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Marianne VestergaardDark Cosmology Centre, Copenhagen
First Galaxies, Quasars, and GRBs, June 8 2010First Galaxies, Quasars, and GRBs, June 8 2010
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
Source Distance from central source
X-Ray Fe K 3-10 RS
Broad-Line Region 600 RS Megamasers 4 104 RS Gas Dynamics 8 105 RS Stellar Dynamics 106 RS
In units of the Schwarzschild radius RS = 2GM/c2 = 3 × 1013 M8 cm .
Note: the reverberation technique is independent of
angular resolution
MBH = v2 RBLR/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 × 107 M.
Highest ionizationlines have smallestlags and largest Doppler widths.
Peterson and Wandel 1999
R (M/V2)
R
V
Radius – Luminosity Relation
• Variability Studies: RBLR=cτ, vBLR
(Kaspi et al.
2005; Bentz et al. 2006, 2009)
RBLR Lλ(nuclear)0.50
(Data from Bentz et al., 2006)
L(1350Å) [erg s-1]
(Kaspi ea 2007)
1039 1047
Hβ
CIV
Virial Mass Estimates:
MBH = v2 RBLR/G
• Variability Studies: RBLR=cτ, vBLR
(Kaspi et al.
2005; Bentz et al. 2006, 2009)
• For individual spectra:
MBH = k(line) FWHM2 Lβ ; 0.5
Lines: Hβ, MgII 2800, CIV 1549
RBLR Lλ(nuclear)0.50
(see e.g. MV 2002, McLure & Jarvis 2002, MV & Peterson 2006; MV & Osmer 2009)
Mergs/s10
)2100(λL
km/s10
FWHM(MgII)106.2M
0.50
44λ
2
36
BH
M ergs/s10
)5100(λL
km/s10
β) FWHM(H108.3M
0.50
44λ
2
36
BH
Scaling Relationships: (calibrated to 2004 Reverberation MBH)
• Hβ:
• MgII:
• CIV: 1σ absolute uncertainty: factor ~3.5 – 4
Virial Mass Estimates: MBH=f v2 RBLR/G
Mergs/s10
)1350(λL
km/s10
FWHM(CIV)104.5M
0.53
44λ
2
36
BH
(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
RBLR Lλ(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 MBH values crucial for cosmological studies!
S/N Matters: Hβ & MgII
FWHM difference: MgII - HβDenney 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 - CIVDenney 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
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 +. 2006; Shen + 2007)
•Radiation Pressure? (Marconi + 2008)
Masses of Distant Quasars
• Ceilings at MBH ≈ 1010 M LBOL < 1048
ergs/s
• MBH ≈ 109 M - even beyond space density drop at z ≈ 3
(DR3 Qcat: Schneider et al. 2005)(DR3 Qcat: Schneider et al. 2005) (MV et al. in prep)
Hβ
MgII
CIV
SDSS DR3: ~41,000 QSOs
Kurk et al. 2007; Jiang et al. 2007, 2010
z~6
• BQS: 10 700 sq. deg; B16.16mag
• LBQS: 454 sq. deg; 16.0BJ18.85mag
• SDSS: 182 sq. deg; i* 20mag
• DR3: 1622 sq. deg.; i* >15, 19.1, 20.2
(H0=70 km/s/Mpc; ΩΛ = 0.7)
Mass Functions of Active Supermassive Black Holes
Factor ~ 17
(Vestergaard & Osmer 2009)
Summary• At present MBH can be estimated to
within a factor of a few: M FWHM2 L0.5
• 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 MBH can be estimated to
within a factor of a few: M FWHM2 L0.5
• 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
Virial Relationships
(Peterson & Wandel 1999, 2000; Onken & Peterson 2002)
Emission lines:SiIV1400, CIV1549, HeII1640, CIII]1909, H4861, HeII4686
•All 4 testable AGNs comply:– NGC 7469: 1.2 107 M
– NGC 3783: 3.0 107 M
– NGC 5548: 6.7 107 M
– 3C 390.3: 2.9 108 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 extremeR – L defined for
– 1041 –1046 erg/s Optical (Bentz et al. 2009)
– 1040 – 1047 erg/s UV (Peterson + 2005; Kaspi + 2007)
– (Data from Bentz et al., 2006)
L(1350Å) [erg s-1]
(Kaspi ea 2007)
1039 1047
Hβ
CIV
Luminosities of Distant Quasars
• Ceilings at LBOL< 1048 ergs/s
• LBOL
4.5 · L(1350Å)
10 · L(5100Å)
• Maximum LBOL value does not extend much beyond R-L relation: 47dex & 47.65 dex
(DR3 Qcat: Schneider et al. 2005)(DR3 Qcat: Schneider et al. 2005) (Vestergaard et al. in prep)
Hβ
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 dex 0.2 dex
MBH = f v2 RBLR/G
Reverberation Mapping:
•RBLR= c τ
•vBLR
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)
HHβ [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 yearsof 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
MBH = f v2 RBLR/G
f depends on structure and geometry of broad line region
f 1 for v = FWHM
(based on Korista et al. 1995)
Radius – Luminosity Relations
2HH
24
)H(
rn
L
cnr
QU
r L1/2
To first order, AGN spectra look the same
Þ Same ionization
parameterÞ Same density
[Kaspi et al (2000) data]
Radius-UV Luminosity Relationship for High-z Quasars
(Korista et al. 1997)
M = VFWHM2 RBLR/G
↑ ↑ ↓0.1109 M 4500km/s 33 lt-days
Ф RBLR-2 L
Log Ф Log n(H)
<L> ≈ 1047 ergs/s
Radius-UV Luminosity Relationship for High-z Quasars
(Dietrich et al. 2002)
M = VFWHM2 RBLR/G
Ф RBLR-2