The Spectral Energy Distributions and Bolometric Luminosities of Local AGN: Study of the Complete 12 μm AGN Sample

We measure the bolometric luminosity of a complete and unbiased 12 μm-selected sample of active galactic nuclei (AGN) in the local Universe. For each galaxy, we used a 10-band radio-to-X-ray spectral energy distribution (SED) to isolate the genuine AGN continuum in each band, including subarcsecond measurements where available, and correcting those contaminated by the host galaxy. We derive the median SED of Seyfert type 1 AGN, Seyferts with hidden broad lines (HBLs), Seyferts of type 2, and LINER nuclei in our sample. The median Seyfert 1 SED shows the characteristic blue bump feature in the UV, but nevertheless, the largest contribution to the bolometric luminosity comes from the IR and X-ray continua. The median SEDs of both HBL and type 2 AGN are affected by starlight contamination in the optical/UV. The median SED of HBL AGN is consistent with that of Seyfert 1s, when an extinction of A V ∼ 1.2 mag is applied. The comprehensive SEDs allowed us to measure accurate bolometric luminosities and derive robust bolometric corrections for the different tracers. The 12 μm and K-band nuclear luminosities have good linear correlations with the bolometric luminosity, similar to those in the X-rays. We derive bolometric corrections for either continuum bands (K band, 12 μm, 2–10 keV, and 14–195 keV) or narrow emission lines (mid-IR high-ionization lines of [O iv] and [Ne v] and optical [O iii] 5007 Å) as well as for combinations of IR continuum and line emission. A combination of continuum plus line emission accurately predicts the bolometric luminosity up to quasar luminosities (∼1046 erg s−1).


Introduction
The determination of the bolometric luminosity of active galactic nuclei (AGN) is important to study the AGN phenomenon itself, which is sustained by an accreting supermassive black hole (SMBH; see, e.g., Rees 1984), and, on the other hand, to understand the role of AGN in galaxy evolution.
The need to place the Seyfert nucleus phenomenon in the framework of galaxy evolution was already clear more than 40 yr ago.It was realized that the most universal major contributions to the bolometric luminosity of AGN come from the hard X-ray and mid-IR bands.For the former, we know that the X-ray band emission is characteristic of AGN: X-ray emission is ubiquitous in AGN and is thought to be produced by Comptonization of UV/optical disk photons by a corona of hot electrons located above the black hole.For the latter, in fact, the mid-IR, and in particular the IRAS 12 μm band, has been used to select a complete sample of AGN (Spinoglio & Malkan 1989;Rush et al. 1993;Spinoglio et al. 1995) because it was realized that this band was carrying a constant fraction of the bolometric luminosity of different types of low-redshift AGN, including Seyfert galaxies of types 1 and 2, and quasars.This result arises from the fact that AGN energy distributions are roughly described by a one-parameter family: a relatively blue quasar continuum altered by varying amounts of nuclear dust.The dust preferentially absorbs continuum at the shortest wavelengths and reemits it in the far-infrared.These two processes make the resulting energy distribution redder in the optical/ultraviolet and IR.However, there is a pivot wavelength, at which the absorption of the original continuum is balanced by the thermal reemission.This occurs in the mid-IR and in fact, 7-12 μm is the only wavelength range where both of these effects (absorption and reemission) are relatively small (Spinoglio & Malkan 1989).
This study was based on the large-aperture IRAS data (Neugebauer et al. 1984), possibly contaminated by emission from the host galaxy.It therefore needed to be reexamined using mid-IR observations of the intrinsic nuclear emission of the AGN.
The first determination of the bolometric luminosity of lowredshift quasars has been done by Sanders et al. (1989), who presented multiwavelength observations (10 9.7 -10 18 Hz) of 109 bright quasars from the Palomar-Green (PG) survey (Schmidt & Green 1983) and showed that the PG quasars emit the bulk of their luminosity (typically more than 90%) between 3000 Å and 300 μm.A few years later, Elvis et al. (1994) integrated the energy distributions of 47 quasars selected mainly from the PG, 3C, and Parkes catalogs using a simple linear interpolation through the data points in L log n n space, i.e., connecting the individual points with a power law and derived bolometric corrections for UV, visible, and infrared monochromatic luminosities.They lacked complete data from the hard X-ray bands, and their sample was primarily an ultraviolet-excess-selected sample and biased toward relatively X-ray-loud quasars.
Following that pioneering work, there have been a few determinations of the bolometric luminosity of AGN, either from selective measurements of the continuum in various spectral ranges and assuming templates to reproduce the spectral energy distributions (SEDs) of AGN (e.g., Marconi et al. 2004;Hopkins et al. 2007;Lusso et al. 2012) or from observations of spectral lines (e.g., Meléndez et al. 2008;Spinoglio et al. 2022).These estimates assume that the measured radiation is isotropic and that simple bolometric corrections can recover the total luminosities of most AGN.Marconi et al. (2004) used the following approach to derive the bolometric corrections, i.e., the corrections to be applied to an observed luminosity to derive the total intrinsic, i.e., bolometric, luminosity of the AGN.Their argument is that although the observed SED of an AGN provides the total observed luminosity (L obs ), this does not give an accurate estimate of the BH mass accretion rate because it often includes reprocessed radiation (i.e., radiation absorbed along other lines of sight and reemitted isotropically).In their view, the accretion rate is related to the total luminosity directly produced by the accretion process, which they call the total intrinsic luminosity L int .In AGN, L int is given by sum of the optical-ultraviolet and X-ray luminosities radiated by the accretion disk and hot corona, respectively.They consider that, in order to estimate L int , one has to remove the IR bump (2.5-60 μm) from the observed SED of unobscured AGN to avoid double counting the source luminosity, i.e., extinction-corrected X-ray emission and reprocessed IR emission.Marconi et al. (2004) used a template spectrum for the AGN, based on the observed optical-UV and X-ray spectra, excluding the observed IR bump, following the above argument.From the assumed template, they compute the bolometric corrections with respect to the optical B band and the soft and hard X-ray bands.
With the aim of determining the bolometric quasar luminosity function, Hopkins et al. (2007) have taken a similar approach to the one of Marconi et al. (2004) in calculating the template spectrum, but they included in the template the observed IR bump, giving a more detailed treatment of the optical/IR.In particular, they used the Richards et al. (2006) template spectrum in the B, g, and i optical bands and a different determination of the spectral index between optical and X-rays (α ox ).
They also found a dependence of the bolometric correction on the luminosity.They compiled a large number of luminosity functions measurements in different redshift ranges, observed wave bands and luminosity intervals from various AGN samples (see Table 1 of Hopkins et al. 2007), selected from the optical, the soft X-rays, the hard X-rays and also at 8-15 μm, including the 12 μm AGN sample (Rush et al. 1993).Vasudevan & Fabian (2007) showed that the variations in the disk emission in the ultraviolet are important by construction of an optical-to-X-ray SED for 54 AGN using Far Ultraviolet Spectroscopic Explorer UV and X-ray data from the literature to constrain the disk emission as well as possible.They also found evidence for a very significant spread in the bolometric corrections, with no simple dependence on luminosity being evident.Populations of AGN such as narrow-line Seyfert 1 nuclei (Osterbrock & Pogge 1985) and radio-loud and X-ray-weak AGN may have bolometric corrections that differ systematically from the rest of the AGN population.Lusso et al. (2012) obtained accurate estimates of bolometric luminosities, bolometric corrections, and Eddington ratios of a large X-ray-selected sample of broad-line (type 1) and narrowline (type 2) AGN from the COSMOS (Scoville et al. 2007) XMM-Newton survey for which extensive data from the far-IR to the optical and ultraviolet regimes were available.They assumed that the intrinsic nuclear luminosity is the sum of the IR and X-ray luminosities (L bol = L IR + L X ).They used an SED fitting code to disentangle the various contributions (using starburst, AGN, and host galaxy templates) in the observed SED by using a standard χ 2 minimization procedure, and they integrated the nuclear component from 1 to 1000 μm to obtain the total IR luminosity L IR .To derive the nuclear accretion disk luminosity from this value, they applied a geometric correction factor based on the models by Pier & Krolik (1992) to account for the torus geometry and their associated anisotropy (see Pozzi et al. 2010).The total X-ray luminosity L X is estimated by integrating the X-ray SED in the 0.5-100 keV range.They found that the bolometric correction is significantly lower at high luminosities with respect to the previous estimates of Marconi et al. (2004) and Hopkins et al. (2007).The main limitation of the study of Lusso et al. (2012) is that it is entirely based on an X-ray-selected sample of AGN and therefore can be biased toward X-ray-bright AGN with most of the sources showing relatively low hydrogen column densities (N H  10 23.5 cm −2 ), thus missing heavily absorbed Comptonthick nuclei.
Other attempts have been made to derive the AGN bolometric luminosity from optical and IR lines originated in the narrow-line regions (NLRs) of AGN.Meléndez et al. (2008)  Our approach to measure the bolometric luminosity of AGN is different from the other derivations summarized above.
(i) We do not assume an a priori template AGN SED as was done in the other derivations (e.g., Marconi et al. 2004;Hopkins et al. 2007), but we have defined 10 photometric bands from the radio to the X-rays to cover the SED of the AGN of the chosen local AGN sample, and we computed the correlations first among the various bands and then, after having integrated a total bolometric nuclear luminosity for as many AGN in the sample as possible, we computed the correlations of the various bands, and combinations of them, with the estimated bolometric luminosity.(ii) With respect to the work of Marconi et al. (2004), we now include subarcsecond measurements of the IR bump, which might also be due to reprocessed radiation reradiated by hot dust, because-even if reprocessedthis radiation ultimately originates in the accretion process in the AGN.

Sample of Local AGN and Multifrequency Data Set
The sample of local AGN used to compute the bolometric luminosity is the 12 μm AGN (hereafter 12MAGN) sample, originally selected from the IRAS catalog from Spinoglio & Malkan (1989) and updated in Rush et al. (1993).The chosen sample is essentially a bolometric flux-limited survey outside the galactic plane and therefore largely unbiased, given the empirical fact that galaxies emit an approximately constant fraction of their total bolometric luminosity at 12 μm.This fraction is ∼15% for AGN, including Seyfert types 1 and 2 and quasars (Spinoglio & Malkan 1989), and 7% for normal and starburst galaxies, independent of star formation activity (Spinoglio et al. 1995).The sample is given in Table 1 and is the same as the one used in Spinoglio et al. (2022).This sample has been selected from the 12 μm flux-limited survey of 893 galaxies (Rush et al. 1993) extracted from the IRAS Faint Source Catalog, version 2 (Moshir et al. 1990), with the classification of galaxy nuclear activity with catalogs of active galaxies available at the time of the selection (Helou et al. 1991;Hewitt & Burbidge 1991;Veron-Cetty & Veron 1991).It contains in total 117 AGN, divided into 48 Seyfert type 1, 27 hidden broad-line (HBL) galaxies, 30 Seyfert type 2, 10 low-ionization nuclear emission-line region (LINER) galaxies, and two other galaxies, one classified as "non-Seyfert" (NGC 1056) and one classified as a starburst galaxy (NGC 6810).We have adopted here the class of HBL galaxies because they are indistinguishable in their IR properties from the Seyfert type 1 galaxies and therefore belong to the broader class of type 1 AGN (see, e.g., Tommasin et al. 2010).The 10 radio-loud objects in the sample are flagged in Table 1.The average redshift(s) and dispersion(s) for the whole sample are 〈z〉 = 0.025 ± 0.029, while for the four classes of galaxies considered, they are Sy1: 〈z〉 = 0.032 ± 0.039; HBL: 〈z〉 = 0.023 ± 0.019; Sy2: 〈z〉 = 0.019 ± 0.016; and LIN: 〈z〉 = 0.016 ± 0.021.
To compute the bolometric luminosity of local AGN, we have considered the following photometric bands, from low to high frequencies: radio 8.4 GHz; the mid-IR 12, 7, 5.8, and 4.5 μm bands; near-IR 2.2 μm; the near-ultraviolet (NUV) Galaxy Evolution Explorer (GALEX; Morrissey et al. 2007) band at an effective wavelength of 2316 Å and the farultraviolet (FUV) GALEX band at 1539 Å; and the 2-10 and 14-195 keV hard X-ray bands.
Our main concern in this analysis has been to derive, from the available observations, the nuclear fluxes of the AGN of our sample, because many local AGN are contaminated by the galactic component, which at some frequencies can be dominant.In order to isolate the nuclear emission from the total observed emission in the various mid-IR bands that we have considered, we have used the subarcsecond observations at 12 μm to correct the other observations, and we have corrected the near-IR K-band observations as well as the ultraviolet fluxes.However, the 8.4 GHz flux densities are already detecting the nuclei at subarcsecond resolution, and the hard X-ray emission is intrinsically produced mainly by the AGN.
From the low-frequency data (radio) to the high-energy data (X-rays), we have adopted the following methodology.
(i) The radio data at 8.4 GHz have been taken from the Very Large Array (VLA; Thompson et al. 1980) with a resolution of 0 25 (Thean et al. 2000) and therefore are sampling the nuclear emission.At the average distance of the whole AGN sample, the angular distance of 0 25 corresponds to a linear distance of 134 pc.Considering the different AGN classes, at the average distance of Seyfert 1, the angular distance of 0 25 corresponds to 142 pc, at that of Seyfert 2, it corresponds to 102 pc and at that of LINER, it corresponds to 86 pc, thus confirming that the radio VLA observations are mainly sampling the nuclear emission.The presence of a jet core in the data would in any case be due to the AGN.(ii) The 12 μm continuum flux density has been taken from Very Large Telescope (VLT) VISIR (Lagage et al. 2004) subarcsecond-resolution observations (Asmus et al. 2014); when these observations were not available, we used the small-aperture ∼10 μm observations from Gorjian et al. (2004) and in only two cases from Rieke (1978; see Table 2).(iii) The 7 and 12.8 μm continuum fluxes have been derived using Spitzer-IRS (Houck et al. 2004) spectroscopy of the [Ar II] 7.0 μm and [Ne II] 12.8 μm lines, respectively, using the line intensities together with the measured equivalent widths (EWs) from Gallimore et al. (2010).These data include galactic emission and therefore need to be corrected.(iv) The Spitzer-IRS data at 7 μm and the Spitzer-IRAC (Fazio et al. 2004) data at 5.8 and 4.5 μm have been corrected using the observed ratio of the Spitzer-IRS 12.8 μm continuum to the VLT-VISIR 12 μm subarcsecond continuum flux density (or the small-aperture ∼10 μm flux density; see the above point (ii)).(v) The K-band nuclear flux has been derived from Keck and Two Micron All Sky Survey (2MASS) observations as reported and fully explained in Spinoglio et al. (2022).(vi) The GALEX NUV and FUV fluxes have been derived using the GALEX point-spread functions (PSFs) of the two UV bands, following the work of Morrissey et al. (2007).(vii) The 2-10 and 14-195 keV hard X-ray data are intrinsically emitted by the AGN, so we assume that they do not need to be corrected.The compilation for the 12 μm sample has been taken from Spinoglio et al. (2022), and the observations have been reported in Ricci et al. (2017) and Oh et al. (2018).

Deriving the Nuclear Fluxes for the Mid-IR and UV Bands
To build up the AGN bolometric luminosity, we have compiled, for our sample of galaxies, in Table 2 the lowfrequency (from radio to near-IR) nuclear fluxes and in Table 3 the high-frequency (from UV to X-rays) nuclear fluxes.In Table 2 we give, for each galaxy of the 12MAGN sample observed, the 8.4 GHz radio flux, measured with the VLA (Thean et al. 2000) with a 0 25 effective aperture, and the 12 μm nuclear flux density measured with the VLT-VISIR in most cases (Asmus et al. 2014; where these data were not available, we have used the 10 μm small-aperture flux taken from Rieke 1978;Gorjian et al. 2004 and inserted a note in Table 2).
We have then extracted from the fluxes and EW measurements of the two fine-structure lines of [Ar II] 7.0 μm and [Ne II] 12.8 μm from Gallimore et al. (2010), who made systematic Spitzer observations of the 12MAGN sample, the corresponding flux densities of the continuum at 7.0 and 12.8 μm.The spectral information was extracted from synthetic 20″ diameter circular apertures centered on the brightest compact IR source; therefore, the derived continuum flux densities are relative to the extended 20″ emission.In order to remove the extended emission and obtain nuclear flux densities, we have computed the ratio of the 12.8 μm 20″ diameter flux density from Spitzer-IRS to the nuclear 12 μm flux density measured by VLT-VISIR (Asmus et al. 2014).We ignored the small difference in wavelength between the two observations.Using the same ratio, R12 in Table 2, we have corrected the 4.5 and 5.8 μm flux densities from Spitzer-IRAC, measured by Gallimore et al. (2010) using a synthetic 20″ diameter circular aperture centered on the brightest infrared source associated with the active galaxy.We have also corrected the 7.0 μm continuum derived from the Spitzer-IRS observations of the [Ar II] 7.0 μm line, as described above.We have included in Table 2 the corrected 7.0, 5.8, and 4.5 μm flux densities only for objects for which the R12 ratio is less than 3 (R12 < 3), discarding all objects for which this ratio is greater than this threshold.The latter has been chosen because we have estimated a reasonable correction only below this threshold.The number of objects above this threshold (with R12 > 3) is 14 plus two galaxies with upper limits in the VLT-VISIR data (see Table 2).
The near-IR nuclear K-band flux density has been derived in Spinoglio et al. (2022), and we refer to this work for the details.
The high-frequency (from UV to X-rays) nuclear flux densities reported in Table 3 include the NUV and FUV ultraviolet flux densities derived from GALEX observations and the 2-10 and 14-195 keV band hard X-ray fluxes, together with the photon indexes Γ 1 and Γ 2 relative to the 2-10 and 14-195 keV observations, respectively.The GALEX (Morrissey et al. 2007)   (This table is available in its entirety in machine-readable form.)(This table is available in its entirety in machine-readable form.) data have been extracted from the Mikulski Archive for Space Telescopes (MAST; Conti et al. 2011) GALEX Catalog Search. 4 For each AGN in our sample, we have extracted the NUV and FUV fluxes and errors in the four smallest apertures and the given values of the galactic interstellar reddening E(B − V ).The GALEX absolute calibration and extinction coefficients have been taken from Morrissey et al. (2007) and Wall et al. (2019), respectively.In order to obtain the best approximation of the nuclear UV fluxes, we have used the fluxes from APER_1 to APER_3, corresponding to radii of 1 5-3 8.For the 23 AGN for which upper limits were present in the APER_1 FUV flux, we have taken the APER_2 flux, for the 9 AGN for which also the APER_2 flux was an upper limit, we have taken the APER_3 flux, while when also the APER_3 flux was an upper limit, we have used this latter as the final upper limit to the FUV flux.The APER_n (with n = 1-3) fluxes have then been corrected using the GALEX photometric curve of growth published in Morrissey et al. (2007) to derive the nuclear fluxes.
The 2-10 keV X-ray fluxes, corrected for absorption, and the 14-195 keV band hard X-ray fluxes have been taken from the references given in Table 3.Because these fluxes are intrinsically produced by the AGN, no further correction should be needed.

Building the Bolometric Luminosity from the Available Nuclear Luminosities
Once the nuclear fluxes were computed, we used trapezoidal integration to calculate the total, or bolometric, luminosity for our AGN sample.The integration has been performed in two separate spectral regions: the first interval is from the radio (8.4 GHz band) to the FUV band, while the second interval includes only the two X-ray bands (2-10 and the 14-195 keV).For those AGN where only one X-ray band flux was available, we computed the missing flux using the median spectral index between 2-10 and 14-195 keV for each of the four AGN classes.The resulting bolometric luminosity is simply the sum of these two integrations.No interpolation has been included between the UV and X-ray data because this spectral region is not observable, and a power-law interpolation would likely have overestimated the bolometric luminosity.
To assign a bolometric luminosity to an AGN of our sample, we require a minimum number of detections over the 10 photometric bands considered.We require at least three available detections in three bands, and these must include either the 2-10 or the 14-195 keV X-ray band.When no X-ray data were available, we were nevertheless able to assign a lower limit to the bolometric flux and luminosity, because the low-frequency domain, from the radio to the K band, is carrying a substantial part of the total luminosity, as can be seen from the shape of the SEDs (see Figures 12-15).
The derived bolometric luminosities and bolometric fluxes for our sample are given in Table 3 For only two objects we were not able to assign even a lower limit to the bolometric luminosity and flux, namely, NGC 1056 and NGC 3511, because of the lack of observations both in the mid-IR (only IRS large-aperture data are available) and at X-rays.

Monochromatic Luminosities
We have selected three observables as the best AGN bolometric luminosity indicators: the corrected 2-10 keV hard X-ray luminosity, the nuclear 12 μm luminosity, and the luminosity of the [O IV] 26 μm line.These three physical quantities have been chosen for the following reasons.(i) X-ray emission is ubiquitous in AGN and is believed to be produced by Comptonization of UV/optical disk photons by a corona of hot electrons located near the black hole.(ii) The mid-IR, and in particular the nuclear 12 μm emission, is the spectral region that has been found to have the minimum scatter in the ratio of the observed to total luminosity among various types of AGN (Spinoglio & Malkan 1989); therefore, the mid-IR flux is considered one of the best general indicators of the bolometric luminosity of all types of AGN.(iii) The [O IV] 26 μm line emission is mainly produced in the AGN NLRs; therefore, it is indirectly linked to the accretion power of the AGN.It is a good measure of the AGN bolometric luminosity, as recently demonstrated by, e.g., Spinoglio et al. (2022).Shorter wavelengths, from the soft X-rays through the optical, can suffer from large extinctions, which are difficult to determine.
To quantify the statistical significance of the relations that we present in the following sections, we used an orthogonal distance regression (ODR) fit (see, e.g., Spinoglio et al. 2022).The best empirical correlations that we have found with the corrected 2-10 keV hard X-ray luminosity are the nuclear 12 μm luminosity (Figure 1), the nuclear K-band luminosity (Figure 2), and the [O IV] 26 μm line luminosity (Figure 3).The statistics of these correlations are given in Table 4, broken out for each of the subsets of data, i.e., the whole 12MAGN sample for which these observations are available; the type 1 objects, which include both Seyfert type 1s and the so-called HBL AGN; and the type 2 objects, i.e., the pure Seyfert type 2 galaxies.In Table 4, for each correlation, are listed: the number of objects (N), the Pearson correlation coefficient ρ, the null hypothesis probability, the linear regression fit parameters (α and β), and the residual variance σ, measuring the goodness of the fit.The linear equation is defined in the notes of Table 4.

Monochromatic versus Bolometric Luminosities
Having obtained the bolometric luminosities for most (82.9%) of our AGN sample (excluding the lower limits and the two objects with no determination), which are given in the last column of Table 3, we computed the correlations between 12 μm nuclear luminosity, K-band nuclear luminosity, NUVcorrected luminosity, FUV-corrected luminosity, 8.4 GHz luminosity, 2-10 keV luminosity, 15-145 keV luminosity, and the computed bolometric luminosity.We have also computed the correlations of the luminosities of the three mid-IR fine-structure lines, which mainly originate in the AGN NLRs, namely, [O IV] 26 μm, [Ne V] 14.3 μm, and [Ne V] 24.3 μm, with the bolometric luminosities.All correlations are given in Table 5 and shown in Figures 4-9.
In Figure 4(a), the well-known correlation between the 2 and 10 keV absorption-corrected luminosity and the computed bolometric luminosity is shown; including all classes of AGN, the correlation is linear (slope 1.00 ± 0.04) and becomes slightly flatter for the type 1 AGN (slope ∼ 0.90) and slightly steeper for the type 2 AGN (slope ∼ 1.04) while remaining linear within 2σ.The harder X-ray 14-195 keV (Figure 4(b)) observed luminosity has also a good and almost linear (slope 0.94 ± 0.04) correlation with the bolometric luminosity if all classes are included, while it becomes significantly steeper for type 2 objects only.
In Figures 5(a) and (b) are shown the correlations between the NUV-and FUV-corrected luminosities with the bolometric luminosity, respectively.The NUV luminosity for all classes together correlates almost linearly (within 2σ) with the bolometric luminosity, while the correlation becomes steeper for the type 1 class (α ∼ 1.40), showing that type 1 objects have a stronger UV excess at higher luminosities.For the same reason, the FUV luminosity has a correlation steeper than linear with the bolometric luminosity.The slope is ∼1.3 for the whole sample and ∼1.6 for type 1 AGN only, while no correlation is apparent for the type 2 AGN.This is partly due to the increased contribution of the accretion disk energy in the UV for the more luminous AGN (Sun & Malkan 1989).Moreover, in these two plots, most AGN at bolometric luminosities greater than ∼10 45 erg s −1 are Seyfert type 1, known to have more powerful directly observed accretion disks.
Figure 6(a) shows the correlation between the radio 8.4 GHz luminosity and the bolometric luminosity.The 8.4 GHz luminosity always has a steeper than linear correlation with the bolometric luminosity, and its slope increases from the whole sample through type 1 AGN to type 2 objects, showing that at higher luminosities, radio-loudness is increasing.
The nuclear K-band luminosity (Figure 6(b)) has a very good linear correlation with the bolometric luminosity for all types of objects (slope ∼ 1.04 ± 0.05).Therefore, the nuclear K-band flux, once corrected for starlight emission, is a good indicator for the bolometric flux.
Figures 7(a) and (b) show the correlations between the nuclear 12 μm luminosity and the [O IV] 26 μm luminosity and the bolometric luminosity, respectively.The nuclear 12 μm luminosity has a strong and linear correlation with the bolometric luminosity.This linearity has been known since the pioneering work of Spinoglio & Malkan (1989), who selected galaxies in the IRAS 12 μm band to produce an unbiased sample of active galaxies.The IRAS large-aperture flux densities were indeed contaminated in galaxies by stellar emission; however, for the Seyfert galaxies, the emission from the AGN tends to dominate the power in this spectral region.Also, the [O IV] 26 μm luminosity, originating mostly in the NLR of the AGN, has an almost linear correlation for the whole AGN sample (α = 0.96 ± 0.05) with the AGN bolometric luminosity, albeit with a larger scatter with slopes ranging from 0.7 for the type 1 objects to 1.1 for the type 2s.We note that the higher bolometric luminosity type 1 AGN have a weaker emission in the NLR mid-IR fine-structure lines, which flattens the slope of the correlation.
Figures 8(a) and (b) show the correlations between the [Ne V] 14.3 μm luminosity and the [Ne V] 24.3 μm luminosity with the bolometric luminosity, respectively.These correlations are shallower than linear for the whole sample and especially for the brighter type 1 objects, showing again, as for the case of [O IV] 26 μm, that at high bolometric luminosity, the NLR becomes relatively weaker than expected from a linear correlation.This indicates that the relation between the NLR fine-structure mid-IR lines and the bolometric luminosity may  not extend linearly up to the regime of quasars, i.e., AGN with bolometric luminosities above 10 46 erg s −1 .Studies based on brighter AGN samples suggest that at these high luminosities, the forbidden line luminosities can no longer "keep up" with the nonstellar continuum (see discussion of [O III] in the Appendix of Malkan et al. 2017).A possible explanation for this "forbidden line saturation" may be that the NLR is becoming "matter-bounded" (Pronik & Chuvaev 1972;Gaskell et al. 2021).There may not be enough gas around luminous quasars to intercept as many of their ionizing photons.
Figures 9(a The K-band nuclear luminosity was chosen in this case because it has a good linear correlation with the bolometric luminosity (see Table 5), and it is at the closest wavelength (about four times longer) to the [O III] 5007 Å line, which has already been used to estimate the bolometric luminosity of AGN.
The combination of a continuum-band nuclear luminosity in the IR (both mid-IR and near-IR) with a line luminosity-when this line is mainly powered by the AGN-gives a better correlation with the bolometric luminosity compared to the correlations between the line luminosities and the bolometric luminosity.This can be clearly seen by comparing Figure 7 .Moreover, in analogy with the measurement of the star formation rate (SFR) in galaxies using both the 24 μm continuum and the optical Hα line by Kennicutt & Evans (2012), the logic behind the composite tracers is that lines are complementary to continuum because they account for photons that are not captured by the dust, so the combination of the two is expected to reduce the scatter, as we show in Figures 7-10.
In Table 6, we give our derived bolometric corrections for the full AGN population.The bolometric corrections are given for the continuum X-ray (both 2-10 and 14-195 keV) and IR luminosities (nuclear 12 μm and K-band) for the luminosities of the brightest lines emitted by the NLR ([O IV] 26 μm, [Ne V] 14.3 μm, [Ne V] 24.3 μm, and [O III] 5007 Å) and for a combination of the mid-IR and near-IR luminosities with the mid-IR fine structure and the [O III] 5007 Å line luminosities, respectively.
We note here that our derived bolometric correction for the [O III] 5007 Å line luminosity is lower by about a factor of 2 compared to the derivation of Heckman et al. (2004), who give a linear correlation (L bol ∼ 3500L [O III] 5007 Å ), while we find a shallower slope of α ∼ 0.90.Similar correlations were found for the AGN monochromatic versus bolometric luminosities when the luminosities are expressed in Eddington units, as shown in Figures 25, 26, and 27 and Table 8 in Appendix B.

Flux-Flux Correlations
We show in Figures 11(a) and (b) the correlations between the observed 12 μm flux and the [O IV] 26 μm line flux, respectively, with the derived bolometric flux of our sample galaxies.The statistics of these correlations are given in Table 9.Although the scatter is large, these correlations are consistent with linearity within 2σ.We show this example to demonstrate that our luminosity-luminosity correlations, even if they are boosted by the distance-squared factors, are indeed real, because the corresponding correlations in flux are almost linear.Additionally, we also explored the flux-flux correlations for the 2-10 keV and 2.2 μm bands.Figure 28 and Table 9 in Appendix C show that the correlation with the bolometric flux is also significant without the distance term.

Median SEDs
We have computed the median SEDs of the four classes of AGN in our sample, Seyfert type 1, HBL, Seyfert type 2, and LINER galaxies, which are shown in Figures 12-15, respectively, and the relevant values for each of the 10 photometric bands are reported in Table 7.The individual SEDs of all galaxies of our sample, normalized to their bolometric luminosity, are shown in Appendix A. The Seyfert b a = + ( ) ( ) (note here that the slope of the correlations are given in bold); and column (7) residual variance of the fit σ.Our purpose is twofold.First, we define the median distributions of the four classes of AGN, because they can be used as local templates, to be compared with SEDs of highredshift AGN.Second, we want to explore if and how the four subsamples of AGN may still include, even after the aperture corrections we have applied to subtract the galaxy contribution, a significant contribution from starlight emission or may be affected by dust obscuration (see Section 4.1).
For each AGN class, the median SED has been derived from the median value of the individual SED distribution evaluated at each frequency sampled (solid line and symbols in Figures 12-15).Prior to the median computation, the individual SEDs were normalized to their median L n ñ value over the frequency range.This approach avoids the arbitrary selection of a reference wavelength for the normalization that would produce a zero dispersion band in the median SED.To  account for the dispersion around the median SED we also compute, at each wavelength, the 10th, 30th, 70th, and 90th percentiles (see Table 7).The dark-shaded areas in Figures 12-15 indicate the SED distribution between percentiles 30 and 70, whereas the light-shaded areas correspond to the interval between percentiles 10 and 90.

Median SEDs and Host Galaxy Contribution
Overall, the median SEDs show two maximum values, one in the mid-IR and another in the X-ray range.Sy1 galaxies clearly show a rising optical/UV continuum with increasing   frequency, whereas HBL, Sy2, and LINER galaxies tend to show a rather flat or depressed optical/UV continuum, possibly contaminated by the host galaxy light (see discussion below).For comparison, we have included in Figure 12 the median SED of the radio-quiet quasars of the sample of Shang et al. (2011).The two determinations agree very well in the spectral region from the radio to the UV, while at X-ray frequencies, the derivation of Shang et al. (2011) is about 1 order of magnitude fainter.The blue optical/UV continuum in Sy1 nuclei is similar to the big blue bump associated with the accretion disk emission in bright quasars (Malkan & Sargent 1982), although the median quasar SEDs show a more pronounced blue bump,   a relatively fainter IR bump, and fainter X-ray emission (Elvis et al. 1994;Krawczyk et al. 2013;Saccheo et al. 2023).This is in agreement with the median SED changes reported by Krawczyk et al. (2013) for the less luminous quasars in their sample (∼10 44.9 erg s −1 ), which show a less pronounced blue bump component.The median Sy1 SED in Figure 12 extends this trend to lower luminosities, with a prominent IR bump brighter than the blue bump component in agreement with the median Seyfert SEDs derived from subarcsecond-resolution observations by Prieto et al. (2010).These changes in the SED are probably due to the decreasing contribution of the accretion disk to the total energy output or the increasing fraction of the reprocessed emission in AGN with decreasing luminosity.
When compared to Seyfert galaxies, the median SED of LINERs is brighter at radio wavelengths, in agreement with the results obtained by Ho (2008).For comparison, we have included in Figure 15 the median SED of the radio-loud quasars of the sample of Shang et al. (2011).These SEDs do agree to first order, showing a certain radio-loudness in the LINER SED, in spite of the fact that our LINER sample is small and not fully representative.Obscured nuclei, namely HBL and Sy2, shown in Figures 13 and 14, respectively, have a depressed optical/UV continuum when compared to Seyfert 1 nuclei and a larger scatter in both the optical/UV and X-ray ranges, suggesting that obscuration by dust and gas is still a source of scatter even after the absorption corrections have been applied.On the other hand, LINERs show a relatively flat SED in the optical/UV range, possibly dominated by the starlight contribution from the host galaxy.
Irrespective of the type of AGN considered, the four median SEDs have their minimum scatter in the mid-IR, namely, in the four photometric bands at 4.5, 5.8, 7.0, and, to a lesser extent, 12 μm.This result confirms that the mid-IR continuum contains a constant fraction of the bolometric flux for all types of active galaxies (Spinoglio & Malkan 1989), a discovery that was initially based on large-aperture flux densities from IRAS (Neugebauer et al. 1984).In this work, we come to the same conclusion using nuclear 12 μm flux measurements at subarcsecond resolution, avoiding most of the contribution by the host galaxy emission and the corresponding corrected mid-IR fluxes from Spitzer.
To evaluate the possible contamination in the optical/UV range of the median AGN SEDs due to current star formation in the host galaxies, we use the EW of the polycyclic aromatic hydrocarbon (PAH) feature at 11.25 μm as a proxy for the SFR (see, e.g., Förster Schreiber et al. 2004;Mordini et al. 2021), which is not affected by AGN contamination (e.g., Lai & Armus 2022).Additionally, dust obscuration can also affect the shape of the optical/UV continuum, either due to nuclear dust (i.e., the torus) or due to host galaxy dust.To investigate this scenario, we use the strength of the silicate feature at 9.7 μm (S sil ; Spoon et al. 2007), which becomes negative for obscured sources but can also be positive for unobscured sources if dust irradiated by the active nucleus is seen along the line of sight.We have therefore divided the objects into each of the four classes on the basis of these two observed quantities, using as a threshold (between low and high values) the median value of the PAH at 11.25 μm and negative or positive values of S sil .The spectroscopic data have been taken from Wu et al. (2009), who measured most of the 12MAGN sample with the Spitzer-IRS spectrograph in the low-resolution mode.
Figure 12 ´[ ] we obtain a median SFR ∼ 0.7-0.8M e yr −1 for both subsamples, consistent with moderate star formation in the host galaxies of Seyfert 1s.Analogously, in Figure 12(b), the population of type 1 Seyferts has been divided into those with the silicates in emission (long-dashed light gray line) and in absorption (short-dashed dark gray line).The differences in the median SEDs between the Seyfert 1 subsamples separated by EW(PAH 11.25 μm) or S sil are negligible for all the wavelengths sampled, suggesting that the median Seyfert type 1 SED is not contaminated by stellar light and does not suffer from heavy dust absorption.
Figures 13(a) and (b) show the same analysis for HBL galaxies, which present a similar median EW(PAH 11.25 μm) value of 0.12 μm as Seyfert galaxies.Nevertheless, the HBL populations with EW(PAH 11.25 μm) > 0.12 μm or positive S sil values show a significantly higher continuum in both the   NUV and FUV bands (long-dashed light gray lines in Figures 13(a) and (b)) when compared with those below EW(PAH 11.25 μm) < 0.12 μm or negative S sil (short-dashed dark gray lines).When the PAH 11.25 luminosities are translated into SFRs, the subsample with EW(PAH 11.25 μm) > 0.12 μm has a median SFR ∼ 0.9 M e yr −1 , while the subsample with EW(PAH 11.25 μm) < 0.12 μm shows a median SFR ∼ 0.6 M e yr −1 .As in the case of Seyfert 1 nuclei, the contribution from star formation is moderate.However, HBL nuclei are dust obscured; therefore, at similar SFR values, the host galaxy dominates in the UV range.Sources with lower SFRs tend to show a decreasing IR-to-UV continuum and the silicate feature in absorption, consistent with a reddened nuclear continuum, as discussed in Section 4.2.
Seyfert 2 galaxies a significantly larger EW(PAH 11.25 μm) with a median value of 0.54 μm, i.e., about 5 times that of Seyfert 1 and HBL galaxies, meaning that their host galaxies are relatively more active at forming stars, in agreement with previous studies (Edelson et al. 1987;Maiolino et al. 1995;Buchanan et al. 2006).As in the case of HBL, Figures 14(a) and (b) show that the median SED of the Seyfert 2 population with large EW (PAH 11.25 μm) or positive S sil values present a brighter continuum in the UV but also the K band (long-dashed light gray line in Figure 14), in agreement with their higher median SFR of ∼4 M e yr −1 .However, the population with lower EW (PAH 11.25 μm) or negative S sil values may still be affected by this contribution, since it shows a relatively flat IR-to-UV continuum (short-dashed dark gray line), their median SFR ∼ 0.6 M e yr −1 is comparable to that of Seyfert 1 and HBL host galaxies.
The differences between Seyfert 1, HBL, and Seyfert 2 galaxies are clearly shown in the diagram of the silicate strength at 9.7 μm as a function of the PAH 11.25 μm feature-S sil versus EW(PAH 11.25 μm)-reported in Figure 16.Both HBL and Seyfert 2 galaxies are obscured by a similar amount according to their median S sil ∼ −0.23, which is larger than that in Seyfert 1s (median S sil ∼ 0.0).However, the host galaxies of HBLs and Seyfert 1s form stars at a similar rate (0.6-0.9 M e yr −1 ), about 4-6 times lower than that of Seyfert 2 hosts with EW(PAH 11.25 μm) > 0.54 μm.
The LINER population in our sample is less numerous and more heterogeneous with a large dispersion in EW(PAH 11.25 μm) and S sil (Figure 16).The median EW(PAH 11.25 μm) of 0.34 μm is not representative of the population, with about half of the sources showing values similar to the Seyfert 1 nuclei (median SFR ∼ 0.1 M e yr −1 ) and the others showing high values indicative of more intense star formation activity (median SFR ∼ 1.7 M e yr −1 ).On the other hand, only two sources show strong silicate absorption, with a median S sil ∼ −0.05.This dual behavior in the IR spectroscopic properties of LINERs is in agreement with previous studies (Dudik et al. 2009;Fernández-Ontiveros & Muñoz-Darias 2021).The differences between the median SEDs for the subpopulations with large/small EW(PAH 11.25 μm) or positive/negative S sil are relatively small (Figures 15(a 2)-( 6)) calculated at each frequency for the νF ν distribution of individual sources.The latter have been previously normalized by their median νF ν over the frequency range.The last four columns (7)-( 10) correspond to the median νF ν distribution for sources below (<EW113) or above (>EW113) the median EW(PAH 11.3 μm) value of their class (0.095 for Sy1, 0.119 for HBL, 0.539 for Sy2) and sources with negative (−Ssil) or positive (+Ssil) silicate strength values.
(b)) and may be attributed to the small number statistics and the large heterogeneity in the LINER class.In summary, as can be seen in Figure 16, most of the Seyfert type 1 AGN have a low 11.25 μm PAH EW (only five Sy1s have EW(PAH 11.25 μm) > 0.4 μm) and have a silicate strength of around zero.HBL galaxies have a larger spread in the silicate strength while keeping a low number of high-PAH EWs (six HBLs have EW(PAH 11.25 μm) > 0.4 μm).In contrast, the majority of the Seyfert type 2 galaxies have a large PAH EW (14 Sy2s have EW(PAH 11.25 μm) > 0.4 μm, while only seven have EW(PAH 11.25 μm) < 0.4 μm).

Dust Properties in Obscured Seyferts
Figures 13(a) and (b) show that the continuum shape of the median HBL SED with low SFRs (low EW(PAH 11.25 μm) or negative S sil (dashed green lines) can be reproduced by the     median Sy1 template after applying a moderate amount of dust reddening.Assuming a foreground dust screen and the extinction curve from Cardelli et al. (1989), a total extinction of A V ∼ 1.2 mag (dashed blue line in Figures 13(a) and (b)) is required.This moderate amount of dust obscuration is enough to hide the continuum emission of a Sy1 and thus reproduce the observed SED shape of an HBL nucleus.
An additional estimate of the dust extinction in these nuclei is provided by the strength of the silicate feature.For a foreground dust screen, the silicate strength corresponds to the optical depth (S sil = −Δτ 9.7 ).Comparing the differential extinction in the optical between Seyfert 1 and HBL nuclei (A V ∼ 1.2 mag), the silicate optical depth (Δτ 9.7 ∼ 0.23) provides some information about the dust properties.We obtain a ratio of A V /Δτ 9.7 ∼ 5.2, in agreement with typical values in AGN (e.g., Lyu et al. 2014), as opposed to the much larger A V /Δτ 9.7 ∼ 18 derived for the local interstellar medium dust in the Milky Way (Roche & Aitken 1984).This suggests that the obscuration may be dominated by large grains that lead to a flatter and featureless extinction curve (Maiolino et al. 2001a(Maiolino et al. , 2001b;;Shao et al. 2017).Nevertheless, the effect of a more complex geometry in the dust distribution should be explored in the future to confirm this scenario.

Comparison with Other Bolometric Corrections
We compare here the bolometric luminosities derived for type 1 and type 2 AGN in our sample with those from other methods.First, in Figure 17, we compare them with the bolometric luminosities computed from the 2-10 keV intrinsic flux using the bolometric correction of Lusso et al. (2012).We adopted the polynomial formula for the bolometric luminosity y , L is the bolometric luminosity in units of L e , y = L L log 2 10 keV -
In Figure 18, we show the comparison of our determination of the bolometric luminosity with the one derived using the [O III] 5007 Å line compiled in Spinoglio et al. (2022) using the bolometric correction of L bol ∼ 3500L [O III] 5007 Å (Heckman et al. 2004).The correlation here is flatter than linear, especially for type 2 objects (α = 0.66 ± 0.16), indicating a deficit of optical forbidden line emission from type 2 AGN, possibly due to obscuration of the emitting NLR.
A recent computation of the hard X-ray 2-10 keV bolometric correction has been provided by Duras et al. (2020), who emphasize the dependence of their bolometric corrections on the bolometric luminosity and separately analyze type 1 and type 2 AGN.In the luminosity range of 10 40 erg s −1  L bol  10 45.5 erg s −1 , we have a similar result when we compare our constant of 15.3, with no dependence on luminosity (see the first line in Table 6), with their result presented in the lower panel of their Figure 4, relative to the average values for type 1 and type 2 sources.Only at higher bolometric luminosities, i.e., for L bol  10 46 erg s −1 , do the predictions of Duras et al. (2020) show higher bolometric corrections by factors of 3-4, with a strong dependence on luminosity.This discrepancy can be due to the fact that our study is based on a local sample of AGN with moderate luminosities, with L bol  10 46 erg s −1 , with the only exception being 3C 273 with L bol ∼ 4 × 10 47 erg s −1 (see Table 3).In contrast, Duras et al. (2020) include in their study various samples of X-ray-selected AGN covering different redshift ranges.In particular, they include 41 sources of the WISE-SDSS Selected Hyper-luminous sample with L bol > 10 47 erg s −1 in the redshift range 2 < z < 4, observed in the X-rays (Martocchia et al. 2017), as well as 31 high-luminosity type 1 AGN with L bol > 10 46.5 erg s −1 in the redshift range 0.9 < z < 5 from the XXL sample (see Table 2 of Liu et al. 2016).The inclusion of these high-luminosity type 1 AGN has the effect of strongly increasing the 2-10 keV bolometric correction, as can be seen from the upper panel of Figure 4 of Duras et al. (2020).
We show in Figure 19 our 2-10 keV bolometric correction as a function of the bolometric luminosity.For comparison, we have included in the plot the fit of the hard X-ray bolometric correction derived from Duras et al. (2020; see their Equation (2) and Figure 4) for both the general case and for type 1 AGN.In the luminosity range shown in the figure, our results are in a reasonably good agreement with their result.Nevertheless, it can be seen that the derived statistics shown in Figure 19 indicates a poor correlation that is consistent with a flat distribution, i.e., a constant bolometric correction as a function of luminosity.The same conclusion of a constant bolometric correction is also valid for the combination of the 12 μm luminosity and the [O IV] 26 μm line luminosity, as shown in Figure 20.

Summary and Conclusions
In this work, we have used the 12 μm sample of local AGN to derive the nuclear SED and the AGN bolometric luminosities, as much as possible free from galactic contamination.
For each galaxy, we used a 10-band SED, from the radio to the hard X-rays.To isolate genuine AGN continuum, we included subarcsecond photometric data where available and corrected the bands contaminated by stellar light from the host galaxy.Both the radio observations at 8.4 GHz and most of the 12 μm photometric data are taken with subarcsecond apertures, while the mid-IR bands at 7.0, 5.8, and 4.5 μm have been corrected using the 12 μm data.The nuclear K-band photometry was taken from Spinoglio et al. (2022), and the UV data from GALEX have been corrected for the telescope PSF in the two NUV and FUV bands.Finally, the absorption-corrected 2-10 keV and observed 14-195 keV X-ray fluxes intrinsically originate in the active nuclei.
Using the 10-band nuclear photometric data, we derived the median SED for each AGN type, namely, Seyfert type 1, Seyfert nuclei with HBLs, Seyfert type 2, and LINERs.The median Seyfert 1 SED shows the characteristic big blue bump feature in the UV; nevertheless, the largest contribution to the bolometric luminosity comes from the IR peak and the X-ray continuum.The median SEDs of both HBL and type 2 nuclei are affected by starlight contamination in the optical/UV range.The median nuclear SED of obscured type 1 nuclei can be reproduced by applying a moderate foreground dust extinction of A V ∼ 1.2 mag to the median Seyfert 1 SED.
We find that the 12 μm and K-band nuclear luminosities have good linear correlations with the bolometric luminosity, similar to those in the X-rays.We derive bolometric corrections for either continuum bands (K band, 12 μm, 2-10 keV, and 14-195 keV) or narrow emission lines (mid-IR high-ionization lines of [O IV] and [Ne V] and optical [O III] 5007 Å) as well as for combinations of IR continuum and line emission.We find that a combination of continuum plus line emission accurately predicts the bolometric luminosity up to quasar luminosities (10 46 erg s −1 ).This is the case of the 12 μm continuum plus the [O IV] 26 μm or the [Ne V] 14.3 μm mid-IR lines and the 2.2 μm continuum plus the [O III] 5007 Å optical line.This result reflects the fact that the IR continuum includes a large fraction of (and is proportional to) the bolometric luminosity of the AGN through both the nuclear continuum emission from the hot dust/torus and the gas emission from the NLR.
The James Webb Space Telescope (Gardner et al. 2006) will be able to measure this bolometric luminosity in virtually any AGN in the local Universe.For AGN at redshifts z < 1, the [Ne V] 14.3 μm line can also be used.
have studied the relations of the [O IV] 26 μm and [O III] 5007 Å luminosities with the 2-10 and 14-195 keV luminosities.They concluded that [O IV] is a good indicator of the AGN power.Rigby et al. (2009) calibrate the [O IV] 26 μm line as a measure of AGN intrinsic luminosity.Finally, Spinoglio et al. (2022) have recently computed the AGN bolometric luminosities using the Lusso et al. (2012) bolometric correction and the corrected (2-10) keV luminosities as a function of the luminosities of the three mid-IR high-ionization lines of [O IV] 26 μm, [Ne V] 14.3 μm, and [Ne V]24.3 μm.

(
iii) Compared to the other works, we separated the nuclear emission due to the AGN from the extended emission due to stellar emission in the galaxy.(iv) We also use the mid-IR spectroscopy of the lines of [O IV] 26 μm and [Ne V] 14.3 and 24.3 μm, which are mainly emitted in the NLRs excited by the accreting SMBH.(v) Our sample includes only local AGN, avoiding possible cosmic evolution in the bolometric corrections derived when different samples obtained at different redshift intervals are combined.

Figure 1 .
Figure 1.Nuclear 12 μm luminosity as a function of the corrected 2-10 keV luminosity.The position of the outlier Arp 220 has been indicated.In each figure (from Figures 1 to 11 and from Figures 17 to 20) representing the correlations between physical quantities, the error bar at the lower left corner has been computed using the median value of the relative errors of the plotted data (from Figures 1 to 11 and from Figures 17 to 20).

Figure 2 .
Figure 2. Nuclear K-band luminosity as a function of the corrected 2-10 keV luminosity.The position of the outlier Arp 220 has been indicated.

Figure 3 .
Figure 3. [O IV] 26 μm line luminosity as a function of the corrected 2-10 keV luminosity.The position of the outlier NGC 5953, which has been recently classified as a non-AGN (Osorio-Clavijo et al. 2023), has been indicated.
) and (b), respectively, show the correlations between a combination of the nuclear 12 μm luminosity and the NLR [O IV] 26 μm and [Ne V] 14.3 μm line luminosities with the bolometric luminosity.The addition of a particular percentage of the luminosity of one of the mid-IR highionization fine-structure lines of [O IV] 26 μm or [Ne V] 14.3 μm to the nuclear 12 μm luminosity has the effect of linearizing the correlation with the bolometric luminosity.Finally, Figures 10(a) and (b) show, respectively, the [O III] 5007 Å luminosity as a function of the bolometric luminosity and a combination of the nuclear K-band luminosity and the [O III] 5007 Å line luminosity with the bolometric luminosity.

type 1 ,
HBL region, Seyfert type 2, and LINERs together with the two non-Seyferts (NGC 1056 and NGC 5953) and the starburst galaxy (NGC 6810) normalized SEDs are shown in the Figures 21-24 figure sets, respectively.
(a) shows the median SEDs obtained from the Seyfert 1 sample with EW(PAH 11.25 μm) values below (short-dashed dark gray line) and above (long-dashed light gray line) 0.1 μm.Following the SFR calibration based on the luminosity of the PAH 11.25 μm derived by Xie & Ho (2019),

Figure 11 .
Figure 11.(a) 12 μm nuclear flux as a function of the estimated bolometric flux.(b) [O IV] 26 μm line flux as a function of the estimated bolometric flux.

Figure 12 .
Figure12.Median rest-frame SED for the Seyfert type 1 galaxies compared to the SED of the radio-quiet quasar population fromShang et al. (2011), shown as a red dotted-dashed line.(a) The population has been divided between the galaxies with high and low values of the EW of the PAH 11.3 μm feature.(b) The population has been divided between the galaxies with the silicate 9.7 μm feature in emission and in absorption.
) and

Figure 15 .
Figure 15.Median rest-frame SED for the LINER galaxies compared to the SED of the radio-loud quasar population from Shang et al. (2011), shown as a red dotteddashed line.(a) Same as Figure 12(a).(b) Same as Figure 12(b).

Figure 16 .
Figure16.Silicate strength as a function of the EW of the PAH 11.3 μm feature for the four AGN populations of Sy1 (blue triangles), HBL (pink diamonds), Sy2 (red squares), and LINERs (green circles).The median EW(PAH 11.3 μm) and silicate strength values for Sy1 (dashed blue), HBL (solid pink), Sy2 (dotted red), and LINERs (dotted-dashed green) are indicated by the horizontal and vertical lines, respectively.

Figure 17 .
Figure17.Correlation between the bolometric luminosity computed in this work and the bolometric luminosity computed from the 2-10 keV corrected flux using the bolometric correction ofLusso et al. (2012).

Figure 18 .
Figure 18.Correlation between the bolometric luminosity computed in this work and the bolometric luminosity computed from the [O III] 5007 Å line compiled in Spinoglio et al. (2022) using the bolometric correction of L bol ∼ 3500L [O III] 5007 Å(Heckman et al. 2004).

Figure 19 .
Figure 19.The 2-10 keV bolometric correction as a function of the bolometric luminosity.The ODR fits to the total population and the type 1 AGN samples have a low Pearson correlation coefficient (ρ = 0.46 and 0.36 for 57 and 90 objects, with P(null) = 3 × 10 −4 and 4 × 10 −4 , respectively) indicating that the correlations are not strong.For comparison, the hard X-ray bolometric correction from Duras et al. (2020) has been included for both the general case and type 1 AGN.

Figure 20 .
Figure 20.The composite 12 μm and [O IV] 26 μm bolometric correction as a function of the bolometric luminosity.The ODR fits to all populations show very low Pearson correlation coefficients, indicating a constant bolometric correction.

Figure 27 .
Figure 27.(a) Ratio of the composite 12 μm and [O IV] 26 μm luminosity to the Eddington luminosity as a function of the ratio of the bolometric luminosity to the Eddington luminosity.(b) Ratio of the composite 12 μm and [Ne V] 14.3 μm luminosity to the Eddington luminosity as a function of the ratio of the bolometric luminosity to the Eddington luminosity.

Table 2
Low-frequency Nuclear Photometry of the AGN Sample No.

Table 3
High-frequency Nuclear Photometry of the AGN Sample and Derived Bolometric Fluxes and Luminosities

Table 4
Correlation of Various Luminosities with the Best Bolometric Indicators (2-10 keV, Nuclear 12 μm, and [O IV] 26 μm Line Luminosities) Fit results.Column (1): the columns give for each correlation variables; column (2): the subset of the sample on which the fit was computed, where "all" indicates the entire sample and type 1 and type 2 indicate the Seyfert type subsets; column (3): number of sources; column (4): Pearson correlation coefficient ρ (1:

Table 5
Logarithmic Correlations of Various Continuum and Line Luminosities and Their Combinations with the Bolometric Luminosities Fit results.Column (1): the columns give for each correlation variables; column (2): the subset of the sample on which the fit was computed, where "all" indicates the entire sample and Type 1 and Type 2 indicate the Seyfert type subsets; column (3): number of sources; column (4): Pearson correlation coefficient ρ (1:

Table 6
Single and Composite Continuum-and Line-based Bolometric Corrections in AGN V ´+ ḿ [ ]

Table 7
Percentiles of the Normalized SED Distribution as a Function of Frequency for the Four AGN Classes Note.For each observed frequency (Hz; column (1)), we give the percentiles 10, 30, 50 (median), 70, and 90 (columns (