The applicability and apparent uncertainties of the techniques currently
available for measuring or estimating black-hole masses in AGNs are briefly
summarized.Comment: 6 pages. Invited review at `AGN Physics with the Sloan Digital Sky
  Survey' conference (July 2003), eds. G. Richards and P. Hall (ASP Conf.
  Series, 2004

Vestergaard, M.

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Vestergaard, Marianne

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u n i ve r s i t y  o f  co pe n h ag e n  Københavns UniversitetBlack-Hole Mass MeasurementsVestergaard, MariannePublished in:ASP Conference SeriesPublication date:2004Citation for published version (APA):Vestergaard, M. (2004). Black-Hole Mass Measurements. ASP Conference Series, 311.Download date: 03. Feb. 2020arXiv:astro-ph/0401436v1  21 Jan 2004AGN Physics with the Sloan Digital Sky SurveyASP Conference Series, Vol. **VOLUME***, 2004G.T. Richards and P.B. Hall, eds.Black-Hole Mass MeasurementsM. VestergaardDepartment of Astronomy, The Ohio State University, 140 West 18thAvenue, Columbus, OH43210Abstract. The applicability and apparent uncertainties of the tech-niques currently available for measuring or estimating black-hole massesin AGNs are briefly summarized.1. IntroductionKnowledge of the mass of the central black hole in active galaxies is importantfor many studies of early structure formation and of the central engine and itsevolution. The hope is that we will learn how the formation and growth of theblack hole affects the formation, the evolution, and the characteristics of thegalaxy by which it is hosted. The SDSS promises to provide valuable insight.Black-hole mass determination methods fall in two distinct categories: pri-mary and secondary methods. Their differences are important to recognize.With primary methods, the black-hole mass (MBH) is directly measured fromgas and stars whose dynamics are dictated by the black hole. These methodsare often very challenging or time consuming. In contrast, secondary methodsare often more easily applied to large data sets, but only provide estimates ofthe mass by adopting approximations to the primary methods or by measuringparameters with which MBH is known to correlate.Due to space limitations, all the work done on this subject cannot be cited;my apologies in advance. Emphasis is placed on a few key papers providingcalibration of the methods and assessments of the uncertainties.2. Primary Mass Determination MethodsStellar and Gas Kinematics. To determine the virial black-hole mass ofnearby quiescent galaxies requires high spatial resolution spectroscopy of thenuclear regions in order to measure the velocity dispersion of the stars (or gas)within the sphere of influence of the central black hole. This method can alsobe used for weakly active galactic nuclei (AGNs), such as low-luminosity AGNs,LINERs, and Seyfert 2s (Table 1). For more luminous AGNs (Type 1 sources)the strong nuclear emission washes out the stellar features in the spectrum. Thescatter in theMBH−σbulge∗ relationship, established for nearby quiescent galaxies(e.g., Tremaine et al. 2002), suggests that black-hole masses determined fromstellar and gas kinematics are accurate to within a factor of about 2.12 VestergaardTable 1. Primary Mass Determination MethodsLow-z High-z BestLow-L High-L High-L AccuracyLINERs, QSOs, Sy 1s QSOs (dex)Sy 2s BL LacsStellar & Gaskinematics (√) ÷ ÷ 0.15− 0.3Megamasers Type 2 ÷ ÷ ≤ −1.0ReverberationMapping Type 1 Type 1√0.15− 0.3Megamasers. Spectroscopy of water-vapor maser emission from circumnu-clear disks in nearby AGNs reveals the kinematics of the disk and the locationof the maser. Megamasers can yield highly accurate MBH measurements, espe-cially in highly inclined sources: for NGC4258, which is inclined 83◦±4◦, themass is determined to within a few per cent (Miyoshi et al. 1995). However,this method is only useful for selected ‘edge-on’ sources and so far relatively fewobjects are known to have megamasers (e.g., Greenhill et al. 2003).Reverberation Mapping. The reverberation-mapping technique is the bestand most robust mass measurement method to apply to AGNs and quasars: uti-lizing the variability properties of the source the technique does not require highspatial resolution and is not affected by the nuclear glare. Peterson & Onken(2004, this volume) outline the basic principle of the reverberation mapping tech-nique and discuss the importance of the zero-point calibration of reverberationmasses and of the unknown, order unity, scale factor f .For a given AGN the rms velocity width and time lag for different broademission lines correlate such that higher ionization lines have larger widths andsmaller lags (consistent with the same central mass for each object). This virialrelationship for multiple lines is seen for all four AGNs for which this is testable(NGC7469, NGC3783, NGC5548, 3C 390.3) and for the well-measured emissionlines of Si iv λ1400, C iv λ1549, He ii λ1640, C iii] λ1909, Hβ λ4861, and He iiλ4686 (Peterson & Wandel 1999, 2000; Onken & Peterson 2002).Notably, nearby AGNs with measurements of both reverberation mass andbulge velocity dispersion fall along theMBH −σ∗ relationship established by qui-escent galaxies and with a similar scatter (Ferrarese et al. 2001). This suggeststhat reverberation mapping masses are accurate to within a factor 2 to 3.Reverberation mapping is fully applicable to distant quasars (Table 1), butis less practical as it is extremely time and resource consuming: luminous AGNsvary with smaller amplitudes and on longer time scales than lower-luminosity,nearby AGNs. The time scales are further increased by time dilation owing tothe cosmological distances of quasars. Even for the 17 nearby quasars monitoredso far, ten years of variability data are necessary to obtain reasonable results(Kaspi et al. 2000). Secondary methods are more practical for distant quasars.Black-Hole Mass Measurements 3Table 2. Secondary Mass Determination MethodsLow-z High-z Best FutureLow-L High-L High-L Accu- WorkLINERs, QSOs, Sy 1s QSOs racySy2s BL Lacs (dex)Scaling Relations√ √ √0.4− 0.5 note aVia MBH−σ∗:− σ∗√ √ ÷ 0.3 note b− [O iii] FWHM √ √ √ 0.7 note c− FundamentalPlane:∑e, re√ √ ÷ >0.7 note dVia MBH−Lbulge& scaling rel.:− MR√ √ ÷ 0.5− 0.6 note eNotes − (a) Improve R−L relation; understand outliers, (b) Extend to moredistant AGNs and luminous quasars, (c) Understand scatter and outliers,(d) Quantify and improve accuracy, (e) Calibrate to Reverberation masses3. Secondary MethodsSince the primary mass determination methods are either inapplicable or imprac-tical for more luminous and more distant AGNs and quasars, several secondarymethods have been adopted in the literature to estimate the central mass. Thesemethods, summarized in Table 2, are either approximations to the reverberationmapping technique or rely on the empirical relationships between the black-holemass, MBH, and the properties of the host galaxy bulge: velocity dispersion,σ∗, or bulge luminosity, Lbulge. The measurements of the bulge properties aremost useful for AGNs at low redshift (z <∼ 1) where the host galaxy is easierto characterize. It is noteworthy that, even so, these methods can yield massestimates that are currently quite uncertain, as explained below.3.1. Scaling RelationshipsBased on single-epoch spectroscopy the scaling relationships are approximationsto the virial-mass measurements obtained from reverberation mapping. Themethod relies on the radius – luminosity relationship, established by reverbera-tion mapping. For a photoionized BLR, its size R should scale with the squareroot of the source luminosity, R ∝ L0.5. Kaspi et al. (2000) found empiricallythat the size of the H β emitting region scales with the continuum luminosity at5100A˚ to the power of 0.7: R(H β) ∝ L0.7λ(5100A˚). While this difference is yet tobe understood (work is in progress; e.g., Peterson & Onken, this volume), thismeans thatMBH can be estimated when we have measurements of the continuumluminosity and the emission-line width: MBH ∝ FWHM2 L0.7λ . (Note, the slopeadopted in the literature is not uniform but ranges between 0.5 and 0.7). The useof FWHM is a single-epoch approximation to the velocity dispersion of the line-4 Vestergaardemitting gas responding to continuum variations (Peterson & Onken 2004, thisvolume). Vestergaard (2004b, this volume) explains why these scaling relationsare reasonable and why they can be applied to luminous, high-z quasars.Three different broad emission lines (H β, Mg ii, and C iv) have been adoptedalong with continuum luminosities (at 5100A˚, 3000A˚, and 1350A˚, respectively)to estimate black-hole masses in large samples of quasars and AGNs [H β, C iv:Vestergaard (2002; 2004b, this volume); Mg ii: McLure & Jarvis (2002); Jarvis& McLure (2004, this volume)]. There are pros and cons to each method as out-lined next. Using optical spectroscopy, the Hβ method probes redshifts below0.9, Mg ii probes redshifts between 0.3 and 2.3, while C iv is accessible at red-shifts between 1.2 and 4.9. While Fe ii emission heavily contaminates the Mg iiline profile (e.g., Francis et al. 1991; Vestergaard & Wilkes 2001) and thus needsto be subtracted to allow measurements of FWHM(Mg ii), typically only strongFe ii emission affects the H β line width. C iv is only affected in the extremewings by He iiλ1640, and occasionally by N iv]λ1486, and (weak) Fe ii multi-plets. However, the contribution to Hβ from the narrow-line region needs to besubtracted. The only concern about C iv is the possible presence of outflowinghigh-ionization BLR gas, which may yield blue asymmetric broad profiles. Thisis seen very clearly in the case of narrow-line Seyfert 1 galaxies (e.g., Leighly2000) for which the C iv method is not well suited. But very few quasars appearto display such asymmetric profiles, so emitting outflows are probably not a gen-eral concern for quasars (Vestergaard 2004). A notable assumption enters theMg ii method, namely that Mg ii should be emitted co-spatially with Hβ andshould therefore have similar line widths (which seems to be the case; McLure &Jarvis 2002). Then FWHM(Mg ii) can be used as a direct surrogate for H β inthe scaling relation. Unfortunately, the only published data on Mg ii constrainthe Mg ii lag (or the distance from which it is emitted) very poorly but theanalysis by Clavel et al. (1991) and Dietrich & Kollatschny (1995) suggest thatMg ii is not necessarily emitted co-spatially with Hβ. The additional advan-tage of the available Hβ and C iv scaling relations is that they are calibratedto the more accurate reverberation mapping masses of nearby AGNs (Wandel,Peterson, & Malkan 1999; Kaspi et al. 2000; Vestergaard 2002). The statisticalscatter indicates 1σ uncertainties of factors 2.5 to 3 (relative to the reverbera-tion masses) for these scaling relations. Similar uncertainties are argued to beobtainable with Mg ii (McLure & Jarvis 2002). Nonetheless, individual massestimates may be uncertain by as much as a factor 10. The power of scalingrelations is in their application to large statistical AGN samples.The uncertainties of these scaling relations are dominated by the scatter inthe R − L relation, and improvements to this relation is thus desirable. Also,there is a need to understand the outliers in the scaling relations (Table 2).Dramatically improving the accuracy of the reverberation masses, on which thescaling relations rely, will require a dedicated space-based observatory, such asthe proposed MIDEX mission Kronos (e.g., Peterson et al. 2004).The radius R can also be estimated with the reasonable assumption that theproduct of the ionization parameter and the electron density is roughly similarin all objects (the photoionization method). In this case the mass estimate isa function of L0.5 FWHM2 and seems accurate to within a factor two of thereverberation masses (Wandel, Peterson,&Malkan 1999).Black-Hole Mass Measurements 53.2. Via the MBH − σ∗ RelationshipAs theMBH−σ∗ relation for quiescent galaxies is relatively tight and AGNs alsofall on this relationship, good measurements of the bulge velocity dispersion inAGN host galaxies can be used to estimate the black-hole mass (and with a sim-ilar uncertainty; Table 2). So far, only AGNs at z < 0.06 have had σ∗ measuredbecause the Ca iiλλ8498, 8542, 8662 absorption lines used for this measurementmove into the atmospheric water vapor bands at z ≥ 0.06 (Ferrarese et al. 2001).Nelson (2000) suggested using FWHM([O iii]) as a proxy for σ∗ since thenear-nuclear stellar velocity dispersion correlates with FWHM([O iii]) for a sam-ple of 75 Seyfert galaxies (Nelson & Whittle 1996). Boroson (2003) used datafrom the SDSS Early Data Release to assess and confirm that the 1σ uncertaintyof this method is a factor of 5. For this method to be more useful, both thescatter and the outliers need to be understood (Table 2). Some line asymme-tries are suspected to be connected with outflows and can be prominent in radiosources where the narrow-line region and the radio source may interact.Studies in the literature have used AGN host galaxy imaging and the Fun-damental Plane for elliptical galaxies to measure the effective surface brightness,∑e, and the effective radius, re, to derive first σ∗ and then MBH. The reasoningis that especially nearby quasars and radio galaxies seem to reside in giant ellip-tical galaxies, which should fall on the Fundamental Plane. Unfortunately, thismethod potentially has large uncertainties because (a)∑e and re are very hardto measure accurately in the presence of the bright nucleus of most AGNs, (b)the bulge/disk decomposition process is difficult even for nearby quiescent galax-ies and is particularly challenging for AGNs, and (c) the method is subject tothe uncertainties of both the Fundamental Plane and theMBH −σ∗ relation. Forradio galaxies, unaffected by nuclear glare, a factor 4 (or larger) uncertainty inestimating σ∗ alone seems appropriate (Woo & Urry 2002). The combined uncer-tainty of the Fundamental Plane method is thus expected to exceed a factor 5.3.3. Via the MBH − Lbulge and Scaling RelationshipsThe black-hole mass of quiescent galaxies correlates, in addition to σ∗, with thebulge luminosity, Lbulge, although with larger scatter. For this reason, the MBH−Lbulge relation is generally not preferred for mass estimates of normal galaxies.This method has also proven difficult and prone to significant uncertainties owingto the nuclear glare affecting the bulge/disk decomposition process (e.g., Wandel2002). Nonetheless, McLure & Dunlop (2001, 2002) argue that with careful R-band measurements of the AGN host galaxy, first Lbulge and then MBH can beestimated to within a factor 3 to 4. Unfortunately, this method has not yetbeen calibrated to reverberation mapping masses, but rather to mass estimatesbased on scaling laws. This may not be a severe problem since the authors findtheir AGNs to have the same slope and scatter as the inactive galaxies withdynamical mass measurements to within the errors.4. Future EffortsTable 2 lists suggestions to how we may improve the mass estimation methods.In addition, it is important to understand their limitations as well as their ef-6 Vestergaardficacy. Since reverberation masses provide the anchor of the scaling relationsa few comments thereon are in order. An understanding of the BLR structureand kinematics is required to determine the absolute zero-point of the reverber-ation masses (the ‘f ’ factor). This is a non-trivial but an achievable task witha dedicated observatory like Kronos and existing advanced analysis techniques(Peterson et al. 2004; Peterson & Horne 2004). Also, direct comparisons of stel-lar dynamics and reverberation mapping need to be effected. Moreover, the oddobjects need to be understood: for example, for 3C 390.3 the lower ionizationlines appear to have shorter lags, in contrast to other AGNs. As this object isthe only broad-line radio source which has been monitored, it needs to be estab-lished whether or not it belongs to a separate class of objects. Understanding thisbehavior is also important for our understanding of the typical BLR structure.ReferencesBoroson, T. A. 2003, ApJ, 585, 647Clavel, J., et al. 1991, in Variability of Active Galactic Nuclei, ed. H. R. Miller& P. J. Wiita (Cambridge: Cambridge University Press), 301Dietrich, M. ,& Kollatschny, W. 1995, A&A, 303, 405Dietrich, M., et al. 2002, ApJ, 581, 912Ferrarese, L., et al. 2001, ApJ, 555, L79Francis, P., et al. 1991, ApJ, 373, 465Greenhill, L., et al. 2003, ApJ, 582, L11Kaspi, S., et al. 2000, ApJ, 533, 631Leighly, K. 2000, New Astronomy Review, 44, 395McLure, R., & Dunlop, J. 2001, MNRAS, 327, 199McLure, R., & Dunlop, J. 2002, MNRAS, 331, 795McLure, R., & Jarvis, M. 2002, MNRAS, 337, 109Nelson, C. 2000, ApJ, 544, L91Nelson, C., & Whittle, M. 1996, ApJ, 465, 96Onken, C., & Peterson, B. M. 2002, ApJ, 572, 746Peterson, B. M., & Horne, K. 2004, Astron. Nach., in pressPeterson, B. M., Polidan, R. S., & Horne, K. 2004, Astron. Nach., in pressPeterson, B. M., & Wandel, A. 1999, ApJ, 521, L95Peterson, B. M., & Wandel, A. 2000, ApJ, 540, L13Tremaine, S., et al. 2002, ApJ, 574, 740Vestergaard, M. 2002, ApJ, 571, 733Vestergaard, M. 2004, ApJ, 600, in pressVestergaard, M., & Wilkes, B. J., 2001, ApJS, 134, 1Wandel, A. 2002, ApJ, 565, 762Wandel, A., Peterson, B. M., & Malkan, M. A. 1999, ApJ, 526, 579Woo, J.-H., & Urry, C. M. 2002, ApJ, 579, 530

Black-Hole Mass Measurements

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Black-Hole Mass Measurements

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