Marianne Vestergaard Dark Cosmology Centre, Copenhagen First Galaxies, Quasars, and GRBs, June Determining Black Hole Masses in Distant Quasars Collaborators: M. Bentz, S. Collin, K. Denney, X. Fan, C. Grier, L. Jiang, T. Kawaguchi, B. Kelly, P.S. Osmer, B.M. Peterson, G. Richards, C.T. Tremonti

Possible Virial Estimators In units of the Schwarzschild radius R S = 2GM/c 2 = 3 × M 8 cm. Note: the reverberation technique is independent of angular resolution M BH = v 2 R BLR /G

Virialized BLR  Filled circles: 1989 data from IUE and ground-based telescopes.  Open circles: 1993 data from HST and IUE. …Dotted line corresponds to virial relationship with M = 6 × 10 7 M . Highest ionization lines have smallest lags and largest Doppler widths. Peterson and Wandel 1999 R  (M/V 2 ) R V

Radius – Luminosity Relation Variability Studies: R BLR =cτ, v BLR (Kaspi et al. 2005; Bentz et al. 2006, 2009) R BLR  L λ (nuclear) 0.50 (Data from Bentz et al., 2006) L (1350Å) [erg s -1 ] (Kaspi ea 2007) HβHβ CIV

Virial Mass Estimates: M BH = v 2 R BLR /G Variability Studies: R BLR =cτ, v BLR (Kaspi et al. 2005; Bentz et al. 2006, 2009) For individual spectra: M BH = k(line) FWHM 2 L β ;   0.5 Lines: Hβ, MgII 2800, CIV 1549 R BLR  L λ (nuclear) 0.50 (see e.g. MV 2002, McLure & Jarvis 2002, MV & Peterson 2006; MV & Osmer 2009)

Scaling Relationships: (calibrated to 2004 Reverberation M BH ) Hβ: MgII: CIV: 1σ absolute uncertainty: factor ~3.5 – 4 Virial Mass Estimates : M BH =f v 2 R BLR /G ( MgII : MV & Osmer 2009; cf. McLure & Jarvis 2002 )   (Vestergaard 2002; Vestergaard & Peterson 2006) 

Word of Caution Comparing masses from different lines? Use equations on the same mass scale Have multiple lines? –Use equations on the same mass scale. –Use all applicable emission lines. Formula simple but method non- trivial! : care is crucial

Radius – Luminosity Relation R BLR  L λ (nuclear) 0.50 Using the highest quality data only! Scatter: 0.11dex (Peterson 2010) The limitation is thus the profile width!

No Broad Emission Line is Perfect! H  and MgII FWHM are not always the same – contrary to common claims SDSS DR3

No Broad Emission Line is Perfect! H  and MgII FWHM are not always the same – contrary to common claims MgII is strongly contaminated by strong, broad features of FeII, complicating its measurement (Vestergaard & Wilkes 2001) Half the MgII line flux is submerged in FeII emission

No Broad Emission Line is Perfect! H  and MgII FWHM are not always the same – contrary to common claims MgII is strongly contaminated by strong, broad features of FeII, complicating its measurement MgII and CIV FWHM often deviate - but cause is unclear: MgII is likely also problematic due to systematic narrowing with z Note: CIV is prone to strong broad absorption! Better understanding of profile differences needed Investigations of systematic biases needed to improve and enhance black hole mass estimates (Study under way) More accurate M BH values crucial for cosmological studies!

S/N Matters: Hβ & MgII FWHM difference: MgII - Hβ Denney et al 2009: In lower S/N data FWHM is: underestimated in direct measurements: -0.1 dex shift, distr. broader overestimated in fits to profile: +0.1 dex shift, distribution broadens 2008

S/N Matters: MgII & CIV FWHM difference: MgII - CIV Denney et al 2009: In lower S/N data FWHM is: underestimated in direct measurements: -0.1 dex shift, distr. broader overestimated in fits to profile: +0.1 dex shift, distribution broadens

Limitations of UV Scaling Relations? NLS1s: low M BH high L BOL /L Edd Possible outflow component to CIV (Leighly 2001)

Are Quasar CIV Profiles Problematic? (EW) (FWHM) (Richards et al. 2002) ~15%

Improving the Scaling Relationships What causes spread around the M-σ relationship?? Inclination? - BLR kinematics is likely planar (Wills & Browne 1986, Vestergaard et al. 2000) Accretion rate? (Collin ; Shen ) Radiation Pressure? (Marconi )

Masses of Distant Quasars Ceilings at M BH ≈ M  L BOL < ergs/s M BH ≈ 10 9 M  - even beyond space density drop at z ≈ 3 (DR3 Qcat: Schneider et al. 2005) (MV et al. in prep) HβHβ MgII CIV SDSS DR3: ~41,000 QSOs Kurk et al. 2007; Jiang et al. 2007, 2010 z~6

BQS: sq. deg; B  mag LBQS: 454 sq. deg; 16.0  B J  mag SDSS: 182 sq. deg; i*  20 mag DR3: 1622 sq. deg.; i* >15,  19.1, 20.2 (H 0 =70 km/s/Mpc; Ω Λ = 0.7) Mass Functions of Active Supermassive Black Holes Factor ~ 17 (Vestergaard & Osmer 2009)

LBQS MF(z|M) (MV & Osmer 2009) Evidence of ‘downsizing’

Summary At present M BH can be estimated to within a factor of a few: M  FWHM 2 L 0.5 R-L relation scatter is low for best data: Profile width is the limitation Line profile depends on multiple factors – under investigation Important points: –No emission line is perfect –Profile issues: not a show stopper –S/N ratio of data matters for mass accuracy! Quasar Mass Functions: –Not simple scalings of Luminosity Function –We see downsizing from redshifts of 3

Luminosity Functions of Active Supermassive Black Holes DR3: 1622 sq. deg.; i* >15,  19.1, 20.2 (Richards et al. 2006)

Mass Functions of Active Supermassive Black Holes DR3: 1622 sq. deg.; i* >15,  19.1, 20.2 (MV et al. 2008)  =  3.3

Summary At present M BH can be estimated to within a factor of a few: M  FWHM 2 L 0.5 R-L relation scatter is low for best data: Profile width is the limitation Line profile depends on multiple factors – under investigation Important points: –No emission line is perfect –Profile issues: not a show stopper –S/N ratio of data matters for mass accuracy! Quasar Mass Functions: –Not simple scalings of Luminosity Function –We see downsizing from redshifts of 3

Extra Slides

Virial Relationships (Peterson & Wandel 1999, 2000; Onken & Peterson 2002) Emission lines: SiIV 1400, CIV 1549, HeII 1640, CIII] 1909, H  4861, HeII 4686 All 4 testable AGNs comply: –NGC 7469: 1.2  10 7 M  –NGC 3783: 3.0  10 7 M  –NGC 5548: 6.7  10 7 M  –3C 390.3: 2.9  10 8 M  R-L relation extends to high-z and high luminosity quasars: –spectra similar (Dietrich ea 2002) –luminosities are not extreme (Dietrich et al 2002)

Radius – Luminosity Relation Luminosities are not extreme R – L defined for –10 41 –10 46 erg/s Optical (Bentz et al. 2009) –10 40 – erg/s UV (Peterson ; Kaspi ) – (Data from Bentz et al., 2006) L (1350Å) [erg s -1 ] (Kaspi ea 2007) HβHβ CIV

Luminosities of Distant Quasars Ceilings at L BOL < ergs/s L BOL  4.5 · L (1350Å)  10 · L (5100Å) Maximum L BOL value does not extend much beyond R-L relation: 47dex & dex (DR3 Qcat: Schneider et al. 2005) (Vestergaard et al. in prep) HβHβ MgII CIV SDSS DR3: ~41,000 QSOs

S/N Matters: Mass Estimates Ratio: MgII / CIVRatio: MgII / Hβ Note: here MgII and CIV are not on entirely same mass scale!

(Data from Vestergaard & Peterson 2006, Marconi et al. 2008) Improve Mass Estimates Reduce scatter further − Can we account for radiation pressure on broad line gas? (eg Marconi et al. 2008) 0.4 dex0.2 dex

Reverberation Mapping Masses

M BH = f v 2 R BLR /G Reverberation Mapping: R BLR = c τ v BLR Line width in variable spectrum Virial Mass Estimates  t t +  24

Reverberation Mapping NGC 5548, the most closely monitored active galaxy (Peterson et al. 1999) HH Hβ [OIII] Hδ H  25

Reverberation Mapping Results NGC 5548, the most closely monitored active galaxy Continuum Emission line Light Curves (Peterson et al. 2002) 13 years of data galaxy 23

Velocity dispersion is measured from the line in the rms spectrum. –The rms spectrum isolates the variable part of the lines. –Constant components (like narrow lines) vanish in rms spectrum Velocity Dispersion of the Broad Line Region and the Virial Mass M BH = f v 2 R BLR /G f depends on structure and geometry of broad line region f  1 for v = FWHM (based on Korista et al. 1995)

Are black hole masses overestimated, eg by factor of 10?

To first order quasar spectra look similar at all redshifts (Dietrich et al 2002)

Radius – Luminosity Relations r  L 1/2 To first order, AGN spectra look the same Þ Same ionization parameter Þ Same density [Kaspi et al (2000) data]

Radius-UV Luminosity Relationship for High-z Quasars (Korista et al. 1997) M = V FWHM 2 R BLR /G ↑ ↑ ↓ 0.1  10 9 M  4500 km/s 33 lt-days Ф  R BLR -2 L Log Ф  Log n(H)  ≈ ergs/s

Radius-UV Luminosity Relationship for High-z Quasars (Dietrich et al. 2002) M = V FWHM 2 R BLR /G Ф  R BLR - 2