Spectral Models for Low-luminosity Active Galactic Nuclei in LINERs: The Role of Advection-dominated Accretion and Jets
Rodrigo S. Nemmen, Thaisa Storchi-Bergmann, Michael Eracleous
MMon. Not. R. Astron. Soc. , 1–23 (2013) Printed 26 August 2018 (MN L A TEX style file v2.2)
Spectral Models for Low-luminosity Active Galactic Nucleiin LINERs: The Role of Advection-dominated Accretionand Jets
Rodrigo S. Nemmen, (cid:63) Thaisa Storchi-Bergmann, Michael Eracleous, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA Instituto de F´ısica, Universidade Federal do Rio Grande do Sul, Campus do Vale, Porto Alegre, RS, Brazil Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802
Accepted 2013 June 18. Received 2013 June 17; in original form 2013 March 31
ABSTRACT
We perform an exploratory study of the physical properties of accretion flows and jetsin low-luminosity active galactic nuclei (LLAGNs) by modeling the spectral energydistributions (SEDs) of 12 LLAGNs in low-ionization nuclear emission-line regions(LINERs). These SEDs we constructed from high-resolution radio, X-ray and opti-cal/UV observations of the immediate vicinity of the black hole. We adopt a coupledaccretion-jet model comprising an inner advection-dominated accretion flow (ADAF)and an outer standard thin disk. We present best-fit models in which either the ADAFor the jet dominate the X-ray emission. Six sources in our sample display an optical-UV excess with respect to ADAF and jet models; this excess can be explained asemission from the truncated disk with transition radii 30 − R S in four of them. Inalmost all sources the optical emission can also be attributed to unresolved, old stellarclusters with masses ∼ − M (cid:12) . We find evidence for a correlation between theaccretion rate and jet power and an anti-correlation between the radio-loudness andthe accretion rate. We confirm previous findings that the radio emission is severely un-derpredicted by ADAF models and explained by the relativistic jet. We find evidencefor a nonlinear relation between the X-ray and bolometric luminosities and a slight IRexcess in the average model SED compared to that of quasars. We suggest that thehardness of the X-ray spectrum can be used to identify the X-ray emission mechanismand discuss directions for progress in understanding the origin of the X-rays. Key words: accretion, accretion disks — black hole physics — galaxies: active —galaxies: nuclei — galaxies: jets — galaxies: Seyfert
In the present-day universe, supermassive black holes(SMBHs) are underfed compared to the ones at high red-shifts and are “sleeping”. Most of SMBH activity at low z isdominated by the weak end of the AGN luminosity func-tion in the form of low-luminosity AGNs (LLAGNs; Ho,Filippenko & Sargent 1995, 1997b; Nagar, Falcke & Wil-son 2005; Ho 2008). LLAGNs are extremely sub-Eddingtonsystems which are many orders of magnitude less lumi-nous than quasars, with average bolometric luminosities L bol (cid:46) erg s − and an average Eddington ratio of L bol /L Edd ∼ − (Ho 2009) where L Edd is the Edding-ton luminosity. Though the LLAGN phase dominates thetime evolution of SMBHs, it contributes little to their mass (cid:63)
E-mail: [email protected] growth (Hopkins & Hernquist 2006; Sijacki et al. 2007; Mer-loni & Heinz 2008; Xu & Cao 2010). The bulk of the LLAGNpopulation ( ≈ /
3; Ho 2008, 2009) reside in low-ionizationnuclear emission-line regions (LINERs; Heckman 1980; Ho,Filippenko & Sargent 1997a).The observational properties of LLAGNs are quite dif-ferent from those of more luminous AGNs. Regarding thebroadband spectral energy distributions (SEDs), LLAGNsseem not to have the thermal continuum prominence in theultraviolet (UV) – the “big blue bump” – which is one of thesignatures of the presence of an optically thick, geometricallythin accretion disk (Ho 1999; Nemmen et al. 2006; Wu, Yuan& Cao 2007; Ho 2008; Eracleous, Hwang & Flohic 2010b).Regarding the emission-lines, LLAGNs typically have weakand narrow Fe K α emission (Terashima et al. 2002) and ahandful of LINERs display broad double-peaked H α lines(e.g., Storchi-Bergmann et al. 2003); these properties of the c (cid:13) a r X i v : . [ a s t r o - ph . H E ] D ec Nemmen et al. emission-line spectrum are consistent with the absence ofa thin accretion disk, or a thin accretion disk whose innerradius is truncated at (cid:38)
GM/c (Chen, Halpern & Filip-penko 1989; Chen & Halpern 1989). Last but not least, withthe typical gas supply available via ordinary mass loss fromevolved stars and gravitational capture of gas from the hotinterstellar medium (i.e. Bondi accretion) in nearby galaxies,LLAGNs would be expected to produce much higher lumi-nosities than observed on the assumption of standard thindisks with a 10% radiative efficiency (Soria et al. 2006b; Ho2009). Taken together, this set of observational propertiesfavors the scenario in which the accretion flow in LLAGNsis advection-dominated or radiatively inefficient.Advection-dominated accretion flows (ADAFs ; for re-views see Narayan, Mahadevan & Quataert 1998; Yuan 2007;Narayan & McClintock 2008) are very hot, geometricallythick, optically thin flows which are typified by low radia-tive efficiencies ( L (cid:28) . Mc ) and occur at low accretionrates ( ˙ M (cid:46) .
01 ˙ M Edd ). SMBHs are thought to spend mostof their lives in the ADAF state (Hopkins, Narayan & Hern-quist 2006; Xu & Cao 2010), the best studied individual casebeing Sgr A* (e.g., Yuan 2007).In many LLAGNs, another component in the accretionflow besides the ADAF is required in order to account for anumber of observations, including a prominence in the midor near-IR and steep fall-off of the spectrum in the optical-UV region – a “red bump” (Lasota et al. 1996; Quataertet al. 1999; Nemmen et al. 2006; Ho 2008; Yu, Yuan & Ho2011; Wu, Yan & Yi 2013) – as well as the presence of double-peaked Balmer emission lines (e.g., Storchi-Bergmann et al.2003; Eracleous, Lewis & Flohic 2009): the emission from athin accretion disk whose inner radius is truncated at theouter radius of the ADAF. The accretion flow may beginas a standard thin disk but somehow at a certain transitionradius it gradually switches from a cold to a hot ADAFmode. The details of how this transition might happen arestill not well understood (Manmoto et al. 2000; Yuan &Narayan 2004; Narayan & McClintock 2008), but it seems tobe analogous to the transition between the different spectralstates in black hole binary systems (Remillard & McClintock2006; Done, Gierli´nski & Kubota 2007).Maoz (2007) challenged the scenario of the central en-gines of LLAGNs consisting of ADAFs and truncated thindisks. Maoz argues that LLAGNs in LINERs have UV/X-ray luminosity ratios similar on average to those of brighterSeyfert 1s and based on that observation he posits that thindisks extending all the way down to the radius of the inner-most stable circular orbits (ISCO) persist even for LLAGNs,despite their smaller accretion rates. Yu, Yuan & Ho (2011)showed that the SEDs compiled by Maoz (2007) are natu-rally fitted by ADAF models with the addition of a trun-cated thin disk and also discussed on theoretical groundswhy the ADAF model has a superior explanation capabil-ity than the pure thin disk model. The ADAF model is theonly model that can naturally account for the set of obser-vational properties of LLAGNs within a self-contained theo- In this paper, we consider ADAFs and radiatively inefficientaccretion flows (RIAFs) to be the same kind of accretion flowsolution. For a clarification regarding the terminology, see Yu,Yuan & Ho 2011. retical framework. Hence, it is the physical scenario adoptedin this work.ADAFs are relevant to the understanding of AGN feed-back since they are quite efficient at producing powerfuloutflows and jets, as suggested by theoretical studies includ-ing analytical theory (Narayan & Yi 1994; Nemmen et al.2007; Begelman 2012) and numerical simulations (McKin-ney & Gammie 2004; Hawley & Krolik 2006; Tchekhovskoy,Narayan & McKinney 2011; McKinney, Tchekhovskoy &Blandford 2012; Yuan, Bu & Wu 2012). This is in line withthe different observational studies that demonstrate thatLLAGNs are generally radio-loud (Nagar et al. 2000; Nagar,Wilson & Falcke 2001; Ho 2002, 2008; Younes et al. 2012)and accompanied by powerful jets (e.g., Heinz, Merloni &Schwab 2007; Merloni & Heinz 2008).It is clear then that an understanding of the physicalnature of LLAGNs in LINERs will shed light on the natureof black hole accretion, outflows and consequently black holegrowth and AGN feedback in present-day galaxies. One ofthe best ways of exploring the astrophysics of black holeaccretion and outflows is by using multiwavelength observa-tions of black hole systems and comparing the spectra pre-dicted by specific models with the data. The goal of this workis therefore to probe the physics of accretion and ejectionin the LLAGN population, by carrying out an exploratorymodeling of their nuclear, broadband, radio to X-rays SEDswhich provide constraints on physical models for the emis-sion of the accretion flow and the jet. Furthermore, witha large enough sample of systems, we can derive from thefits to the data the parameters that characterize the cen-tral engines and build a census of the “astrophysical diet”of low-state AGNs.The structure of this paper is as follows. In Section 2 wedescribe the sample of 21 LLAGNs in LINERs that we used,the data and the criteria that we use to select the 12 best-sampled SEDs. Section 3 describes the physical model thatwe adopted in order to interpret and fit the SEDs and derivethe central engine parameters. In Section 4 we describe themodel fits to the SEDs. In Section 5 we describe the param-eters resulting from our model fits and possible correlationsbetween accretion and jet production. We present the aver-age SED resulting from our fits in §
6, including the predictedemission in wavebands which can be observed with futurefacilities such as ALMA. We discuss the role of the ADAFand jet in explaining the X-ray emission, the constraints onthe transition radius and the limitations of our models in §
7, outlining along the way the directions for progress onthese issues. We conclude by presenting a summary of ourresults in §
8. In the Appendix, we discuss the uncertaintiesin the model parameters that we derive and present illustra-tive model fits to the 9 sparsely-sampled SEDs which wereleft out of the main analysis.
Eracleous, Hwang & Flohic (2010b) (hereafter EHF10) com-piled a sample of 35 SEDs of LLAGNs found in LINERswhich include high spatial resolution optical and UV ob-servations with the
Hubble Space Telescope (HST), as wellas X-ray observations with
Chandra and high-resolution ra- c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs dio observations with the Very Large Array – VLA – orVLBA/VLBI.LINERs constitute quite a heterogeneous class of ob-jects. For instance, their nature and particularly the natureof the source of power for their line emission has been re-peatedly questioned (e.g. Eracleous, Hwang & Flohic 2010a;Sarzi et al. 2010; Yan & Blanton 2012; Singh et al. 2013).For example, Yan & Blanton (2012) concluded that the lineemission observed in large-aperture ( >
100 pc) spectroscopyin most of the LINER-like galaxies in their sample is notprimarily powered by an accreting black hole and thus urgecaution in associating the corresponding line emission withthe AGN bolometric luminosity. Therefore, in order to selectfrom the sample of EHF10 the sources for which the nuclearemission is most probably associated with black hole accre-tion – thus providing the best SEDs to be compared againstaccretion flow and jet models – we carefully applied the fol-lowing selection criteria.
Availability of black hole mass estimates –
We limited our-selves only to galaxies with black hole mass estimates sincethe mass is one of the fundamental input parameters to thespectral models.
Presence of a compact nuclear radio core and availabilityof at least one high-resolution radio detection with VLA orVLBA/VLBI –
Radio measurements constrain the relativeimportance of the synchrotron emission from the jet andADAF.
Presence of nuclear X-ray point source and availability of itsX-ray spectra –
Given that the X-ray spectrum is a crucialconstraint for the models, we only selected objects for whichthere is detected nuclear X-ray emission as opposed to upperlimits.
Availability of at least one high spatial resolution nuclear ob-servation in the µ m − ˚ A waveband – Measurementsin the optical/near-IR potentially constrain the emission ofthe truncated thin accretion disk, whereas observations inoptical/UV can constrain the inverse Compton emission pro-duced in the inner regions of the ADAF. Therefore, we se-lected only sources which have at least one observation athigh spatial resolution ( < (cid:48)(cid:48) ) in the 1 µ m − Absence of prominent absorption features from hot stars inthe nuclear UV spectrum (when available) –
We discardedfrom our analysis three sources (NGC 404, NGC 5055 andNGC 6500) from the EHF10 sample which display promi-nent absorption lines in their UV spectra, suggestive thatstellar emission dominates the UV light (cf. Maoz et al. 1998;EHF10 for more details).These selection criteria leave us with 12 LINERs whichare listed in Table 1. This table also lists their correspondingHubble and LINER Types, black hole masses, bolometricluminosities and Eddington ratios.We treat the observations in the IR band taken withlower spatial resolutions ( > (cid:48)(cid:48) ) – i.e. larger apertures – asupper limits because they include considerable contamina-tion from the emission of the host galaxy.The masses of the SMBHs were estimated from the stel-lar velocity dispersions using the M BH − σ relationship (Fer-rarese & Merritt 2000; Gebhardt et al. 2000; Tremaine et al.2002), with the exception of NGC 3031 (M81) and NGC4486 (M87) whose black hole masses were estimated fromthe stellar and/or gas kinematics (Bower et al. 2000; Dev- ereux et al. 2003; Gebhardt & Thomas 2009; see Table 1).As EHF10 note, for the objects with multiple mass determi-nations using different methods, the estimated masses areconsistent with each other within a factor of 2 or better.The optical-UV data of all objects were corrected forextinction (EHF10), unlike previous similar SED modelingefforts (e.g. Wu, Yuan & Cao 2007; Yuan, Yu & Ho 2009;Yu, Yuan & Ho 2011). In order to compute the bolometricluminosities from the SEDs, EHF10 used two methods. Forthe objects with the best sampled SEDs, they computed L bol by integrating the SEDs directly, ignoring upper limit datapoints. These objects are NGC 3031, NGC 3998, NGC 4374,NGC 4486, NGC 4579 and NGC 4594. For these objectsthey assumed that pairs of neighboring points in the SEDsdefined a power law, integrated each segment individuallyand summed the segments to obtain L bol . From this set ofbest sampled SEDs they estimated the average “bolometriccorrection” from the 2-10 keV luminosity to the bolometricluminosity ( L bol = 50 L X ), which they used to obtain L bol for the remaining objects, for which the SEDs are not as wellsampled. These bolometric luminosities are listed in Table1. The sources in our sample were selected based on theavailability of data. As discussed by EHF10, there may besome biases inherited from the surveys from which the datawas obtained which rely on objects bright in the radio, UVand X-ray bands. For instance, transition objects are under-represented while type 1.9 LINERs are over-represented.It is not clear at present whether the relative number ofLINER types in our sample could impact our modeling re-sults. Therefore, the resulting sample cannot be consideredcomplete since it only consists of objects for which the neces-sary data are available. The biases resulting from this selec-tion are hard to quantify but we refer the reader to EHF10for further discussion. We fit the observed broadband SEDs of the LLAGNs in oursample using a model which consists of three components:an inner ADAF, an outer truncated thin accretion disk anda jet. The components of the model are illustrated in Figure1. We describe here the main features of this model.
The inner part of the accretion flow is in the form of anADAF which is a hot, geometrically thick, optically thintwo-temperature accretion flow, which has low radiative ef-ficiency (e.g., Narayan, Mahadevan & Quataert 1998; Kato,Fukue & Mineshige 1998). ADAFs are characterized by thepresence of outflows or winds, which prevent a considerablefraction of the gas that is available at large radii from be-ing accreted onto the black hole. This has been suggestedby numerical simulations (Stone & Pringle 2001; Hawley &Krolik 2001; Igumenshchev, Narayan & Abramowicz 2003;De Villiers, Hawley & Krolik 2003; Proga & Begelman 2003;McKinney & Gammie 2004; Yuan, Bu & Wu 2012) and an-alytical work (Narayan & Yi 1994; Blandford & Begelman c (cid:13)000
The inner part of the accretion flow is in the form of anADAF which is a hot, geometrically thick, optically thintwo-temperature accretion flow, which has low radiative ef-ficiency (e.g., Narayan, Mahadevan & Quataert 1998; Kato,Fukue & Mineshige 1998). ADAFs are characterized by thepresence of outflows or winds, which prevent a considerablefraction of the gas that is available at large radii from be-ing accreted onto the black hole. This has been suggestedby numerical simulations (Stone & Pringle 2001; Hawley &Krolik 2001; Igumenshchev, Narayan & Abramowicz 2003;De Villiers, Hawley & Krolik 2003; Proga & Begelman 2003;McKinney & Gammie 2004; Yuan, Bu & Wu 2012) and an-alytical work (Narayan & Yi 1994; Blandford & Begelman c (cid:13)000 , 1–23 Nemmen et al.
Table 1.
Sample of galaxies and their basic properties a .Galaxy Hubble Distance b log LINER L X L bol L bol /L Edd
Type (Mpc) ( M BH /M (cid:12) ) Type (erg s − ) c (erg s − ) d NGC 1097 SB(rl)b 14.5 (1) 8.1 L1 4 . × . × × − NGC 3031 (M81) SA(s)ab 3.6 (3) 7.8 S1.5/L1 1 . × . × × − NGC 3998 SA(r)0 13.1 (2) 8.9 L1 2 . × . × × − NGC 4143 SAB(s)0 14.8 (2) 8.3 L1 1 . × . × × − NGC 4261 E2-3 31.6 (2) 8.7 L2 1 . × . × × − NGC 4278 E1-2 14.9 (2) 8.6 L1 9 . × . × × − NGC 4374 (M84, 3C 272.1) E1 17.1 (2) 8.9 L2 3 . × . × × − NGC 4486 (M87, 3C 274) E0-1 14.9 (2) 9.8 L2 1 . × . × × − NGC 4552 (M89) E 14.3 (2) 8.2 T2 2 . × . × × − NGC 4579 (M58) SAB(rs)b 21.0 (4) 7.8 L2 1 . × . × × − NGC 4594 (M104) SA(s)a 9.1 (2) 8.5 L2 1 . × . × × − NGC 4736 (M94) (R)SA(r)ab 4.8 (2) 7.1 L2 5 . × . × × − Notes:(a) The information in this table was obtained from EHF10, see text.(b) The number in parenthesis gives the source and method of the distance measurement, as follows: (1) From the catalog of Tully &Fisher (1988), determined from a model for peculiar velocities and assuming H = 75 km s − Mpc − ; (2) From Tonry et al. (2001),who used the surface brightness fluctuation method. Following Jensen et al. (2003), the distance modulus reported by Tonry et al.(2001) was corrected by subtracting 0.16 mag; (3) From Freedman et al. (1994, 2001), who used Cepheid variables; (4) From Gavazziet al. (1999) who used the Tully-Fisher method.(c) L X is the X-ray luminosity in the 2 −
10 keV range.(d) The bolometric luminosities of NGC 1097, NGC 3031, NGC 3998, NGC 4374, NGC 4486, NGC 4579 and NGC 4594 were estimatedby integrating the SEDs. For all other galaxies L bol was determined by scaling L X as described in § Figure 1.
Cartoon illustrating the model for the central enginesof LLAGNs. It consists of three components: an inner ADAF, anouter truncated thin disk and a relativistic jet. s by˙ M = ˙ M o (cid:18) RR o (cid:19) s , (1)to describe the radial variation of the accretion rate ˙ M o mea-sured at the outer radius of the ADAF, R o . The results ofthe numerical simulations of the dynamics of ADAFs previ-ously mentioned as well as Chandra
X-ray studies of NGC3115 and Sgr A* (e.g., Wong et al. 2011; Wang et al. 2013) together with submillimeter polarization and Faraday rota-tion measurements of Sgr A* (Marrone et al. 2007) suggestthat 0 . (cid:46) s (cid:46) s = 0 . M ; the viscosity parameter α ; themodified plasma β parameter, defined as the ratio betweenthe gas and total pressures, β = P g /P tot ; δ , the fractionof energy dissipated via turbulence that directly heats elec-trons; and the adiabatic index γ . Following Nemmen et al.(2006), in our calculations we adopt α = 0 . β = 0 . γ = 1 .
5. Traditional ADAF models adopted δ to be small( δ (cid:46) .
01; e.g., Narayan & Yi 1995). On the other hand,it has been argued that the value of δ can be potentiallyincreased due to different physical processes - such as mag-netic reconnection - that affect the heating of protons andelectrons in hot plasmas (e.g., Quataert & Gruzinov 1999;Sharma et al. 2007). Given the theoretical uncertainty re-lated to the value of δ , we allow it to vary over the range0 . (cid:54) δ (cid:54) . c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs the eigenvalue j (the specific angular momentum of the flowat the horizon) until the sonic point condition at the sonicradius R s is satisfied, in addition to the outer boundary con-ditions (Yuan, Quataert & Narayan 2003).There are three outer boundary conditions that theADAF solution must satisfy, specified in terms of the threevariables of the problem: the ion temperature T i , the elec-tron temperature T e and the radial velocity v (or equiv-alently the angular velocity Ω). Following Yuan, Ma &Narayan (2008), when the outer boundary of the ADAF isat the radius R o = 10 R S (where R S is the Schwarzschildradius) we adopt the outer boundary conditions T out , i =0 . T vir , T out , e = 0 . T vir and λ out = 0 .
2, where the virialtemperature is given by T vir = 3 . × ( R S /R ) K, λ ≡ v/c s is the Mach number and c s is the adiabatic sound speed.When the outer boundary is at R o ∼ R S we adoptthe boundary conditions T out , i = 0 . T vir , T out , e = 0 . T vir and λ out = 0 .
5. After the global solution is calculated, thespectrum of the accretion flow is obtained (see e.g., Yuan,Quataert & Narayan 2003 for more details). We verified thatif these boundary conditions are varied by a factor of a few,the resulting spectrum does not change much.
Our model posits that outside the ADAF there is an outerthin accretion disk with an inner radius truncated at R tr = R o and extending up to 10 R S such that the outer radiusof the ADAF corresponds to the transition radius to thethin disk. The other parameters that describe the thin disksolution are the inclination angle i , the black hole mass andthe accretion rate ˙ M o (the same as the accretion rate at theouter boundary of the ADAF).The thin disk emits locally as a black body and we takeinto account the reprocessing of the X-ray radiation fromthe ADAF. This reprocessing effect has only a little impacton the spectrum of the thin disk though, with the resultingSED being almost identical to that of a standard thin disk(e.g., Frank, King & Raine 2002).For sources without optical/UV constraints, we adopt R o ∼ R S ; in this case we simply ignore the contributionof the thin disk emission since for R tr ∼ R S the thindisk contributes very little to the emission compared to theADAF. In sources for which we have available optical/UVdata to constrain this component of the flow, we then exploremodels with R tr < R S . The SEDs of LLAGNs are generally radio-loud (Ho 1999; Ho& Peng 2001; Ho 2002; Terashima & Wilson 2003; EHF10);but see Maoz 2007; Sikora, Stawarz & Lasota 2007). Theradio prominence of these SEDs is usually explained by in-voking the synchrotron emission of relativistic jets, since thethe accretion flow does not produce enough radio emissionto account for the observed radio luminosity (e.g., Ulves-tad & Ho 2001; Wu & Cao 2005; Nemmen et al. 2006; Wu,Yuan & Cao 2007; Yuan, Yu & Ho 2009; but see Liu &Wu 2013). Some authors even argue that the entire SEDof LLAGNs may be explained by the jet component (e.g.,Falcke, K¨ording & Markoff 2004; Markoff et al. 2008). We therefore include in our modeling the contribution from theemission from a relativistic jet.We adopt a jet model based on the internal shock sce-nario which is used to interpret gamma-ray burst afterglows(e.g., Piran 1999; Spada et al. 2001; Nemmen et al. 2012; seeYuan, Cui & Narayan 2005 for more details). This model hasbeen adopted in previous works to understand the broad-band SEDs of X-ray binaries and AGNs (Spada et al. 2001;Yuan, Cui & Narayan 2005; Nemmen et al. 2006; Wu, Yuan& Cao 2007). According to this jet model, some fraction ofthe material in the innermost regions of the accretion flowis transferred to the jet producing an outflow rate ˙ M jet anda standing shock wave in the region of the jet closest tothe black hole is formed. This shock wave is created fromthe bending of the supersonic accretion flow near the blackhole in the direction of the jet. We calculate the shock jump(Rankine-Hugoniot) conditions to find the electron and iontemperatures of the plasma ( T e and T i ). We find that thejet spectrum is not very sensitive to changes in T e and T i ,since the emission is completely dominated by non-thermalelectrons (see below). We therefore adopt T i = 6 . × Kand T e = 10 K in our calculations of the jet emission.The jet is modeled as having a conical geometry withhalf-opening angle φ and a bulk Lorentz factor Γ j which areindependent of the distance from the black hole. The jet isalong the axis of the ADAF and makes an angle i with theline of sight. The internal shocks in the jet are presumablycreated by the collisions of shells of plasma with differentvelocities. These shocks accelerate a small fraction ξ e of theelectrons into a power-law energy distribution with index p .The energy density of accelerated electrons and the ampli-fied magnetic field are described by two free parameters, (cid:15) e and (cid:15) B .Following Nemmen et al. (2006); Wu, Yuan & Cao(2007), we adopt in our calculations of the jet emission thevalues φ = 0 . ξ e = 10% and Γ j = 2 .
3, which cor-responds to v/c ≈ . j available). For six sources wehave independent constraints on the value of i (cf. Table 2).For the other six, we simply adopt i = 30 ◦ . Therefore, thereare four free parameters in the jet model: ˙ M jet , p , (cid:15) e and (cid:15) B . We allow p to vary in the range 2 − Throughout this paper we will use the dimensionless massaccretion rates ˙ m = ˙ M/ ˙ M Edd , noting that the Eddingtonaccretion rate is defined as ˙ M Edd ≡ M/ (10 M (cid:12) ) M (cid:12) yr − assuming a 10% radiative efficiency. We will also expressthe black hole mass in terms of the mass of the sun, m = M/M (cid:12) , and the radius in terms of the Schwarzschild radius, r = R/R S .We have 8 free parameters in the SED fits with ourcoupled accretion-jet model. Four of these parameters de-scribe the emission of the accretion flow: the accretion rate˙ M o , the fraction of viscously dissipated energy that directlyheats the electrons δ , the transition radius between the in- c (cid:13)000
3, which cor-responds to v/c ≈ . j available). For six sources wehave independent constraints on the value of i (cf. Table 2).For the other six, we simply adopt i = 30 ◦ . Therefore, thereare four free parameters in the jet model: ˙ M jet , p , (cid:15) e and (cid:15) B . We allow p to vary in the range 2 − Throughout this paper we will use the dimensionless massaccretion rates ˙ m = ˙ M/ ˙ M Edd , noting that the Eddingtonaccretion rate is defined as ˙ M Edd ≡ M/ (10 M (cid:12) ) M (cid:12) yr − assuming a 10% radiative efficiency. We will also expressthe black hole mass in terms of the mass of the sun, m = M/M (cid:12) , and the radius in terms of the Schwarzschild radius, r = R/R S .We have 8 free parameters in the SED fits with ourcoupled accretion-jet model. Four of these parameters de-scribe the emission of the accretion flow: the accretion rate˙ M o , the fraction of viscously dissipated energy that directlyheats the electrons δ , the transition radius between the in- c (cid:13)000 , 1–23 Nemmen et al. ner ADAF and the outer truncated thin disk R tr and theADAF mass-loss parameter s . The other four parameterscharacterize the jet emission: the mass-loss rate in the jet˙ M jet , the electron energy spectral index p , and the electronand magnetic energy parameters (cid:15) e and (cid:15) B .Our fitting procedure can be summarized as follows.We begin with a model characterized by the initial values˙ m o = 0 . r tr = 10 , δ = 0 . s = 0 .
3, ˙ m jet = 10 − , p = 2 . (cid:15) e = 0 . (cid:15) B = 0 .
01. We adopt an iterative pro-cedure, in which we vary one parameter each time and keepthe others fixed, computing the total emitted spectrum re-sulting from the sum of the radiation from the jet, truncateddisk and ADAF for each iteration. We repeat this processuntil we obtain an acceptable fit of the total SED to theradio, optical, UV and X-ray observations. We judge thegoodness of fit of the models by eye instead of using an au-tomatic model fitting technique (e.g. maximum likelihood,Bayesian analysis etc). The main difficulty with implement-ing a more rigorous spectral model fitting is that computingthe dynamics and radiative transfer for the ADAF is com-putationally demanding and hence the evaluation time andparameter space sampling of the models is very time con-suming (see also Yu, Yuan & Ho 2011). Therefore, our goalis to find models which are approximately consistent withthe spectral data as opposed to exhaustively exploring thefull parameter space of the models.We stress that the model components are not indepen-dent from each other. For instance, since the ADAF is con-nected to the thin disk at R o , the accretion rate at the ADAFouter radius is the same as the one in the truncated disk aswe note in § M o and ˙ M jet are expected tobe correlated and we require in our fits that ˙ M jet / ˙ M o < M jet and ˙ M o independentlyin our fits.Regarding the contribution of the jet to the emission,this component produces X-rays through optically thin syn-chrotron emission with its hardness being controlled by thethe parameter p ; for instance, the X-ray photon index isgiven by Γ X = 1 + p/ (cid:54) p (cid:54) X <
2. For such sources, we favor the ADAF as theX-ray production site. On the other hand, for LLAGNs withΓ X (cid:62)
2, we also consider fits to the X-ray spectrum in whichthe jet dominates the emission.We have also searched the literature for independentconstraints from other works on the values of the model pa-rameters, such as the mass accretion rate, inclination angle,transition radius and jet power. We list such independentconstraints in Table 2.
In the optical and near-IR, even though the HST apertureis small ( ≈ . (cid:48)(cid:48) ), it corresponds to ≈ −
15 pc for thegalaxies in our sample. A ≈
10 pc aperture will include upto a few 10 stars, as estimated by adopting a typical bulgestellar density of ∼ stars per cubic parsec (Kormendy & Kennicutt 2004). The enclosed mass is estimated roughly as M b ∼ × (cid:18) ρ b × M (cid:12) pc − (cid:19) (cid:18) R (cid:19) M (cid:12) , (2)where ρ b ∼ × M (cid:12) pc − is the typical Milky Way bulgedensity (e.g., Genzel, Eisenhauer & Gillessen 2010). Sincetypical, evolved stellar populations in bulges emit mostly inthe near-IR and optical, it is prudent to consider the possi-ble contribution of unresolved, nuclear stellar population atthese wavebands in our sample. Thus, for the 12 LLAGNsfor which we have optical observations available, we alsoconsider the possibility that the nuclear optical data is re-produced with simple stellar population spectral models.We adopt a 10 Gyr-old stellar population with solarmetallicity and a Salpeter initial mass function as represen-tative of the typical evolved stellar populations in galacticbulges (Wyse, Gilmore & Franx 1997). We perform a least-squares fit of the compact nuclear stellar population spec-tral model (Bruzual & Charlot 2003) to the HST opticalmeasurements (and to the optical spectrum in the case ofNGC 1097) by simply varying the mass of the stellar popu-lation. The resulting stellar population spectral models aredisplayed alongside the accretion flow and jet models in Fig-ures 2-8, for illustration. We did not try to perform a de-tailed simultaneous fit of the accretion flow/jet models andthe stellar population to the observations. We simply wantto illustrate the potential of unresolved stellar populationsto account for the optical observations.Given that the luminosity of the stellar population fallsquite rapidly for λ < λ < We describe in this section the results obtained from fit-ting our coupled accretion-jet model to the SEDs. In theSED plots that follow below, the points in the optical-UVwaveband correspond to the data without any extinctioncorrection while the upper bars represent the same obser-vations after a maximal extinction correction (see EHF10);hence, these bars illustrate the uncertainty in the extinctioncorrections.The arrows represent upper limits to the nuclear lu-minosity. These upper limits are either a result of non-detections, or because the corresponding observations weretaken through a large aperture ( > (cid:48)(cid:48) ). In the latter case, theupper limits include a potentially significant contributionby the emission from dust and the stellar population of thegalaxy bulge as discussed in the previous section. In orderto illustrate this point, we consider the case of NGC 1097.The IR observations for this LINER were taken through an c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs aperture of diameter ≈ (cid:48)(cid:48) (Nemmen et al. 2006) which cor-responds to ≈
364 pc. The bulge stellar mass enclosed withinthis aperture can be roughly estimated using equation 2 as ∼ × M (cid:12) . Figure 2 shows the spectrum of an old stellarpopulation with this amount of mass, demonstrating thatthe bulge stellar emission can account for at least part ofthe IR upper limits in our sample. Therefore, even thoughthe IR upper limits are not very useful to constrain the ac-cretion and jet models, we display the corresponding datapoints in Figures 3-9 for completeness.Table 2 lists the model parameters. We list wheneveravailable the Bondi accretion rate and the correspondingreference from which ˙ m Bondi was taken. P obsjet correspondsto the jet power estimated either from observations or us-ing the correlation between jet power and radio luminosityof Merloni & Heinz (2007). P modjet represents the jet powerresulting from our jet model, calculated as P jet = ˙ M jet Γ j c .Table 3 shows the stellar mass potentially enclosed within0 . (cid:48)(cid:48) as obtained from the stellar populations fits to the HSToptical observations.For completeness, we present model fits to the 9 SEDsfrom EHF10 which did not pass our data quality cut in theAppendix. However, due to the lower quality of their SEDs,we refrain from drawing conclusions based on those sources.We demonstrate in this section that there are two pos-sible types of models which can accommodate the observedSED of M81 (and the SEDs of other LINERs in our sam-ple as we will show below): In the first type, the emissionfrom the ADAF dominates the observed X-rays; in the sec-ond type of model, the jet emission dominates the X-rays.We will hereafter use the abbreviations AD (as in ADAF-dominated ) and JD (as in jet-dominated ) when referring tothe former and latter types of models, respectively.
The SED of this object was previously studied in detail byNemmen et al. (2006) and the model displayed in Figure 2corresponds to the model obtained by Nemmen et al. (2006).The transition radius is independently constrained from themodeling of the broad double-peaked H α emission line ( r tr ∼ Chandra observations. The jetemission is not able to reproduce the X-ray spectrum since itwould require p < § ≈ ≈ . (cid:48)(cid:48) . × M (cid:12) (cf. § ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC1097
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 2.
The observed SED and ADAF-dominated model forNGC 1097. The dashed blue, dotted red and dot-dashed greenlines correspond to the emission from the ADAF, truncated thindisk and jet, respectively. The solid black line represents the sumof the emission from all components. The inset shows the zoomed2-10 keV spectrum. The upper solid magenta line shows the spec-trum of an old stellar population with ∼ × M (cid:12) which ac-counts for the near-IR upper limits observed at lower spatial res-olution. The lower solid gray line displays the spectrum of an oldstellar population fitted to the optical observations. a mass ∼ × M (cid:12) . As discussed in the previous section,this is presumably the case for the other galaxies in our sam-ple which also have lower spatial resolution IR observations,although the stellar mass will vary from source to source. This source is among the brightest LLAGNs known since itis the nearest AGN besides Centaurus A and has been thesubject of a broadband multiwavelength monitoring cam-paign (Markoff et al. 2008; Miller et al. 2010).Devereux & Shearer (2007) modeled the profile of thebroad double-peaked H α line with a relativistic thin diskmodel. They were able to explain the profile with an inclina-tion angle of 50 ◦ . Such a high inclination angle is supportedby radio observations of the jet (Bietenholz, Bartel & Ru-pen 2000). The H α line profile of M81 is consistent with aninner radius of ≈ − R S for the line-emitting thin disk(Devereux & Shearer 2007). In our models for the SED, wetherefore adopt i = 50 ◦ and r tr = 360. The resulting IR-luminous thin disk spectrum is not strongly constrained bythe available IR upper limits and optical-UV observations.On the other hand, the optical data points at 6000 ˚A and4700 ˚A are consistent with a stellar population with mass6 . × M (cid:12) .Figure 3 shows two models for the SED of M81 con-sistent with the above constraints: in the left-hand side, anADAF with δ = 0 .
01 dominates the X-ray emission whereasin the model to the right a jet with p = 2 is the dominantX-ray emitter. c (cid:13)000
01 dominates the X-ray emission whereasin the model to the right a jet with p = 2 is the dominantX-ray emitter. c (cid:13)000 , 1–23 Nemmen et al. ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3031
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3031
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3998
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3998
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 3.
SEDs and coupled accretion-jet models for NGC 3031 and NGC 3998. The left panel shows the AD models for each objectwhile the right panel displays the JD models. The dashed, dotted and dot-dashed lines correspond to the emission from the ADAF,truncated thin disk and jet, respectively. The solid line when present represents the sum of the emission from all components. The insetshows the zoomed 2-10 keV spectrum. The old stellar population fitted to the optical data is displayed as the gray solid line.
The shortest wavelength (1750 ˚A) UV data point in theSED of NGC 3998 presented in EHF10 is anomalously highbecause of variability (Devereux 2011). As discussed by De-vereux this data point was obtained many years before allthe other observations, when the source was much brighter.For this reason, we exclude this UV measurement from ouranalysis and plots.In our models we adopted a large outer radius for theADAF, but smaller radii are not ruled out by the data. Forinstance, we are also able to obtain a reasonable fit to theSED with r tr = 500 and ˙ m o = 10 − . This model is consis-tent with the IR upper limits and accounts for the X-raydata. The transition radius cannot be much smaller than this value, otherwise the emission of the truncated thin diskwould exceed the IR upper limits. Furthermore, as notedby Ptak et al. (2004), the lack of Fe K α line emission alsosuggests that the value of r tr is not so small.A JD model accounts quite well for the X-rays but some-what underestimates the optical-UV data. The optical data point can be reproduced by emission fromthe truncated thin disk emission with the somewhat smalltransition radius of r tr = 70. Alternatively, the optical ob-servation can be fitted with an old stellar population withmass 5 × M (cid:12) . Since the jet model requires p < c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4143
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4261
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4278
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 4.
Same as in Figure 3 for NGC 4143, NGC 4261 andNGC 4278, displaying only AD models. duce the X-ray spectrum, a jet origin for the X-ray emissionin disfavored.
Estimates of the Bondi rate, inclination angle and jet powerare available (Gliozzi, Sambruna & Brandt 2003; Merloni& Heinz 2007) and there are two independent estimates ofthe jet power. We adopt i = 63 ◦ in our models (Gliozzi,Sambruna & Brandt 2003). The accretion rate we obtainfrom the ADAF fit is somewhat smaller than ˙ m Bondi . A jetorigin for the X-rays is disfavored since it would require p <
2. This AGN is likely to be strongly affected by extinctionin the optical-UV (OUV) band (EHF10). Hence, the OUVmeasurements probably do not capture the emission of thecentral engine. For this reason, it is not surprising that themodels overpredict the OUV emission by almost one orderof magnitude in Fig. 4.
Di Matteo, Carilli & Fabian (2001) also estimated that theBondi rate is ˙ m Bondi ∼ . − .
01. Giroletti, Taylor &Giovannini (2005) found a two-sided radio structure for thejet using VLA data, and estimated that the jet is orientedclose to the line of sight (2 ◦ (cid:46) i (cid:46) ◦ ) and mildly relativistic(Γ j ∼ . i = 3 ◦ andΓ j = 1 . r tr ∼ −
40. If weallow s to vary, we can also reproduce the SED with a largertransition radius, r tr = 100, ˙ m o = 4 × − , δ = 0 . s = 0 .
77. Alternatively, the optical observation can be fittedwith a 10 M (cid:12) stellar population. A JD model is disfavoredfor this source. A prominent jet resolved with the VLA is observed to cre-ate cavities in the X-ray emitting gas (Allen et al. 2006;Finoguenov et al. 2008).We find adequate AD and JD models for the data. Aswas the case for NGC 4594, the mid to near-IR data areinsufficient to make the case of a truncated thin disk com-pelling and similar models with much larger values of r tr are not ruled out by the available IR data. The jet power inboth models is in good agreement with the power estimatedby Merloni & Heinz (2007) based on the calorimetry of theX-ray cavities observed with Chandra . A 5 × M (cid:12) stellarpopulation nicely reproduces the optical excess above themodels. Di Matteo et al. (2003) previously estimated the Bondiaccretion rate using
Chandra
X-ray data ( ˙ M Bondi ∼ . M (cid:12) yr − ; ˙ m Bondi ≈ × − ). Biretta, Sparks & Mac-chetto (1999) analyzed HST observations of the jet in M87and estimated that Γ j (cid:62) ◦ < i < ◦ . Basedon the results of Biretta, Sparks & Macchetto (1999), we c (cid:13)000
X-ray data ( ˙ M Bondi ∼ . M (cid:12) yr − ; ˙ m Bondi ≈ × − ). Biretta, Sparks & Mac-chetto (1999) analyzed HST observations of the jet in M87and estimated that Γ j (cid:62) ◦ < i < ◦ . Basedon the results of Biretta, Sparks & Macchetto (1999), we c (cid:13)000 , 1–23 Nemmen et al. ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4374
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4374
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4486
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4486
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 5.
Same as Figure 3 for NGC 4374 and NGC 4486. adopt in our jet modelling the parameters Γ j = 6 and i = 10 ◦ . The jet kinetic power is estimated to be in therange 10 − erg s − (e.g., Bicknell & Begelman 1999;Owen, Eilek & Kassim 2000; Allen et al. 2006; Merloni &Heinz 2007).We find adequate AD and JD models for the data, al-though the JD model underpredicts the OUV data by afactor of a few. The SED of M87 was previously fitted usingADAF and/or jet models (Di Matteo et al. 2003; Yuan, Yu& Ho 2009; Li et al. 2009). Di Matteo et al. (2003) modelledthe SED of M87 with an ADAF model using different val-ues of δ but not including mass-loss (i.e., s = 0). The modeladopted by Li et al. (2009) is quite similar to that of DiMatteo et al. (2003) although the former incorporate generalrelativistic corrections. Di Matteo et al. (2003) and Li et al.(2009) obtained that the ADAF emission with no mass-lossapproximately reproduces the SED and results in accretion rates consistent with the Bondi rate. Our AD model is simi-lar to that of Di Matteo et al. (2003) but it also incorporatesmass-loss as suggested by numerical simulations.Yuan, Yu & Ho (2009) tried to model the SED using anADAF model with δ = 0 . δ ( δ > . m o (cid:28) .
01) the ADAF X-rayspectrum is harder than the data. Yuan, Yu & Ho (2009)instead successfully fit the data with a JD model using p =2 . The Bondi accretion rate was estimated by Merloni & Heinz(2007) (see also Allen et al. 2006) from the X-ray profilesof density and temperature. The kinetic power carried bythe jet was estimated by Merloni & Heinz (2007) (see also c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4552
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 6.
The SED and jet-dominated model for NGC 4552. Theinset shows the zoomed 2-10 keV spectrum.
Allen et al. 2006) from the energy deposited in the X-raycavities. Since the X-ray spectrum is quite soft, AD modelsare unable to account for the X-ray emission. The JD modelin Fig. 6 is roughly consistent with the radio observationsand explains quite well the X-ray data, but overpredicts theoptical data. The resulting jet power is roughly consistentwith the value estimated by Allen et al. (2006); Merloni &Heinz (2007). A likely explanation for the unusually faintUV emission compared to the X-rays is source variability(Maoz et al. 2005) and hence we did not attempt to fit the2500 ˚A and 3300 ˚A measurements with a stellar populationas in the other LLAGNs.
NGC 4579 shares many characteristics with NGC 3031(M81) and NGC 1097: its nucleus features broad double-peaked Balmer emission lines (Barth et al. 2001) and a lackof the iron K α line emission (Eracleous et al. 2002). Fromthe width of the broad H α line, Barth et al. (2001) obtaineda rough estimate of the inner radius of the line-emitting por-tion of the accretion disk r tr ∼ r tr = 150 and i = 45 ◦ . The resulting thin diskspectrum peaks in the IR and its high-frequency tail extendsinto the optical-UV; however, the available IR upper limitsand HST optical-UV data do not allow us to set strong con-straints on the thin disk emission. A jet origin for the X-raysis disfavored by the hardness of the spectrum. The left panel of Figure 8 shows an AD model which is con-sistent with the available optical-UV and X-ray data. In thismodel, the jet dominates the radio emission and contributesonly weakly to the X-ray flux. The inferred accretion rate isconsistent with the Bondi accretion rate estimated by Pel-legrini (2005). The available data are not sufficient to con-strain the presence of a truncated thin disk in this source, ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4579
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 7.
Same as Fig. 2 for NGC 4579 (AD model). ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4736
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 9.
Same as Fig. 2 for NGC 4736 (AD model). hence we adopt r tr = 10 . The right panel of Fig. 8 showsa jet model for the SED of NGC 4594 which is consistentwith the data for p = 2. As was the case of NGC 1097, NGC 4143 and NGC 4278,this LINER requires a relatively small transition radius inorder to explain its UV data. The 3300 ˚A observation canalso be reproduced by a ≈ . × M (cid:12) stellar population.The X-ray spectrum is too hard to be explained by a jetmodel (Figure 9). c (cid:13)000
Same as Fig. 2 for NGC 4736 (AD model). hence we adopt r tr = 10 . The right panel of Fig. 8 showsa jet model for the SED of NGC 4594 which is consistentwith the data for p = 2. As was the case of NGC 1097, NGC 4143 and NGC 4278,this LINER requires a relatively small transition radius inorder to explain its UV data. The 3300 ˚A observation canalso be reproduced by a ≈ . × M (cid:12) stellar population.The X-ray spectrum is too hard to be explained by a jetmodel (Figure 9). c (cid:13)000 , 1–23 Nemmen et al. ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4594
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4594
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 8.
Same as Figure 3 for NGC 4594.
Table 2.
Model parameters resulting from the SED fits discussed in Section 4. The meaning of the parameters is described in Section 3.
Galaxy Model ˙ m o r tr δ s ˙ m jet p (cid:15)e (cid:15)B i ( ◦ ) P modjet P obsjet ˙ m Bondi Refs.and notesNGC 1097 AD 6 . × − × − × − . × − − . × . × × − × − × . × − × − . × . × × − . × − − × . × − . × − . × . × − × − × × − . × − × . × − . × . × × − . × − × − × × − . × − × − . × − × − . × . × − . × . × . × − . × × − . × − × × − × × − . × Notes: (a) Black hole mass estimated from the fundamental plane of black holes (Merloni, Heinz & di Matteo 2003), using the X-ray and radioluminosities.(b) Observed jet power estimated using the radio data and the Merloni & Heinz (2007) correlation.(c) For NGC 1097, Γ = 10 (for consistency with the work of Nemmen et al. 2006).(d) 5 GHz luminosity estimated using the Merloni, Heinz & di Matteo (2003) correlation.(e) The lower limit on P obsjet was derived by Gliozzi, Sambruna & Brandt (2003) and the upper limit results from using the radio dataand the Merloni & Heinz (2007) correlation. The Bondi rate and inclination angle is from Gliozzi, Sambruna & Brandt (2003). References:
1. Pellegrini (2005), 2. David et al. (2005), 3. Gliozzi, Sambruna & Brandt (2003), 4. Di Matteo, Carilli & Fabian (2001),5. Giroletti, Taylor & Giovannini (2005), 6. Allen et al. (2006), 7. Merloni & Heinz (2007), 8. Biretta, Sparks & Macchetto (1999), 9. DiMatteo et al. (2003), 10. Barth et al. (2001) c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs Our detailed SED modeling allows us to place constraints – within the framework of ADAF and jet models – on themass accretion rate onto the black hole and kinetic powerfor the LLAGNs in our sample. In this section, we evaluatepossible correlations among the parameters describing theaccretion flow and jet resulting from our SED models. Inparticular, when discussing correlations between the massaccretion rate and other parameters, we restrict ourselvesonly to AD models. The reason is that in most JD fits theestimate of ˙ m that we obtain from the fits should be re-garded as a rough lower limit to the accretion rate. In fact,for most of the JD models, the contribution of an underlyingADAF to the emission is not necessarily required (cf. the JDmodels for NGC 4594, M87 and NGC 4579).We show in the panel a of Figure 10 the relation be-tween the accretion rate at the outer radius of the ADAFand the global radiative efficiency of the systems, definedas η rad ≡ L bol / ( ˙ M o c ) where we obtain L bol by integratingthe synthetic spectra obtained in the SED fits including allcomponents (thin disk, ADAF and jet). The values of η rad for our sample are in the range ∼ (10 − − m ≈ − − .
01. There is noapparent correlation between the global efficiency and ˙ m o ,keeping in mind the significant uncertainties in ˙ m o and L bol .The error bars are estimated as described in the Appendix.Panel b of Figure 10 shows the relation between theaccretion rate and the jet power in Eddington units, whilepanel c displays the relation between the accretion rate andjet kinetic efficiency P jet / ( ˙ M BH c ) defined in terms of theaccretion rate at 3 R S , ˙ M BH ≡ ˙ M (3 R S ). Panel b shows thatthere is a hint of a correlation which is significant at the ≈ σ level. However, panel c shows no clear evidence forcorrelation between the accretion rate and the kinetic effi-ciency.Low power radio galaxies exhibit a correlation betweenthe jet power – derived from X-rays cavities which were pre-sumably created by the AGN outflows – and the Bondi ac-cretion rates ˙ M Bondi – inferred from the density and tem-perature profiles that are obtained from the X-ray observa-tions (Allen et al. 2006; Balmaverde, Baldi & Capetti 2008;but see Russell et al. 2013). The Bondi rates are usuallyparametrized in the literature as a “Bondi power” assuminga 10% efficiency ( P Bondi ≡ . M Bondi c ). Therefore, in orderto compare our results with these independent estimates ofjet powers and ˙ M Bondi , we use the accretion rates that wederived to define the “Bondi power” P Bondi ≡ . M o c /α, (3)taking into account that ˙ M o = α ˙ M Bondi in the ADAF model(Narayan & McClintock 2008). Figure 11 displays the rela-tion between P Bondi defined using the equation above andthe jet powers we derived from our SED models. The un-certainties in P Bondi and P jet are both ∼ . P Bondi and P jet derived by Balmaverde, Baldi& Capetti (2008). Within the uncertainties, we can see thatour SED fitting results are consistent with the Balmaverdeet al. correlation.We then proceed to estimate the radio loudness param- log ˙ m o l og L b o l / ( ˙ M c ) log ˙ m o l og P j e t / L E dd log ˙ m o l og P j e t / ( ˙ M B H c ) Figure 10.
The relation between the mass accretion rate ˙ m o atthe outer radius of the ADAF (in Eddington units) and the globalradiative efficiency [ L bol / ( ˙ M o c )] (panel a, top), jet power nor-malized in Eddington units (panel b, center) and the jet kineticefficiency defined in terms of the accretion rate at 3 R S (panel c,bottom). The error bars are estimated as described in the Ap-pendix. eter from the SED fits. The radio loudness can be quantifiedas the optical to radio ratio R o ≡ L ν (6 cm) /L ν (B) (Keller-mann et al. 1989) where radio-quiet objects correspond to R o = 10. Figure 12 shows the relation between R o and themass accretion rate. There is a hint of an anti-correlation be-tween these variables, significant at the 1 . σ level (keepingin mind the non-negligible uncertainties). This is in generalagreement with previous evidence for an anti-correlation be- c (cid:13)000
The relation between the mass accretion rate ˙ m o atthe outer radius of the ADAF (in Eddington units) and the globalradiative efficiency [ L bol / ( ˙ M o c )] (panel a, top), jet power nor-malized in Eddington units (panel b, center) and the jet kineticefficiency defined in terms of the accretion rate at 3 R S (panel c,bottom). The error bars are estimated as described in the Ap-pendix. eter from the SED fits. The radio loudness can be quantifiedas the optical to radio ratio R o ≡ L ν (6 cm) /L ν (B) (Keller-mann et al. 1989) where radio-quiet objects correspond to R o = 10. Figure 12 shows the relation between R o and themass accretion rate. There is a hint of an anti-correlation be-tween these variables, significant at the 1 . σ level (keepingin mind the non-negligible uncertainties). This is in generalagreement with previous evidence for an anti-correlation be- c (cid:13)000 , 1–23 Nemmen et al.
42 43 44 45 46 47 log P Bondi l og P j e t Figure 11.
The relation between the Bondi power P Bondi asdefined in equation 3 and the jet power, using the parametersinferred from the SED models in our sample. The dashed linecorresponds to the P Bondi − P jet relation obtained by Balmaverde,Baldi & Capetti (2008). log ˙ m o l o g ( r a d i o l o u d n e ss ) Figure 12.
Relation between the mass accretion rate ˙ m o and theradio loudness R o . The anti-correlation is only significant at the1 . σ level. tween radio-loudness and the Eddington ratio in radio-loudAGNs (Ho 2002; Sikora, Stawarz & Lasota 2007; Broderick& Fender 2011).We consider the relation between the X-ray luminosityand the bolometric luminosity. Figure 13 displays the cor-relation between L X and L bol as well as the correspondinguncertainties. These variables display a correlation signifi-cant at the 3 . σ level. We perform a linear regression usingthe least-squares BCES( Y | X ) method with bootstrapping(Akritas & Bershady 1996). The best-fit model correspondsto the solid line (log L bol = A log L X + B ; shaded regioncorresponds to the 1 σ confidence band). The best-fit param-eters are A = 0 . ± .
12 and B = 16 . ± .
9. The scatterabout the best-fit is 0.3 dex. Hence, this result suggests that log L X l og L b o l Figure 13.
The relation between 2 −
10 keV X-ray luminosity andthe bolometric luminosity. The solid line shows the best-fit power-law model as described in the text (shaded region, 1 σ confidenceband). The dashed line corresponds to L bol = 52 L X as in EHF10. the best-fit 2 −
10 keV X-ray bolometric correction is givenby κ X ≈ (cid:18) L X erg s − (cid:19) − . . (4)EHF10 performed a linear interpolation (in log space)of the SED data points of a control sample of 7 LLAGNsand estimated the median X-ray bolometric correction as52. Within the uncertainties, this bolometric correction isconsistent with our results, as can be seen in Fig. 13 (dashedline corresponds to L bol = 52 L X ). We discuss how our valuesof κ X compare to those typical of quasars in Section 7.3.Finally, we computed the α ox parameter for our sampleof AD model SEDs. α ox is a simple parametrization of theUV to X-ray ratio defined in terms of the spectral index ofa power law between L ν at 2500 ˚A and at 2 keV definedas α ox ≡ .
384 log[ L ν (2 keV) /L ν (2500 ˚A)]. We find a me-dian value for α ox of -1.1 with a standard deviation of 0.1.An extrapolation of the α ox − L ν (2500 ˚A) relation obtainedfrom Seyferts and quasars (Steffen et al. 2006; Young, Elvis& Risaliti 2009) to the low luminosities typical of our samplepredict α ox values in the range − . (cid:46) α ox (cid:46) − .
6. There-fore, the typical α ox values in our sample of LLAGNs seem tobe lower than what would be expected based on a direct ex-trapolation of trends obtained from brighter AGNs. We cau-tion the reader, however, that our α ox estimates should beregarded with caution. For instance, given the uncertaintyin the degree of extinction affecting the UV luminosities inour sample, we estimate that uncertainties as high as ∼ . L (2500 ˚A) – and correspondingly in α ox – are likely(cf. appendix A). c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs It is of interest to compute the average SEDs resulting sepa-rately from the AD and JD scenarios. These SEDs are usefulfor different purposes. Since the observed SEDs are the mainobservables that we use to derive the central engine parame-ters via our fitting, as a consistency check the average modelSEDs should reproduce the average SED obtained directlyfrom the observed ones.Secondly, SEDs obtained from averaging observed datapoints are obviously limited by the observed bands. Outsidethe observed bands different authors adopt ad-hoc interpo-lations between the data, usually a linear interpolation inlog-log space (Ho 1999; EHF10), which might not reflectthe actual physical processes involved in the emission. Theaverage from the AD and JD scenarios that we obtained canhence serve as guidelines – with a physical justification – tothe typical shape of the SEDs in the bands which have notbeen constrained yet.Motivated by the reasons above, we show in Fig. 14athe average SEDs computed separately for the AD and JDscenarios. We first normalized the individual SEDs to thesame X-ray luminosity of 10 erg s − in the band 2-10 keV.This value is approximately the average X-ray luminosityfor the LINERs in our sample. After normalizing the SEDs,for each frequency bin we computed the mean of the modelSEDs as (cid:104) log νL ν (cid:105) . Following EHF10 we choose to computethe average of the logarithm of the luminosities instead ofusing the values of νL ν themselves in order to reduce theeffect of outliers in the resulting average.The average JD SED is relatively featureless and has asmall bump in the IR between a few × µ m – a few × µ mwhich is due to the truncated thin disk. The average ADSED on the other hand is more complex given the richervariety of radiative processes which take place. Overall, thespectral shapes of the average JD and AD SEDs are similar.The bumps in the average SEDs are much less pronouncedthan the bumps in the individual SEDs. This occurs becausethe bumps in the individual SEDs do not peak at the sameplace and when the SEDs are averaged these bumps aresmoothed out. For this reason, the average model SEDs willnot resemble any one of the individual SEDs.Figure 14a also displays the average data points com-puted from the observed SEDs in a similar way by EHF10where the error bars represent the uncertainty in the emis-sion due to the uncertainty affecting the amount of extinc-tion correction involved. The shaded region around the av-erage best-fit X-ray power-law represents the standard de-viation in the value of the LINER photon index. In orderto illustrate the wide diversity of the individual SEDs, weshow in Figure 14b the 1 σ scatter affecting the model SEDs(where we show only the AD average SED for simplicity)and the observed ones.As expected, the average model SEDs agree well withthe observed constraints. There are some details that areworth mentioning. The shape of the X-ray spectrum of theaverage JD SED is slightly softer than the correspondingshape of the average AD SED. Both are within the 1 σ un-certainty in the photon index of the average observed SED.In the OUV, even though the model SEDs agree with the ob-served constraints they are quite different from each other.For instance, the red bump is stronger in the average AD ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) AD meanJD meanRadio-quiet QSOsRadio-loud QSOs
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 15.
The average JD and AD model SEDs compared tothe average radio-loud and radio-quiet quasar SEDs computed byShang et al. (2011). All SEDs are normalized to the same 2-10keV luminosity.
SED. The average JD SED predicts a lower UV flux. In theradio band, the model SEDs are quite similar to each other.Figure 15 shows the average AD and JD SEDs com-pared to the average ones of radio-loud and radio-quietquasars computed by Shang et al. (2011). The averagequasar SEDs computed by Shang et al. (2011) are very sim-ilar to the ones of Elvis et al. (1994) but the former includemore detailed features and are based on more recent dataobtained with improved instrumentation. As in Fig. 14a,the SEDs were normalized such that they all have the sameX-ray luminosity in the 2-10 keV band of 10 erg s − . TheUV excess in the quasar SEDs (the big blue bump) is clearlyapparent in comparison to the LLAGN ones. It is also in-teresting that for ν > Hz the average AD, average JDand the radio-loud quasar SEDs are quite similar.It is worth investigating how the luminosity is par-titioned in different wavebands for the SEDs plotted inFig. 15. For this purpose, we computed the luminosity con-tained in the radio (10 − . Hz), IR (10 . − . ),optical-UV (10 . − . ), X-rays (2 −
10 keV) and “other”(10 . Hz − E >
10 keV) wavebands by integrat-ing the SEDs, with the values in parenthesis denoting therange of frequencies or energies that we adopted for eachwaveband. The pie charts in Fig. 16 display the L band /L bol for each waveband defined above, for the average SEDs ofLLAGNs and quasars. In the case of quasars, as is wellknown, the emission is dominated by the UV bump withthe IR emission corresponding to the reprocessed emissionof the accretion disk by the dust torus. In the case of the av-erage AD and JD SEDs for the LLAGNs in our sample, theIR, optical-UV and “other” bands release comparable frac-tions of the bolometric luminosity contrary to the case ofquasars. In particular, the IR dominates the energy budgetof the SED in the AD case. It is also notable that a higher c (cid:13)000
10 keV) wavebands by integrat-ing the SEDs, with the values in parenthesis denoting therange of frequencies or energies that we adopted for eachwaveband. The pie charts in Fig. 16 display the L band /L bol for each waveband defined above, for the average SEDs ofLLAGNs and quasars. In the case of quasars, as is wellknown, the emission is dominated by the UV bump withthe IR emission corresponding to the reprocessed emissionof the accretion disk by the dust torus. In the case of the av-erage AD and JD SEDs for the LLAGNs in our sample, theIR, optical-UV and “other” bands release comparable frac-tions of the bolometric luminosity contrary to the case ofquasars. In particular, the IR dominates the energy budgetof the SED in the AD case. It is also notable that a higher c (cid:13)000 , 1–23 Nemmen et al. ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) AD meanJD mean
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − )
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure 14. a, left:
The average SEDs (geometric mean) computed separately for the AD and JD models (dashed and dotted linesrespectively). The data points correspond to the geometric mean computed by EHF10. The “error bars” on the optical-UV data pointsrepresent the range of extinction corrections. b, right: σ scatter around the average (model and observed) SEDs illustrating the diversityof individual SEDs. The solid line shows the average AD SED and the shaded region corresponds to the standard deviation from theAD models. The points correspond to the mean computed by EHF10 and the error bars show the scatter in the measurements. In theOUV, the filled circles correspond to measurements without any reddening correction whereas the open circles correspond to the maximalextinction correction. fraction of the energy is released in the radio and X-rayscompared to the quasar SEDs.We remind the reader that the shape of the SEDs ofindividual objects may display a significant variance withrespect to the average SEDs (e.g., Shang et al. 2011; Run-noe, Brotherton & Shang 2012; see also the discussion insection 7.3). As such, although the energy budget displayedin Fig. 16 is an average representation of the whole sam-ple of LLAGNs studied in our work and the Shang et al.quasar SEDs, it should be regarded with care when appliedto individual sources. We discuss the caveats that affect our analysis in Section 7.1.In Section 7.2 we discuss the nature of X-rays in LLAGNsand in Section 7.5 we suggest directions for making progressin this issue.
From an observational point of view, even though we arecarrying one of the largest systematic analysis of the SEDsof LLAGNs to date (see also Wu, Yuan & Cao 2007; Yu,Yuan & Ho 2011), for most of the sources that we consideredwe only have a few data points available to fit. The lackof observational constraints, of course, impacts our abilityto rule out the different scenarios for the central engine ofLLAGNs – AD vs JD models – and to probe the transitionbetween the ADAF and the thin disk. Therefore, it is clearthat a strong case exists for obtaining more measurementsand better detections of the sample over a broader range of
Radio IR Optical-UV
X-rays Other
LLAGNs (AD)
Radio IR Optical-UV
X-rays Other
LLAGNs (JD)
Radio2%IR32% Optical-UV54%X-rays4%Other7%
Radio-loud quasars
Radio1%IR28% Optical-UV61%X-rays1%Other8%
Radio-quiet quasars
Figure 16. L band /L bol ratios for different wavebands, computedfor the average AD and JD model SEDs, compared to the corre-sponding ratios for the average radio-loud and radio-quiet quasarSEDs of Shang et al. (2011). These average SEDs are displayedtogether in Figure 15. wavelengths in order to better constrain the models for thecentral engine. We discuss specific observational strategiesin the Section 7.2. Furthermore, the size of our sample islimited. We need to extend our modeling to a larger numberof LLAGNs in order to draw further conclusions.From a theoretical perspective, there are considerable c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs theoretical uncertainties involved in the the ADAF-jet mod-els. For instance, we cannot expect to constrain the ADAFparameters s and δ from the SED fitting since there is adegeneracy between these parameters (Quataert & Narayan1999). Previous modeling efforts overcome the particular dif-ficulty of the s/δ degeneracy by fixing the values of theseparameters (e.g., Wu, Yuan & Cao 2007; Yuan, Yu & Ho2009) to the ones consistent with constraints from Sgr A*Yuan, Quataert & Narayan (2003). Despite recent progress(e.g., Sharma et al. 2007), the value of δ is essentially un-constrained. For this reason, the values of the parametersinferred in our fits do not correspond necessarily to uniquechoices but rather should be considered as illustrative of rea-sonable fits. Furthermore, our jet model is basically a phe-nomenological one: we have more freedom in the jet fittingcompared to the ADAF model. The nature of the X-ray emission in LLAGNs has been de-bated in the last few years by several authors favoring insome cases the AD or JD models based on the analysisof individual sources (e.g., Falcke & Markoff 2000; Yuan,Markoff & Falcke 2002; Yuan et al. 2002; Yuan, Quataert &Narayan 2003; Wu, Yuan & Cao 2007; Markoff et al. 2008;Miller et al. 2010) or in a statistical sense based on the fun-damental plane of black hole activity (Merloni, Heinz & diMatteo 2003; Falcke, K¨ording & Markoff 2004; Yuan & Cui2005; Yuan, Yu & Ho 2009; Plotkin et al. 2012; Younes et al.2012).In our AD models, the X-rays are produced predomi-nantly by inverse Compton scattering by the ADAF of seedsynchrotron photons produced in the accretion flow itself; incontrast, in our JD models, the X-rays are dominated by theoptically thin synchrotron emission at the base of the jet. Inthis regard, the X-ray spectrum is an important observablethat can be used in order to disentangle the dominant com-ponent responsible for the LLAGNs. Internal shocks in thejet will favor electron energy distributions with power-lawindices in the range p ≈ − p results in Γ X ≈ − . X (cid:54) X <
2. In our sample, 6 LINERs havehard X-ray spectra which cannot be easily explained as jetemission whereas for only one source, NGC 4552, we werenot able to find an AD model able to account for the softX-ray SED with Γ X = 2 (cf. Table 2).Based on the observations above, we suggest that thespectral shape of the X-ray spectrum could be used to dif-ferentiate between an AD versus a JD origin for the X-rays.Namely, soft X-ray LLAGNs (Γ X ∼ − .
5) would be likelyjet-dominated whereas hard X-ray emitters (Γ X <
2) wouldbe ADAF-dominated.Note that it is still possible that relativistic shocks in δ Γ X Jet with p =2 − ˙ m out =10 − ˙ m out =10 − Figure 17.
The X-ray photon index Γ X predicted by ADAFsas a function of δ for different accretion rates. We computed Γ X from a grid of ADAF models computed for R o = 500, s = 0 . m = 10 . The shaded region corresponds to the range ofphoton indexes for jets with spectral index of the electron energydistribution in the range p = 2 − jets could give rise to electron energy distributions with p slightly smaller than 2 in a small fraction of sources (Starlinget al. 2008; Curran et al. 2010) and, as noted by Yuan, Yu &Ho (2009), reconnection effects could also change the elec-tron energy distribution produced by shocks. In addition,ADAFs with relatively high accretion rates ( ˙ m o ≈ .
01) canproduce X-ray spectra with Γ X ≈ . p = 2 .
2. At these accre-tion rates we expect that the thin disk would be truncatedat radii r tr ∼
100 (Yuan & Narayan 2004; Narayan & Mc-Clintock 2008) and hence the SED would be accompaniedby relatively strong thermal emission in the near-IR. In thenext section, we outline additional observations which willbe crucial to disentangle the high-energy contribution of thejet and ADAF.
It is instructive to compare the X-ray bolometric correctionswe estimate in this work with those typical of quasars. Onecommon way is to integrate the SED using the IR emis-sion as a proxy of the intrinsic nuclear luminosity, assum-ing that a dust torus reprocesses the intrinsic optical-UVemission into IR radiation (e.g. Pozzi et al. 2007; Vasude-van et al. 2010; Lusso et al. 2011). Another closely relatedapproach is to integrate the SED directly using the optical-UV emission (e.g., Marconi et al. 2004; Hopkins, Richards &Hernquist 2007; Vasudevan & Fabian 2007; Runnoe, Broth-erton & Shang 2012). For example, Lusso et al. (2011) find (cid:104) κ X (cid:105) ∼
23 for type-I quasars whereas Runnoe, Brotherton& Shang (2012) estimate (cid:104) κ X (cid:105) ∼
38 for their sample. An ex-trapolation of the results of Marconi et al. (2004); Hopkins,Richards & Hernquist (2007) to the luminosities character-istic of LLAGNs predicts values as low as 10 or even lowerfor κ X (cf. also Vasudevan & Fabian 2007; Young, Elvis &Risaliti 2010; Lusso et al. 2011).As we described in section 5, we estimate L bol by in-tegrating the entire SED from radio up to 100 keV and in- c (cid:13)000
38 for their sample. An ex-trapolation of the results of Marconi et al. (2004); Hopkins,Richards & Hernquist (2007) to the luminosities character-istic of LLAGNs predicts values as low as 10 or even lowerfor κ X (cf. also Vasudevan & Fabian 2007; Young, Elvis &Risaliti 2010; Lusso et al. 2011).As we described in section 5, we estimate L bol by in-tegrating the entire SED from radio up to 100 keV and in- c (cid:13)000 , 1–23 Nemmen et al. cluding the IR emission since it is not clear at all whetherthe IR photons in LLAGNs should be treated as reprocessedemission from a dusty torus (e.g., Mason et al. 2013). Wefind κ X ≈ (cid:0) L X / erg s − (cid:1) − . for the LLAGN SEDsin our sample; in other words, our average bolometric cor-rection seems to be in rough agreement with the low valuesexpected from the extrapolations of the quasar results men-tioned above. At lower luminosities, our results suggest that κ X increases slightly ( κ X ≈
32 at L X = 10 erg s − ).We caution that extrapolations of bolometric correc-tions derived from quasar samples to lower luminosities haveto be regarded with caution since, as we previously argued,it is likely that the accretion physics in LLAGNs may be sig-nificantly different compared to quasars. We also remind thereader that our κ X estimates are subject to non-negligibleuncertainties ( ∼ . L bol determinations. In addition,the mean X-ray bolometric corrections can be inaccuratefor individual objects due to variation in the X-ray emissionand the SED shapes (or equivalently, the different degreesof contributions of the ADAF, thin disk and jet emission)from object to object, i.e. there is a large intrinsic scatter inthe values of κ X (cf. the scatter in the SEDs in Figure 14b).Such a large scatter was also noted in the case of quasarSEDs (e.g., Marchese et al. 2012; Runnoe, Brotherton &Shang 2012).We now discuss a few individual sources and their asso-ciated X-ray bolometric corrections. Two examples of SEDswith relatively low κ X correspond to the AD model for NGC3998 (Fig. 4; κ X ≈
10) and the JD model for NGC 4594 (Fig.8; κ X ≈ κ X (cid:46)
10 are roughlyflat (to first order) in the IR to the X-rays range. On theother hand, many of the modeled SEDs in our sample – inparticular, the AD models – have considerable imbalances inthe fraction of the luminosity radiated in the different wave-bands. For instance, the integrated luminosity contained inthe IR, optical-UV and > . L X (see Fig. 16). For example, the modelsfor NGC 1097 and NGC 4278 ( κ X values of 24 and 67, re-spectively) with their pronounced IR “bumps” due to thetruncated thin disk emission, and the extreme case of NGC4143 with κ X ≈ The peak of the emission for a thin disk truncated at r ∼ − m ∼ is typically located in the wave-length range 1 − µ m with a high-frequency tail extend-ing into the optical and UV (e.g., Nemmen et al. 2006; Yu,Yuan & Ho 2011; Taam et al. 2012). Indeed, six sources(NGC 1097, NGC 3031, NGC 4143, NGC 4278, NGC 4374and NGC 4736) display an optical-UV excess with respectto the ADAF and jet models. In four of these sources (NGC1097, NGC 4143, NGC 4278 and NGC 4736), on the as-sumption that the optical-UV observations are dominatedby the AGN, we were able to reproduce the data with thetruncated thin disk emission with reasonable accretion ratesand transition radii. For NGC 1097, NGC 3031 and NGC4579 in particular, the transition radius is fixed by the mod-eling of the H α double-peaked emission-line (e.g., Storchi-Bergmann et al. 2003; Nemmen et al. 2006 and references Table 3.
Masses of stellar populations required to fit the HSToptical emission for the galaxies in our sample.Galaxy log mass( M (cid:12) )NGC 1097 8.2NGC 3031 7.8NGC 3998 8.5NGC 4143 7.7NGC 4261 7.1NGC 4278 8NGC 4374 7.7NGC 4486 8.3NGC 4552 –NGC 4579 8.1NGC 4594 7.6NGC 4736 8.1 therein); for these three LLAGNs, the thin disk componentis significantly luminous (note that 4579 does not displayan optical-UV excess with respect to the ADAF emission),given the relatively small transition radii implied by the H α emission line. While the optical spectrum of NGC 1097 isexplained by the thin disk emission, the available IR up-per limits and optical-UV observations for NGC 3031 andNGC 4579 do not allow us to put useful constraints on theemission of the truncated thin disk for these sources. Forthe remaining sources in the sample, the lack of appropriateIR constraints – i.e. observations with high enough spatialresolution to accurately isolate the AGN – prevents us frombetter constraining the outer thin disk emission. We discussobservations that will be helpful in order to shed light intothis issue in section 7.5.Even though the truncated thin disk is an appealingexplanation for the optical-UV observations in many of theLINERs in our sample, we are unable to rule out the pos-sibility that the optical emission in our sources is producedby a unresolved stellar population based solely on the SEDmodeling. This possibility was already pointed out by Maozet al. (2005); Maoz (2007). From the fits of stellar populationmodels to the optical data we obtained stellar masses in therange ∼ a few 10 − M (cid:12) (Table 3). In fact, as we arguedin section 3.5, such an amount of mass due to unresolvedstellar populations in the bulge within the HST aperture isquite feasible.In addition, some of the galaxies in our sample could po-tentially host a compact nuclear star cluster, similarly to theMilky Way (Sch¨odel, Merritt & Eckart 2009; Genzel, Eisen-hauer & Gillessen 2010). The compact nuclear star cluster inour Galaxy has a density ρ NC ∼ M (cid:12) pc − (Sch¨odel, Mer-ritt & Eckart 2009; Genzel, Eisenhauer & Gillessen 2010).If the galaxies in our sample host nuclear star clusters withsimilar densities as the Milky Way, then the implied starcluster mass enclosed within a radius R is M NC ∼ × (cid:18) ρ NC M (cid:12) pc − (cid:19) (cid:18) R (cid:19) M (cid:12) . (5)This mass estimate is likely to be on the high-end for oursample; however we do note that studies of galaxies hostingboth nuclear star clusters and massive black holes suggestthat the masses of these components are quite similar (Sethet al. 2008). c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs We suggest different routes to clarify the issue of the natureof X-ray emission in LLAGNs in the future. The AD andJD models should predict different characteristic radio andX-ray variability timescales (e.g., Ptak et al. 1998), hencewe should be able to test which component is dominant inX-rays by carrying out a simultaneous monitoring of thevariability of radio and X-rays. By comparing the variabilitypattern predicted by jet/ADAF models we could pinpointthe X-ray dominant component. This promising strategy isquite similar to what the observational campaigns carriedout for M81 (Markoff et al. 2008; Miller et al. 2010) andcould be applied to many other LLAGNs.The
Fermi
Gamma-ray Space Telescope can be quitehelpful in this regard. LLAGNs are potential sources of γ -rays (Takami 2011) and in fact one of the source in thissample (NGC 4486) has already been detected by the Fermi
LAT (Abdo et al. 2009). By using the model parameters thatwe derived in our radio-to-X-rays fits we should be able topredict the γ -ray spectrum (Mahadevan, Narayan & Krolik1997; Takami 2011) and compare with future Fermi detec-tions. In this way we should be able to compare AD/JDpredictions and through γ -ray observations place furtherconstraints on the production site responsible for the high-energy emission and the jet-disk connection in LLAGNs.Observations in the mm and sub-mm are also very help-ful because they constrain the ADAF synchrotron emissionand hence also the X-ray emission. This follows becausethe synchrotron photons in the ADAF are inverse-Compton-scattered to X-rays.Another future direction for a shedding light on the roleof the jet in the SEDs of LLAGNs lies in refining and betterunderstanding of the fundamental plane of black hole activ-ity (Merloni, Heinz & di Matteo 2003; Falcke, K¨ording &Markoff 2004; G¨ultekin et al. 2009; Yuan, Yu & Ho 2009;Plotkin et al. 2012) as a tool for constraining the radia-tive processes shaping the radio and X-ray emission in sub-Eddington black hole sources.Finally, it is crucial to observe the LLAGNs of our sam-ple at high spatial resolution in the IR wavebands in orderto probe the presence of the outer thin disk component.There has been recent observational progress on this front(Asmus et al. 2011; Fern´andez-Ontiveros et al. 2012; Masonet al. 2012). Since emission from hot dust is also importantin these IR bands, the contribution of the putative dustytorus (Ramos Almeida et al. 2011) must also be taken intoaccount. Modeling these recent observations is beyond thescope of this work (cf. Mason et al. 2013, in preparation). We performed a detailed exploratory modeling of the broad-band spectral energy distributions of a sample of 12 low-luminosity AGNs in LINERs selected from EHF10 based onthe presence of a compact radio cores and nuclear X-raypoint sources as well as the availability of high-resolutionoptical/UV observations. Our coupled accretion-jet modelconsists of an accretion flow which is radiatively inefficientin the inner parts and becomes a thin disk outside a cer-tain transition radius. The relativistic jet is modeled in the framework of the internal shock scenario. In the frameworkof our model, our main results are as follows.(i) We find that there are two broad classes of mod-els that can explain the majority of the observed SEDs. Wecall the first one AD which stands for “ADAF-dominated”since the ADAF dominates most of the broadband emis-sion, particularly in X-rays. In the second class of models,the jet component dominates the majority of the continuumemission and for this reason we call this scenario JD as in“jet-dominated”.(ii) We suggest that the spectral shape of the X-rayspectrum could be used to differentiate between an AD ver-sus a JD origin for the X-rays: soft X-ray LLAGNs (pho-ton spectral indices ∼ − .
5) are likely jet-dominatedwhereas hard X-ray emitters (photon indices <
2) are likelyADAF-dominated. We discuss different observational strate-gies to make progress in understanding the origin of X-raysin LLAGNs.(iii) The radio band is almost always dominated by thesynchrotron emission from the jet, confirming previous re-sults.(iv) Six sources in our sample display an optical-UV ex-cess with respect to ADAF and jet models; in four of them(NGC 1097, NGC 4143, NGC 4278 and NGC 4736), this ex-cess can be reproduced by emission from a truncated thin ac-cretion disk with transition radii in the range 30 − R S . Al-ternatively, unresolved, old stellar populations with masses ∼ − M (cid:12) located within ≈ −
15 pc of the nuclei canalso reproduce the HST optical observations.(v) The mass accretion rates that reach the outer radiusof the ADAF – based on the AD models – lie in the range ∼ × − − .
02 in Eddington units. These accretion ratesare likely to represent upper limits if the jet is the dominantcontributor to the broadband high-energy emission.(vi) Typically ∼
10% of these accretion rates reach 3 R S with the remaining gas being presumably lost due to out-flows.(vii) The efficiency of conversion of rest mass energy as-sociated with gas supplied to the accretion flow into disk+jetradiation is in the range ∼ (10 − − . ∼ − erg s − . The efficiency with whichthe rest mass energy associated with gas supplied to theblack hole is converted into jet kinetic power is in the range0 . − σ ) and anti-correlation ( ≈ . σ )between the radio-loudness – estimated using core radio lu-minosity – and the accretion rate.(x) We compute the average SED for LLAGNs usingour model fits. The average SEDs are quite different fromthe quasar ones and display a slight IR bump. High spa-tial resolution IR observations are required in order betterconstrain the physics of IR emission in LLAGNs.(xi) There is evidence for a nonlinear relation betweenthe 2 −
10 keV and the bolometric luminosity for the sourcesin our sample [log L bol = (0 . ± .
12) log L X + 16 . ± . c (cid:13)000
12) log L X + 16 . ± . c (cid:13)000 , 1–23 Nemmen et al. we computed can be useful for a number of different appli-cations.
ACKNOWLEDGMENTS
We are grateful to: Feng Yuan for useful discussions as wellas help with the models and allowing us to use some of hiscodes; Renyi Ma and Hui Zhang for their help with settingup the models; Jo˜ao Steiner, Michael Brotherton, Rog´erioRiffel, Francesco Tombezi, Judith Racusin, Rafael Eufrasio,Rachel Mason and Roman Shcherbakov for productive dis-cussions; and to the referee for the useful comments and thesuggestion of considering the contribution of stellar popula-tions. RSN was supported by an appointment to the NASAPostdoctoral Program at Goddard Space Flight Center, ad-ministered by Oak Ridge Associated Universities through acontract with NASA. TSB acknowledges the financial sup-port of the Brazilian institutions CNPq and CAPES. Thisresearch has made use of the NASA/IPAC ExtragalacticDatabase (NED) which is operated by the Jet PropulsionLaboratory, California Institute of Technology, under con-tract with the National Aeronautics and Space Administra-tion.
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APPENDIX A: UNCERTAINTIES IN DERIVEDPARAMETERS OF LLAGNS
In this section, we estimate the uncertainties in the mainparameters obtained from the SED models such as massaccretion rates and jet powers.
Accretion rate –
In order to estimate the uncertainty in ˙ m from the AD models, we assume that the bolometric lumi-nosity of LLAGNs can be approximated as the ADAF totalluminosity, L bol ∼ L adaf . We note that this may not be a good approximation for systems in which the thin diskis truncated at low radii, since in such situations the trun-cated disk can contribute a significant part of the luminosity.Correspondingly, for LLAGNs in which the emission is dom-inated by the jet, this approximation is also not appropriate.We use the fitting formulae for the ADAF radiative efficien-cies computed by Xie & Yuan (2012) for different values of δ , assuming s = 0 . R o = 100 (cf. their Table 1). Weevaluate how much ˙ m o varies by changing the value of δ be-tween 10 − and 0.5, for L bol = const. We find that ˙ m o isaffected by a systematic uncertainty of 0.2 dex due to ouruncertain knowledge of the value of δ .The above estimate is appropriate for fixed values of s and R o . It is possible that ADAFs have systematically differ-ent amounts of mass-loss due to outflows or convection thanwhat we considered (e.g., Shcherbakov, Penna & McKinney2012). If this is the case, then our values of ˙ m could be bi-ased towards higher rates if s > . s < . s that we adopted in our SED models).In order to estimate the degree to which different values of s could affect the estimated accretion rates, we computed agrid of ADAF SED models for R o = 10 , δ = 0 . m = 10 and α = 0 . s in the ranges ˙ m o = 10 − − .
01 and s = 0 . − . L bol , we estimate rough un-certainties in ˙ m o of a factor of 5 in each direction (0.7 dex;slightly smaller for smaller values of R o ).Combining the above uncertainties in quadrature withthe systematic scatter of 0.23 dex resulting from the M − σ relation (Tremaine et al. 2002), we estimate a systematicuncertainty in ˙ m o of ∼ . s and δ should be correlated). Theuncertainty in the “Bondi accretion power” P Bondi as definedin the main text is estimated to be of the same order.We expect that the uncertainty in the accretion ratedue to our lack of understanding in the structure of ADAFs(values of s and δ ) and the uncertainty in the black hole masswill dominate over the observational sources of uncertainty(i.e., error in the observed fluxes, paucity of SED samplingin some sources). Bolometric luminosity –
The bolometric luminosities andEddington ratios for the LINERs in our sample are affectedby a factor of 5 ( ∼ . η rad is ∼ . σL X /L X ≈ . ≈ . Jet power –
In order to estimate the uncertainty in the jetpowers derived from the SED models, we consider for il-lustration how the relativistic jet model ( § (cid:15) e = 0 . (cid:15) B = 0 .
01, we consider two values of the bulk Lorentz fac-tor, 2.3 (the fiducial one) and 7 as suggested by Merloni &Heinz (2007), and vary ˙ m jet in order to fit the radio SED.The uncertainty in the value of Γ j results in a factor of 5systematic uncertainty in P jet , similarly to the uncertaintyaffecting L bol . The uncertainty in P jet /L Edd corresponds to ∼ .
76 dex. The uncertainty affecting the jet kinetic effi-ciency should be of the same order of magnitude as the oneaffecting P jet /L Edd . Radio loudness –
The uncertainty in the radio loudness de- c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC0266
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure B1.
The SED and ADAF-dominated model for NGC266. The dashed, dotted and dot-dashed lines correspond to theemission from the ADAF, truncated thin disk and jet, respec-tively. The solid line represents the sum of the emission from allcomponents. The inset shows the zoomed 2-10 keV spectrum. pends on the corresponding errors affecting the radio andoptical luminosities. We estimate that the typical uncer-tainties in L ν (6 cm) and L ν (4400˚A) correspond to ∼ . ∼ . R o estimates have a ∼ . APPENDIX B: FITS TO SPARSELY SAMPLEDSEDS
We present in this section the model fits to the 9 SEDsthat, although displaying nuclear X-ray point sources ob-served with
Chandra , did not pass the quality cut discussedin Section 2 for lacking a radio core or HST optical/UVobservations.but nevertheless have estimates of the black holes massand X-ray SEDs available. The SED fits are shown in Fig-ures B1-B5. In the subsections below, we briefly describethe details of the fits to the SED of each object. The basicproperties of the LLAGNs and the model parameters aresummarized in tables B1 and B2, respectively.
B1 NGC 0266
The AD model accounts slightly better for the best-fit X-rayslope, but note the pronounced uncertainty on the value ofobserved photon index. The JD model requires p < < p < ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC1553
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure B2.
Same as Figure B1 for NGC 1553.
B2 NGC 1553
The Bondi accretion rate was estimated by Pellegrini (2005).Even though the JD model roughly accounts for the esti-mated L X , it fails to fit the slope of the X-ray spectrumeven with a small value of p . We take this as evidence thatthis source is unlikely to be JD (Fig. B2). The estimated˙ m o is consistent with the lower limit on ˙ m Bondi obtained byPellegrini (2005).
B3 NGC 2681
For this LLAGN, there are not enough optical observationsto fit the truncated thin disk model and estimate the tran-sition radius (Fig. B3).
B4 NGC 3169
As was the case of NGC 2681, for this LLAGN there are notenough optical observations to fit the truncated thin diskmodel and estimate the transition radius. The JD modelaccounts well for the available data. The inferred extremevalues of (cid:15) e and (cid:15) B imply that essentially all the energy inthe post-shock region of the jet is carried by the particles. B5 NGC 3226
The SED of this LLAGN is well fitted by both an AD andJD type of models. As is the case of NGC 2681, there are nogood optical band constraints on the emission of the trun-cated thin disk.
B6 NGC 3379
This source has only two data points outside the X-ray band,one in the radio and the other in the optical, both of whichcorrespond to upper limits. Therefore, there are few con-straints for the accretion-jet model. The Bondi rate was es-timated by David et al. (2005). c (cid:13)000
This source has only two data points outside the X-ray band,one in the radio and the other in the optical, both of whichcorrespond to upper limits. Therefore, there are few con-straints for the accretion-jet model. The Bondi rate was es-timated by David et al. (2005). c (cid:13)000 , 1–23 Nemmen et al.
Table B1.
Sample of galaxies with sparsely sampled SEDs and their basic properties. Notation is the same as in Table 1.Galaxy Hubble Distance b log LINER L X L bol L bol /L Edd
Type (Mpc) ( M BH /M (cid:12) ) Type (erg s − ) c (erg s − ) d NGC 266 SB(rs)ab 62.4 (1) 7.6 e L1 7 . × . × × − NGC 2681 SBA(rs)0/a 16.0 (2) 7.1 L1 6 . × . × × − NGC 3169 SA(s)a 19.7 (1) 7.8 L2 1 . × . × × − NGC 3226 E2 21.9 (2) 8.1 L1 5 . × . × × − NGC 3379 E1 9.8 (2) 8.2 L2/T2 1 . × . × × − NGC 4457 SAB(s)0/a 10.7 (4) 6.9 L2 1 . × . × × − NGC 4494 E1-2 15.8 (2) 7.6 L2 9 . × . × × − NGC 4548 SBb(rs) 15.0 (3) 7.6 L2 5 . × . × × − Notes:(e) The mass estimate for NGC 266 is subject to a large uncertainty ( ≈ ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC2681
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC2681
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure B3.
SEDs and coupled accretion-jet models for NGC 1553. The left panel shows the AD models for each object while the rightpanel displays the JD models.
The AD model is able to reproduce the observed SEDgiven the few constraints available, but there are no radiodata to constrain the jet model in this case so we don’tinclude it. The available data are not enough to constrainwell the transition radius. The accretion rate required by theAD model is more than an order of magnitude higher than˙ m Bondi . One possible explanation for this result is that theaccretion rate is enhanced by gas released by stars. This isin line with the findings of Soria et al. (2006a,b) for a sampleof quiescent early-type galaxies.
B7 NGC 4457
Since there are only upper limits in the radio band, the jetpower for this object was estimated using the observation at ν = 1 . × Hz and the Merloni & Heinz (2007) correla-tion.
B8 NGC 4494
Same as NGC 4457.
B9 NGC 4548
Same as NGC 4457. Given the large uncertainty in the pho-ton index, the X-ray spectrum does not provide good con-straints for the models.This paper has been typeset from a TEX/ L A TEX file preparedby the author. c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3169
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3169
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3226
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3226
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3379
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC3379
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure B4.
Same as Figure 3 for NGC 2681, NGC 3169 and NGC 3226.c (cid:13)000
Same as Figure 3 for NGC 2681, NGC 3169 and NGC 3226.c (cid:13)000 , 1–23 Nemmen et al. ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4457
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4457
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4494
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4494
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4548
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV ν / Hz)35363738394041424344 l o g ( ν L ν / e r g s − ) NGC4548
1m 10cm 1cm 1mm 100 µ m 10 µ m 1 µ m 1000 .1keV 1keV 10keV100keV Figure B5.
Same as Figure 3 for NGC 4278, NGC 4457 and NGC 4494.c (cid:13) , 1–23 pectral Models for LLAGNs in LINERs Table B2.
Model parameters resulting from the sparsely sampled SED fits. For all models listed below, R o = 10 , s = 0 . i = 30 ◦ . Galaxy Model ˙ m o δ ˙ m jet p (cid:15) e (cid:15) B P modjet P obsjet ˙ m Bondi
Refs.and notesNGC 0266 AD 5 . × − × − . × -NGC 1553 AD 2 . × − × − . × NGC 2681 JD - - 5 × − . × . × - bNGC 2681 AD 7 . × − − . × -NGC 3169 JD - - 3 × − . × − . × - bNGC 3169 AD 0.03 0.01 2 . × − -NGC 3226 JD - - 10 − × − . × . × - bNGC 3226 AD 0.12 0.01 5 × − . × -NGC 3379 JD - - 2 × − . × - 1 . × − . × − . × − × < × - bNGC 4457 AD 2 . × − × − × -NGC 4494 JD - - 10 − . × < . × -NGC 4494 AD 6 . × − − . × -NGC 4548 JD - - 1 . × − . × . × - bNGC 4548 AD 8 × − × − . × - c (cid:13)000