H0LiCOW VII. Cosmic evolution of the correlation between black hole mass and host galaxy luminosity
Xuheng Ding, Tommaso Treu, Sherry H. Suyu, Kenneth C. Wong, Takahiro Morishita, Daeseong Park, Dominique Sluse, Matthew W. Auger, Adriano Agnello, Vardha N. Bennert, Thomas E. Collett
MMNRAS , 1–14 (2017) Preprint 5 September 2017 Compiled using MNRAS L A TEX style file v3.0
H0LiCOW VII. Cosmic evolution of the correlationbetween black hole mass and host galaxy luminosity
Xuheng Ding, , , (cid:63) Tommaso Treu, Sherry H. Suyu, , , Kenneth C. Wong, Takahiro Morishita, , , Daeseong Park, Dominique Sluse, Matthew W. Auger, Adriano Agnello, , Vardha N. Bennert, Thomas E. Collett School of Physics and Technology, Wuhan University, Wuhan 430072, China Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095-1547, USA Department of Astronomy, Beijing Normal University, Beijing 100875, China Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan Physik-Department, Technische Universit¨at M¨unchen, James-Franck-Straße 1, 85748 Garching, Germany National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Astronomical Institute, Tohoku University, Aramaki, Aoba, Sendai 980-8578, Japan Institute for International Advanced Research and Education, Tohoku University, Aramaki, Aoba, Sendai 980-8578, Japan Korea Astronomy and Space Science Institute, Daejeon, 34055, Republic of Korea STAR Institute, Quartier Agora - All´ee du six Aoˆut, 19c B-4000 Li`ege, Belgium Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK European Southern Observatories, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany Physics Department, California Polytechnic State University, San Luis Obispo CA 93407, USA; [email protected] Institute of Cosmology and Gravitation, University of Portsmouth, Burnaby Rd, Portsmouth PO1 3FX, UK
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Strongly lensed active galactic nuclei (AGN) provide a unique opportunity to makeprogress in the study of the evolution of the correlation between the mass of super-massive black holes ( M BH ) and their host galaxy luminosity ( L host ). We demonstratethe power of lensing by analyzing two systems for which state-of-the-art lens mod-elling techniques have been applied to deep Hubble Space Telescope imaging data. Weuse i) the reconstructed images to infer the total and bulge luminosity of the hostand ii) published broad-line spectroscopy to estimate M BH using the so-called virialmethod. We then enlarge our sample with new calibration of previously publishedmeasurements to study the evolution of the correlation out to z ∼ .
5. Consistentwith previous work, we find that without taking into account passive luminosity evo-lution, the data points lie on the local relation. Once passive luminosity evolution istaken into account, we find that BHs in the more distant Universe reside in less lumi-nous galaxies than today. Fitting this offset as M BH / L host ∝ (1 + z ) γ , and taking intoaccount selection effects, we obtain γ = 0 . ± . . ± . M BH - L bulge and M BH - L total , respectively. To test for systematic uncertainties and selectioneffects we also consider a reduced sample that is homogeneous in data quality. We findconsistent results but with considerably larger uncertainty due to the more limitedsample size and redshift coverage ( γ = 0 . ± . . ± . M BH - L bulge and M BH - L total , respectively), highlighting the need to gather more high-quality data forhigh-redshift lensed quasar hosts. Our result is consistent with a scenario where thegrowth of the black hole predates that of the host galaxy. Key words: galaxies: evolution — black hole physics — galaxies: active (cid:63)
E-mail: [email protected]
It is commonly accepted that almost all the galaxies have asupermassive black hole (BH) in their center, whose mass c (cid:13) a r X i v : . [ a s t r o - ph . GA ] S e p X. Ding et al. ( M BH ) is known to be correlated with the host proper-ties. The tight correlations are usually, but not uniquely,explained as the results of their co-evolution (e.g., Magor-rian et al. 1998; Ferrarese & Merritt 2000; Gebhardt et al.2001; Marconi & Hunt 2003; H¨aring & Rix 2004; G¨ultekinet al. 2009; Graham et al. 2011; Beifiori et al. 2012; Parket al. 2015; Kormendy & Ho 2013) (see, however, Peng 2007;Jahnke & Macci`o 2011, for a different view). A powerful wayto explore the origin of this physical coupling and under-stand the role of active galactic nuclei (AGN) feedback ingalaxy formation is to measure the correlations directly athigh redshift and determine how and when they emerged andevolved over cosmic time (e.g., Treu et al. 2004; Salvianderet al. 2006; Woo et al. 2006; Jahnke et al. 2009; Schramm &Silverman 2013; DeGraf et al. 2015).The most common technique used to estimate M BH beyond the local Universe ( z > .
1) is the so-called virialmethod, based on the properties of broad emission lines intype 1 AGN (Shen 2013; Peterson 2014). However, the brightsource associated with the AGN makes the study of its hostgalaxy very difficult. Strong gravitational lensing (see, e.g.,Courbin et al. 2002; Schneider et al. 2006; Treu 2010; Treu& Ellis 2015, for reviews) stretches the host galaxy out fromthe wings of the bright point source as point spread function(PSF), providing a unique opportunity to infer its magni-tude robustly (Peng et al. 2006). However, in order to mea-sure host luminosity ( L host ) and construct the M BH - L host correlation from strongly lensed AGN, it is necessary to en-sure that any systematic uncertainties associated with thegravitational lens model can be controlled to the desiredlevel of accuracy.Recently, Ding et al. (2017) studied the fidelity of themeasurement of lensed AGN host brightness through a set ofextensive and realistic simulations of Hubble Space Telescope observation and lens modeling. First, the mock images of thelensed AGNs in our sample (see Ding et al. (2017), Table1) were generated as realistically as possible. Second, thesimulated AGN host galaxy images were reconstructed withthe state-of-the-art lens modelling tool ( glee ). Third, byfitting the host magnitude with the software galfit (Penget al. 2002) and comparing the inference to the input value,Ding et al. (2017) found that the L host can be recovered withbetter accuracy and precision than the uncertainty on singleepoch M BH estimates ( ∼ . − − − with thegoal of measuring cosmological parameters from gravita-tional time delays (Suyu et al. 2017; Bonvin et al. 2017). M BH is inferred by applying a set of self-consistent calibra-tions of the virial method to the broad emission line proper-ties measured by Sluse et al. (2012). In addition, we combineour new measurements with a large sample of AGNs taken Developed by Suyu & Halkola (2010) based on Suyu et al.(2006) and Halkola et al. (2008). H Lenses in COSMOGRAIL’s Wellspring, . from the literature and consistently recalibrated, and studythe evolution of the M BH - L host relation for 146 objects inthe redshift range 0 < z < .
5. It is still unclear whether thebulge or the total luminosity provides the tightest correla-tion with M BH (Jahnke et al. 2009; Bennert et al. 2011b;Park et al. 2015). Thus, we consider both of them in thisstudy.This paper is organized as follows. We briefly describethe sample selection in Section 2. The host galaxy sur-face photometry and the M BH are inferred in Section 3and 4, respectively. In Section 5, we present our main re-sult. Discussion and conclusion are presented in Section 6and 7. Throughout this paper, we adopt a standard concor-dance cosmology H = 70 km s − Mpc − , Ω m = 0 .
30, andΩ Λ = 0 .
70. Magnitudes are given in the AB system.
First, we analyze the two quadruply-imaged AGNHE0435 − − .
693 and 0 . L host .Second, we combine and compare our new measure-ments with those by Peng et al. (2006) (hereafter, P06).P06 explored the M BH - L host based on 20 non-lensed AGNsand 31 gravitationally lensed AGNs (including HE0435 andRXJ1131). P06 is so far the only paper in which the M BH - L host relation has been comprehensively investigated usinglensed AGNs observed with HST . We note that for the twosystems in common, the
HST images used in our work aremuch deeper than those used by P06, and the lens modelsare much more detailed. Also, P06 was based on NIC2 im-ages, as opposed to the much more powerful more moderncameras used in our work. Therefore, our measurements su-percede those by P06 for these two systems. Furthermore, weexclude MG 2016+112 because it is a type II AGN (Koop-mans et al. 2002) and the black hole mass using the virialmethod cannot be considered reliable. We also exclude thelens system B2045+265 used by P06 because of the incorrectredshift identification of the AGN spectrum by Fassnachtet al. (1999) (Nierenberg et al. 2017, in preparation).Third, we combine our new measurements with sam-ples of non-lensed AGN that have been measured by mem-bers of our team using the same techniques as those appliedhere. The samples consist of 52 intermediate redshift AGNs(0 . < z < .
57) summarized by Park et al. (2015) (here-after P15), 27 distant AGNs (0 . < z < .
9) measured byBennert et al. (2011b) and Schramm & Silverman (2013)(hereafter, B11 and SS13), and 19 local AGNs measurements(Bennert et al. 2010; Peterson et al. 2004). It is worth notic-ing that they are so far the largest
HST imaging sampleswhich are carefully selected as moderate-luminosity AGN,for which the contrast between nucleus and host galaxies ismuch more favorable for the inference of L host than for highluminosity lensed quasars. Thus, their host luminosities aremeasured with high accuracy even without lensing. MNRAS000
HST imaging sampleswhich are carefully selected as moderate-luminosity AGN,for which the contrast between nucleus and host galaxies ismuch more favorable for the inference of L host than for highluminosity lensed quasars. Thus, their host luminosities aremeasured with high accuracy even without lensing. MNRAS000 , 1–14 (2017) osmic evolution of M BH - L host Overall, our sample consists of two new lensed systemsand active galaxies from the literature, including ellipticaland spiral hosts with redshift up to 4.5. This total sampleof 146 objects is the largest compilation of AGNs from
HST which are cross-calibrated to study the M BH - L host relation.The objects and their basic properties are listed in Tab. 1and 2. In this section, we describe the measurement of host lumi-nosity. For HE0435 and RXJ1131, we first derived their hostmagnitude from the reconstructed surface brightness mapsin the source plane. Then, we inferred the rest-frame R-band luminosities based on their spectral energy distribution(SED). For the other AGNs, we collected and homogenizedtheir luminosities from the literature.
We used the software galfit to model the reconstructionsfrom Wong et al. (2017) and Suyu et al. (2013). The recon-struction of HE0435 was fitted as the S´ersic profile with n limited between 1 −
4. It has been tested that this prior on n does not bias the inference of magnitude (Ding et al. 2017).In the case of RXJ1131 a clearly visible residual image waspresent and the resulting parameters were physically accept-able when fitted with an additional profile, we concludedthat the host galaxy is composed of a disk and a bulge.In this case, we fixed the reconstruction as two-componentS´ersic profiles with n equals to 1 and 4, corresponding to ex-ponential disk profile and de Vaucouleurs (1948) profile, re-spectively. Although the luminosities of lens systems are cor-rected from lensing magnification using a lens model, smalldifferences exist between models of different groups. The de-rived magnification rarely differs by more than 20%. Accord-ing to detailed simulations presented by Ding et al. (2017),the inferred values of L host can be recovered with sufficientaccuracy and precision to study the M BH - L host relation us-ing our approach. Finally, we derived the rest-frame R-bandluminosity using a standard K-correction. These steps aredescribed below in more detail for each system. HE0435 was imaged with
HST /WFC3-IR through filterF160W from program
HST -GO-12889 (PI: S. H. Suyu).Wong et al. (2017) produced a set of twelve reconstructionsfor this system, based on different assumptions, in order toestimate the amplitude of systematic errors associated withthese choices. In 9/12 cases the source plane resolution wasset to 40 ×
40 pixels. For the other three cases a higher res-olution of 50 ×
50 pixels was adopted. The reconstructionswere based on an image plane size of ∼ . (cid:48)(cid:48) m host = 21 . ± .
13; the inferred effective radius and S´ersicindex are R eff = 0 . ± .
14 arcsecond; n = 3 . ± .
14, asshown in Tab. 3. Furthermore, to test the type of the host
Table 3.
The inference of HE0435 and RXJ1131.Object magnitude R eff S´ersic index ( n )(arcsec)HE0435 21 . ± .
13 0 . ± .
14 3 . ± . disk . ± .
06 0.84 ± .
09 fixed 1RXJ1131 bulge . ± .
28 0.20 ± .
08 fixed 4 -0.042 0.01 0.062 0.11 0.17 0.22 0.27 0.32 0.38 0.43 0.48 (a) Lens reconstruction of HE0435 (left), the best-fit by galfit (mid-dle) and residual image (right). (b) Observed image of HE0435 (left) and simulationwith key parameters equal to inferred value (right).
Figure 1.
Illustration of the surface photometry study ofHE0435, presented with the same stretch for each panel, basedon
HST /WFC3-IR images through filter F160W. galaxy, we fitted the reconstructions as two-component S´er-sic profile. However, we obtained unphysical results and noimprovements in the fit indicating that the host galaxy ofHE0435 is consistent with being a pure elliptical. One ex-ample of the reconstruction and its corresponding galfit best-fit are shown in Fig. 1, panel (a). We also note thatthere is a small structure at the lower left of the host. How-ever, its brightness is negligible compared to the host whichdo not affect the inference of the L host . Interestingly, thiscould correspond tidal features in the host galaxies. If true,the mergers could be related to triggered AGN activity. Itis beyond the scope of this work to pursue this further, butit would be intriguing to simulate the hosts with mergersignature and to see if they can be recovered in the sourcereconstruction.We can verify the accuracy of our result by carrying outsimulations as described in our previous paper (Ding et al.2017), using our inferred parameters as input. The observedand simulated HE0435 images are shown in Fig. 1, panel(b). By repeating the analysis on the simulated image, werecover the input value (input: m host = 21 .
75 mag; output21.88 mag) showing an accuracy much better than our target1.25 mag (0.5 dex). We note that while in the simulations thePSF is assumed to be perfectly known, for the real data thePSF is inferred from the data using an iterative correctionprocedure (see Chen et al. 2016; Wong et al. 2017, Suyu etal. in preparation).Following P06, we made no corrections for dust extinc-
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X. Ding et al. tion of the host galaxy because they are likely to be small fora pure elliptical. The observed magnitudes were then trans-formed to rest-frame R-band by applying K-correction withSbc template spectrum, using Coleman et al. (1980) tem-plates. We used the Sbc template because the stellar popula-tions cannot be older than a few Gyrs at this redshift and thelocal elliptical template would be too red. Nevertheless, sincethe HE0435 is observed through the F160W filter, whichroughly corresponds to the rest-frame R-band at z ∼ . L host of HE0435 in rest-frame R-band is log L host = 10 .
96 which isvery close to the one inferred in P06 (i.e. log L host = 11 . HST
Advanced Camerafor Surveys (ACS) in the filter F555W and F814W are alsoavailable from Wong et al. (2017). Unfortunately, due to theshort exposure time, the signal to noise ratio of the recon-structed host images in these bands is insufficient to inferthe luminosity robustly in these bands and study the colorsof the host. Thus they are not considered in this study.
RXJ1131 is imaged with
HST /ACS through filter F814W.A set of seven source resolutions including 50 ×
50, 52 × ×
54, 56 ×
56, 58 ×
58, 60 ×
60, and 64 ×
64 pixels were se-lected when modelling the host image into source plane(Suyu et al. 2013), with a frame size of ∼ . (cid:48)(cid:48) .As noted by Suyu et al. (2013), all the reconstructionof the host show a compact peak near the center (see Fig. 2,panel (a), left panel), exhibiting the boundary line betweenthe dominated area of bulge and disk which indicates thehost galaxy is a spiral galaxy. Similarly, Claeskens et al.(2006) reconstructed the host of RXJ1131 and found it tobe a spiral, disk dominated galaxy. Thus, we fitted the re-constructions as two-component S´ersic profiles, and the in-ferred properties of the disk are m disk = 20 . ± .
06 mag; R eff disk = 0 . ± .
09 arcsecond and the properties of thebulge are m bulge = 21 . ± .
28 mag; R eff bulge = 0 . ± . m host and R eff ) equal to the inferred values. The realand mock RXJ1131 image are shown in Fig. 2, panel (b).We first use a single S´ersic profile to fit the reconstruction,but applying this model is a poor representation with anobvious residual in the central image (i.e. Fig. 2, panel (c),left). This result suggests the lens model of RXJ1131 recon-structs the host with sufficiently high resolution to distin- Suyu et al. (2014) updated the model of RXJ1131. Given thesimilarity in the composite and power-law model by Suyu et al.(2014), a similar time delay distance is obtained (within ∼ ∼ -0.44 0.11 0.66 1.2 1.8 2.3 2.9 3.4 4 4.5 5.1 (a) Source plane reconstruction of RXJ1131 (left), the best-fit by galfit using a two-S´ersic components profile (middle) and residualimage (right). -0 17 34 51 67 84 101 118 135 152 168 (b) Observed image of RXJ1131 (left) and simulatedimages with key parameters equal to inferred value(right). -0.37 -0.19 -0.013 0.17 0.34 0.52 0.7 0.88 1.1 1.2 1.4 (c) Residual map of modelling the simu-lated reconstruction with single (left) and two-component (right) profile. Figure 2.
Illustration of the surface photometry study ofRXJ1131, presented with the same stretch for each panel, basedon
HST /ACS images through filter F814W. guish a bulge+disk model from a single component. Fittingwith two-component S´ersic profile, we find that the residualmap is much improved and both components can be recon-structed accurately with our data and analysis techniques:input m disk = 20 .
07 mag and m bulge = 21 .
80 mag; inferredvalues are m disk = 20 .
37 mag and m bulge = 22 .
07 mag.As for HE0435, we derived the rest-frame R-band mag-nitude using a standard K-correction. At the redshift ofRXJ1131, the conversion to R-band magnitude depends sig-nificantly on the adopted SED. Therefore, we determinedthe K-correction directly from the color of lensed host arc,based on the multi-band SED fitting available in the archive(GO-9744; PI: C. S. Kochanek). The final estimations are∆mag disk (R − F814W) ≈ − . bulge (R − F814W) ≈− .
7. For detail, see Appendix A.
In this section we describe our inference of the rest-frameR-band luminosity for the P06 and P15 samples.P06 used the galfit (for non-lensed source) and lens-
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MNRAS000 , 1–14 (2017) osmic evolution of M BH - L host fit (for lensed source) softwares to infer the brightness ofthe AGN hosts, describing the host galaxy as single S´ersicprofile. In P06, they reported a single value of luminosity foreach object, suggesting that the host galaxies are ellipticals.However, in our analysis, we find the RXJ1131 is a spiralgalaxy which suggests the approach in P06 may not be ac-curate for all the host galaxies. We will return to this issuein Section 6. Their measurements of absolute magnitude arepresented by P06 (Tab 3 and 4 therein) in rest-frame R-band, Vega system. Thus, we transfer to AB system using m AB , R − m Vega , R = 0 .
21 (Blanton & Roweis 2007).Similarly, for the P15 sample, which includes the sam-ples from B11 and SS13, the host galaxy was fitted as a n = 4 profile to model the bulge component; an exponentialdisk profile was added if deemed necessary. The rest-frameV-band luminosity is derived (see P15, Tab. 4, Column 3)by applying the K-correction with an early-type galaxy tem-plate spectrum. The same template is taken, we convertedtheir results to rest-frame R-band. As the scatter in V-Rcolors is small, the associated uncertainty is estimated tobe 0.16 mag (i.e. 0.06 dex in luminosity). Likewise, the lu-minosities for 19 local active galaxies are converted to rest-frame R-band.Having obtained the R-band mag, the luminosity is de-rived by log L R /L R, (cid:12) = 0 . M R, (cid:12) − M R ), where M R, (cid:12) =4 .
61 (Blanton & Roweis 2007). We summarized the homog-enized R-band luminosities in Tab. 1 and 2.
Assuming that the dynamics of the broad-line region (BLR)is dominated by the gravity of the central supermassive blackhole, M BH can be derived by applying the so-called virialmethod, based on the size of the BLR ( R BLR ) and the line-of-sight velocity width (∆ V ) which can be inferred in turnfrom continuum luminosity and emission line width, respec-tively. Usually, the C IV ( λ II ( λ β ( λ λ L λ (1300˚A), λ L λ (3000˚A) and λ L λ (5100˚A) are used, respec-tively.Sluse et al. (2012), P06, and P15 used different lines anddifferent calibrations of the virial method. Thus we need tocross-calibrate them in order to avoid any systematic biasbetween the samples.We first choose the recipe of P15 as the baseline:log (cid:18) M BH M (cid:12) (cid:19) = 7 .
536 + 0 .
519 log (cid:18) λL erg s − (cid:19) + 2 log (cid:16) σ H β − (cid:17) . (1)Then we align the self-consistent recipes (including emissionlines using H β and Mg II ) from McGill et al. (2008) with thisbaseline, by adding a small constant to the intercept (i.e. − . IV -based estimator,we exploit the nine AGNs in our sample for which both Mg II and C IV are available. We take the C IV recipe from P06 andadd a small constant intercept (i.e. − . lensfit is a version of galfit that has been extended to fitlensed host galaxies while optimizing the mass model for the lensgalaxy. For details, see P06. average the value inferred from Mg II . Overall, we adopt thefollowing virial formalism:log (cid:18) M BH M (cid:12) (cid:19) = a + b log (cid:18) λ L λ line erg s − (cid:19) + 2 log (cid:18) FWHM(line)1000 km s − (cid:19) , (2)with a { C IV , Mg II , H β } = { } , b { C IV , Mg II ,H β } = { } , λ line { C IV , Mg II , H β } = { } . Having achieved a consistent cross-calibration,the M BH is estimated by adopting the emission line prop-erties measured by Sluse et al. (2012), P06 and P15.For the 19 local AGNs, rather than using continuumluminosity, R BLR was derived from time lags between con-tinuum and emission-line variations (Peterson et al. 2004).Thus, same as P15, we adopt the reverberation-mapping M BH measurements with virial factor (log f = 0 .
71, Parket al. 2012; Bentz et al. 2009), noting that they are theanchor for the virial method and thus are inherently self-consistent. M BH estimates are listed in Tab. 1 and 2, together withdetails on the emission line used. For RXJ1131, since theestimated M BH using Mg II and H β are very similar, weadopt their average. Moreover, we note that the values of M BH for HE0435 and RXJ1131 inferred in this paper arelarger than the estimates by P06 (∆ log M BH = 0 .
25 and0 .
44 for HE0435 and RXJ1131, respectively), due to the factthat the properties of the emission lines of these two systemshave been revised upwards by Sluse et al. (2012) based ondata of superior quality.
Following P15 and Ding et al. (2017), for the distant objects,we adopt total uncertainty for L host and M BH of 0.2 dex( ∼ M BH - L host relation The M BH - L bulge and M BH - L total relation defined by oursamples are shown in Fig. 3, panel (a) and (b). There is aclearly positive correlation between M BH and L host as inlocal samples. For a direct comparison to local samples, wefit the local M BH - L host as:log (cid:0) M BH M (cid:12) ) = α + β log( L R L (cid:12) ) . (3)Using a Markov Chain Monte Carlo (MCMC) process we de-rive α = 0 . ± . β = 0 . ± .
09 for the M BH - L bulge and α = 0 . ± . β = 0 . ± .
15 for the M BH - L total , with in-trinsic scatter σ int ∼ .
25 for both of them. Consistent withprevious work (e.g. P06, P15), the observed correlation athigh redshift is nearly identical to the local. This is perhapssurprising, considering that both the black hole mass andhost galaxy luminosity are expected to evolve over cosmictime. For example, in a minimal evolution toy model, the el-liptical galaxies and their black hole are formed at high red-shift and evolve passively thereafter. Thus, we expect L host to fade over time, owing to aging stellar populations. To al-low a direct comparison to the local samples, we consideredthis scenario in the next section. MNRAS , 1–14 (2017)
X. Ding et al. log ( L R,bulge /L fl ) l o g ( M B H / M fl ) log( M BH / M fl ) =0.68+0.74 log( L R / L fl ) assumed uncertainties (a) Observed, M BH − L bulge relation HE0435RXJ1131AGNs from P15 lensed AGNs in P06non-lensed AGNs in P06local AGNs S ou r ce r e d s h i f t log ( L R,total /L fl ) l o g ( M B H / M fl ) log( M BH / M fl ) =0.33+0.95 log( L R / L fl ) assumed uncertainties (b) Observed, M BH − L total relation HE0435RXJ1131AGNs from P15 lensed AGNs in P06non-lensed AGNs in P06local AGNs S ou r ce r e d s h i f t log ( L R, ,bulge /L fl ) l o g ( M B H / M fl ) log( M BH / M fl ) =0.78+0.75 log( L R / L fl ) assumed uncertainties (c) Evolution-corrected, M BH − L bulge relation HE0435RXJ1131AGNs from P15 lensed AGNs in P06non-lensed AGNs in P06local AGNs S ou r ce r e d s h i f t log ( L R, ,total /L fl ) l o g ( M B H / M fl ) log( M BH / M fl ) =0.53+0.94 log( L R / L fl ) assumed uncertainties (d) Evolution-corrected, M BH − L total relation HE0435RXJ1131AGNs from P15 lensed AGNs in P06non-lensed AGNs in P06local AGNs S ou r ce r e d s h i f t Figure 3.
Illustration of observed (top) and evolution-corrected (bottom) correlations of M BH - L bulge (left) and M BH - L total (right).For distant AGNs, the redshifts are color-coded. The local data and their linear fitting (using an MCMC process) are colored in gray(1- σ region) with the best-fitted coefficients in blue color. We use the star symbol to highlight our new lensed-based measurements ofHE0435 and RXJ1131. The total uncertainty for L host and M BH of distant AGNs are adopted to be 0.2 dex ( ∼000
Illustration of observed (top) and evolution-corrected (bottom) correlations of M BH - L bulge (left) and M BH - L total (right).For distant AGNs, the redshifts are color-coded. The local data and their linear fitting (using an MCMC process) are colored in gray(1- σ region) with the best-fitted coefficients in blue color. We use the star symbol to highlight our new lensed-based measurements ofHE0435 and RXJ1131. The total uncertainty for L host and M BH of distant AGNs are adopted to be 0.2 dex ( ∼000 , 1–14 (2017) osmic evolution of M BH - L host M BH - L host relation In order to test the passive evolution scenario, we correct theobserved L host to its expected value at z = 0 by accountingfor the aging of the stellar populations. It has been shownthat the evolution of the mass-to-light ratio of early-typegalaxies can be effectively described as that of a single burststellar population formed at appropriate redshifts (e.g., Treuet al. 2005). In order to represent the uncertainty in thestar formation history we consider a range of single burstmodels formed at z f equals to 2, 3 and 5 . We choose toparametrize the evolution with the functional form d mag R = δ m d log(1 + z ), i.e. d log L R /d log(1 + z ) = δ, (4)with δ = − δ m / .
5, so thatlog( L R, ) = log( L R ) − δ log(1 + z ) . (5)For this parametrization, we derive that δ m (cid:39) − . ± . δ = 1 . ± .
08) provides a good representation of typicalstar formation histories.This formalism is more accurate when considering abroad range in redshift with respect to adopting a singleslope as a function of d mag /dz as done by P06 and P15. Fora direct comparison, we also plot the passive evolution cor-rection as a function of redshift in Fig. 4. Note that our cho-sen functional form describes well the P15 form at z < z ∼ z implied by previous parametriza-tions. Furthermore, our chosen functional form facilitate theanalysis of the M BH - L host evolution in the following way.Combining Eq. 3 with the passive evolving correction, i.e.Eq. 5, and adding γ (cid:48) term which describes the evolution ofthe correlation between M BH and observed L host , leads tothe following formalism:log (cid:0) M BH M (cid:12) ) = α + β log( L R, L (cid:12) )+ βδ log(1 + z ) + γ (cid:48) log(1 + z ) . (6)In this equation, βδ represents the effects of passive evolu-tion. The evolution at fixed present-day luminosity is givenby γ = γ (cid:48) + βδ . In this way the effects of the passive evolu-tion correction can be easily separated and a different passiveevolution model can be applied to the data, if desired. In ourspecific case, since we derived β = 0 . ± .
09 for the M BH - L bulge relation, the passive evolution term corresponds toapproximately βδ = 0 . × . ∼ .
0, neglecting the effectsof scatter and errors. Likewise, the passive evolution term is βδ = 0 . × . ∼ . M BH - L total relation.The resulting M BH - L host relation after applying thepassive evolution correction is shown in Fig. 3, panels (c)and (d). Clearly, after the correction, the high redshift sam-ples are offset with respect to the local samples, indicatinga tendency of BH in the more distant Universe to reside inless luminous hosts at fixed M BH . This tendency is consis-tent with previous work, and also consistent with the studiesof the M BH - σ ∗ (stellar velocity dispersion) and M BH - M ∗ Stellar evolution is calculated with
Galaxev (Bruzual & Char-lot 2003), based on Padova-1994 stellar evolutionary tracks, as-suming Salpeter IMF, Solar metallicity, and no dust attenuation. z C o rr ec t e d m a g f o r p a ss i v e e vo l u ti on d mag V /dz = − . d mag R /dz = − . d mag R /d log(1 + z ) = − . Adopted by P15Adopted by P06Adopted here
Figure 4.
Illustration of the comparison of the passive evolutioncorrection adopted by P15, P06 and in this work. Note that all thesamples in P15 are at low redshift ( z (cid:46) d mag V /dz (cid:39)− .
55 is derived by assuming z f = 2 which is appropriate at theseredshifts. P06 adopted d mag R /dz (cid:39) − . z f = 5. (stellar mass) correlations, which do not require correctionfor passive evolution (Treu et al. 2004; Woo et al. 2006, 2008;Bennert et al. 2011a).We fit the offset in black hole mass at fixed passivelyevolved luminosity as a function of redshift in the form:∆ log M BH = γ log(1 + z ) , (7)where ∆ log M BH = log (cid:0) M BH M (cid:12) ) − α − β log( L R, L (cid:12) ) , andobtain γ = 0 . ± .
11 for the M BH - L bulge and γ = 0 . ± .
11 for the M BH - L total , as shown in Fig. 5, panels (a), (b).We also obtain γ (cid:48) = − . ± .
11 for the M BH - L bulge and γ (cid:48) = − . ± .
12 for the M BH - L total , when not taking intoaccount the passive evolving correction. As expected, thedifference γ − γ (cid:48) is consistent with the effects of the passiveevolving correction, i.e. βδ ∼ . M BH - L bulge and βδ ∼ . M BH - L total .We conclude by noting that this fit does not take intoaccount selection effects, which are discussed in the nextsection. From Fig. 3, we can see that at high redshift we preferen-tially study systems with the larger M BH and L total . Thisis expected as observational samples tend to be flux limitedand thus favor the high luminosity tail (and hence typicallyhigh M BH ) of the distribution. Like many other instancesin astronomy, it is essential to take into account the selec-tion function when estimating the evolution of the black holemass host galaxy correlations (Treu et al. 2007; Lauer et al.2007; Bennert et al. 2011a; Schulze & Wisotzki 2014; Parket al. 2015). MNRAS , 1–14 (2017)
X. Ding et al. log (1 + z ) ∆ l og M B H ∆ log M BH = (0 . ± . log (1 + z ) z HE0435RXJ1131AGNs from P15AGNs from Schramm et al. 2013lensed AGNs in P06 using Mg II lensed AGNs in P06 using H β lensed AGNs in P06 using C IV non-lensed AGNs in P06local AGNs (a) Offset for M BH - L bulge relation using entire sample log (1 + z ) ∆ l og M B H ∆ log M BH = (0 . ± . log (1 + z ) z HE0435RXJ1131AGNs from P15AGNs from Schramm et al. 2013lensed AGNs in P06 using Mg II lensed AGNs in P06 using H β lensed AGNs in P06 using C IV non-lensed AGNs in P06local AGNs (b) Offset for M BH - L total relation using entire sample log (1 + z ) ∆ l og M B H ∆ log M BH = (0 . ± . log (1 + z ) z HE0435RXJ1131 AGNs from P15local AGNs (c) Offset for M BH - L bulge relation using reduced sample log (1 + z ) ∆ l og M B H ∆ log M BH = (0 . ± . log (1 + z ) z HE0435RXJ1131 AGNs from P15local AGNs (d) Offset for M BH - L total relation using reduced sample Figure 5.
Illustration of the offset in log M BH for a given L bulge (left) and L total (right) as a function of redshift, after passive evolutioncorrection. Top panels corresponds to the fitting using the whole sample. We also highlight the subsamples from SS13. Bottom panelscorresponds to the fitting excluding the samples from P06 and SS13. The red solid line represents the best-fit trend for all distant objectsas a functional of ∆ log M BH = γ log(1 + z ), with the 1- σ region confidence range shaded in grey. The orange band is the intrinsic scatterof local linear relation. MNRAS000
Illustration of the offset in log M BH for a given L bulge (left) and L total (right) as a function of redshift, after passive evolutioncorrection. Top panels corresponds to the fitting using the whole sample. We also highlight the subsamples from SS13. Bottom panelscorresponds to the fitting excluding the samples from P06 and SS13. The red solid line represents the best-fit trend for all distant objectsas a functional of ∆ log M BH = γ log(1 + z ), with the 1- σ region confidence range shaded in grey. The orange band is the intrinsic scatterof local linear relation. MNRAS000 , 1–14 (2017) osmic evolution of M BH - L host Following P15, we take selection effects into accountby using a Monte Carlo simulation method based upon themethodology introduced by Treu et al. (2007) and Bennertet al. (2010). The simulated samples are generated froma combination of the local active BH mass function fromSchulze & Wisotzki (2010) and the local M BH - L host rela-tion from Bennert et al. (2010) with Gaussian random noiseadded as a function of the two free parameters γ and in-trinsic scatter of the correlation σ int . Note that the scatteris assumed to be independent of redshift in our description.For each object, the likelihood of the observed M BH with agiven L host is calculated from the simulated sample at thegiven γ and σ int , and taking into account whether the objectwould be selected or not based on our sensitivity. Finally,by adopting uninformative uniform (flat) prior or lognormalprior from Bennert et al. (2010, σ int = 0 . ± . γ and σ int is evaluated. Selectioneffects are modelled in the same way for the lensed-quasarsample, neglecting any second order effects related to lens-ing magnification. We note however, that these effects aresmall (Collett & Cunnington 2016) and magification-relatedbiases should affect the quasar and host galaxy in a similarmanner, thus moving objects mostly along the M BH - L host correlation and not away from it.Taking into account selection effects, the results of theinference are shown in Fig. 6. The fitted values of γ are0 . ± . M BH - L bulge ) and 0 . ± . M BH - L total ), almostindependent of the choice of prior. These values are consis-tent with the previous inference in Section 5.1 and 5.2.Interestingly, the intrinsic scatter of the correlations isfound to be consistent with typical values inferred for localsamples (0 . − . z . It wouldbe beneficial to study how the selection bias changes as afunction of some key factors such as the values of L host and M BH , the level of the uncertainties and the redshift distri-bution of the samples. However, this topic is trivial in thisstudy as we obtained consistent inference by either or nottalking selection effects into account. Moreover, to study thisrelation quantitively requires considerate tests and simula-tions. Thus, we leave it in the future study. In this section, we first estimate the importance of potentialsystematic errors in § § § We have combined our new measurements with ones takenfrom the literature in order to increase the sample size andreduce statistical uncertainties. Even though we have re-stricted our analysis to the samples that have been analyzedin the most similar manner to our new data and we havecross-calibrated the black hole mass estimators, there arestill some residual differences.
Table 4.
The summary for the different inference of γ . Sample Account for M BH - L bulge M BH - L total selection effects?Entire No 0 . ± .
11 0 . ± . a . ± . ± . . ± .
28 0.51 ± . . ± . ± . a : Using lognormal prior. First, P06 obtained the luminosity of one galaxy bycombined the fluxes together, even though some of themmay include a disk component (e.g. RXJ1131). Accordingto morphological studies of AGN host galaxies, the fractionof spiral/elliptical hosts of AGN is approximately one third(Kocevski et al. 2012), with the exact value depending on M BH and luminosity. Thus it is possible that P06 overes-timates the bulge component of some of the host galaxies.The total luminosity should be less affected by this bias,even though not completely immune.Furthermore, the subsample by SS13 included in thecompilation by P15, was X-ray selected as opposed to op-tically selected like the rest of the non-lens sample (someof the lenses are radio-selected). This difference in selectioncould potentially lead to a systematic difference between thetwo samples.In order to estimate these systematic uncertainties, werepeat the analysis by excluding the P06 and SS13 samples.This reduced sample will have significantly less statisticalpower, owing to the reduced size and redshift coverage, butshould be more robust with respect to the systematic uncer-tainties discussed above. Given this reduced sample, we ob-tain γ = 0 . ± .
28 for the M BH - L bulge and γ = 0 . ± . M BH - L total , as shown in Fig. 5, panel (c), (d). More-over, we use the same approach to study the selection ef-fects and obtain the consistent inference, as illustrated inFig. 7. Even though as expected the uncertainties are largerthan for the full sample, the results are statistically mu-tually consistent at 1- σ level. To facilitate the comparisonbetween different γ , we summarize our inference in Tab. 4.We conclude that our inferred trends are not dominated bysystematic differences between the samples, and systematicuncertainties of this kind are smaller than the random ones.In this work, M BH estimates are derived using the C IV ,Mg II and H β emission lines. However, the C IV and Mg II linesare usually in outflow (Baskin & Laor 2005; Richards et al.2011; Denney 2012) and therefore may not be dominated bythe gravity of the central M BH and result in biased M BH estimates, especially for the C IV line (Trakhtenbrot & Net-zer 2012). Following McGill et al. (2008) the potential biashas been mitigated by cross-calibrating the M BH estimatesbased on the different lines. As a further sanity check, wefitted the γ using only H β -based samples. We note that thisH β sample is very smilar to the subsample excluding P06and SS13, and in fact the results are similar ( γ = 1 . ± . M BH - L bulge and γ = 0 . ± .
37 for the M BH - L total ).We conclude that any potential residual bias related to theuse of lines other than H β is smaller than statistical uncer-tainties or biases related to sample selection. MNRAS , 1–14 (2017) X. Ding et al. (a) M BH - L bulge , flat prior (b) M BH - L bulge , lognormal prior(c) M BH - L total , flat prior (d) M BH - L total , lognormal prior Figure 6.
Posterior distribution function given the entire dataset for a model with evolution in the form ∆ log M BH = γ log(1 + z ) withintrinsic scatter σ int , taking into account selection effects. The M BH - L bulge (top) and M BH - L total (bottom) correlations with flat (left)and lognormal prior (right) are shown. P15, using a sample of 79 active galaxies, inferred the fol-lowing evolutionary trends: γ = 0 . ± . M BH - L bulge and γ = 0 . ± . M BH - L total . These are con-sistent with our inference, although their uncertainties aremuch larger, owing to the smaller sample size and reducedhigh redshift coverage. A similar result was obtained by P06,where they found that the ratio between M BH and M ∗ was ∼ z ∼ − γ ∼ . − . M BH - L bulge relation is atopic of intense debate in the literature. Many works have re-ported an evolutionary signal based on different relations in-cluding the M BH - L host (e.g. Treu et al. 2007; Bennert et al.2010), the M BH - M ∗ (e.g. McLure et al. 2006; Jahnke et al. 2009; Decarli et al. 2010; Cisternas et al. 2011; Bennert et al.2011b; Trakhtenbrot et al. 2015) and the M BH - σ ∗ (e.g. Wooet al. 2006, 2008) correlations. Nevertheless, other observa-tional studies (e.g. Shields et al. 2003; Greene & Ho 2005;Komossa & Xu 2007; Shen et al. 2008) found no evidence forevolution. In Shankar et al. (2016), they find serious biasesin the M BH - M ∗ relation and prove that σ ∗ is more funda-mental than any other variable. However, in Shankar et al.(2009), they show that there is no evolution in the M BH - σ ∗ relation once one accounts for the ages of local galaxies andthe So(cid:32)ltan argument. Moreover, Schulze & Wisotzki (2011,2014) concluded that there is no statistically significant ev-idence for evolution once these selection effects are takeninto account and corrected. Taking a different approach, De-Graf et al. (2015) used the results of the high-resolutionnumerical simulation MassiveBlackII to compare the ob-served and intrinsic evolution of the black hole mass hostgalaxy correlations and reproduced the evolutionary trendof the relation. Consistent with other considerations, theyalso found that the observed samples display steeper slopesthan random ones, suggesting the selecting effects can ex-hibit faster evolution than a random sample. Similarly, by
MNRAS000
MNRAS000 , 1–14 (2017) osmic evolution of M BH - L host (a) M BH - L bulge , flat prior (b) M BH - L bulge , lognormal prior(c) M BH - L total , flat prior (d) M BH - L total , lognormal prior Figure 7.
Same as Fig. 6, using the reduced sample. generating Monte Carlo realizations of the M BH - σ ∗ relationat z = 6, Volonteri & Stark (2011) also found that due toselection bias the ’observable’ subsample would suggest anaverage positive evolution even when the intrinsic correla-tions is characterized by no or negative evolution at highredshift. These studies highlight once again the importanceof taking selection effects into account.Clearly, absence of evidence does not imply evidence ofabsence, and one way to make progress is to improve theprecision and accuracy of the measurement. In our work, weattain much higher precision than previous work owing tothe enlarged sample, including lensed quasars. Thanks to thelarge sample size, even when selection effects are taken intoaccount, the evolutionary trend is detected at high signifi-cance ( γ (cid:54) = 0 at more than 5- σ ). However, using a reducedsample by excluding the subsamples from P06 and SS13, weobtain a smaller evolutionary trend, with larger uncertain-ties. These results are consistent at 1- σ level (see Tab. 4),and highlight the importance of studying larger sample ofhigh redshift lenses with the state-of-the-art data. Our results are consistent with a scenario in which BHs inthe distant Universe typically reside in lower stellar massgalaxies than today, assuming that the passively evolvedluminosity tracks approximately stellar mass (see Bennertet al. 2011a; Schramm & Silverman 2013, for a consistent di-rect measurement based on stellar mass determination). Inorder to end up on the local final relation, the stellar massof the host galaxy would have to grow faster than M BH .An interesting clue to the physical mechanism drivingthe evolution could perhaps be found by comparing the in-ferred evolution for the correlation between M BH and thetotal host galaxy luminosity, and that with the bulge lu-minosity. We found those two to be comparable within theuncertainties. Previous work found the M BH - M ∗ bulge cor-relation to evolve somewhat faster than M BH - M ∗ total , al-beit at low statistical significance, suggesting that one ofthe mechanisms at work is the build up of the bulge com-ponent from stars in the disk (Croton 2006). It is difficultto perform a direct comparison, because of the fact thatthe P06 sample did not attempt bulge-disk decomposition,and we have also assumed a single passive evolution trend MNRAS , 1–14 (2017) X. Ding et al. for the entire galaxy. Both effects could potentially suppressthe differences between the evolution of the bulge and totalluminosity with respect to the black hole mass.Also, our sample extends to much larger redshift thanthat of B11. One possible explanation of this possible tensionis that the dominant evolutionary mechanisms changes withredshift. At low redshift ( z (cid:46) z (cid:38) L host of ellipticals would not change when con-sidering the bulge and the total, we examine the offset usingthe sample limited to spiral galaxies. In our sample, there are9 local spirals and 41 distant spirals, excluding SS13. Fittingthe offset with this subsample, we obtain γ = 2 . ± .
41 and1 . ± .
41 for M BH - L bulge and M BH - L total , respectively,which are larger than the previous inference listed in Tab. 4for the entire sample. This difference could suggest the spi-ral galaxies are undergoing a more rapid evolution than theellipticals in order to end up on the local final relation. How-ever, we caution that this result should be taken with a grainsalt, given the small sample size of the local disk comparisonsample. We presented a new measurement of the co-evolution of su-permassive black holes and their host galaxies. First, wecarried out a new analysis of two strongly lensed quasars,HE0435 − − L host is small (0.1 − M BH by using a set of self-consistent single epoch estimatorsbased on the quasar emission line properties as measured bySluse et al. (2012).Second, we combined our measurements with the pub-lished ones from the literature (Peng et al. 2006; Park et al.2015), thus expanding our sample to 146 active galaxies upto z = 4 .
5. We have taken care of using self-consistent recipesto re-derive the black hole mass estimates and convert all theluminosities self-consistently to the rest-frame R-band.Our main findings can be summarized as follows:(i) The observed correlations - without correction for evo-lution - are consistent with those observed in the local Uni-verse. (ii) The data are inconsistent with a passive evolutionscenario. By correcting the host galaxy rest-frame luminosityto z = 0, we find that galaxies are underluminous for a given M BH , even neglecting growth by accretion.(iii) The passively evolved correlations are well describedby a relationship of the form ∆ log M BH = γ log(1 + z ) with γ = 0 . ± . γ = 0 . ± .
2, respectively at fixed bulge andtotal host luminosity, taking into account selection effects.Considering that stellar populations must fade as theyget older, and considering that similar results have beenfound when studying the correlations between M BH andhost galaxy velocity dispersion (Treu et al. 2004; Woo et al.2006, 2008) and stellar mass (Jahnke et al. 2009; Bennertet al. 2011b; Schramm & Silverman 2013), we are forced toconclude that the co-evolution of galaxies and black holesis non-trivial, in the sense that systems do not stay on thecorrelation as they evolve. At least for active galaxies in therange of black hole and stellar masses that can be analyzedwith current technology, it appears that the growth of theblack hole predates that of the bulge (Croton 2006). How-ever, given the complexity and variety of processes involved,direct comparisons with detailed numerical simulations areneeded to further our understanding of the co-evolution ofblack holes and their hosts. Recent cosmological simulationsincluding some prescriptions for black hole growth and feed-back have been shown to reproduce the observations at leastat z < HST imaging data have been obtainedfor six additional strongly lensed systems and their analy-sis will be described in a forthcoming paper. The sample oflensed quasars and their hosts that can be studied at highfidelity is likely to continue to grow as more such systems arediscovered in wide field imaging and spectroscopic surveys(e.g. Agnello et al. 2015; More et al. 2016; Schechter et al.2017; Ostrovski et al. 2017). ACKNOWLEDGEMENTS
Based in part on observations made with the NASA/ESAHubble Space Telescope, obtained at the Space TelescopeScience Institute, which is operated by the Association ofUniversities for Research in Astronomy, Inc., under NASAcontract NAS 5-26555. These observations are associatedwith programs WFI2033 − − HST -GO-12889 (PI: Suyu); SDSS1206+4332, HE0047 − − HST -GO-14254 (PI: Treu). MNRAS000
Based in part on observations made with the NASA/ESAHubble Space Telescope, obtained at the Space TelescopeScience Institute, which is operated by the Association ofUniversities for Research in Astronomy, Inc., under NASAcontract NAS 5-26555. These observations are associatedwith programs WFI2033 − − HST -GO-12889 (PI: Suyu); SDSS1206+4332, HE0047 − − HST -GO-14254 (PI: Treu). MNRAS000 , 1–14 (2017) osmic evolution of M BH - L host We are grateful to Vivien Bonvin, Geoff C.-F. Chen,Frederic Courbin, Matthew A. Malkan, Cristian E. Rusu,Jong-Hak Woo, and Andreas Schulze for useful commentsand suggestions that improved this manuscript. We thankChien Peng for his help with the estimates of black holemass. X.D. is supported by the China Scholarship Coun-cil. T.T. acknowledges support by the Packard Founda-tions through a Packard Research Fellowship and by theNSF through grants AST-1450141 and AST-1412315. S.H.S.gratefully acknowledges support from the Max Planck So-ciety through the Max Planck Research Group. C.E.R. ac-knowledges support from the NSF grant AST-1312329. D.S.acknowledges funding support from a
Back to Belgium grantfrom the Belgian Federal Science Policy (BELSPO). K.C.W.and D.P. is supported by an EACOA Fellowship awardedby the East Asia Core Observatories Association, whichconsists of the Academia Sinica Institute of Astronomyand Astrophysics, the National Astronomical Observatory ofJapan, the National Astronomical Observatories of the Chi-nese Academy of Sciences, and the Korea Astronomy andSpace Science Institute. V.N.B. gratefully acknowledges as-sistance from a National Science Foundation (NSF) Researchat Undergraduate Institutions (RUI) grant AST-1312296.Note that findings and conclusions do not necessarily repre-sent views of the NSF. V.B. acknowledge the support of theSwiss National Science Foundation (SNSF).
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APPENDIX A: THE K-CORRECTION FORTHE RXJ1131 HOST
We apply the K-correction to the observed magnitudes toobtain the rest-frame R-band magnitude. At the redshift ofRXJ1131 ( z s = 0 . Fast (Kriek et al. 2009) based on
Galaxev stellar evolution track(Bruzual & Charlot 2003), assuming the solar metallicity,exponentially declining star formation history and Calzettiet al. (2000) dust extinction law, while the redshift is fixedto the spectroscopic one. The error for each pixel is cal-culated based on empty regions of images. We then de-rive the rest-frame R-band magnitude by using the best-fit template for each pixel, and see the offset from the ob-served F814W magnitude. As shown in Fig. A1, panel (b),∆mag disk (R − F814W) ≈ − . > bulge (R − F814W) ≈ − . This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS000
Galaxev stellar evolution track(Bruzual & Charlot 2003), assuming the solar metallicity,exponentially declining star formation history and Calzettiet al. (2000) dust extinction law, while the redshift is fixedto the spectroscopic one. The error for each pixel is cal-culated based on empty regions of images. We then de-rive the rest-frame R-band magnitude by using the best-fit template for each pixel, and see the offset from the ob-served F814W magnitude. As shown in Fig. A1, panel (b),∆mag disk (R − F814W) ≈ − . > bulge (R − F814W) ≈ − . This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS000 , 1–14 (2017) osmic evolution of M BH - L host Table 1.
Properties of AGNs in the distant sample.
Object Line(s) Used redshift log M BH log L host ,R ( M (cid:12) ) ( L (cid:12) ) ± . ± . II bulge Mg II /H β disk Mg II /H β β II II II /C IV II II II /C IV II /C IV II II II II IV IV II /C IV IV IV IV IV IV β IV IV II /C IV IV IV II /C IV IV II II II II II II IV II /C IV II /C IV IV IV IV IV IV IV IV IV II /C IV IV IV L bulge / L total )S09 a H β β β β β β β β β β β β β β β β β β β β β Table 1. —continued.
Non-lensed AGNs from P15 log L bulge /log L total S31 H β β β β β β β β β β β β β β β β β β β β β β β β β β β β β β β II II II II II II II II II II II b Mg II II II II II II II II II II II II II II II II Note: − Column 1: object ID. Column 2: Emission line used toestimate M BH . Column 3: redshift as listed in the literature. Col-umn 4: M BH calibrated from Eq. 2 using the corresponding lines.Column 5: Inferred rest-frame R-band luminosity not correctedfor evolution. Note that all the host galaxies in P06 are assumedto be pure ellipticals. a ID taken from Park et al. (2015). b ID taken from Schramm & Silverman (2013).MNRAS , 1–14 (2017) X. Ding et al.
Table 2.
Properties of local AGNs.Object redshift log M BH log L bulge ,R /log L total ,R ( M (cid:12) ) ( L (cid:12) ) ± . ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − Local AGNs measurements, taken from Bennert et al.(2010). Following Park et al. (2015), we adopted virial factor aslog f = 0 .
71. Note that Bennert et al. (2010) adopted log f = 0 . -1 Age (Gyr)1.00.80.60.40.20.00.20.4 R R F . − F W o b s . ( m a g ) Z fl , E1.0 Z fl , E2.5 Z fl , E0.4 Z fl , Sb1.0 Z fl , Sb2.5 Z fl , Sb (a) K-correction from observed F814w band tothe rest-frame R-band magnitude, as a functionof stellar population age. The colors are calcu-lated based GALAXEV stellar evolution trackwith metallicities of Z = 0 . Z (cid:12) , 1 . Z (cid:12) , 2 . Z (cid:12) for E-type and Sb-type galaxies. x (pixel) y ( p i x e l ) R R F . − F W o b s . ( m a g ) (b) Color map (the rest-frame R magnitude - observedF814W magnitude) of RXJ1131, calculated by SED fit-ting with three broadband imaging (F555W, F814Wand F160W). For bulge region, a direct measurementof SED is affected by the residual AGN contamination,and hence half blue and half red. For the disk region,i.e. around the area where lensing-distorted spiral armpatterns and star forming regions are clearly visible,∆mag is approximately − . Figure A1.
Illustration of the K-correction for RXJ1131.MNRAS000