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

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 +. 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)

LBQS MF(z|M)

(MV & Osmer 2009)

Evidence of ‘downsizing’

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

Extra Slides

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

Reverberation Mapping Masses

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)

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

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