Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Pancoast, B. Brewer, T. Treu (2014)
Modelling reverberation mapping data – I. Improved geometric and dynamical models and comparison with cross-correlation resultsMonthly Notices of the Royal Astronomical Society, 445
A. Pancoast, B. Brewer, T. Treu, Daeseong Park, A. Barth, M. Bentz, J. Woo (2013)
Modelling reverberation mapping data – II. Dynamical modelling of the Lick AGN Monitoring Project 2008 data setMonthly Notices of the Royal Astronomical Society, 445
J. Smith, A. Robinson, S. Young, D. Axon, E. Corbett (2005)
Equatorial scattering and the structure of the broad-line region in Seyfert nuclei: evidence for a rotating discMonthly Notices of the Royal Astronomical Society, 359
C. Onken, L. Ferrarese, D. Merritt, B. Peterson, R. Pogge, M. Vestergaard, A. Wandel (2004)
Supermassive Black Holes in Active Galactic Nuclei. II. Calibration of the Black Hole Mass-Velocity Dispersion Relationship for Active Galactic NucleiThe Astrophysical Journal, 615
A. Barth, B. Boizelle, J. Darling, A. Baker, D. Buote, L. Ho, J. Walsh (2016)
MEASUREMENT OF THE BLACK HOLE MASS IN NGC 1332 FROM ALMA OBSERVATIONS AT 0.044 ARCSECOND RESOLUTIONThe Astrophysical Journal Letters, 822
S. Collin, T. Kawaguchi, B. Peterson, M. Vestergaard (2006)
Systematic effects in measurement of black hole masses by emission-line reverberation of active galactic nuclei: Eddington ratio and inclinationAstronomy and Astrophysics, 456
L. Ho, M. Astronomy, Astrophysics, T. Science, Korea Astronomy, S. Institute (2014)
THE BLACK HOLE MASS SCALE OF CLASSICAL AND PSEUDO BULGES IN ACTIVE GALAXIESThe Astrophysical Journal, 789
Yan-Rong Li, Jian-Min Wang, L. Ho, P. Du, J. Bai (2013)
A BAYESIAN APPROACH TO ESTIMATE THE SIZE AND STRUCTURE OF THE BROAD-LINE REGION IN ACTIVE GALACTIC NUCLEI USING REVERBERATION MAPPING DATAThe Astrophysical Journal, 779
J. Krolik, C. McKee, C. Tarter (1981)
Two-phase models of quasar emission line regionsThe Astrophysical Journal, 249
V. Afanasiev, L. Popović (2015)
POLARIZATION IN LINES—A NEW METHOD FOR MEASURING BLACK HOLE MASSES IN ACTIVE GALAXIESThe Astrophysical Journal Letters, 800
P. Du, Jian-Min Wang, Zhi-Xiang Zhang (2017)
Hidden Broad-line Regions in Seyfert 2 Galaxies: From the Spectropolarimetric PerspectiveThe Astrophysical Journal Letters, 840
M. Sikora, Ł. Stawarz, J. Lasota (2006)
Radio Loudness of Active Galactic Nuclei: Observational Facts and Theoretical ImplicationsThe Astrophysical Journal, 658
L. Gallo, P. Edwards, E. Ferrero, Jun Kataoka, D. Lewis, D. Lewis, S. Ellingsen, Z. Misanovic, William Welsh, Matthew Whiting, T. Boller, W. Brinkmann, J. Greenhill, Alicia Oshlack (2006)
The spectral energy distribution of PKS 2004–447: a compact steep-spectrum source and possible radio-loud narrow-line Seyfert 1 galaxyMonthly Notices of the Royal Astronomical Society, 370
P. Du, K. Lu, Zhi-Xiang Zhang, Ying-Ke Huang, Kai Wang, Chen Hu, Jie Qiu, Yan-Rong Li, X. Fan, X. Fang, J. Bai, W. Bian, Ye-Fei Yuan, L. Ho, Jian-Min Wang (2016)
SUPERMASSIVE BLACK HOLES WITH HIGH ACCRETION RATES IN ACTIVE GALACTIC NUCLEI. V. A NEW SIZE–LUMINOSITY SCALING RELATION FOR THE BROAD-LINE REGIONThe Astrophysical Journal, 825
B. Peterson, K. Horne (2004)
Echo Mapping of Active Galactic NucleiAstronomische Nachrichten, 325
M. Miyoshi, J. Moran, J. Herrnstein, L. Greenhill, N. Nakai, P. Diamond, M. Inoue (1995)
Evidence for a black hole from high rotation velocities in a sub-parsec region of NGC4258Nature, 373
Joseph Miller, R. Goodrich, W. Mathews (1991)
Multidirectional views of the active nucleus of NGC 1068The Astrophysical Journal, 378
R. Antonucci (1983)
Optical polarization position angle versus radio structure axis in Seyfert galaxiesNature, 303
A. Pancoast, B. Brewer, T. Treu (2011)
GEOMETRIC AND DYNAMICAL MODELS OF REVERBERATION MAPPING DATAThe Astrophysical Journal, 730
Alicia Oshlack, Rachel Webster, Matthew Whiting (2001)
A Very Radio Loud Narrow-Line Seyfert 1: PKS 2004–447The Astrophysical Journal, 558
M. Bentz, K. Denney, C. Grier, A. Barth, B. Peterson, M. Vestergaard, V. Bennert, G. Canalizo, G. Rosa, A. Filippenko, E. Gates, J. Greene, Weidong Li, M. Malkan, R. Pogge, D. Stern, T. Treu, J. Woo (2013)
THE LOW-LUMINOSITY END OF THE RADIUS–LUMINOSITY RELATIONSHIP FOR ACTIVE GALACTIC NUCLEIThe Astrophysical Journal, 767
R. Baldi, A. Capetti, A. Robinson, A. Laor, E. Behar, U. Southampton, UK., Technion, Haifa, Israel, I. Torino, Italy., R. Technology, Usa (2016)
Radio-loud Narrow Line Seyfert 1 under a different perspective: a revised black hole mass estimate from optical spectropolarimetryMonthly Notices of the Royal Astronomical Society, 458
R. Antonucci, J. Miller (1985)
Spectropolarimetry and the nature of NGC 1068The Astrophysical Journal, 297
A. Laor (2000)
On Black Hole Masses and Radio Loudness in Active Galactic NucleiThe Astrophysical Journal Letters, 543
P. Du, Chen Hu, K. Lu, Fang Wang, Jie Qiu, Yan-Rong Li, J. Bai, S. Kaspi, H. Netzer, Jian-Min Wang (2013)
SUPERMASSIVE BLACK HOLES WITH HIGH ACCRETION RATES IN ACTIVE GALACTIC NUCLEI. I. FIRST RESULTS FROM A NEW REVERBERATION MAPPING CAMPAIGNThe Astrophysical Journal, 782
R. Antonucci (1984)
Optical spectropolarimetry of radio galaxies.The Astrophysical Journal, 278
B. Peterson (2014)
Measuring the Masses of Supermassive Black HolesSpace Science Reviews, 183
James Smith, S. Young, A. Robinson, E. Corbett, M. Giannuzzo, D. Axon, J. Hough (2002)
A spectropolarimetric atlas of Seyfert 1 galaxiesMonthly Notices of the Royal Astronomical Society, 335
J. Krolik (2000)
Systematic Errors in the Estimation of Black Hole Masses by Reverberation MappingThe Astrophysical Journal, 551
H. Tran, Joseph Miller, L. Kay (1992)
Detection of obscured broad-line regions in four Seyfert 2 galaxiesThe Astrophysical Journal, 397
IN Dusty, Dusty Nebulae (2020)
Radiative transfer
J. Woo, T. Treu, A. Barth, S. Wright, J. Walsh, M. Bentz, P. Martini, V. Bennert, G. Canalizo, A. Filippenko, E. Gates, J. Greene, Weidong Li, M. Malkan, D. Stern, T. Minezaki (2010)
THE LICK AGN MONITORING PROJECT: THE MBH–σ* RELATION FOR REVERBERATION-MAPPED ACTIVE GALAXIESThe Astrophysical Journal, 716
C. Brindle, J. Hough, J. Bailey, D. Axon, M. Ward, W. Sparks, I. McLean (1990)
An optical and near-infrared polarization survey of Seyfert and broad-line radio galaxies. I, Statistical propertiesMonthly Notices of the Royal Astronomical Society, 244
MNRAS 473, L1–L5 (2018) doi:10.1093/mnrasl/slx154 Advance Access publication 2017 September 28 Measuring black hole mass of type I active galactic nuclei by spectropolarimetry 1,2 1,2,3‹ Yu-Yang Songsheng and Jian-Min Wang Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, China University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China National Astronomical Observatories of China, Chinese Academy of Sciences, 20A Datun Road, Beijing 100020, China Accepted 2017 September 25. Received 2017 September 19; in original form 2017 July 18 ABSTRACT Black hole (BH) mass of type I active galactic nuclei (AGNs) can be measured or estimated through either reverberation mapping or empirical R–L relation, however, both of them suffer from uncertainties of the virial factor (f ), thus limiting the measurement accuracy. In BLR this letter, we make an effort to investigate f through polarized spectra of the broad-line BLR regions (BLR) arisen from electrons in the equatorial plane. Given the BLR composed of discrete clouds with Keplerian velocity around the central BH, we simulate a large number of spectra of total and polarized flux with wide ranges of parameters of the BLR model and equatorial scatters. We find that the f -distribution of polarized spectra is much narrower BLR than that of total ones. This provides a way of accurately estimating BH mass from single spectropolarimetric observations of type I AGN whose equatorial scatters are identified. Key words: polarization – galaxies: active – quasars: supermassive black holes. found in inactive galaxies (Onken et al. 2004; Woo et al. 2010). 1 INTRODUCTION f as an averaged one can only remove the systematic bias BLR Reverberation mapping (RM) is nowadays the most common tech- between the virial product ct V /G and M for a large sample, FWHM nique of measuring black hole (BH) mass of type I active galac- however, f is poorly understood individually. Furthermore, the BLR tic nuclei (AGNs), except for a few local AGNs spatially resolved zero-point and scatters of the M –σ relation depend on bulge types • ∗ (Peterson 1993; Peterson 2014). RM measures time lags t of broad of the host galaxy, and virial factors of classical bulges and pseudo- emission lines with respect to varying continuum as ionizing pho- bulges can differ by a factor of ∼2(Ho &Kim 2014). The calibrated tons, allowing us to obtain the emissivity-averaged distance from values of f lead to δM /M ∼ 2, yielding only rough estimations • • BLR the broad-line regions (BLR) to the central BH. Assuming fully of BH mass in AGNs. random orbits of the BLR clouds with Keplerian velocity, we have Recently, a motivated idea to test the validity of f factor has BLR the BH mass as been suggested by Du, Wang & Zhang (2017) in type II AGNs through the polarized spectra. In principle, the polarized spectra are ct V FWHM M = f , (1) viewed with highly face-on orientation to observers, and f in BLR BLR type II AGNs should be the same as with type I AGNs. They reach where f is the virial factor, V is the full width at half- a conclusion of f ∼ 1 from a limited sample. For type I AGNs, BLR FWHM BLR maximum (FWHM) of the broad emission line profiles, c is the the polarized spectra received by a remote observer correspond to light speed and G is the gravity constant. The total error budget on ones viewed by an edge-on observer, lending an opportunity to the BH mass can be simply estimated by δM /M ≈ [(δ ln f ) + • • BLR measure BH mass similar to cases of NGC 4258 through water 1/2 0.08] ,where t and V are usually of 20 per cent and FWHM maser (Miyoshi et al. 1995) or others through CO line (Barth et al. 10 per cent for a typical measurement of RM observations, respec- 2016). tively. Obviously, the major uncertainty on the BH mass is due to In this letter, we investigate f in type I AGNs through mod- BLR f ; however, it could be different by a factor of more than one elling the scattering polarized spectra quantitatively. In Section 2, BLR order of magnitude (Pancoast et al. 2014b). Its dependence on kine- we build a dynamical model for BLR and scattering region of type matics, geometry and inclination of the BLR is poorly understood I AGNs for polarized spectra. In Section 3, we simulate a large (Krolik 2001; Collin et al. 2006). number of spectra for a large range of model parameters to get the For those AGNs with measured stellar velocity dispersions σ of ∗ distribution of f for both total and polarized spectra. We find that BLR bulges and RM data, f can be calibrated by the M –σ relation • ∗ f is in a very narrow range for polarized spectra. In Section 4, BLR BLR we draw conclusions and discuss potential ways of improving the accuracy of BH mass determination. E-mail: wangjm@ihep.ac.cn 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Downloaded from https://academic.oup.com/mnrasl/article-abstract/473/1/L1/4265274 by Ed 'DeepDyve' Gillespie user on 16 March 2018 L2 Y.-Y. Songsheng and J.-M. Wang Figure 1. Panel (a) is a cartoon of a type I AGN with an equatorial scattering region. The blue points represent clouds in the BLR and the grey region the scatters on the equatorial plan. i is the inclination angle to a remote observer in the O–YZ plane. Panel (b) is the frame for the BLR geometry. O–XY is the equatorial plane. O–X Y is the orbital plane of one specific cloud, which can be obtained by rotating X around Z by φ and then rotating Z around X by θ . C C C C C The phase angle of the cloud relative to OX is φ . Panel (c) is the scattering geometry used here. BP is the incident light from point B on one orbit. n is obs C B the direction of sight of the observer (i.e. the direction of scattered light). The vectors of n , n , n , n and n are explained in the appendix. obs ⊥ z x 2 POLARIZED SPECTRA FROM EQUATORIAL R ≡ GM /c and orbits of the clouds are circular. The velocity of g • SCATTERS the cloud is ⎛ ⎞ Optical spectropolarimetric observations of type II AGNs dis- − sin φ cos φ − cos φ sin φ cos θ B C B C C cover that there is a broad component of emission line in polar- ⎜ ⎟ ⎜ ⎟ v = V − sin φ sin φ + cos φ cos φ cos θ , (2) cloud K ized spectra, indicating the appearance of (1) a BLR hidden by B C B C C ⎝ ⎠ the torus; and (2) at least one scattering region outside the torus cos φ sin θ B C (Antonucci & Miller 1985; Miller, Goodrich & Mathews 1991; −1/2 Tran, Miller & Kay 1992). Radio observations also show that radio where V = cr . The half opening angle of the BLR is , BLR axes of most type II AGNs are nearly perpendicular to the position the inner and outer radii of the BLR are r and r , respectively. B,i B,o angle of polarization (Antonucci 1983;Brindleetal. 1990), show- Then we have r ∈ [r ,r ],θ ∈ [0, ]. The distribution of B B,i B,o C BLR ing that scattering regions of Type II AGNs situated outside the clouds can be modelled by power law as well. The number density −β torus but aligned with the axes of the AGNs, called polar scattering of the clouds is n (r ,θ ,φ ,φ ) = n (r /r ) ,where n is the B B C C B B0 B B,i B0 region. In contrast, observations of type I AGNs reveal that position number density at r . B,i angles of the polarization are more often aligned with radio axes A single scattering process is illustrated by Fig. 1(c). Expres- (Antonucci 1983, 1984; Smith et al. 2002). Equatorial scattering sions of the scattering angle and rotation angle χ are derived in regions may exist, which are hidden by the torus, but can be seen in appendix. Assuming the ionizing source is isotropic and line in- the polarized spectra of type I AGNs (Smith et al. 2005). tensity of one cloud at B is linearly proportional to the intensity −2 We follow the geometry of equatorial scatters as in Smith et al. of local ionizing fluxes, the line intensity at B is i = kr ,where (2005). The geometry of the scattering regions and BLR are shown k is a constant. We further assume that all clouds emit unpolar- in Fig. 1(a). The details of the geometric relations are provided in ized Hβ photons isotropically and neglect multiple scatterings of the appendix. If the half opening angle of the scattering region is optically thin regions. Thus the intensity at P is simply given by , the inner and outer radii of the scattering region are r and r , i = i S/4πr ,where S is the surface area of the cloud. Given in- P P,i P,o P B BP then we have r ∈ [r ,r ],θ ∈ [π/2 − ,π/2 + ]. Scatter- cident photons with the Stokes parameters of (i , 0, 0, 0), the Stokes P P,i P,o P P P ings caused by intercloud electrons in the BLR have been esti- parameters in the (n –n ) frame are (Chandrasekhar 1960). mated as τ ≈ 0.04R (see equation 5.13 in Krolik, McKee & 0.1pc BLR ⎛ ⎞ Tarter 1981), where R = R /0.1 pc is a typical size of the 1 1 0.1pc BLR 2 2 ⎛ ⎞ (1 + cos ) (1 − cos )0 0 BLR (Bentz et al. 2013), which can be totally neglected for polar- ⎜ 2 2 ⎟ P ⎜ ⎟ ⎜ ⎟ ized spectra. We thus assume that the scattering region is composed ⎜ 1 1 ⎟ ⎜ 0 ⎟ 2 2 3σ ⎜ ⎟ (1 − cos ) (1 + cos )0 0 ⎜ ⎟ of free cold electrons beyond the BLR, and the whole region is ⎜ ⎟ 2 2 ⎜ ⎟ 8πR ⎜ ⎟ ⎝ ⎠ optically thin, i.e. the optical depth τ ∼ nσ ¯ < 1, where n¯ is the ⎜ ⎟ es T 00 cos 0 ⎝ ⎠ average number density of the electrons, is the typical scale of 00 0 cos the region and σ is the Thomson cross-section. The distribution ⎛ ⎞ of the number density of electrons is assumed to be a power law as 1 + cos −α n (r ,θ ,φ ) = n (r /r ) ,where n is the number density at P P P P P0 P P,i P0 ⎜ ⎟ ⎜ 1 − cos ⎟ inner radius r . P,i ⎜ ⎟ = A , (3) ⎜ ⎟ We assume BLR is composed of a large quantity of indepen- ⎝ 0 ⎠ dent clouds rotating around the BH, and has a geometry indicated by Fig. 1(b) (Pancoast, Brewer & Treu 2011;Lietal. 2013;Pan- coast, Brewer & Treu 2014a). The detailed geometric relations of where A = 3σi /16πR , R is the distance between the observer BLR are given in the appendix. Suppose that the unit of length is and AGN. Converting the Stokes parameter to the fixed coordinate MNRASL 473, L1–L5 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/473/1/L1/4265274 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Measuring black hole mass L3 − n system, we have Table 1. The dependence of f on model parameters. z x BLR ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ i 10 0 0 1 + cos Parameter Range Meaning δ ln f BLR ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Total Polarized ⎜ q ⎟ ⎜ 0cos2χ sin 2χ 0 ⎟ ⎜ 1 − cos ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ = A ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ r (10 R ) [1, 5] SR inner radius 0.01 0 u 0 − sin 2χ cos 2χ 0 0 g ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ P,i r (10 R ) [2, 10] SR outer radius 0 0 P,o v 00 0 cos 0 ◦ ( ) [20, 50] SR opening angle −0.04 0 α [0, 1.5] Index of DF of electrons 0.01 0 ⎛ ⎞ 1 + cos 3 r (10 R ) [1, 5] Inner radius of BLR −0.01 0.01 B,i ⎜ ⎟ r (10 R ) [2, 10] Outer radius of BLR 0.01 −0.01 B,o ⎜ (1 − cos )cos2χ ⎟ ⎜ ⎟ ( ) [20, 50] Opening angle of BLR −0.38 0.03 = A . (4) 0 BLR ⎜ ⎟ −(1 − cos ) sin 2χ ⎝ ⎠ β [0, 1.5] Index of DF of clouds 0 −0.02 i( ) [0, 45] Inclination angle −0.64 0 Note. SR: scattering region and DF: distribution function. δ ln f describes BLR The velocity of the cloud v projected to the direction of incident cloud the dependence on parameters of the BLRs. See details for its definition in light n is BP the main text. It shows that f is sensitive to and i for the total BLR BLR spectra, but it is almost a constant for polarized spectra. V 1 r (q cos φ + q sin φ ) 1 2 P B B = , (5) 1/2 1/2 2 2 r + r + 2r r (q cos φ − q sin φ ) B 2 1 B P B B P B where q = cos θ sin θ + sin θ cos θ sin(φ − φ ), q =− sin θ 1 2 P C P C P C P cos(φ − φ ). If the intrinsic wavelength of the line is λ ,the wave- P C length after scattering is λ = λ (1 − V /c) due to Doppler shifts. Integrating over all the clouds and electrons, we have the total po- larized spectrum, ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ 2π ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ = dV n dV n L(λ, λ )dφ , ⎜ ⎟ P P BLR B B ⎜ ⎟ ⎝ ⎠ U V V 0 u ⎝ ⎠ P BLR (6) where the intrinsic profile of Hβ line is assumed to be a Lorentzian 2 2 function of L(λ, λ ) ∝ /[(λ − λ ) + ], is the intrinsic width much smaller than the broadening due to rotation of clouds (the Figure 2. Total, polarized spectra and polarization degrees of a type I AGN Lorentzian profiles are a very good approximation in the present with an equatorial electron scattering region. The left-hand column is spectra context). for different inclinations, whereas the right-hand column is for different BLR Similarly, we can calculate the spectrum of non-scattered pho- opening angles. The tops of the total spectra become flatter and polarization tons. The velocity of the cloud v projected to the direction of cloud decreases with increasing (tends to 90 ). BLR observer n is obs V 1 = q˜ cos φ + q˜ sin φ , (7) 1 2 1/2 B B ◦ ◦ ◦ ◦ ◦ τ = σn (r − r ) = 1, i = (1 ,10 ,20 ,30 ,40 )and = es P0 P,o P,i BLR where q˜ = sin θ cos i + cos θ cos φ sin i, q˜ =− sin φ sin i. 1 2 C C C C ◦ ◦ ◦ ◦ ◦ (10 , 20 , 30 , 40 , 50 ). As shown in the left-hand panel of Fig. 2 The observed wavelength is λ = λ (1 − V /c). Integrating over , the total spectra get broader as i increases and show double- all the clouds, we have peaked profiles when i exceeds a critical inclination. By contrast, 2π i S the width and the profile of the polarized spectra are not sensitive to F = dV n L(λ, λ )dφ , (8) BLR B B 4πR i (can be found from normalized spectra). This interesting property V 0 BLR results from the fact that the polarized spectra are equivalent to the and the expression for polarization degree and position angle, ones seen by observers at edge-on orientations. Generally, the line 2 2 centres have lowest polarization degrees. However, the polarization Q + U 1 Q λ λ P = ,θ = arccos . (9) λ λ degrees become smaller with i. 2 2 I + F 2 λ λ Q + U λ λ Total spectra show strong dependence on . As shown in the BLR If U > 0, θ ∈ (0, π/2). If U < 0, θ ∈ (−π/2, 0). Position angles right-hand panel of Fig. 2,large- BLRs show a broader width λ λ λ λ BLR represent the angle between the direction of maximum intensity and get narrower with decreasing of until double-peaked pro- BLR and n . files. However, does not change the polarized profiles too BLR Table 1 summarises all the parameters of the present model. much. A large indicates that the system tends to be more BLR We calculate a series of profiles for different values of parameters spherically symmetric and to decrease the polarization degree. Com- and find that the profiles are only sensitive to and i. Fig. 2 paring with the total spectra, the width of the polarized spectrum BLR shows typical spectra of a type I AGN with an equatorial electron is insensitive to and i. This property allows us to infer f BLR BLR scattering region. The parameters of the model are r = 10 , r = from the polarized spectrum and improve the accuracy of BH mass P,i P,o 4 ◦ 3 3 2 × 10 , = 30 , r = 2 × 10 , r = 6 × 10 , α = 1, β = 1, measurement, as shown in Section 3. P B,i B,o MNRASL 473, L1–L5 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/473/1/L1/4265274 by Ed 'DeepDyve' Gillespie user on 16 March 2018 L4 Y.-Y. Songsheng and J.-M. Wang originating from the equatorial scatters. Actually, this can be done 3 THE VIRIAL FACTOR by checking if the position angles are parallel to radio axis in AGNs. With the BLR model, we have the emissivity-averaged time lag of We apply the current f to the radio-loud narrow BLR a broad emission line as line Seyfert 1 galaxy PKS 2004−447 with V (H α) = FWHM −1 dV ri n R g 1500 km s (z = 0.240). The BH mass estimated by single BLR B B t = dV i n c total spectra is about 5 × 10 M (Oshlack, Webster & BLR B B Whiting 2001), which is much smaller than the critical mass 2−β 1 − β 1 − q r R 8 r B,i (M ∼ 10 M ) invariably associated with classical radio-load = , (10) 1−β 2 − β c 1 − q AGNs (Laor 2000). Fortunately, the polarized spectra of VLT ob- servations show its H α FWHM of (280 ± 50)Å (Baldi et al. 2016). where r = r − r · n and the corresponding virial factor from obs B B 44 −1 Since the 5100Å luminosity is L = 1.25 × 10 erg s (Gallo equation (1) can be written as et al. 2006), R–L relation indicates that the average time lag 1−β 1.6 ± 0.14 1 − β 1 − q V between emission line and continuum is about 10 d −1 r FWHM f = r , (11) B,i BLR 2−β (Bentz et al. 2013) for sub-Eddington AGNs (Du et al. 2016). 2 − β c 1 − q Taking log f =−0.63 for the polarized spectra of H α line, BLR where q = r /r , V is the FWHM of profiles either from the r 8.45 ± 0.2 B,o B,i FWHM we have M = 10 M . Employing the standard ac- total or polarized spectra. We generate profiles according to param- cretion disc model, we have the dimensionless accretion rates eters listed in Table 1 and measure V to show dependences of −2 2 3/2 FWHM ˙ ˙ ˙ of M = Mc /L = 20.1(L / cos i) m ≈ 0.05, where M is Edd 44 f on each parameter. 38 −1 BLR the accretion rates, L = 1.4 × 10 (M /M )ergs , L = Edd • 44 We did Monte Carlo simulations for all the parameters listed in 44 −1 7 L /10 erg s ,cos i = 0.75 (inclination) and m = M /10 M 5100 7 • Table 1 and then get the ln f –ln X relations, where X is any one i i BLR (Du et al. 2014). Such a low accretion rate agrees with the of the parameters. The f dependence on X can then be obtained BLR radio-loudness and accretion rate relation (Sikora, Stawarz & by δ ln f = (∂ ln f /∂ ln X )δ ln X ,where ∂ ln f /∂ ln X is i i i BLR BLR BLR Lasota 2007). the slope of the ln f –ln X relations and δln X is its range. The i i BLR Finally, we would like to point out the temporal properties of slope is estimated from the line regression of ln f –ln X relations BLR polarized spectra. The equatorial distributions of scatters lead to from the Monte Carlo simulations. The dependence listed in Table 1 delays of polarized photons with different frequencies relative to shows that only i and are the major drivers in the total spectra, BLR the BLR, and such a delay may need to be considered for polarized but f is insensitive to all the parameters (only slightly relies on BLR spectra at different epochs. Such a kind of polarization campaigns ). We estimate the entire uncertainties of f due to all pa- BLR BLR will provide a new way of accurately measuring the BH mass in 2 2 1/2 rameters as log f = [ (∂ ln f /∂ ln X ) ( log X ) ] . i i BLR i=1 BLR type 1 AGNs. We have log f = (0.74, 0.04) for total and polarized spectra, BLR respectively. 4 CONCLUSION AND DISCUSSION We plot the log f -distributions and contour maps versus BLR BLR and i in Fig. 3. It shows that the distribution from total spectra is In this Letter, we show that the factor f has a wide range for BLR much broader than that from polarized spectra. The 68 per cent con- total spectra of the virialized BLR. We investigate the polarized fidence interval of the former is log f ∈ [−0.41, 0.08] agreeing BLR spectra of the BLR arisen from the equatorial scatters for f in BLR with values from detailed Markov chain Monte Carlo modelling determination of the BH mass in type I AGNs. It is found that (Pancoast et al. 2014b), but log f ∈ [−0.65, −0.62] from the BLR log f ∈ [−0.65, −0.62] for polarized spectra. This arises from BLR polarized spectra. For a typical RM campaign, we have the uncer- the fact that the electrons on the equatorial plane scatter the broad- tainties of BH mass δM /M ≈ (0.8, 0.3) from total and polarized • • line photons to observers, assembling to view the BLR as edge- spectra, respectively. Obviously, spectropolarimetry provides much on orientation. The polarized spectra provide a way of accurately better f for BH mass from RM campaign. However, the polarized BLR measuring BH mass from single-epoch polarized spectra, which spectra as the prerequisites of applications should be identified as is much better than that from single-epoch total spectra. For an individual application, equatorial scatters must be checked for the validity of the polarized spectra. We note the work of Afanasiev & Popovic( ´ 2015), who employed the angles of polarization arisen by scatters on the inner edge of the dusty torus in order to alleviate dependence of BH mass on inclinations. This is different from what we suggest in this Letter. We would like to point out the major assumptions used in this Letter that scattering region is equatorial, but static. The geometry of scatters is supported by observations but the dynamics could be more complicated. We also neglect scatters of dust particles. This simple model shows the potential functions of polarized spectra in measuring BH mass. Fitting the polarized spectra leads to a more accurate BH mass, but we will conduct it in a forthcoming paper. Figure 3. The upper three panels display the distribution of log f ob- BLR tained from total spectra, while the lower three panels display polarized spectra. In each row, the first panel is the probability density function of ACKNOWLEDGEMENTS log f and the shadow area marks out the 68 per cent confidence interval, BLR and the second and third indicate correlations of log f with model pa- The authors thanks the referee for a useful report. We acknowl- BLR rameters of and i, respectively. f is sensitive to both and i BLR edge the support of the staff of the Lijiang 2.4-m telescope. Fund- BLR BLR for the total spectra, whereas f only very weakly depends on . BLR BLR ing for the telescope has been provided by Chinese Academy of MNRASL 473, L1–L5 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/473/1/L1/4265274 by Ed 'DeepDyve' Gillespie user on 16 March 2018 Measuring black hole mass L5 Sciences and the People’s Government of Yunnan Province. This APPENDIX research is supported by the National Key Program for Science and For type I AGN, the polarized spectra observed by a remote observer Technology Research and Development (grant 2016YFA0400701), are mostly caused by electron scattering of the equatorial regions. Natural Science Foundation of China grants through Natural Sci- Suppose the coordinate of the electron in spherical system is (r , ence Foundation of China-11503026, -11173023 and -11233003, θ , φ ), we have and an Natural Science Foundation of China – Chinese Academy P P of Sciences joint key grant U1431228, by the Chinese Academy of ⎪ x = r sin θ cos φ , P P P P Sciences Key Research Program through KJZD-EW-M06, and by y = r sin θ sin φ , (A.1) the Key Research Program of Frontier Sciences, Chinese Academy P P P P of Sciences, grant No. QYZDJ-SSW-SLH007. z = r cos θ . P P P As for a cloud in BLR at (r cos φ ,r sin φ ,0),weuse therotation B B B B REFERENCES matrix ⎛ ⎞ Afanasiev V. L., Popovic´ L. C., 2015, ApJ, 800, L35 cos φ − sin φ cos θ sin φ sin θ C C C C C Antonucci R. R., 1983, Nature, 303, 158 ⎜ ⎟ ⎜ ⎟ R = sin φ cos φ cos θ − cos φ sin θ , (A.2) Antonucci R., 1984, ApJ, 278, 499 C C C C C ⎝ ⎠ Antonucci R., Miller J., 1985, ApJ, 297, 621 0sin θ cos θ C C Baldi R. D., Capetti A., Robinson A., Laor A., Behar E., 2016, MNRAS, 458, L69 for the position of the cloud Barth A. J., Boizelle B. D., Darling J., Baker A. J., Buote D. A., Ho L. C., ⎪ x = r (cos φ cos φ − sin φ sin φ cos θ ), B B B C B C C Walsh J. L., 2016, ApJ, 822, L28 ⎪ Bentz M. C. et al., 2013, ApJ, 767, 149 y = r (cos φ sin φ − sin φ cos φ cos θ ), (A.3) B B B C B C C Brindle C., Hough J., Bailey J., Axon D. J., Ward M. J., Sparks W. B., z = r sin θ sin φ , McLean I. S., 1990, MNRAS, 244, 577 B B C B Chandrasekhar S., 1960, Radiative Transfer. Dover Press, New York in the O − XYZ frame. Collin S., Kawaguchi T., Peterson B. M., Vestergaard M., 2006, A&A, 456, One cloud is at (x ,y ,z ) and one scattering electron is at B B B (x ,y ,z ), we have the direction vector of incident light Du P. et al., 2014, ApJ, 782, 45 P P P Du P. et al., 2016, ApJ, 825, 126 Du P., Wang J.-M., Zhang Z.-X., 2017, ApJ, 840, L6 n = (x − x )i + (y − y ) j + (z − z )k , (A.4) BP P B P B P B BP Gallo L. et al., 2006, MNRAS, 370, 245 Ho L. C., Kim M., 2014, ApJ, 789, 17 2 2 2 where r = (x − x ) + (y − y ) + (z − z ) . The direc- BP P B P B P B Krolik J. H., 2001, ApJ, 551, 72 tion of the observer at infinity is taken to be n = (0, sin i, cos i). obs Krolik J., McKee C. F., Tarter C., 1981, ApJ, 249, 422 The scattering angle is given by Laor A., 2000, ApJ, 543, L111 Li Y.-R., Wang J.-M., Ho L. C., Du P., Bai J.-M., 2013, ApJ, 779, 110 cos = n · n = (y − y )sin i + (z − z )cos i . (A.5) obs BP P B P B Miller J., Goodrich R., Mathews W. G., 1991, ApJ, 378, 47 BP Miyoshi M., Moran J., Herrnstein J., Greenhill L., Nakai N., Diamond P., The unit vector perpendicular to the scattering plane is Inoue M., 1995, Nature, 373, 127 Onken C. A., Ferrarese L., Merritt D., Peterson B. M., Pogge R. W., Vester- n × n obs BP n = . (A.6) gaard M., Wandel A., 2004, ApJ, 615, 645 |n × n | obs BP Oshlack A., Webster R., Whiting M., 2001, ApJ, 558, 578 Pancoast A., Brewer B. J., Treu T., 2011, ApJ, 730, 139 We take the fixed coordinate system at celestial sphere of the ob- Pancoast A., Brewer B. J., Treu T., 2014a, MNRAS, 445, 3055 server to be n − n , n = (0, − cos i, sin i),n = (1, 0, 0). The z x z x Pancoast A., Brewer B. J., Treu T., Park D., Barth A. J., Bentz M. C., Woo angle between n and n satisfies that ⊥ z J.-H., 2014b, MNRAS, 445, 3073 x − x Peterson B. M., 1993, PASA, 105, 247 P B cos χ = . 1/2 2 2 Peterson B. M., 2014, Space Sci. Rev., 183, 253 [(z − z )sin i − (y − y )cos i] + (x − x ) P B P B P B Sikora M., Stawarz Ł., Lasota J.-P., 2007, ApJ, 658, 815 (A.7) Smith J., Young S., Robinson A., Corbett E., Giannuzzo M., Axon D., Hough J., 2002, MNRAS, 335, 773 Smith J., Robinson A., Young S., Axon D., Corbett E. A., 2005, MNRAS, 359, 846 Tran H. D., Miller J. S., Kay L. E., 1992, ApJ, 397, 452 Woo J. -H. et al., 2010, ApJ, 716, 269 This paper has been typeset from a T X/LT X file prepared by the author. E E MNRASL 473, L1–L5 (2018) Downloaded from https://academic.oup.com/mnrasl/article-abstract/473/1/L1/4265274 by Ed 'DeepDyve' Gillespie user on 16 March 2018
Monthly Notices of the Royal Astronomical Society Letters – Oxford University Press
Published: Sep 28, 2017
Keywords: polarization; galaxies: active; quasars: supermassive black holes
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.