Systematic Redshift of the Fe III UV Lines in Quasars. Measuring Supermassive Black Hole Masses under the Gravitational Redshift Hypothesis
E. Mediavilla, J. JimÉnez-Vicente, C. Fian, J. A. MuÑoz, E. Falco, V. Motta, E. Guerras
SSystematic Redshift of the Fe III UV Lines in Quasars.Measuring Supermassive Black Hole Masses under theGravitational Redshift Hypothesis.
E. MEDIAVILLA , , J. JIM ´ENEZ-VICENTE , , C. FIAN , , J. A. MU ˜NOZ , , E.FALCO , V. MOTTA & E. GUERRAS ABSTRACT
We find that the Fe III λλ λλ M BH R ( ∆ λλ (cid:39) Gc M BH R ) and using different estimates of the emitting region size, R (eitherfrom gravitational microlensing, reverberation mapping or from the scaling of sizewith intrinsic quasar luminosity), we obtain masses for 10 objects which are inagreement within uncertainties with previous mass estimates based on the virialtheorem. Reverberation mapping estimates of the size of the Fe III λλ Instituto de Astrof´ısica de Canarias, V´ıa L´actea S/N, La Laguna 38200, Tenerife, Spain Departamento de Astrof´ısica, Universidad de la Laguna, La Laguna 38200, Tenerife, Spain Departamento de F´ısica Te´orica y del Cosmos, Universidad de Granada, Campus de Fuentenueva, 18071Granada, Spain Instituto Carlos I de F´ısica Te´orica y Computacional, Universidad de Granada, 18071 Granada, Spain Departamento de Astronom´ıa y Astrof´ısica, Universidad de Valencia, 46100 Burjassot, Valencia, Spain. Observatorio Astron´omico, Universidad de Valencia, E-46980 Paterna, Valencia, Spain Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA Instituto de F´ısica y Astronom´ıa, Facultad de Ciencias, Universidad de Valpara´ıso, Avda. Gran Breta˜na1111, 2360102 Valpara´ıso, Chile Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, OK,73019, USA a r X i v : . [ a s t r o - ph . GA ] J u l λλ Subject headings: (black hole physics — gravitational lensing: micro)
1. Introduction
In the classical picture of quasars, a central supermassive black hole (BH) is surroundedby an inspiraling disk that transports matter into the depth of the gravitational well of theBH, releasing huge quantities of energy (Zeldovich 1964, Salpeter 1964). This central engineilluminates gas clouds located in a larger region (Broad Line Region, BLR) giving rise to verybroad emission lines (BEL) whose width and shape are determined by the kinematics of thegas clouds, ultimately ruled by the central BH. Thus, the kinematics of the BLR potentiallyprovides a means of measuring the central masses of supermassive BH and of studying thestructure of the accretion disk.Specifically, the methods for estimating BH masses in distant quasars are mainly basedon the measure of the broadening of the BEL in combination with the virial theorem (see,e.g., Peterson 2014). According to this theorem, the square of the line-broadening, (∆ v ) , isa proxy for M/R that, in combination with a determination of the size, R , can provide anestimate of the mass, M = f (∆ v ) RG . (1)The dimensionless factor, f , includes the effects of the unknown BLR geometry, kinematicsand inclination. Without more information, it is a common practice to use an average valuefor f obtained by calibrating with other methods , even when f is different for each object.This virial factor, by itself, limits the accuracy of individual estimates of mass to ∼ In the nearby universe, masses of supermassive black holes have been determined in around 70 galaxiesby direct modeling of the stellar or gas dynamics (see, e.g., McConnell & Ma 2013). The M BH − σ ∗ relationship, for instance (Ferrarese & Merritt 2000, Gebhardt et al. 2000, Tremaine etal. 2002). f ), arises from the determination of the line widths(Peterson 2014), due to both, the ambiguity in the definition of ∆ v (FWHM, σ , use of thevariable or constant part of the spectra, etc.), and the presence of contaminating features(extra components, blended lines, pseudo-continuum, etc.).An alternative path to BH masses is the gravitational redshift of the BEL. If we considerthe width of the BEL as caused by motion in the gravitational field of a central mass, a simplecalculation shows that we should expect measurable gravitational and transverse Dopplerredshifts (see, e.g., Netzer 1977, Anderson 1981, Mediavilla & Insertis 1989). Indeed, inthe weak limit of the Schwarzschild metric, the velocity of the emitters is proportional to (cid:112) GM/R , and the gravitational plus transverse Doppler redshift will tend to Gc MR . Thus,line broadenings typical of the BEL, ∆ v (cid:38) km s − , will result in redshifts z grav = ∆ λλ (cid:38) . λ (cid:38) β in many cases) can showredward asymmetries (Peterson et al. 1985, Sulentic 1989, Zheng & Sulentic 1990, Popovi´cet al. 1995, Corbin et al. 1997), that have been sometimes interpreted as the result ofgravitational redshift (Joni´c et al. 2016), although the presence of an extra componentredshifted due to inflow is, perhaps, a more accepted explanation for the line asymmetry. Ina few cases in which spectroscopic monitoring is available, the redshift between the meanand rms profiles of Balmer lines has been associated with gravitational redshift (Kollatschny2003, Liu et al. 2017) . There has also been continued controversy about the existence ofredshifts in Fe II emission. Hu et al. (2008) interpreted the redshift measured in the FeII optical lines of a sample of SDSS spectra in terms of kinematics dominated by infall. Inthis scenario, to prevent the gas from being accelerated away from the central source by theradiation force, Ferland et al. (2009) propose that we only observe the shielded face of near-side infalling clouds. However, Kovaˇcevi´c et al. (2010) report only a slight redshift of the Fe Hereafter we refer to the combined gravitational and transverse Doppler effects as gravitational redshift. In any case, the presence of gas cold enough as to generate the Balmer lines so close to the BH as tojustify the redshift needs to be explained (Bon et al. 2015). , so that the larger the changes the smaller the size. According to previousstudies (Guerras et al. 2013a,b, Fian et al. 2018), the Fe III λλ § λλ § § When a distant quasar is lensed by the gravitational potential of an intervening (lens) galaxy, the relativemovement between the quasar and the distribution of stars in the lens galaxy can change the brightnessesof the images, an effect called quasar gravitational microlensing (Chang & Redfsdal 1979, 1984, see also thereview by Wambsganss 2006).
2. Results: Fe III λλ The data analyzed in this work have different origins. The 14 lensed quasar spectrafitted in § § § We model the Fe III λλ . , . . , . σ (= FWHM / . λ , and scale factor. In Figure 1 we can see that this template is ableto reproduce very well the shape of the Fe III λλ , but the fitted features are redshifted in all the objects except one(SDSS 1004+4112, which is strongly affected by microlensing). Leaving aside this object,we find that the average of this systematic redshift is (cid:104) ∆ λ (cid:105) = 10 . ± . , R = 1 . × . +5 − light-days, we can estimate the average mass ofthe supermassive black holes of the lensed quasars under the hypothesis of a gravitationalorigin for the redshift. If we assume that gravitational and transverse Doppler are thephysical phenomena giving rise to the redshift, we have (see, e.g., Mediavilla & Insertis,1989), ν = ( ν /γ ) (cid:112) − GM BH /Rc with γ = (1 − ( v/c ) ) − / . In the weak limit of theSchwarzschild metric, v (cid:39) GM BH /R , and we have, See also other fits in the upper panel of Figure 2, and Figures 3 and 4. Fiann et al. (2018) consider a disk with a Gaussian radial profile, for which the half-light radius, R , isobtained from the reported Gaussian sigma, r s , through R = 1 . r s . z grav = ∆ λλ (cid:39) Gc M BH R , (2)and, M BH (cid:39) c G ∆ λλ R = (cid:16) z grav . (cid:17) (cid:18) R
10 light days (cid:19) (cid:0) . × M (cid:12) (cid:1) . (3)Susbtituting in Equation 3 the mean redshift of the iron lines and the microlensing basedsize, we obtain for the average mass of the supermassive black holes, (cid:104) M BH (cid:105) (cid:39) (0 . ± . × M (cid:12) , where the uncertainty arises partly from the method and partly from theintrinsic scatter between objects. This value is in good agreement, in mean and scatter,with virial based estimates for lensed quasars (see, e.g., Figure 8 of Mosquera et al. 2013).In fact, if we consider the 8 lensed quasars in our sample (HE 0047-1756, SDSS 0246-0285,SDSS 0924+0219, FBQ 0951+2635, Q 0957+561, HE 1104-1805, SDSS 1335+0118 and HE2149-2745) that have virial mass estimates by Peng et al. (2006) and Assef et al. (2011),we obtain from Eq. 3, (cid:104) M microBH (cid:105) (cid:39) (0 . ± . × M (cid:12) , in very good agreement with theaverage of their virial masses, (cid:104) M virialBH (cid:105) (cid:39) . × M (cid:12) .Because of the interesting implications of these results, and to exclude any systematicissue in our sample of lensed quasars, we fit the Fe III λλ ∼ λ λλ λ λ λλ z = ∆ λ/λ , of these features are: 0 . ± . λλ . ± . λ . ± . λλ σ/λ , we obtain: 0 . ± . λλ . ± . λ . ± . λλ λλ χ red ≤
2, although some of the spectra have a low S/N ratio. We can use BOSS compositesto discuss virialization. If the kinematics is virialized (Eq. 1), we should have, 7 –
G M BH R = f (∆ v ) = f (cid:16) σλ (cid:17) c , (4)where we have taken σc/λ as representative of the line broadening , ∆ v . Combining Eq. 4with the expression for the mass in terms of the redshift (Eq. 2), we obtain,∆ λλ = 32 f (cid:16) σλ (cid:17) . (5)Taking logarithms, we can write this condition of virialized kinematics in a linear shapeconvenient for quantitative fitting,log (cid:16) σλ (cid:17) = − log 3 f (cid:18) ∆ λλ (cid:19) . (6)The measured redshifts, z = ∆ λ/λ , and widths of the Fe III lines, (cid:0) σλ (cid:1) , obtained from theBOSS composite spectra (excluding the cases with S/N < .
0) follow this correlation thoughwith a relatively high scatter (Figure 5). Fitting Eq. 6 to the data we obtain (R-squared ∼ . (cid:16) σλ (cid:17) = − . ± .
64 + (0 . ± .
26) log (cid:18) ∆ λλ (cid:19) . (7)The large uncertainties in the fit parameters (Eq. 7) can have an intrinsic origin, for thevirial factors, f , can be significantly different from system to system depending on physicalunknowns like the flatness of the emitter’s distribution, its orientation, or the presence ofnon gravitational forces (e.g., radiation pressure). It is likely that the criteria to form theBOSS composites may be biased with respect to any of these unknowns giving rise to anintrinsic scatter in f . On the other hand, radial motions may also contribute to the redshiftin a variable way from object to object, increasing the scatter. In any case, alternativeexplanations (inflow, for instance, may be another mechanism giving rise to the redshifts)would need additional physics to explain the observed trend between broadening and red-shift. Thus, while a tight correlation between ∆ λ/λ and (cid:0) σλ (cid:1) is not generally expected, thetrend found between these two quantities among the composite spectra of BOSS supportsthe gravitational interpretation of the Fe III λλ For our Gaussian based fits, σ = F W HM/ .
35 but in many applications of the virial theorem based onemission-line profiles, σ is the second moment of the experimental line profile, and F W HM/σ depends onthe profile shape (Collin et al. 2006). λλ λ c = (cid:104) λ (cid:105) , in eachcomposite spectrum. The standard deviation between the redshift measurements based oneither the fit of the template or the centroid of the blend is ∼ . − , randomly dis-tributed between blue- and red-shifts while we are measuring exclusively redshifts of aboutone thousand km s − . In addition, this problem should be mitigated in the case of BOSScomposites resulting from the average of many spectra.
3. Discussion: Black Hole Mass Estimates Based on Fe III λλ Under the hypothesis that the redshift of the Fe III λλ R F eIII can be obtained (see Eq. 3). We are going to consider three differentmethods for computing sizes: reverberation mapping, scaling of the size of the BLR withluminosity and gravitational microlensing. λλ NGC 5548 is a widely studied AGN for which reverberation mapping has yielded es-timates of the size for the continuum and several strong emission lines (see, e.g., Clavel etal. 1991, Korista et al. 1995, Peterson et al. 2002; see also Pei et al. 2017 and referencestherein).We fit the Fe III λλ Notice, however, that some common conceptions about this AGN could change if the suspected existenceof a supermassive BH binary in the center of this galaxy (Li et al. 2016) is confirmed. λ . ± . . ± .
4) days whenthe centroid (peak) of the cross correlation centroid (peak) distribution CCCD (CCPD)is taken as reference. The errors have been estimated applying flux randomization MonteCarlo methods. Adopting these lags as estimates of R F eIII and using the measurement of theredshift from the fit to the average spectra, z grav ( F eIII ) = (∆ λ/λ ) F eIII = 0 . ± . M BH = 2 . +0 . − . × M (cid:12) ( M BH = 1 . +1 . − . × M (cid:12) ) for the centroid (peak). Thesevalues are relatively large but in agreement within uncertainties with recent estimates ofthe black hole mass derived from the virial theorem ( M = 1 . +0 . − . × M (cid:12) , Ho & Kim,2015; M = 6 . +2 . − . × M (cid:12) , Pei et al 2017), taking into account a 30% uncertainty in theaverage virial factor f (Woo et al. 2015), and the intrinsic scatter between objects (0.35 dexaccording to Ho & Kim 2015).We also fit the Fe III λλ z grav ( F eIII ) = 0 . ± . ∼ . M BH ≤ . +0 . − . × M (cid:12) , compatible with previousvirial estimates ( M = 1 . +0 . − . × M (cid:12) , Ho & Kim, 2015, 1 − × M (cid:12) , Shapovalova et al.2017).Finally, it is also important to stress that, once the size is known via reverberationmapping, the mass of the object is directly obtained from the redshift without using anyprevious calibration, i.e., in combination with reverberation mapping, the gravitational red-shfit of the Fe III λλ primary method to determine masses. In fact,because gravitational redshift does not depend on geometrical considerations, it may becomethe primary calibrator of all the other methods used to measure the mass of the BH. λλ Reverberation mapping is an observationally expensive technique to estimate sizes. Analternative is to use the scaling of the size of the BLR with luminosity, R ∝ ( λL λ ) α (Kaspi etal. 2000, 2005). In combination with the line width of the BLR lines as an estimator of thevirial velocity, empirical BH mass calibrations, M BH ∝ F W HM ( λL λ ) α , can be obtained.The most reliable R − L λ relationship is based on H β and L . Other determinations,related to H α , Mg II or CIV, are re-calibrated from the R ( Hβ ) − L relationship. In spite 10 –of some problems associated with it (see, e.g., Mej´ıa-Restrepo et al. 2016), the calibrationusing the CIV line is important because it is the only prominent broad emission line thatlies within the optical window at high-z as is the case in many of the objects we studied.Specifically, for high redshift quasars, BH masses can be estimated from the CIV λ (Mej´ıa-Restrepo et al. 2016), M BH ( CIV ) = 10 . ± . (cid:18) F W HM
CIV km s − (cid:19) (cid:18) λL λ (1450 ˚A)10 erg s − (cid:19) . ± . M (cid:12) . (8)Thus, we can use the F W HM
CIV measurements available for the BOSS composites (Jensenet al. 2016) to re-calibrate Eq. 8 in terms of the Fe III gravitational redshift . Onaverage, we find for the BOSS composite spectra: < F W HM CIV > = (0 . ± . < (cid:112) z grav ( F eIII ) > c , where the uncertainty is the standard error in the mean. Substitutingthis in Eq. 8 we obtain a mass scaling relationship based on the gravitational redshift of FeIII, M BOSSBH ( F eIII ) = 10 . +0 . − . (cid:18) z grav ( F eIII ) c km s − (cid:19) (cid:18) λL λ (1350 ˚A)10 erg s − (cid:19) . ± . M (cid:12) . (9)To check the validity of this relationship, we compare in Figure 7 the mass estimates obtainedapplying Eq. 9 to the measured Fe III gravitational redshifts of the lensed quasars in oursample (Fian et al. 2018) with the virial based masses obtained by Peng et al. (2006) andAssef et al. (2011). We have 8 objects in common: HE 0047-1756, SDSS 0246-0285, SDSS0924+0219, FBQ 0951+2635, Q 0957+561, HE 1104-1805, SDSS 1335+0118 and HE 2149-2745. We have also included NGC 5548 and NGC 7469 in the plot (gravitational redshiftmasses obtained from Eq. 9 and virial masses from Vestergaard & Peterson 2006). Theglobal agreement over two orders of magnitude in mass is very noticeable, showing that theFe III λλ R ∝ L . , and (ii) use the available virial based mass estimates to calibrate The use of other standard calibrations (e.g. Vestergaard & Peterson 2006, Assef et al. 2011) do notsubstantially affect the results. This is supported by Eq.5 which relates broadenings and redshifts.
11 –our unscaled masses, µ = ( z grav ( F eIII ) c/ km s − ) (cid:0) λL λ (1350 ˚A) / erg s − (cid:1) . M (cid:12) .The relatively small value of the shift in the calibration, 0.04 dex, as compared with the 1 σ scatter of the masses with respect to the best fit, 0.26 dex, indicates that there is a goodagreement between the BOSS composite spectra based calibration and the independent cal-ibration that would be obtained fitting the virial masses. The 0.26 dex scatter of the massesrelative to the fit, also indicates that Eq. 9 is reliable taking into account that virial massesare themselves uncertain typically by ∼ . λλ ∼
200 SDSS individual quasars (S/N (cid:38)
20) shows that the redshift can bemeasured with a reasonable accuracy in 25% of them. This implies a number of potential BHmass determinations of more than one thousand from available and future quasar surveys. λλ Using microlensing based sizes, we can also estimate the BH masses directly from theequation of the redshift in the weak limit of the Schwarzschild metric (Eq. 3). We do nothave individual estimates of size for each object, but we can use the average microlensingsize estimated by Fian et al. (2018) re-scaling it by applying the R ∝ √ λL λ relationship: M BH (cid:39) c G ∆ λλ (cid:104) R (cid:105) √ λL λ (cid:104)√ λL λ (cid:105) . (10)This equation is, indeed, very similar to Equation 9 but has been derived on different grounds.Inserting the value of (cid:104) R (cid:105) from Fian et al. (2018) and the average of the square root of theluminosities of the quasars, (cid:104)√ λL λ (cid:105) , used by these authors to infer (cid:104) R (cid:105) , we can write, M BH (cid:39) ∆ λ . (cid:115) λL λ . erg s − × (0 . ± . × M (cid:12) . (11)It is convenient to rewrite this equation to compare it with the equivalent expression (Eq.9) based on the BOSS composite spectra calibration, M microBH ( F eIII ) = 10 . +0 . − . (cid:18) z grav ( F eIII ) c km s − (cid:19) (cid:18) λL λ (1350 ˚A)10 erg s − (cid:19) . M (cid:12) . (12) 12 –Thus, Eqs. 9 and 12 agree within uncertainties. This agreement is noteworthy takinginto account that the calibration of Eq. 11 (and hence Eq. 12) resides on gravitationalmicrolensing while Eq. 9 has been calibrated from the widths of the CIV lines of BOSScomposites. Figure 8 shows the good agreement, 0.27 dex of scatter (1 σ ), between the massestimates obtained using Eq. 11 and the virial masses. R ∝ L b Law.
Finally, it is also interesting to perform a fit of Equation 10 to the virial masses of our10 objects but now leaving free the exponent of the R-L relationship, R ∝ λL bλ . A changeof scale, a , is also allowed. Specifically we fit a and b parameters in,log (cid:18) M vir . × M (cid:12) (cid:19) = log (cid:18) a ∆ λ . (cid:19) + b log (cid:18) L λ (cid:104) λL bλ (cid:105) /b (cid:19) , (13)where (cid:104) λL bλ (cid:105) is computed taking into account all the objects used by Fian et al. (2018) toestimate the average microlensing size. We obtain a = 1 . ± . b = 0 . ± .
08. That is,Eq. (10) agrees within uncertainties with the best fit to virial masses. To show this explicitlywe can, once more, write Eq. 13 as, M best fitBH ( F eIII ) = 10 . +0 . − . (cid:18) z grav ( F eIII ) c km s − (cid:19) (cid:18) λL λ (1350 ˚A)10 erg s − (cid:19) . ± . M (cid:12) , (14)in agreement within uncertainties with both, M microBH (Eq. 12) and M BOSSBH (Eq 9). In Figure9 we compare the results of M bestfitBH with the virial masses (1 σ = 0 .
26 dex).Thus, according to the results discussed in sections 3.2, 3.3 and 3.4, from three differentmethods (Eqs. 9, 12 and 14), we have obtained consistent (within uncertainties) coefficientsof the relationship that scales the masses of the BH with redshift and luminosity.
4. Conclusions
We have studied the Fe III λλ λλ λ λλ λλ (cid:104) M BH (cid:105) (cid:39) (0 . ± . × M (cid:12) , in goodagreement with previous virial based estimates.4 - We present a scaling relationship of mass with redshift and luminosity useful tomeasure the BH mass of one individual object from a single spectrum. This relationshipcan be formally derived from the Schwarzschild metric and is consistently calibrated usingthree different methods: the broadening of the CIV lines of the BOSS composite spectra, thestrength of gravitational microlensing in the Fe III UV lines, and the best fit to the availablevirial masses. The two first methods are completely independent and the estimated massesusing any of them are in statistical agreement with virial masses over two orders of magnitude(1 σ scatter of 0.27 dex comparable to the intrinsic scatter of the virial masses).5 - If the gravitational redshift hypothesis is correct, the application of the scalingrelationship to spectra of available quasar surveys will provide thousands of estimates of su-permassive BH masses. Future mass estimates based on the Fe III redshift and reverberationmapping may become the primary calibrator for all BH mass measurement methods.Although the good matching between the masses derived from the measured redshiftsof the Fe III λλ λλ REFERENCES
Anderson, K. S. 1981, ApJ, 246, 13Assef, R. J., Denney, K. D., Kochanek, C. S., et al. 2011, ApJ, 742, 93Bentz, M. C., Peterson, B. M., Netzer, H., Pogge, R. W., & Vestergaard, M. 2009, ApJ, 697,160Bon, N., Bon, E., Marziani, P., & Jovanovi´c, P. 2015, Ap&SS, 360, 7Chang, K., & Refsdal, S. 1979, Nature, 282, 561Chang, K., & Refsdal, S. 1984, A&A, 132, 168Clavel, J., Reichert, G. A., Alloin, D., et al. 1991, ApJ, 366, 64Collin, S., Kawaguchi, T., Peterson, B. M., & Vestergaard, M. 2006, A&A, 456, 75Corbin, M. R. 1997, ApJ, 485, 517Ferland, G. J., Hu, C., Wang, J.-M., et al. 2009, ApJ, 707, L82Ferrarese, L., & Merritt, D. 2000, ApJ, 539, L9Fian, C., Guerras, E., Mediavilla, E., et al. 2018, arXiv:1805.09619Gebhardt, K., Bender, R., Bower, G., et al. 2000, ApJ, 539, L13 15 –Guerras, E., Mediavilla, E., Jimenez-Vicente, J., et al. 2013a, ApJ, 764, 160Guerras, E., Mediavilla, E., Jimenez-Vicente, J., et al. 2013b, ApJ, 778, 123Harris, D. W., Jensen, T. W., Suzuki, N., et al. 2016, AJ, 151, 155Ho, L. C., & Kim, M. 2014, ApJ, 789, 17Ho, L. C., & Kim, M. 2015, ApJ, 809, 123Hu, C., Wang, J.-M., Ho, L. C., et al. 2008, ApJ, 687, 78-96Jensen, T. W., Vivek, M., Dawson, K. S., et al. 2016, ApJ, 833, 199Joni´c, S., Kovaˇcevi´c-Dojˇcinovi´c, J., Ili´c, D., & Popovi´c, L. ˇC. 2016, Ap&SS, 361, 101Kaspi, S., Smith, P. S., Netzer, H., et al. 2000, ApJ, 533, 631Kaspi, S., Maoz, D., Netzer, H., et al. 2005, ApJ, 629, 61Kollatschny, W. 2003, A&A, 412, L61Korista, K. T., Alloin, D., Barr, P., et al. 1995, ApJS, 97, 285Kovaˇcevi´c, J., Popovi´c, L. ˇC., & Dimitrijevi´c, M. S. 2010, ApJS, 189, 15Kovaˇcevi´c-Dojˇcinovi´c, J., & Popovi´c, L. ˇC. 2015, ApJS, 221, 35Kriss, G. A., Peterson, B. M., Crenshaw, D. M., & Zheng, W. 2000, ApJ, 535, 58Li, Y.-R., Wang, J.-M., Ho, L. C., et al. 2016, ApJ, 822, 4Liu, H. T., Feng, H. C., & Bai, J. M. 2017, MNRAS, 466, 3323McConnell, N. J., & Ma, C.-P. 2013, ApJ, 764, 184Mediavilla, E., & Insertis, F. M. 1989, A&A, 214, 79Mej´ıa-Restrepo, J. E., Trakhtenbrot, B., Lira, P., Netzer, H., & Capellupo, D. M. 2016,MNRAS, 460, 187Mosquera, A. M., Kochanek, C. S., Chen, B., et al. 2013, ApJ, 769, 53Netzer, H. 1977, MNRAS, 181, 89PPei, L., Fausnaugh, M. M., Barth, A. J., et al. 2017, ApJ, 837, 131 16 –Peng, C. Y., Impey, C. D., Rix, H.-W., et al. 2006, ApJ, 649, 616Peterson, B. M., Meyers, K. A., Carpriotti, E. R., et al. 1985, ApJ, 292, 164Peterson, B. M. 1993, PASP, 105, 247Peterson, B. M., Berlind, P., Bertram, R., et al. 2002, ApJ, 581, 197Peterson, B. M., Ferrarese, L., Gilbert, K. M., et al. 2004, ApJ, 613, 682Peterson, B. M. 2006, Astronomical Society of the Pacific Conference Series, 360, 191Peterson, B. M. 2014, Space Sci. Rev., 183, 253Popovic, L. C., Vince, I., Atanackovic-Vukmanovic, O., & Kubicela, A. 1995, A&A, 293, 309Salpeter, E. E. 1964, ApJ, 140, 796Shapovalova, A. I., Popovi´c, L. ˇC., Chavushyan, V. H., et al. 2017, MNRAS, 466, 4759Sulentic, J. W. 1989, ApJ, 343, 54Sulentic, J. W., Marziani, P., Zamfir, S., & Meadows, Z. A. 2012, ApJ, 752, L7Tremaine, S., Gebhardt, K., Bender, R., et al. 2002, ApJ, 574, 740Vanden Berk, D. E., Richards, G. T., Bauer, A., et al. 2001, AJ, 122, 549Vestergaard, M., & Wilkes, B. J. 2001, ApJS, 134, 1Vestergaard, M., & Peterson, B. M. 2006, ApJ, 641, 689Wambsganss, J. 2006, Saas-Fee Advanced Course 33: Gravitational Lensing: Strong, Weakand Micro, 453Woo, J.-H., Yoon, Y., Park, S., Park, D., & Kim, S. C. 2015, ApJ, 801, 38Zel’dovich, Y. B. 1964, Soviet Physics Doklady, 9, 195Zheng, W., & Sulentic, J. W. 1990, ApJ, 350, 512Zu, Y., Kochanek, C. S., & Peterson, B. M. 2011, ApJ, 735, 80
This preprint was prepared with the AAS L A TEX macros v5.2.
17 –Fig. 1.— Fits to the Fe III λλ σ ,and shift, d = ∆ λ , of the iron lines are indicated for each spectrum (in ˚A). The continuous(dashed) curve corresponds to the data (fit). Vertical dashed lines are located at the wave-lengths corresponding to the Fe III lines of the Vestergaard & Wilkes (2001) template atrest. The spectra have been shifted by an amount − d to match the template rest frame. 18 – ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) Fig. 2.— Fits of three UV iron features, Fe III λλ λλ λλ λ λ ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) Fig. 3.— Fits of the Vestergaard & Wilkes (2001) template to the 27 composite spectra ofthe BOSS survey. Open circles correspond to the data, the blue line to the template andthe other lines to the Gaussians representing each of the Fe III lines. The number of eachcomposite is indicated and, in parentheses, the reduced chi-squared value, χ red (see text). 20 – ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ λ Å F l u x ( a r b i t r a r y un i t s ) ( ) Fig. 4.— Continuation of Figure 3. 21 – - - - - - - - - - - Δλλ l og σ λ Fig. 5.— Fe III λλ (cid:0) σλ (cid:1) , versus redshift, ∆ λλ , obtained from thecomposite spectra of the BOSS survey with S/N >
3. The straight line is the best fit to thedata points (see text). 22 – F l u x ( a r b i t r a r y un i t s )
10 5 0 5 10Lag (days)0.80.60.40.20.00.20.40.60.81.0 CC F Fig. 6.— Reverberation lag of Fe III λλ λλ M vir M ⊙ l og M g r a v M ⊙ Fig. 7.— Comparison between the virial and gravitational redshift based masses (calibrationbased on the widths of the CIV lines in the BOSS composite spectra). The solid linecorresponds to M BOSSgrav = M vir . The dashed line corresponds to the best linear fit to thedata with slope unity. The small separation between both lines indicates the good agreementbetween the BOSS based calibration and the calibration that would be obtained using thevirial based mass estimates (see text). Errors in M vir are from Assef et al. (2011) orcorrespond to the dispersions of the virial relationships (Peng et al. 2006, Vestergaard &Peterson 2006). Errors in M BOSSgrav include a (conservative) error of ± . M vir M ⊙ l og M g r a v M ⊙ Fig. 8.— Comparison between the virial and gravitational redshift based masses (cali-brated using microlensing to determine a reference size). The continuous line correspondsto M micrograv = M vir . The dashed line corresponds to the best linear fit to the data with slopeunity. The very small separation between both lines indicates the excellent agreement be-tween the microlensing based calibration and the calibration that would be obtained usingthe virial based mass estimates. Errors in M vir are from Assef et al. (2011) or correspond tothe dispersions of the virial relationships (Peng et al. 2006, Vestergaard & Peterson 2006).Errors in M micrograv include the scatter in the estimate of the average gravitational redshift, theerror in the microlensing estimate of the size, and 0.13 dex of intrinsic scatter in the R-Lrelationship (Peterson 2014). 25 – M vir M ⊙ l og M g r a v M ⊙ Fig. 9.— Best fit of the mass scaling relationship based on the redshift to the virial massesleaving free the R ∝ L b law. The continuous line corresponds to M best fitgrav = M vir . The bestlinear fit to the data with slope unity is indistinguishable from this line. Errors in M best fitvir are from Assef et al. (2011) or correspond to the dispersions of the virial relationships(Peng et al. 2006, Vestergaard & Peterson 2006). Errors in M best fitgravbest fitgrav