasars containing very massive black holes, it might be a poor indicator (see also Vasudevan & Fabian 2007; Vasudevan et al. 2009) in lower luminosity AGNs with less massive black holes (such as Seyfert galaxies), because the maximum of their accretion disk emission is expected to be located in the extreme-UV rather than in the near-UV band (e.g., Shakura & Sunyaev 1973; Hubeny et al. 2001). Mid-infrared observations, such as used in the present study, make it possible to disclose the true bolometric luminosity of the accretion disk by measuring the luminosity of the obscuring torus, which serves as a calorimeter of the power radiated by the central engine.

Furthermore, there is probably no discrepancy at all, because our study probes relatively low-luminosity AGNs compared to the quasars used in the studies. Indeed, assuming again a power-law spectrum with an exponential cutoff at  keV, the  erg s luminosity range effectively probed by INTEGRAL in the 17–60 keV band corresponds to a range of 2 keV-monochromatic luminosities of to  erg s Hz. As can be seen, e.g., from Fig. 4 in Steffen et al. (2006), such AGNs are located in the low-luminosity part of the diagram, where the data are consistent with being proportional to , whereas the evidence for a decreasing luminosity trend of / comes from more luminous AGNs with </