Estimating black hole masses in obscured AGN using X-rays
MMNRAS , 1–14 (2015) Preprint 20 January 2021 Compiled using MNRAS L A TEX style file v3.0
Estimating black hole masses in obscured AGN using X-rays
Mario Gliozzi ★ and James K. Williams and Dina A. Michel Department of Physics and Astronomy, George Mason University, 4400 University Drive, Fairfax, VA 22030
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Determining the black hole masses in active galactic nuclei (AGN) is of crucial importance to constrain the basic characteristicsof their central engines and shed light on their growth and co-evolution with their host galaxies. While the black hole mass( 𝑀 BH ) can be robustly measured with dynamical methods in bright type 1 AGN, where the variable primary emission and thebroad line region (BLR) are directly observed, a direct measurement is considerably more challenging if not impossible forthe vast majority of heavily obscured type 2 AGN. In this work, we tested the validity of an X-ray-based scaling method toconstrain the 𝑀 BH in heavily absorbed AGN. To this end, we utilized a sample of type 2 AGN with good-quality hard X-ray dataobtained by the NuSTAR satellite and with 𝑀 BH dynamically constrained from megamaser measurements. Our results indicatethat, when the X-ray broadband spectra are fitted with physically motivated self-consistent models that properly account forabsorption, scattering, and emission line contributions from the putative torus and constrain the primary X-ray emission, thenthe X-ray scaling method yields 𝑀 BH values that are consistent with those determined from megamaser measurements withintheir respective uncertainties. With this method we can therefore systematically determine the 𝑀 BH in any type 2 AGN, providedthat they possess good-quality X-ray data and accrete at a moderate to high rate. Key words:
Galaxies: active – Galaxies: nuclei – X-rays: galaxies
Historically, radio-quiet active galactic nuclei (AGN) have been di-vided into two main categories based on their optical spectroscopy:type 1 AGN, whose spectra are characterized by the presence ofbroad permitted lines (with full width at half maximum FWHM > − ) along with narrow forbidden lines, and type 2 AGN,where only narrow forbidden lines are detected (e.g., Khachikian &Weedman 1974; Antonucci 1983).According to the basic AGN unification model, type 2 AGN can beconsidered as the obscured counterpart of type 1 AGN and their maindifferences can be simply ascribed to different viewing angles, dueto the presence of an obscuring toroidal structure made of gas anddust surrounding the AGN (e.g., Osterbrock 1978; Antonucci 1993;Tadhunter 2008; Urry & Padovani 1995). However, over the years,theoretical and observational studies have revealed that the simplestversion of the unification model, based on a smooth donut-shapedtorus, is unable to explain several observations, favoring instead ascenario where the torus is clumpy, with a covering factor dependingon various AGN properties, and where the overall obscuration occurson different scales with significant contribution from the galaxy itself.See Netzer (2015) and Ramos Almeida & Ricci (2017) for recentcomprehensive reviews on the unification model of AGN.Regardless of the nature of the obscuration, in type 2 AGN, thecentral engine – an optical/UV emitting accretion disk, coupled withan X-ray emitting Comptonization corona – and the broad line re-gion (BLR) are not directly accessible to observations. This makes it ★ E-mail: [email protected] more difficult to determine the properties of obscured AGN, whichrepresent the majority of the AGN population and thus play a crucialrole in our understanding of the AGN activity, census, and cosmo-logical evolution (see Hickox & Alexander 2018 for a recent reviewon obscured AGN).In order to shed light on the properties of the AGN central engineand its accretion state, we need to accurately determine the black holemass ( 𝑀 BH ). In type 1 AGN, a reliable dynamical method frequentlyused is the so-called reverberation mapping method, where intrinsicchanges in the continuum emission of the central engine, measuredwith some time delay in the line emission produced by the BLR, areused to constrain the 𝑀 BH , modulo a geometric factor (Blandford& McKee 1982; Peterson et al. 2004). On the other hand, in type 2AGN, by definition the BLR is not visible and hence the reverberationmapping technique cannot be applied. Nevertheless, there is a smallfraction of heavily obscured AGN for which it is still possible tomeasure the 𝑀 BH in a reliable way via a dynamical method. These arethe sources that display water megamaser emission; if this emissionis located in the accretion disk and is characterized by the Keplerianmotion, then the 𝑀 BH can be constrained with great accuracy (e.g.Kuo et al. 2011).In this work, we use a sample of heavily obscured type 2 AGNwith 𝑀 BH constrained by megamaser measurements and with good-quality hard X-ray spectra obtained with the Nuclear SpectroscopicTelescope Array ( NuSTAR ), a focusing hard X-ray telescope launchedin 2012 with large effective area and excellent sensitivity in the energyrange 3–78 keV, where the signatures of absorption and reflection aremost prominent. Our main goal is to test whether an X-ray scalingmethod that yields 𝑀 BH values broadly consistent with those ob- © a r X i v : . [ a s t r o - ph . H E ] J a n Gliozzi, Williams, & Michel
Table 1.
Properties of the sample Source Distance 𝑀 BH 𝜆 Edd
NuSTAR
Exposurename (Mpc) (10 M (cid:12) ) ( 𝐿 bol / 𝐿 Edd ) observation ID (ks)(1) (2) (3) (4) (5) (6)NGC 1068 14 . a . ± . . ± .
053 60002033002 52.1NGC 1194 53 . b . ± . . ± .
002 60061035002 31.5NGC 2273 25 . b . ± . . ± .
034 60001064002 23.2NGC 3079 17 . c . + . − . . ± .
009 60061097002 21.5NGC 3393 50 . d . ± . . ± .
016 60061205002 15.7NGC 4388 19 . b . ± . . ± .
009 60061228002 21.4NGC 4945 3 . e . ± . . ± .
075 60002051004 54.6IC 2560 26 . f . ± . . ± .
050 50001039004 49.6Circinus 4 . g . ± . . ± .
044 60002039002 53.9Columns: 1 = megamaser AGN name. 2 = distance used computing the 𝑀 BH from the maser measurements. References for the distances and black hole massesare (a) Lodato & Bertin (2003), (b) Kuo et al. (2011), (c) Kondratko, Greenhill, & Moran (2005), (d) Kondratko, Greenhill, & Moran (2008), (e) Greenhill et al.(1997), (f) Yamauchi et al. (2012), and (g) Greenhill et al. (2003). 3 = black hole mass. 4 = Eddington ratio with Brightman’s bolometric correction of 10 × to 𝐿 X from Brightman et al. (2016). 5 = NuSTAR observation ID. 6 = exposure time. tained from reverberation mapping in type 1 AGN can be extendedto type 2 AGN.The paper is structured as follows. In Section 2, we describe thesample properties and the X-ray data reduction. In Section 3, wereport on the spectral analysis of
NuSTAR data. The application ofthe X-ray scaling method and the comparison between the 𝑀 BH values derived with this method and those obtained from megamasermeasurements are described in Section 4. We discuss the main resultsand draw our conclusions in Section 5. We chose our sample of type 2 AGN based on the following two cri-teria: these objects must have 1) the 𝑀 BH dynamically determined bymegamaser disk measurements, and 2) good-quality hard X-ray data.The former criterion is crucial to quantitatively test the validity of theX-ray scaling method applied to heavily obscured AGN, whereas thelatter criterion is necessary to robustly constrain the properties of theprimary X-ray emission by accurately assessing the contributions ofabsorption and reflection caused by the putative torus. These criteriaare fulfilled by the sample described by Brightman et al. (2016),which is largely based on the sample of megamasers analyzed byMasini et al. (2016) and spans a range in X-ray luminosity between10 erg s − and a few units in 10 erg s − . The general propertiesof this sample, including the distance used to determine the 𝑀 BH from maser measurements, the 𝑀 BH itself, and the Eddington ratio 𝜆 Edd = 𝐿 bol / 𝐿 Edd , are reported in Table 1.The archival
NuSTAR data of these nine objects were calibrated andscreened using the
NuSTAR data analysis pipeline nupipeline withstandard filtering criteria and the calibration database
CALDB version20191219. From the calibrated and screened event files we extractedlight curves and spectra, along with the RMF and ARF files necessaryfor the spectral analysis, using the nuproduct script. The extractionregions used for both focal plane modules, FPMA and FPMB, arecircular regions of radii ranging from 40 (cid:48)(cid:48) to 100 (cid:48)(cid:48) depending onthe brightness of the source, and centered on the brightest centroid.Background spectra and light curves were extracted by placing circlesof the same size used for the source in source-free regions of the samedetector. No flares were found in the background light curves. All spectra were binned with a minimum of 20 counts per bin using theHEASoft task grppha 𝜒 statistics to be valid. The X-ray spectral analysis was performed using the xspec v.12.9.0 software package (Arnaud 1996), and the errors quoted on the spec-tral parameters represent the 1 𝜎 confidence level.The NuSTAR spectra of this sample have already been reasonablywell fitted with self-consistent physically motivated models suchas
MYTorus (Murphy & Yaqoob 2009) and
Torus (Brightman &Nandra 2011) to account for the continuum scattering and absorp-tion, as well as the fluorescent line emission produced by the torus,whereas the primary emission was parametrized with a phenomeno-logical power-law model. However, in order to apply the X-ray scalingmethod (whose key features are described in the following section),the primary emission needs to be parametrized by the Bulk Mo-tion Comptonization model (
BMC ), which is a generic Comptoniza-tion model that convolves thermal seed photons producing a powerlaw (Titarchuk, Mastichiadis, & Kylafis 1997). This model, whichcan be used to parametrize both the bulk motion and the thermalComptonization, is described by four spectral parameters: the nor-malization 𝑁 BMC , the spectral index 𝛼 , the temperature of the seedphotons 𝑘𝑇 , and log 𝐴 , where 𝐴 is related to the fraction of scatteredseed photons 𝑓 by the relationship 𝐴 = ( 𝑓 + )/ 𝑓 . Unlike the phe-nomenological power-law model, the BMC parameters are computedin a self-consistent way, and the power-law component produced bythe
BMC does not extend to arbitrarily low energies.We carried out a homogeneous systematic reanalysis of the
Nu-STAR spectra of these sources. We started from the best-fit modelsreported in the literature but utilized the
Borus model (Baloković etal. 2018), which can be considered as an evolution of the previoustorus models. Specifically,
Borus has the same geometry imple-mented in
Torus but can also be used in a decoupled mode, wherethe column density 𝑁 H responsible for the continuum scattering andfluorescent line emission is allowed to be different from the 𝑁 H re-sponsible for the attenuation of the primary component. Additionally,unlike Torus , this model correctly accounts for the absorption expe-rienced by the photons backscattered from the far side of the inner
MNRAS , 1–14 (2015) stimating black hole masses in obscured AGN (cid:239) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) NGC 1068
105 20 50 (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV) (cid:239) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) NGC 1194
105 20 50 (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV) (cid:239) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) NGC 2273
105 20 (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV) (cid:239) (cid:239) (cid:239) (cid:239) (cid:239) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) NGC 3079
105 20 50 (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV) (cid:239) (cid:239) (cid:239) (cid:239) (cid:239) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) NGC 3393
105 20 50 (cid:239) (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV) (cid:239) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) NGC 4388
105 20 50 (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV) (cid:239) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) NGC 4945
105 20 50 (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV) (cid:239) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) IC 2560
105 20 (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV) (cid:239) no r m a li ze d c oun t s s (cid:239) k e V (cid:239) Circinus
105 20 50 (cid:239) ( d a t a (cid:239) m od e l ) / e rr o r Energy (keV)
Figure 1.
The top panels show the
NuSTAR spectra (black data points indicate FPMA data whereas the red ones indicate FPMB data) with the best-fit models,whereas the bottom panels show the data-to-model ratios. MNRAS000
NuSTAR spectra (black data points indicate FPMA data whereas the red ones indicate FPMB data) with the best-fit models,whereas the bottom panels show the data-to-model ratios. MNRAS000 , 1–14 (2015)
Gliozzi, Williams, & Michel
Table 2.
Spectral ResultsSource 𝑁 H Gal log ( 𝑁 H bor ) cos 𝜃 CFtor 𝐴 Fe 𝑁 H mytz Γ 𝑁 BMC log
𝐴 𝑓 s ( 𝜒 / dof)name (10 cm − ) (%) (10 cm − ) (%)(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)NGC 1068 2 .
59 23 . ± . . . ± . . + . − . . + . − . × − .
53 23 . ± . . . ± . . + . − . . + . − . × − .
80 25 . ± . . . ± . . + . − . . + . − . × − .
87 24 . ± . . . ± . . + . − . . + . − . × − .
13 25 . ± . . . ± . . + . − . . + . − . × − .
57 23 . ± . . . ± . . + . − . . + . − . × − -0.55 17.0 435.2/420NGC 4945 14 . . ± . . . ± . . + . − . . + . − . × − .
51 25 . ± . . . ± . . + . − . . + . − . × − . . ± . . . ± . . + . − . . + . − . × − -0.43 3.3 1713.2/1714Columns: 1 = megamaser AGN name. 2 = Galactic column density from NASA’s HEASARC. 3 = column density calculated with the Borus model. 4 = cosineof the inclination angle. 5 = covering factor. 6 = iron abundance relative to the solar value. 7 = column density calculated with the
MYTorus model. 8 = photonindex. 9 = normalization of the BMC model. 10 = logarithm of 𝐴 , where 𝐴 = ( 𝑓 + )/ 𝑓 and 𝑓 is the fraction of seed photons that are scattered. 11 = fractionof the primary emission scattered along the line of sight by an extended ionized reflector. 12 = 𝜒 divided by degrees of freedom. torus. With respect to MYTorus , Borus contains additional emissionlines, has a larger range for 𝑁 H , and directly yields the value of thecovering fraction. However, since Borus only parametrizes the scat-tered continuum and the fluorescent line components associated withthe torus, to account for the absorption and scattering experiencedby the primary emission, we utilized the zeroth-order component of
MYTorus ( MYTZ ), which properly includes the effects of the Klein-Nishina Compton scattering cross section that are relevant in heavilyabsorbed AGN at energies above 10 keV. In summary, our procedurecan be summarized in three steps: 1) we started from the spectral bestfits reported in the literature; 2) we then substituted
Borus (morespecifically, we used the borus02_v170323a.fits table) for either
Torus or MYTorus to account for the scattered and line components,and used the zeroth-order component of
MYTorus for the transmittedone; 3) finally, we substituted
BMC for the power-law model used forthe primary emission.In the spectral fitting, in order to preserve the self-consistency ofthese physically motivated torus models, which are created by MonteCarlo simulations using a power law to parametrize the X-ray primaryemission, one needs to link the primary emission parameters – thephoton index Γ and the normalization 𝑁 PL – to the input parametersof the scattered continuum and emission-line components. In the caseof the BMC model, the power-law slope is described by the spectralindex 𝛼 , which is related to the photon index by the relationship Γ = 𝛼 +
1. However, there is not a known mathematical equationlinking the normalizations 𝑁 BMC and 𝑁 PL . We therefore derived thisrelationship empirically by using a sample of clean type 1 AGN (i.e.,AGN without cold or warm absorbers), whose details are described inWilliams, Gliozzi, & Rudzinsky (2018); Gliozzi & Williams (2020).We fitted the 2–10 keV XMM-Newton spectra twice, first with the
BMC model and then with a power law. The results of this analysisare illustrated in Fig. 2, where 𝑁 PL / 𝑁 BMC is plotted versus 𝑁 BMC ,showing that, regardless of the value of 𝑁 BMC , the normalizationratios cluster around the average value, 30 . ± .
9, represented by thelonger-dashed line, with moderate scattering of 𝜎 = .
2, representedby the shorter-dashed lines. Fig. 2, where the data point’s size andcolor provide information about the photon index, also reveals atendency for the AGN with steeper spectra to have larger values of 𝑁 PL / 𝑁 BMC . This trend is formally confirmed by a least-squares best fit of 𝑁 PL / 𝑁 BMC vs. Γ , which yields 𝑁 PL / 𝑁 BMC =-18.9 + 26.3 Γ ,with a Pearson’s correlation coefficient of 0.85.These results are in agreement with those obtained from a seriesof simulations carried out with the fakeit command in xspec.Simulating spectra of the BMC model with the parameters varyingover a broad range, and then fitting them with a power-law model,we found that 𝑁 PL / 𝑁 BMC shows a horizontal trend when plotted vs. 𝑁 BMC with an average value consistent with 30 for
Γ = .
9, whereasthe horizontal trend is consistent with an average value of 24 for
Γ = . Γ = . 𝑁 BMC to be equal to 𝑁 PL /30 by linking theseparameters to reflect this relationship. For completeness, and to takeinto account the weak dependence of 𝑁 PL / 𝑁 BMC on Γ , we have alsocarried out the spectral analysis assuming 𝑁 PL / 𝑁 BMC = 24 (i.e., theaverage value minus one standard deviation) for flat spectrum sourcesand 𝑁 PL / 𝑁 BMC = 38 (average + 𝜎 ) for steep spectrum sources.We note that, compared to Γ and 𝑁 BMC , the remaining
BMC param-eters 𝑘𝑇 and log 𝐴 play a marginal role in the shape of the spectrumand in the determination of the 𝑀 BH , as explicitly assessed in Gliozziet al. (2011). Therefore, to limit the number of free parameters, wefixed 𝑘𝑇 to 0.1 keV, which is consistent with the values generallyobtained when the BMC model is fitted to X-ray AGN spectra (e.g.,Gliozzi et al. 2011; Williams, Gliozzi, & Rudzinsky 2018), whereaslog 𝐴 was fixed to the best-fit value obtained in the first fitting itera-tion.Our baseline model for all type 2 AGN fitted in this work isexpressed in the xspec syntax as follows: phabs * (atable(Borus) + MYTZ * BMC + const * BMC) where the first absorption model phabs accounts for our Galaxycontribution, the Borus table model parametrizes the continuumscattering and fluorescent emission line components associated withthe torus, and
MYTZ models the absorption and Compton scatter-ing acting on the transmitted primary emission, which is describedby the Comptonization model
BMC . The last additive component const*BMC parametrizes the fraction of primary emission directlyscattered towards the observer by a putative optically thin ionized
MNRAS , 1–14 (2015) stimating black hole masses in obscured AGN ¡ ¡ ¡ ¡ ¡ ¡ BMC N P L = N B M C : : : : : G a mm a Figure 2. 𝑁 PL / 𝑁 BMC plotted vs. 𝑁 BMC for a sample of “clean” type 1 AGN(i.e., AGN with negligible warm or cold absorbers). The black longer-dashedline represents the average value, whereas the shorter-dashed lines indicatethe one standard deviation levels from the average. Both the data point’s sizeand color provide information on the source’s photon index Γ : the larger thesymbol and the darker the color, the steeper the Γ . medium, which is often observed below 5 keV in spectra of heavilyobscured AGN (e.g., Yaqoob 2012).Depending on the source and the complexity of its X-ray spec-trum, additional components (such as the host galaxy contribution,individual lines, additional absorption and scattering components,or models describing off-nuclear sources contained in the NuSTAR extraction region) are included and described in the individual notesof each source reported in the Appendix.The spectral parameters obtained by fitting this baseline model arereported in Table 2, and the best fits and model-to-data ratios areshown in Fig 1. 𝑀 BH from the X-ray scaling method The X-ray scaling method was first introduced by Shaposhnikov &Titarchuk (2009), who showed that the BH mass and distance 𝐷 of any stellar mass BH can be obtained by scaling these propertiesfrom those of an appropriate reference source (i.e., a BH system with 𝑀 BH dynamically determined and distance tightly constrained). Inits original form this technique exploits the similarity of the trendsdisplayed by different BH systems in two plots – the photon index Γ vs. quasi-periodic oscillation (QPO) frequency plot and the 𝑁 BMC – Γ diagram – to derive their 𝑀 BH and 𝐷 .Based on the assumption that the process leading to the ubiquitousemission of X-rays – the Comptonization of seed photons producedby the accretion disk – is the same in all BH systems regardlessof their mass, this method can in principle be extended to any BHincluding the supermassive BHs at the cores of AGN. In the lattercase, since the detection of QPOs is extremely rare but the distanceis generally well constrained by redshift or Cepheid measurements,only the 𝑁 BMC – Γ diagram is used to determine the 𝑀 BH . Indeed,over the years, this method has been successfully applied to stellarmass BHs (e.g., Seifina, Titarchuk, & Shaposhnikov 2014; Titarchuk & Seifina 2016) and to ultraluminous X-ray sources (e.g., Titarchuk& Seifina 2016; Jang et al. 2018), as well as to a handful of AGNthat showed high spectral and temporal variability during deep X-ray exposures (e.g., Gliozzi et al. 2010; Giacché, Gilli, & Titarchuk2014; Seifina, Chekhtman, & Titarchuk 2018.)Although the vast majority of AGN do not possess long-term X-ray observations and do not show strong intrinsic spectral variability(i.e., variability described by substantial changes of Γ not caused byobscuration events), the X-ray scaling method can be extended toany type 1 AGN with one good-quality X-ray observation. Indeed,Gliozzi et al. (2011) demonstrated that the 𝑀 BH values determinedwith this method are fully consistent with the corresponding valuesobtained from the reverberation mapping technique. The referencesources, used in that study and then also in this work, are three stellarmass BHs residing in X-ray binaries – GRO J1655-40, GX 339-4, andXTE J1550-564 – with 𝑀 BH dynamically determined and spectralevolution during the rising and decaying phases of their outburstsmathematically parametrized by Shaposhnikov & Titarchuk (2009).The physical properties of the stellar references and the mathematicaldescription of their spectral trends, as well as the details of themethod, are reported in Gliozzi et al. (2011).In summary, all the reference trends yielded 𝑀 BH measurementsconsistent with the reverberation mapping values within their nomi-nal uncertainties, with the decaying trends showing a slightly betteragreement than the rising trends, which have a tendency to underes-timate 𝑀 BH to a moderate degree. Unfortunately, the most reliablereference source – GRO J1655-40 during the 2005 decaying phase(hereafter GROD05) – has a fairly small range of Γ during its spec-tral transition limiting its application to sources with relatively flatphoton indices. Using the reverberation mapping values as calibra-tion, it was determined that for AGN with steep spectra ( Γ >
2) thebest estimate of 𝑀 BH is obtained using the value derived from therising phase of the 1998 outburst of XTE J1550-564 multiplied by afactor of 3 (hereafter 3*XTER98). Below, we summarize the generalprinciples at the base of this technique; a more detailed explanationcan be found in Shaposhnikov & Titarchuk (2009) and Gliozzi etal. (2011). For completeness, in the Appendix we report the basicinformation on the reference sources, including the mathematical ex-pression of their spectral trends, which is necessary to derive 𝑀 BH using the equation reported below.The scaling method assumes that all BH systems accreting at amoderate or high rate undergo similar spectral transitions, character-ized by the “softer when brighter” trend (i.e., the X-ray spectrum soft-ens when the accretion and hence the luminosity increases). Thesespectral transitions are routinely observed in stellar BHs (e.g., Remil-lard & McClintock 2006) and often found in samples of AGN (e.g.,Shemmer et al. 2008; Risaliti, Young, & Elvis 2009; Brightman et al.2013, 2016), which are characterized by considerably longer dynam-ical timescales, making it nearly impossible to witness a genuine statetransition in a supermassive BH system, although a few long mon-itoring studies have observed this spectral trend in individual AGN(e.g., Sobolewska & Papadakis 2009). The “softer when brighter”trend, usually illustrated by plotting the photon index versus the Ed-dington ratio 𝜆 Edd , is seen with some scattering in numerous type 1AGN samples and also in the heavily absorbed type 2 AGN, whichare the focus of our work (Brightman et al. 2016). This lends supportto the hypothesis that the photon index Γ is a reliable indicator of theaccretion state of any BH.Indeed, this is the fundamental assumption of the X-ray scalingmethod: Γ is indicative of the accretion state of the source, and BHsystems in the same accretion state are characterized by the sameaccretion rate (in Eddington units) and the same radiative efficiency MNRAS000
2) thebest estimate of 𝑀 BH is obtained using the value derived from therising phase of the 1998 outburst of XTE J1550-564 multiplied by afactor of 3 (hereafter 3*XTER98). Below, we summarize the generalprinciples at the base of this technique; a more detailed explanationcan be found in Shaposhnikov & Titarchuk (2009) and Gliozzi etal. (2011). For completeness, in the Appendix we report the basicinformation on the reference sources, including the mathematical ex-pression of their spectral trends, which is necessary to derive 𝑀 BH using the equation reported below.The scaling method assumes that all BH systems accreting at amoderate or high rate undergo similar spectral transitions, character-ized by the “softer when brighter” trend (i.e., the X-ray spectrum soft-ens when the accretion and hence the luminosity increases). Thesespectral transitions are routinely observed in stellar BHs (e.g., Remil-lard & McClintock 2006) and often found in samples of AGN (e.g.,Shemmer et al. 2008; Risaliti, Young, & Elvis 2009; Brightman et al.2013, 2016), which are characterized by considerably longer dynam-ical timescales, making it nearly impossible to witness a genuine statetransition in a supermassive BH system, although a few long mon-itoring studies have observed this spectral trend in individual AGN(e.g., Sobolewska & Papadakis 2009). The “softer when brighter”trend, usually illustrated by plotting the photon index versus the Ed-dington ratio 𝜆 Edd , is seen with some scattering in numerous type 1AGN samples and also in the heavily absorbed type 2 AGN, whichare the focus of our work (Brightman et al. 2016). This lends supportto the hypothesis that the photon index Γ is a reliable indicator of theaccretion state of any BH.Indeed, this is the fundamental assumption of the X-ray scalingmethod: Γ is indicative of the accretion state of the source, and BHsystems in the same accretion state are characterized by the sameaccretion rate (in Eddington units) and the same radiative efficiency MNRAS000 , 1–14 (2015)
Gliozzi, Williams, & Michel
NGC 4945 :
001 0 :
002 0 :
005 0 :
01 0 :
02 0 :
05 0 : : : BMC : : : : : : ¡ Figure 3. 𝑁 BMC – Γ plot, showing the data point corresponding to NGC 4945and two reference patterns; the darker trend refers to GROD05, the spectralevolution of GRO 1655-40 during the decay of an outburst that occurred in2005, and the lighter color trend indicates GROR05, the spectral evolutionshown by the same source during the outburst rise. The dashed lines indi-cate the uncertainties in the reference spectral trends, whereas the error barsrepresent the uncertainties of the AGN spectral parameters. 𝜂 . As a consequence, when we compare the accretion luminosity( 𝐿 ∝ 𝜂𝑀 BH (cid:164) 𝑚 ) in BH systems that are in the same accretion state(i.e., with the same Γ ), we are directly comparing their 𝑀 BH . Thisexplains why the comparison of the values of the normalization ofthe BMC model, 𝑁 BMC (which is defined as the accretion luminosityin units of 10 erg s − divided by the distance squared in units of10 kpc), computed at the same value of Γ between the AGN and aknown stellar BH reference source, yields the 𝑀 BH . This is illustratedin Fig. 3 and mathematically described by 𝑀 BH , AGN = 𝑀 BH , ref × (cid:18) 𝑁 BMC , AGN 𝑁 BMC , ref (cid:19) × (cid:32) 𝑑 𝑑 (cid:33) where 𝑁 BMC , ref and 𝑑 ref are the BMC model normalization and dis-tance of the stellar mass BH system used as a reference.Fig. 3 illustrates the X-ray scaling method and its inherent un-certainties that are related to the statistical errors on the spectralparameters Γ and 𝑁 BMC and on the uncertainty of the referencesource spectral trend (shown by the dashed lines), as well as on thespecific reference source trend utilized. Although similar in shape,the reference spectral trends show some differences (e.g., in theirplateau levels and slopes), leading to slightly different 𝑀 BH values.From Fig. 3, it is clear that these differences exist also between therise and decay phases of the same reference source.It is important to note that at very low accretion rates both stellarmass and supermassive BHs show an anti-correlation between Γ and 𝜆 Edd (e.g., Constantin et al. 2009; Gu & Cao 2009; Gültekin etal. 2012). Since the X-ray scaling method is based on the positivecorrelation between these two quantities, it cannot be applied todetermine the 𝑀 BH of objects in the very low-accretion regime. Thiswas explicitly demonstrated by the work of Jang et al. (2014), whoanalyzed a sample of low-luminosity low-accreting AGN.In the following, we systematically estimate the 𝑀 BH using all thereference sources available (depending on the AGN’s Γ , not all refer-ence sources can be used since their photon index ranges vary fromreference source to reference source) and then compute the 𝑀 BH average value and its uncertainty 𝜎 /√ 𝑛 (where 𝜎 is the standarddeviation and 𝑛 is the number of reference trends utilized). As al-ready explained above, for AGN with steep spectra, the most reliableestimate of 𝑀 BH is obtained using the 3*XTER98 reference trend;therefore, we also include this value in Table 3. All 𝑀 BH valueslisted in this table were computed assuming 𝑁 PL / 𝑁 BMC = 30; how-ever, for completeness, we also report the 𝑀 BH obtained assuming 𝑁 PL / 𝑁 BMC = 24 and 38 for flat- and steep-spectrum sources, respec-tively. We note that such changes in 𝑁 PL / 𝑁 BMC lead to 𝑀 BH valuesthat are consistent with the values obtained with the original assump-tion 𝑁 PL / 𝑁 BMC = 30, within the respective 𝑀 BH uncertainties thatare of the order of 10%–40%.The 𝑀 BH values obtained with the different reference sources andtheir average are illustrated in Fig. 4. As already found in Gliozzi etal. (2011) for the reverberation mapping AGN sample, the referencetrends of decaying outbursts yield systematically larger 𝑀 BH valuescompared to those obtained from the rising trends. For each obscuredAGN, several 𝑀 BH values obtained from different reference sourcesand their average appear to be broadly consistent with the valueobtained from megamaser measurements (a quantitative comparisonis carried out in the next subsection). The only noticeable exceptionis NGC 1194, for which the X-ray scaling method yields valuessignificantly lower than the maser one. This discrepancy however isnot surprising, since this source has a fairly low accretion rate and inthat regime the X-ray scaling method cannot be safely applied. To compare the 𝑀 BH values obtained from the X-ray scalingmethod with the maser ones in a quantitative way, we computed,using all the available reference trends, the difference Δ 𝑀 BH = 𝑀 BH , maser − 𝑀 BH , scaling and its uncertainty 𝜎 diff , obtained by addingthe respective errors in quadrature. As explained before, the error onthe 𝑀 BH inferred from the scaling method includes the uncertain-ties on the spectral AGN parameters and on the reference trends inthe 𝑁 BMC – Γ diagram. Depending on the reference trend utilized,the percentage uncertainties range from 10%–15% for GROD05 andGXD03 to 30%–40% for XTER98, which is also the percentageuncertainty of the average 𝑀 BH .The error on the 𝑀 BH obtained with megamaser measurements ac-counts for the uncertainties associated with the source position andwith the fitting of the Keplerian rotation curve (Kuo et al. 2011). Forthe uncertainties on the 𝑀 BH determined via megamaser measure-ments we used the errors quoted in the literature with the exceptionof NGC 4388, for which we multiplied the quoted uncertainty by afactor of 10; this yields a percentage error of ∼ 𝑀 BH in this source, where thereis no systemic maser detected and the five maser spots detected arenot sufficient to demonstrate that the rotation is Keplerian (Kuo etal. 2011). Note that both methods explicitly depend on the sources’distances and hence, in principle, their total uncertainties should ac-count also for the distance uncertainties (indeed some of the sourcesof this maser sample are fairly close and thus their distances cannotbe obtained from the redshift and Hubble’s law). However, since ourgoal is to compare the two methods, we can avoid the uncertaintyassociated with the distance by assuming the exact same distanceused in the maser papers.We used the criterion Δ 𝑀 BH / 𝜎 diff < 𝑀 BH values derived with these two methods are statistically consistent.In other words, the X-ray scaling measurements of the 𝑀 BH areconsidered formally consistent with the corresponding megamaservalues if their difference is less than three times the uncertainty 𝜎 diff . MNRAS , 1–14 (2015) stimating black hole masses in obscured AGN Figure 4. 𝑀 BH values obtained with the X-ray scaling method using different reference sources, compared with 𝑀 BH obtained from megamaser measurements,which are represented by the black symbols at the top of each panel. The results of these comparisons are summarized in Table 4 andillustrated in Fig. 5, where the dashed lines represent the 3 𝜎 levels.From this figure it is evident that every source has at least one 𝑀 BH scaling value that is consistent with the maser one, with GROD05and GXD03 being the most reliable ones, along with the average 𝑀 BH and the value obtained with 3*XTER98. The latter ones arealways within 3 𝜎 from the megamaser value, also by virtue of theirslightly larger uncertainties.An alternative way to compare the two methods is offered by theratio 𝑀 BH , maser / 𝑀 BH , scaling . The ratios, obtained by dividing themegamaser 𝑀 BH by each of the available reference sources, as wellas by the 𝑀 BH average and by 3*XTER98, are reported in Table 5and illustrated in Fig. 6, where the 𝑀 BH values obtained with thescaling method for the most reliable references (GROD05, GXD03,3*XTER98) and the average values are plotted versus their respectivemegamaser values. From this figure, one can see that, for GROD05(top left panel), 3*XTER98 (bottom left panel), and the average(bottom right panel), all values are consistent with the ratio of 1 within a factor of 3, and a good agreement is found also with GXD03(top right panel) with two sources (IC 2560 and NGC 2273) that haveslightly larger values.Based on the values reported in Table 5, all ratios obtained fromthese reference trends are consistent with unity at the 3 𝜎 limit(i.e., their ratio ± 𝜎 is consistent with 1) confirming the statisti-cal agreement between the two methods. Finally, we note that using 𝑁 PL / 𝑁 BMC = 24 (for flat spectrum sources) and 38 (for steep spec-trum sources) confirms and reinforces the conclusions derived fromthe original assumption 𝑁 PL / 𝑁 BMC = 30.
Constraining the 𝑀 BH in AGN is of crucial importance, since itdetermines the space and temporal scales of BHs, constrains theiraccretion rate via the Eddington ratio, and plays an essential rolein our understanding of the BH growth and co-evolution with the MNRAS000
Constraining the 𝑀 BH in AGN is of crucial importance, since itdetermines the space and temporal scales of BHs, constrains theiraccretion rate via the Eddington ratio, and plays an essential rolein our understanding of the BH growth and co-evolution with the MNRAS000 , 1–14 (2015)
Gliozzi, Williams, & Michel
GROR05GXD03GXR04XTER98average3*XTER98 ¡ ¡ ¢ M B H = ¾ d i ff NGC1068
XTER98 3*XTER98GROD05GROR05GXD03GXR04 average ¡ ¡ ¢ M B H = ¾ d i ff NGC2273
XTER98 3*XTER98GROD05GROR05GXD03GXR04 average ¡ ¡ ¢ M B H = ¾ d i ff NGC3079
XTER98 3*XTER98GROD05GROR05GXD03GXR04 average ¡ ¡ ¢ M B H = ¾ d i ff NGC3393
GROD05 GXD03GROR05 GXR04 XTER98 3*XTER98average ¡ ¡ ¢ M B H = ¾ d i ff NGC4388
GROD05 GXD03GROR05 GXR04XTER98 3*XTER98average ¡ ¡ ¢ M B H = ¾ d i ff NGC4945
GROR05GXD03GXR04XTER98 3*XTER98average ¡ ¡ ¢ M B H = ¾ d i ff IC2560
GROR05 XTER983*XTER98average ¡ ¡ ¢ M B H = ¾ d i ff Circinus
Figure 5.
Plots showing the difference between the BH mass determined from megamaser measurements and the values obtained with the X-ray scaling methodfor the different reference sources, divided by the uncertainty of the difference, Δ 𝑀 BH / 𝜎 diff . The horizontal dashed lines enclose the region where the differencebetween the BH masses is within 3 𝜎 .MNRAS , 1–14 (2015) stimating black hole masses in obscured AGN Table 3.
Black hole masses with the X-ray scaling methodSource 𝑀 BH GROD05 𝑀 BH GROR05 𝑀 BH GXD03 𝑀 BH GXR04 𝑀 BH XTER98 𝑀 BH aver 𝑀 BH name (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) )(1) (2) (3) (4) (5) (6) (7) (8)NGC 1068 . . . 1 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 1194 5 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =24 6 . + . − . . + . − . + − . . + . − . . + . − . . + . − . . + . − . NGC 2273 22 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 3079 4 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 3393 40 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 4388 3 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =24 4 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 4945 0 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =24 0 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . IC 2560 . . . 3 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =38 . . . 2 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . Circinus . . . 0 . + . − . . . . . . . 0 . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =38 . . . 0 . + . − . . . . . . . 0 . + . − . . + . − . . + . − . Columns: 1 = AGN name. 2–8 = black hole masses determined with the X-ray scaling method. Subscripts denote GROD05 = reference source GRO J1655-40in the decreasing phase; GROR05 = reference source GRO J1655-40 in the rising phase; GXD03 = reference source GX 339-4 in the decreasing phase; GXR03= reference source GX 339-4 in the rising phase; XTER98 = reference source XTE J1550-564 in the rising phase; 3*XTER98 = reference source XTEJ1550-564 in the rising phase with a multiplicative correction of a factor 3 applied. Note, the average value (in column 7) is obtained averaging all the 𝑀 BH obtained from all the reference sources but excluding 3*XTER98. Note: For each source the first line reports the 𝑀 BH values obtained using 𝑁 PL / 𝑁 BMC = 30in the spectral fitting; the second line (present only for sources with relatively flat or steep spectra) explicitly states the different value of 𝑁 PL / 𝑁 BMC used. host galaxy. The most reliable ways to determine the 𝑀 BH are directdynamical methods, which measure the orbital parameters of “testparticles”, whose motion is dominated by the gravitational force ofthe supermassive BH. For example, the mass of the supermassiveBH at the center of our Galaxy has been tightly constrained bydetailed studies of the orbits of a few innermost stars observed overseveral years (e.g., Ghez et al. 2008; Gillessen et al. 2009). In nearbyweakly active galaxies, the 𝑀 BH is determined by the gas dynamicswithin the sphere of influence of the BH (e.g., Gebhardt et al. 2003).On the other hand, in bright type 1 AGN, the 𝑀 BH measurementis obtained from the dynamics of the BLR via the reverberationmapping technique (e.g., Peterson et al. 2004). Finally, in heavilyabsorbed type 2 AGN, where the BLR is completely obscured, theonly possible direct measurement of the 𝑀 BH is based on megamasermeasurements (e.g., Kuo et al. 2011 and references therein).The main problem with direct dynamical methods is that they arefairly limited in their application. For instance, direct measurementsof 𝑀 BH via gas dynamics are limited to nearby weakly active galax-ies, where the sphere of influence is not outshined by the AGN and aresufficiently close to be resolvable at the angular resolution of ground-based observatories. Similarly, the reverberation mapping technique,which is heavily time and instrument consuming, is limited to type 1AGN with small or moderate masses. Finally, the megamaser emis-sion in type 2 AGN is relatively rare, and only when the megamaseroriginates in the accretion disk (as opposed to the jet and outflows) can this technique be used to constrain the 𝑀 BH (e.g., Panessa et al.2020 and references therein).Fortunately, there are a few robust indirect methods that make itpossible to constrain the 𝑀 BH beyond the range of applicability ofthe direct dynamical ones. For example, the tight correlation between 𝑀 BH and the stellar velocity dispersion in the bulge 𝜎 ∗ , observed innearby nearly quiescent galaxies (e.g., Tremaine et al. 2002), canbe extrapolated to constrain the 𝑀 BH in many distant and moreactive galaxies. Similarly, the empirical relationship between theBLR radius and optical luminosity makes it possible to determine themass of numerous type 1 AGN with only one spectral measurementwithout the need of long monitoring campaigns (e.g., Kaspi et al.2000).Although indirect methods have proven to be very useful to derivegeneral results for large samples of AGN, caution must be appliedwhen these methods are extrapolated well beyond the original rangeof applicability of the direct methods. To check for consistency andavoid potential biases associated with the various assumptions inher-ent in these indirect methods, it is important to develop and utilizealternative techniques to constrain the 𝑀 BH . In this perspective, X-ray-based methods may offer a useful complementary way to the morecommonly used optically based ones, since X-rays that are producedvery close to the BH are less affected by absorption and by star andgalaxy contamination. Indeed, model-independent methods based onX-ray variability yielded 𝑀 BH values broadly consistent with those MNRAS000
Black hole masses with the X-ray scaling methodSource 𝑀 BH GROD05 𝑀 BH GROR05 𝑀 BH GXD03 𝑀 BH GXR04 𝑀 BH XTER98 𝑀 BH aver 𝑀 BH name (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) ) (10 M (cid:12) )(1) (2) (3) (4) (5) (6) (7) (8)NGC 1068 . . . 1 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 1194 5 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =24 6 . + . − . . + . − . + − . . + . − . . + . − . . + . − . . + . − . NGC 2273 22 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 3079 4 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 3393 40 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 4388 3 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =24 4 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . NGC 4945 0 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =24 0 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . IC 2560 . . . 3 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =38 . . . 2 . + . − . . + . − . . + . − . . + . − . . + . − . . + . − . Circinus . . . 0 . + . − . . . . . . . 0 . + . − . . + . − . . + . − . 𝑁 PL / 𝑁 BMC =38 . . . 0 . + . − . . . . . . . 0 . + . − . . + . − . . + . − . Columns: 1 = AGN name. 2–8 = black hole masses determined with the X-ray scaling method. Subscripts denote GROD05 = reference source GRO J1655-40in the decreasing phase; GROR05 = reference source GRO J1655-40 in the rising phase; GXD03 = reference source GX 339-4 in the decreasing phase; GXR03= reference source GX 339-4 in the rising phase; XTER98 = reference source XTE J1550-564 in the rising phase; 3*XTER98 = reference source XTEJ1550-564 in the rising phase with a multiplicative correction of a factor 3 applied. Note, the average value (in column 7) is obtained averaging all the 𝑀 BH obtained from all the reference sources but excluding 3*XTER98. Note: For each source the first line reports the 𝑀 BH values obtained using 𝑁 PL / 𝑁 BMC = 30in the spectral fitting; the second line (present only for sources with relatively flat or steep spectra) explicitly states the different value of 𝑁 PL / 𝑁 BMC used. host galaxy. The most reliable ways to determine the 𝑀 BH are directdynamical methods, which measure the orbital parameters of “testparticles”, whose motion is dominated by the gravitational force ofthe supermassive BH. For example, the mass of the supermassiveBH at the center of our Galaxy has been tightly constrained bydetailed studies of the orbits of a few innermost stars observed overseveral years (e.g., Ghez et al. 2008; Gillessen et al. 2009). In nearbyweakly active galaxies, the 𝑀 BH is determined by the gas dynamicswithin the sphere of influence of the BH (e.g., Gebhardt et al. 2003).On the other hand, in bright type 1 AGN, the 𝑀 BH measurementis obtained from the dynamics of the BLR via the reverberationmapping technique (e.g., Peterson et al. 2004). Finally, in heavilyabsorbed type 2 AGN, where the BLR is completely obscured, theonly possible direct measurement of the 𝑀 BH is based on megamasermeasurements (e.g., Kuo et al. 2011 and references therein).The main problem with direct dynamical methods is that they arefairly limited in their application. For instance, direct measurementsof 𝑀 BH via gas dynamics are limited to nearby weakly active galax-ies, where the sphere of influence is not outshined by the AGN and aresufficiently close to be resolvable at the angular resolution of ground-based observatories. Similarly, the reverberation mapping technique,which is heavily time and instrument consuming, is limited to type 1AGN with small or moderate masses. Finally, the megamaser emis-sion in type 2 AGN is relatively rare, and only when the megamaseroriginates in the accretion disk (as opposed to the jet and outflows) can this technique be used to constrain the 𝑀 BH (e.g., Panessa et al.2020 and references therein).Fortunately, there are a few robust indirect methods that make itpossible to constrain the 𝑀 BH beyond the range of applicability ofthe direct dynamical ones. For example, the tight correlation between 𝑀 BH and the stellar velocity dispersion in the bulge 𝜎 ∗ , observed innearby nearly quiescent galaxies (e.g., Tremaine et al. 2002), canbe extrapolated to constrain the 𝑀 BH in many distant and moreactive galaxies. Similarly, the empirical relationship between theBLR radius and optical luminosity makes it possible to determine themass of numerous type 1 AGN with only one spectral measurementwithout the need of long monitoring campaigns (e.g., Kaspi et al.2000).Although indirect methods have proven to be very useful to derivegeneral results for large samples of AGN, caution must be appliedwhen these methods are extrapolated well beyond the original rangeof applicability of the direct methods. To check for consistency andavoid potential biases associated with the various assumptions inher-ent in these indirect methods, it is important to develop and utilizealternative techniques to constrain the 𝑀 BH . In this perspective, X-ray-based methods may offer a useful complementary way to the morecommonly used optically based ones, since X-rays that are producedvery close to the BH are less affected by absorption and by star andgalaxy contamination. Indeed, model-independent methods based onX-ray variability yielded 𝑀 BH values broadly consistent with those MNRAS000 , 1–14 (2015) Gliozzi, Williams, & Michel
NGC2273NGC 3079 NGC 3393NGC 4388NGC 4945
GROD05
BHmaser M B H X NGC 1068NGC2273NGC 3079 NGC 3393NGC 4388NGC 4945 IC 2560
GXD03
BHmaser M B H X NGC 1068NGC2273NGC 3079 NGC 3393NGC 4388NGC 4945 IC 2560Circinus
BHmaser M B H X NGC 1068NGC2273NGC 3079 NGC 3393NGC 4388NGC 4945 IC 2560
Average
BHmaser M B H X Figure 6. 𝑀 BH , X , the BH mass obtained with the scaling method plotted versus 𝑀 BH , maser obtained from the megamaser. The top left panel shows the X-rayscaling values derived from the GROD05 reference, the top right panel those from GXD03, the bottom left the values from 3*XTER98, and the bottom rightpanel the 𝑀 BH values obtained from the average of all the available reference sources. The longer-dashed line represents the perfect one-to-one correspondencebetween the two methods, i.e., a ratio 𝑀 BH , maser / 𝑀 BH , X =
1, whereas the shorter-dashed lines indicate the ratios of 3 and 1/3, respectively. obtained with dynamical methods (e.g. Papadakis 2004; Nikołajuk etal. 2006; McHardy et al. 2006; Ponti et al. 2012). In a previous workfocused on a sample of AGN with reverberation mapping measure-ments and good quality
XMM-Newton data, we demonstrated thatthe X-ray scaling method also provides results in agreement withreverberation mapping within the respective uncertainties (Gliozzi etal. 2011).It is important to bear in mind that the X-ray scaling method is notequivalent to making some general assumptions on the accretion rateand the bolometric correction and deriving the BH mass from the X-ray luminosity using the formula 𝑀 BH = 𝜅 bol 𝐿 X /( . × 𝜆 Edd ) ,where 𝜅 bol is the bolometric correction that may range from 15 to150 depending on the accretion rate of the source (Vasudevan &Fabian 2009), and 𝐿 X the X-ray luminosity in erg/s. With this simpleequation, without an a priori knowledge of the accretion rate of thesource, one could at best obtain the order of magnitude of the 𝑀 BH .Since 𝜆 Edd can vary over a broad range (for example, for this smallsample of obscured AGN, the Eddington ratio varies from 0.01 to0.3), it is not possible to obtain a specific value of 𝑀 BH that can bequantitatively compared with the value obtained from the dynamicalmethod and find a good agreement, as we did with the scaling method.One may then argue that the only important parameter in thescaling method is 𝑁 BMC (because of its direct dependence on theaccretion luminosity and distance) and that it is still possible to obtaina good agreement with the dynamically estimated 𝑀 BH with anyvalue of the photon index. To test this hypothesis, we have selectedthe two sources with the flattest spectra of our sample (NGC 4388 and NGC 4945) and the two sources with the steepest spectra (IC2560 and Circinus), and recalculated their 𝑀 BH with the scalingmethod assuming Γ = .
17 for the flattest sources and
Γ = .
66 forthe steepest sources. This led to changes of 𝑀 BH by a factor slightlylarger than 2 (note that considerably larger changes of 𝑀 BH wouldhave resulted if we had used a larger difference in the photon indicesinstead of the minimum and maximum values of this small sample).If the photon index did not play any role, then these 𝑀 BH changesshould have not made a difference in the agreement with the valuesobtained via the dynamical method, with some objects showing aslightly better agreement and others a slightly worse agreement.Instead, all four sources, which were originally consistent with theirmaser respective estimates based on the mass ratio criterion describedabove (see Table 5 and Figure 6), showed a clear departure from thedynamical 𝑀 BH values with three sources (NGC 4388, NGC 4945,and IC 2560) that were not formally consistent with the maser valuesanymore (their new mass ratios were 8.0, 7.1, and 6.7, respectively)and only Circinus (ratio of 0.5) still consistent, but only by virtue ofthe fact that the original ratio was basically 1. We therefore concludethat the scaling method works because the photon index accuratelycharacterizes the accretion state of accreting black holes and allowsthe correct selection of the reference source’s 𝑁 BMC value to becompared with the AGN’s value.In this study, we have extended the X-ray scaling method to a sam-ple of heavily obscured type 2 AGN with 𝑀 BH already constrainedby megamaser measurements. This dynamical method is rightly con-sidered one of the most reliable; however, the accuracy of the 𝑀 BH MNRAS , 1–14 (2015) stimating black hole masses in obscured AGN Table 4. Δ 𝑀 BH / 𝜎 diff : Comparison between 𝑀 BH from maser and X-ray scalingSource Δ 𝑀 BH / 𝜎 name GROD05 GROR05 GXD03 GXR04 XTER98 average 3 ∗ XTER98(1) (2) (3) (4) (5) (6) (7) (8)NGC 1068 . . . 16.7 − . . . . . . . 𝑁 PL / 𝑁 BMC =24 17 . . . . . . − . − . − . − . − . − . − . − . − . − . − . − . − . − . . . 𝑁 PL / 𝑁 BMC =24 2 . . . . 𝑁 PL / 𝑁 BMC =24 1 . . − . − . − . − . − . 𝑁 PL / 𝑁 BMC =38 . . . 1.1 − . − . − . − . − . 𝑁 PL / 𝑁 BMC =38 . . . 4.7 . . . . . . 4.0 2.3 1.0Columns: 1 = AGN name. 2–8 = Change in black hole mass over error for each reference source. Reference sources: GROD05 = reference source GROJ1655-40 in the decreasing phase; GROR05 = reference source GRO J1655-40 in the rising phase; GXD03 = reference source GX 339-4 in the decreasingphase; GXR03 = reference source GX 339-4 in the rising phase; XTER98 = reference source XTE J1550-564 in the rising phase; 3*XTER98 = referencesource XTE J1550-564 in the rising phase with a multiplicative correction of a factor 3 applied. Note, the average value (in column 7) is obtained averaging allthe 𝑀 BH obtained from all the reference sources but excluding 3*XTER98. Note: For each source the first line reports the values obtained using 𝑁 PL / 𝑁 BMC =30 in the spectral fitting; the second line (present only for sources with relatively flat or steep spectra) explicitly states the different value of 𝑁 PL / 𝑁 BMC used. derived with this technique depends on the quality of the radio data,on the assumption that the megamaser emission is produced in anedge-on disk, and that its rotation curve is strictly Keplerian. Addi-tionally, one should bear in mind that this technique measures themass enclosed within the megamaser emission. As a consequence,the actual 𝑀 BH may be slightly smaller if the measured enclosedmass encompasses a nuclear cluster or the inner part of a massivedisk, or alternatively slightly larger if radiation pressure (not includedin the 𝑀 BH derivation) plays an important role (Kuo et al. 2011).Specifically, for the sources of our sample, the rotation curve tracedby the megamaser in NGC 1068 is non-Keplerian; the 𝑀 BH wasderived assuming a self-gravitating accretion disk model (Lodato& Bertin 2003). NGC 1194 displays one of the largest maser disks(with inner and outer radii of 0.54 and 1.33 parsecs) which appearsto be slightly bent and is consistent with Keplerian rotation (Kuoet al. 2011). NGC 2273 also shows indications of a warped butmuch smaller disk (with inner and outer disk radii of 0.028 and0.084 pc) with Keplerian rotation (Kuo et al. 2011). In NGC 3079the disk appears to be thick and flared (Kondratko, Greenhill, &Moran 2005), whereas in NGC 3393 the maser seems to describe aflat disk perpendicular to the kpc radio jet, and the positions of themaser points have substantial uncertainties (Kondratko, Greenhill, &Moran 2008). NGC 4388, located in the Virgo cluster, has only fivemegamaser spots, which make it impossible to demonstrate that theylie on a disk or that the rotation is Keplerian (Kuo et al. 2011). Forthis reason, to reflect the actual uncertainty on the 𝑀 BH derived by megamaser measurements, we have increased the statistical error bya factor of 10, leading to an uncertainty of ∼ 𝑀 BH of ∼ 𝑀 BH values determined from megamaser measurements as robustestimates but not as extremely accurate values, and the errors reportedin Table 1 are likely lower limits on their actual uncertainties.With respect to type 1 AGN, the main difficulty of applying theX-ray scaling method to heavily obscured AGN is the need to prop-erly constrain the parameters of the primary emission in sourceswhose X-ray spectra are dominated by absorption and reflection.However, the NuSTAR spectra of these specific sources, often com-plemented with
Chandra and
XMM-Newton data, were the objectof very detailed analyses, which led to the disentanglement and acareful characterization of the different contributions of the AGNdirect and reprocessed emission, of the host galaxy, and of the off-nuclear sources located in the spectral extraction region (e.g., Yaqoob
MNRAS000
MNRAS000 , 1–14 (2015) Gliozzi, Williams, & Michel
Table 5.
Ratio between 𝑀 BH values obtained from maser measurements and the X-ray scaling method: 𝑀 BH , maser / 𝑀 BH , scaling Source Rationame GROD05 GROR05 GXD03 GXR04 XTER98 average 3 ∗ XTER98(1) (2) (3) (4) (5) (6) (7) (8)NGC 1068 . . . 5 . ± . . ± . . ± . . ± . . ± . . ± . ± ±
16 7 ± ± ±
21 17 ± ± 𝑁 PL / 𝑁 BMC =24 10 ± ±
15 6 ± ± ±
18 13 ± ± . ± . . ± . . ± .
02 0 . ± .
03 0 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . 𝑁 PL / 𝑁 BMC =24 2 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . ± . . ± . . ± . 𝑁 PL / 𝑁 BMC =24 2 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . 𝑁 PL / 𝑁 BMC =38 . . . 1 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . 𝑁 PL / 𝑁 BMC =38 . . . 5 . ± . . ± . . ± . . ± . 𝑀 BH obtained fromall the reference sources but excluding 3*XTER98. Note: For each source the first line reports the values obtained using 𝑁 PL / 𝑁 BMC = 30 in the spectral fitting;the second line (present only for sources with relatively flat or steep spectra) explicitly states the different value of 𝑁 PL / 𝑁 BMC used.
Borus (Baloković et al. 2018) instead of the
MYTorus or Torus models usedin the previous analyses. To characterize the primary emission, in-stead of the phenomenological power-law model, we utilized the
BMC
Comptonization model, since the scaling method directly scales thenormalization of this model 𝑁 BMC between AGN and an appropriatestellar reference to determine 𝑀 BH .With our baseline spectral model, where we assumed 𝑁 PL / 𝑁 BMC = 30, as described in detail in Section 3 (see also the Appendix fordetails on the spectral fittings of individual sources), and applyingthe scaling technique summarized in Section 4.1, we obtained thefollowing results: • Many of the 𝑀 BH values, obtained with different referencetrends, are broadly in agreement with the corresponding mega-maser ones. In particular, the estimates derived using GROD05,3*XTER98, and the ones obtained by averaging the values in-ferred from all the available reference sources, are consistent at the3 𝜎 level, based on measurements of Δ 𝑀 BH / 𝜎 diff = ( 𝑀 BH , maser − 𝑀 BH , scaling )/ 𝜎 diff , which are reported in Table 4 and shown in Fig. 5. • The agreement between the two methods is confirmed by the 𝑀 BH , maser / 𝑀 BH , scaling ratio: for all type 2 AGN of our sample ( 𝑀 BH , maser / 𝑀 BH , scaling ) ± 𝜎 ≤
1, when using the best referencesources or the average 𝑀 BH , as summarized in Table 5. Fig. 6 illus- trates the good agreement between the two methods, showing thatGROD05, GXD04 (partially), 3*XTER98, and the average obtainedfrom all reference patterns are all consistent with the one-to-one ratiowithin a factor of three. • The only object of our sample for which the 𝑀 BH inferred fromthe X-ray scaling method is statistically inconsistent with the mega-maser value is NGC 1194, which is the AGN with the lowest accretionrate ( 𝜆 Edd (cid:39) × − ). However, this discrepancy is expected, sincethe X-ray scaling method cannot be applied in this regime, where Γ generally shows an anti-correlation with 𝜆 Edd .In conclusion, our work demonstrates that the same X-ray scalingmethod works equally well for type 1 AGN (given the formal agree-ment with the reverberation mapping sample) and type 2 AGN (basedon the agreement with the megamaser sample). We thus conclude thatthis method can be safely applied to any type of AGN regardless oftheir level of obscuration, provided that these sources accrete abovea minimum threshold and that their primary X-ray emission can berobustly characterized via spectral analysis. This also proves that thismethod is robust and can be used to complement the various indirectmethods, especially when they are applied well beyond the rangeof validity of the direct methods, from which they were calibrated.Finally, the X-ray scaling method offers the possibility to investigatein a systematic and homogeneous way the existence of any intrinsicdifference in the fundamental properties of the central engines in type
MNRAS , 1–14 (2015) stimating black hole masses in obscured AGN ACKNOWLEDGEMENTS
We thank the anonymous referee for constructive comments and sug-gestions that improved the clarity of the paper and helped strengthenour conclusions. This research has made use of data, software, and/orweb tools obtained from the High Energy Astrophysics ScienceArchive Research Center (HEASARC), a service of the AstrophysicsScience Division at NASA/GSFC and of the Smithsonian Astrophys-ical Observatory’s High Energy Astrophysics Division, and of theNuSTAR Data Analysis Software (NuSTARDAS) jointly developedby the ASI Science Data Center (ASDC, Italy) and the CaliforniaInstitute of Technology (Caltech, USA).
DATA AVAILABILITY
The data underlying this article are available in the High EnergyAstrophysics Science Archive Research Center (HEASARC) Archiveat https://heasarc.gsfc.nasa.gov/docs/archive.html.
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APPENDIX A: ADDITIONAL SPECTRAL RESULTSNGC 1068:
A detailed analysis of the
NuSTAR , XMM-Newton , and
Chandra spectra of this source was carried out by Bauer et al. (2015).Thanks to the excellent sensitivities of
XMM-Newton and
NuSTAR over broad complementary energy ranges, and to the sub-arcsecondspatial resolution of
Chandra , the authors were able to disentanglethe contributions of the host galaxy and off-nuclear sources fromthe AGN emission within the
NuSTAR extraction region. The over-all best-fit model is fairly complex and comprises several Fe and Niemission lines, a Bremsstrahlung component to account for the radia-tive recombination continuum and lines, a cutoff power-law modelto account for the off-nuclear X-ray sources, in addition to the AGN-related emission, which is parametrized by two different
MYTorus scattered and line components, in addition to the transmitted one de-scribed by the zeroth-order component of that model. In our fitting,in addition to our baseline model we added the Bremsstrahlung andcutoff power law with all parameters fixed at the values provided byBauer et al. (2015), and a Gaussian line to roughly model the excessaround 6.5 keV. To account for the multiple absorption components,we also added a second
Borus model, whose best-fit parameters arelog ( 𝑁 H bor ) = . ± .
1, CFtor = 83%, and 𝐴 Fe =
1. Our best-fit parameters are broadly consistent with the results presented byBauer et al. (2015). The observed flux in the 2–10 keV energy bandis 5 . × − erg cm − s − , and the intrinsic one (i.e., corrected forabsorption) 1 . × − erg cm − s − . NGC 1194:
The starting model for the spectral fit of this source isprovided by the work of Masini et al. (2016), who fitted the
Nu-STAR spectrum with the
MYTorus model in the decoupled mode,
MNRAS000
MNRAS000 , 1–14 (2015) Gliozzi, Williams, & Michel with the addition of a Gaussian line at 6.8 keV, and a scatteringfraction of the primary continuum of 𝑓 s ∼ Γ , 𝑁 H ,and 𝑓 s ) to be fully consistent with their best-fit results. The 2–10keV observed flux is 1 . × − erg cm − s − , and the intrinsic one1 . × − erg cm − s − . NGC 2273:
The starting spectral model for this source is againprovided by the work of Masini et al. (2016), who fitted the
NuSTAR spectrum with the
Torus model that favored a heavily absorbedscenario with 𝑁 H > × cm − . In our fitting, we used ourbaseline model, which yielded a best fit broadly consistent with theirresults. The 2–10 keV observed flux is 9 . × − erg cm − s − , andthe intrinsic one 3 . × − erg cm − s − . NGC 3079:
The starting spectral model for this source is againprovided by the work of Masini et al. (2016), who fitted the
NuSTAR spectrum with the
MYTorus model in a coupled mode. The resultsobtained with our baseline model are consistent within the respectiveuncertainties with their results. The 2–10 keV observed flux is 6 . × − erg cm − s − , and the intrinsic one 1 . × − erg cm − s − . NGC 3393:
The starting spectral model for this source is providedby the work of Koss et al. (2015) and Masini et al. (2016), who fittedthe
NuSTAR spectrum with both
MYTorus and
Torus models. Theresults obtained with our baseline model are broadly consistent withthe results presented by these authors with a slightly larger value of 𝑁 H (10 vs. 2 . × cm − ). The 2–10 keV observed flux is 4 . × − erg cm − s − , and the intrinsic one 8 . × − erg cm − s − . NGC 4388:
The starting spectral model for this source is once moreprovided by the work of Masini et al. (2016), who fitted the
Nu-STAR spectrum with the
MYTorus and
Torus models, which fa-vor a Compton-thin scenario with a substantial scattered primaryemission that dominates below 5 keV. The results from our base-line model are fully consistent with their results. The 2–10 keVobserved flux is 7 . × − erg cm − s − , and the intrinsic one1 . × − erg cm − s − . NGC 4945:
A detailed analysis of the
NuSTAR , Suzaku , and
Chan-dra spectra of this source was carried out by Puccetti et al. (2014),who in turn, were guided by the results obtained by Yaqoob (2012)based on a comprehensive analysis of all the hard X-ray spectraavailable at that time. The wealth of high-quality broad-band spectraobtained with several observatories made it possible to parametrizeseparately the different contributions of the host galaxy, the AGN,and contaminating sources within the
NuSTAR extraction region.The best-fit model is fairly complex and comprises several emis-sion lines, the galaxy optically thin thermal continuum, which isdescribed by the
APEC model, the contamination from off-nuclearsources parametrized by a power law, and the AGN emission seenthrough a torus described by the
MYTorus model in the decoupledmode. In our fitting procedure, in addition to our baseline model weincluded the
APEC and power-law models with all parameters fixedat the values provided by Yaqoob. Our results are broadly consis-tent with those obtained by both Yaqoob and Puccetti. The 2–10keV observed flux is 3 . × − erg cm − s − , and the intrinsic one2 . × − erg cm − s − . IC 2560:
The starting spectral model for this source is again providedby the work of Masini et al. (2016), who fitted the
NuSTAR spectrumwith the
Torus model, which favors a heavily absorbed primaryemission characterized by a steep photon index. The results from ourbaseline model are broadly consistent with their results. The 2–10keV observed flux is 3 . × − erg cm − s − , and the intrinsic one1 . × − erg cm − s − . Circinus:
A detailed analysis of the
NuSTAR , XMM-Newton , and
Chandra spectra of this source was carried out by Arévalo et al. (2014). Combining the complementary properties of these obser-vatories (i.e., the high sensitivities of
XMM-Newton and
NuSTAR over broad energy ranges and the sub-arcsecond spatial resolutionof
Chandra ), the authors were able to disentangle the contributionsof different contamination sources (diffuse emission from the hostgalaxy, supernova remnant contribution, and off-nuclear X-ray bi-nary sources) from the AGN emission within the
NuSTAR extractionregion. The overall best-fit model is complex and comprises severalemission lines, an
APEC model for the diffuse emission, three
Mekal models to parametrize the supernova remnant, and a power-law modelto account for the off-nuclear point-like sources, in addition to twodifferent
MYTorus models used in the decoupled mode. In our fit-ting, in addition to our baseline model we added all the contaminationmodels with all the parameters fixed at the values provided by Aré-valo et al. (2014) and three Gaussian lines to roughly model theline excess in the 5.5–7.5 keV range. To account for the multiple ab-sorption components, we also added a second
Borus model, whosebest-fit parameters are log ( 𝑁 H bor ) = . ± .
1, CFtor = 10%, and 𝐴 Fe =
1. Our best-fit parameters are broadly consistent with theirresults. The 2–10 keV observed flux is 2 . × − erg cm − s − , andthe intrinsic one 2 . × − erg cm − s − . APPENDIX B: THE X-RAY SCALING METHOD
The X-ray scaling method for determining the mass of a black hole( 𝑀 BH ) was first described by Shaposhnikov & Titarchuk (2009) andfirst applied to AGN by Gliozzi et al. (2011), where the method isdescribed in detail. Here, we only report the essential informationon the stellar reference sources – their 𝑀 BH values and distances(Table B1) and the mathematical expression of the spectral trendwith the best fit parameters for the different sources (Table B2) –that is needed to reproduce the 𝑀 BH values. The two steps belowaccomplish the scaling described in Section 4.1.Step 1. Use the following equation to solve for 𝑁 BMC,r , the BMCnormalization the reference source would have at the same photonindex as the target AGN. The reference source is a Galactic, stellar-mass black hole with known mass and distance. 𝑁 BMC,r ( Γ ) = 𝑁 tr × (cid:26) − ln (cid:20) exp (cid:18) 𝐴 − Γ 𝐵 (cid:19) − (cid:21)(cid:27) ( / 𝛽 ) (B1)where Γ is the photon index of the target AGN as determined by thespectral fit, and 𝐴 , 𝐵 , 𝑁 tr , and 𝛽 are given in Table B2. Note: thisequation was first presented by Jang et al. (2018) with an error: thereshould be a minus sign before the logarithm.Step 2. Use the equation presented in Section 4.1 to solve for 𝑀 BH,t . 𝑀 BH,t = 𝑀 BH,r × (cid:18) 𝑁 BMC,t 𝑁 BMC,r (cid:19) × (cid:18) 𝑑 t 𝑑 r (cid:19) (B2)where 𝑀 BH is the black hole mass, 𝑁 BMC is the BMC normalization,and 𝑑 is the distance. The 𝑡 subscript denotes the target AGN and the 𝑟 subscript denotes the reference source. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS , 1–14 (2015) stimating black hole masses in obscured AGN Table B1.
Characteristics of reference sources Name 𝑀 BH 𝑑 (M (cid:12) ) (kpc)GRO J1655-40 6 . ± . . ± . . ± . . ± . . ± . . ± . Table B2.
Parametrization of Γ – 𝑁 BMC reference patternsTransition
𝐴 𝐵 𝑁 tr 𝛽 (1) (2) (3) (4) (5)GRO J1655-40 D05 1 . ± .
02 0 . ± .
02 0 . ± .
001 1 . ± . . ± .
04 0 . ± .
04 0 . ± .
001 1 . ± . . ± .
03 0 . ± .
04 0 . ± . . ± . . ± .
03 0 . ± .
01 0 . ± .
001 8 . ± . . ± .
02 2 . ± . . ± .
010 0 . ± .000