UNCERTAINTIES ON THE BLACK HOLE MASSES UNCERTAINTIES ON THE BLACK HOLE MASSES

AND CONSEQUENCES FOR THE EDDINGTON RATIOSAND CONSEQUENCES FOR THE EDDINGTON RATIOS

Suzy Collin Suzy Collin

Observatoire de Paris-Meudon, FranceObservatoire de Paris-Meudon, France

Collaborators: Collaborators:

T. Kawaguchi (Tokyo), T. Kawaguchi (Tokyo),

B. Peterson (Ohio U), M. Vestergaard (Steward obs),B. Peterson (Ohio U), M. Vestergaard (Steward obs),

C. Boisson, M. Mouchet (Paris)C. Boisson, M. Mouchet (Paris)

I.I. Uncertainties on direct mass determinationsUncertainties on direct mass determinations

II.II. Indirect mass determinations: super-Eddington accretion Indirect mass determinations: super-Eddington accretion ratesrates

IN 35 SEYFERT AND LOW REDSHIFT QUASARSIN 35 SEYFERT AND LOW REDSHIFT QUASARS BH MASSES ARE DETERMINED BH MASSES ARE DETERMINED DIRECTLY DIRECTLY

BY THE “REVERBERATION MAPPING METHOD”BY THE “REVERBERATION MAPPING METHOD”

It consists in measuring the time delay between the continuum and the line It consists in measuring the time delay between the continuum and the line variations which respond to them; it gives an (approximate) size of the broad variations which respond to them; it gives an (approximate) size of the broad Line Region . Assuming that Line Region . Assuming that the BLR is gravitationally boundthe BLR is gravitationally bound (certainly true for the Balmer line emitting region), the mass of the BH, (certainly true for the Balmer line emitting region), the mass of the BH, , is then: , is then:

where is the dispersion velocity, and where is the dispersion velocity, and a scale factor. a scale factor.It is usually assumed (Peterson & Wandel 1999, Kaspi et al. 2000) thatIt is usually assumed (Peterson & Wandel 1999, Kaspi et al. 2000) that which correspond to an which correspond to an isotropic BLRisotropic BLR with a with a random random distribution of orbitsdistribution of orbits. .

M(BH) = f (c M(BH) = f (c V V22/G) = f (Virial Product) /G) = f (Virial Product)

M(BH)M(BH),,

R(BLR)R(BLR)

VV ff

V = FWHMV = FWHM, and , and f =f = 3/4 3/4

IN ALL OTHER OBJECTS (EXCEPT ONE) THE MASSES ARE IN ALL OTHER OBJECTS (EXCEPT ONE) THE MASSES ARE DETERMINED DETERMINED INDIRECTLYINDIRECTLY USING THIS EMPIRICAL RELATION USING THIS EMPIRICAL RELATION

by-product:by-product: an empirical relation between R(BLR) and L(optical) an empirical relation between R(BLR) and L(optical)

I. I. UNCERTAINTIES ON THE MASS DETERMINATIONSUNCERTAINTIES ON THE MASS DETERMINATIONS

VARIOUS UNCERTAINTIESVARIOUS UNCERTAINTIES

1.1. The scale factor f depends on the geometry and on the kinematics of The scale factor f depends on the geometry and on the kinematics of the BLR, and most probably on the Eddington rate (Collin et al. 2006).the BLR, and most probably on the Eddington rate (Collin et al. 2006).

2.2. What is the best choice for measuring V? The FWHM (all works) or What is the best choice for measuring V? The FWHM (all works) or lineline? ? line line seems more reliable (Peterson et al. 2004), but it is generally seems more reliable (Peterson et al. 2004), but it is generally

not measured. not measured.

3.3. Is it better to use the RMS or the mean spectrum? Is it better to use the RMS or the mean spectrum?

Etc…Etc…

106

107

108

109

1010

106 107 108 109 1010

M(BH) (Kaspi et al., 2000)

Peterson et al. 2004: use Peterson et al. 2004: use (line) instead of FWHM, RMS spectrum instead of mean (line) instead of FWHM, RMS spectrum instead of mean spectrum, and changed the factor spectrum, and changed the factor ff (scaled on the bulge masses by Onken et al. 2004) (scaled on the bulge masses by Onken et al. 2004)

Sample of reverberation mapped objects

Example of systematic uncertaintiesExample of systematic uncertainties

Collin, Kawaguchi, Peterson, Vestergaard (2006)

Reverberation mapped objects, all datasetsReverberation mapped objects, all datasets

broad flat broad flat topped linestopped lines

Mean spectraRMSspectra

NGC5548

narrow narrow peaked linespeaked lines

Gaussian profile

THE SCALE FACTOR IS NOT A CONSTANTTHE SCALE FACTOR IS NOT A CONSTANT

Pop 1

Pop 2

Pop A Pop Bsimilar to Sulentic et al.

Col

lin e

t al

.

Scale factor determined by fitting Scale factor determined by fitting

M(BH) to M(M(BH) to M(**), M(BH) being FWHM-based), M(BH) being FWHM-based

Remember: Remember: f = 0.75 is f = 0.75 is usedused

f = 2.4 1

f = 0.85 0.15

THE INCLINATION OF THE BLR PLAYS A ROLETHE INCLINATION OF THE BLR PLAYS A ROLE

a fraction of Pop1 objects should be seen a fraction of Pop1 objects should be seen at small inclination: at small inclination:

their masses can be underestimated by factors up to tentheir masses can be underestimated by factors up to ten(NGC4051, Mrk590, NGC7469…)(NGC4051, Mrk590, NGC7469…)

Assuming that the velocity includes a plane rotational Assuming that the velocity includes a plane rotational plus an isotropic partplus an isotropic part

VVobsobs =V =VKepKep (a (a 22 + sin + sin))1/21/2

and using the distribution of and using the distribution of M(M(**)) /M(RM), we found that /M(RM), we found that

BH MASSES DETERMINED IN LARGE SAMPLES BH MASSES DETERMINED IN LARGE SAMPLES INDIRECTLY BY THE EMPIRICAL RELATIONINDIRECTLY BY THE EMPIRICAL RELATION

Kaspi et al. 2000, revised by Kaspi et al. 2005Kaspi et al. 2000, revised by Kaspi et al. 2005

Allows to determine M(BH) for single epoch observations, Allows to determine M(BH) for single epoch observations, simply by measuring Lopt (=simply by measuring Lopt (=LL at 5100 at 5100A)A) and the FWHM and the FWHM

Determination of Determination of Lbol/LeddLbol/Ledd

Lbol: generally deduced from LoptLbol: generally deduced from Lopt, assuming , assuming Lbol ~10 LoptLbol ~10 Lopt

CAUTION! CAUTION!

1.1. IT ELIMINATES THE INTRINSIC DISPERSION OF THE L-S RELATIONIT ELIMINATES THE INTRINSIC DISPERSION OF THE L-S RELATION

2.2. THE SCALE FACTOR CAN STILL BE WRONGTHE SCALE FACTOR CAN STILL BE WRONG

3.3. THE INCLINATION CAN STILL AFFECT THE WIDTHSTHE INCLINATION CAN STILL AFFECT THE WIDTHS

Example: from the SDSS, McLure & Dunlop 2004Example: from the SDSS, McLure & Dunlop 2004

The relation leads to very high M(BH) for luminous The relation leads to very high M(BH) for luminous quasars (quasars (~10~101010Mo, Netzer 2003, Vestergaard 2002).Mo, Netzer 2003, Vestergaard 2002).

Narrow line Narrow line objectsobjects

L/Led

d=1

II. EXISTENCE OF SUPER-EDDINGTON ACCRETION RATES

Collin, Boisson, Mouchet, et al. 2002Reverberation mapped sample of Kaspi et al. 2000

““Are quasars accreting at super-Eddington rates?”Are quasars accreting at super-Eddington rates?”

€

M.

/M.

edd

€

M.

edd = Lbol/0.1c2

BUT

1. We have used Ho=50, overestimating the luminosities by a factor 2

2. The masses of the sample have been revised by Peterson et al. (2004)

106

107

108

109

1010

106 107 108 109 1010

M(BH) (Kaspi et al., 2000)

STRONG DECREASE

OF

STRONG DECREASE

OF

€

M.

/M.

edd

BUT THERE ARE OTHER SAMPLES, WITH BH MASSES

DETERMINED INDIRECTLY

BUT THERE ARE OTHER SAMPLES, WITH BH MASSES

DETERMINED INDIRECTLY

10-3

10-2

10-1

100

10-3 10-2 10-1 100 101 102

Lopt (in 1044

erg/s)

€η = Lbolc2M.

M=106

M=107

M=108

cos =0.7, Corr-bol=10

L/Ledd=1

L/Ledd=0.1

Let assume that Lopt is due to a thin accretion disk Let assume that Lopt is due to a thin accretion disk (as usually accepted)(as usually accepted)

In the optical, the AD radiates locally like a BB (Hubeny et al. 2001)In the optical, the AD radiates locally like a BB (Hubeny et al. 2001)

€

Lopt cos θ (MM). 2/3

€

Lopt cos θ (MM). 2/3

€

η ~ 0.05 cosθ 3/2 Cbol10 M7

Lopt44

FOR SMALL MASSES AND FOR SMALL MASSES AND LARGE LOPT, THE LARGE LOPT, THE

EFFICIENCY EFFICIENCY ηη SHOULD SHOULD BE VERY SMALLBE VERY SMALL

FOR SMALL MASSES AND FOR SMALL MASSES AND LARGE LOPT, THE LARGE LOPT, THE

EFFICIENCY EFFICIENCY ηη SHOULD SHOULD BE VERY SMALLBE VERY SMALL

THE ACCRETION RATE MUST THE ACCRETION RATE MUST NOT BE CONFUSED WITH THE LUMINOSITY!NOT BE CONFUSED WITH THE LUMINOSITY!

10-1

100

101

102

106 107 108

M(BH) (in solar mass)

sample of NLS1s of Veron2-Goncalves 2001

Lbol

/Ledd

M/Medd

. .

example of super-Eddington accretion rates:example of super-Eddington accretion rates:

Collin & Kawaguchi, 2004 Collin & Kawaguchi, 2004

€

→ η = 0.1 L bol/L edd

M.

/M.

edd

BH masses deduced from the size-luminosity relationshipBH masses deduced from the size-luminosity relationship

10-1

100

101

102

106 107 108

sample of NLS1s of Boroson 2003

Lbol

/Ledd

M(BH) (in solar mass)

M/Medd

. .

Another example of super-Eddington accretion ratesAnother example of super-Eddington accretion rates

Collin & Kawaguchi, 2004 Collin & Kawaguchi, 2004

1 0-21 0-11 001 011 051 061 071 08M (in s o la r m a s s )€ M. /M. ed d€ L /L ed dB arth et al. 2 0 0 5 sam p leL = 9 L o p t

1 0-21 0-11 001 011 051 061 071 08M (in s o la r m a s s )B a rth e t a l. 2 0 0 5 s a m p leL = 9 L o p tLb o l/Le d dM/Me d d..

10-2

10-1

100

101

105 106 107 108

M (in solar mass)

Barth et al. 2005 sample

L= 9 Lopt

Lbol

/Ledd

M/Medd

. .

Super-Eddington accretion rates are found not only Super-Eddington accretion rates are found not only for NLS1s, but generally for low mass samplesfor NLS1s, but generally for low mass samples

L/Led

d=1

McLure & Dunlop 2004McLure & Dunlop 2004

After correction for the efficiency

COULD THERE BE ANOTHER EXPLANATION?COULD THERE BE ANOTHER EXPLANATION?

1. Super-Eddington accretion rate (not large, ≤ 1 Mo per year) at 1. Super-Eddington accretion rate (not large, ≤ 1 Mo per year) at large distance from the BH, but super-Eddington relativistic large distance from the BH, but super-Eddington relativistic wind at small distance (Pounds et al. 2004, Gierlinski & Done wind at small distance (Pounds et al. 2004, Gierlinski & Done 2004, Chevallier et al. 2006).2004, Chevallier et al. 2006).

2. The optical-UV emission is not due to the accretion disk, even 2. The optical-UV emission is not due to the accretion disk, even taking into account a non-gravitational external heating: but to taking into account a non-gravitational external heating: but to what else?what else?

3. The empirical L-R(BLR) relation may not be valid at large 3. The empirical L-R(BLR) relation may not be valid at large L/Ledd and small masses.L/Ledd and small masses.

4. Alternatively, we observe really super-Eddington accretion 4. Alternatively, we observe really super-Eddington accretion rates. Indeed…rates. Indeed…

3. The empirical L-R(BLR) relation may not be valid at large 3. The empirical L-R(BLR) relation may not be valid at large L/Ledd and small masses.L/Ledd and small masses.

4. Alternatively, we observe really super-Eddington accretion 4. Alternatively, we observe really super-Eddington accretion rates. Indeed…rates. Indeed…

10-2

10-1

100

101

100 101 102 103

sample of NLS1s of Veron2-Goncalves

slim disk

10Lopt/Ledd

3 108M

o

3 106M

o

Schwarzschild BH

dotm

10Lopt/L

Super-Eddington accretion rates Super-Eddington accretion rates

are well explained by slim disksare well explained by slim disks

€

M.

/M.

critCollin & Kawaguchi, 2004 Collin & Kawaguchi, 2004

COSMOLOGICAL CONSEQUENCES OF COSMOLOGICAL CONSEQUENCES OF

SUSUPER-EDDINGTON ACCRETION RATESPER-EDDINGTON ACCRETION RATES

1.1. During their low mass phase, the growth time of the BHs is not During their low mass phase, the growth time of the BHs is not Eddington limited (but most probably mass supply limited); it is Eddington limited (but most probably mass supply limited); it is thus much smaller than the Eddington time (Kawaguchi et al. thus much smaller than the Eddington time (Kawaguchi et al. 2004)2004)..

2. It implies that the BH/bulge mass relationship for NLS1s may 2. It implies that the BH/bulge mass relationship for NLS1s may be more dispersed than for other objects.be more dispersed than for other objects.

Super-Eddington accretion can explain Super-Eddington accretion can explain the rapid early growth of BHsthe rapid early growth of BHs

Super-Eddington accretion can explain Super-Eddington accretion can explain the rapid early growth of BHsthe rapid early growth of BHs

SUMMARYSUMMARY

1.1. There are both random (factor 3) AND systematic uncertainties There are both random (factor 3) AND systematic uncertainties (in particular in the scale factor) in the determination of M(BH) (in particular in the scale factor) in the determination of M(BH) using reverberation mapping technique.using reverberation mapping technique.

2.2. These uncertainties are exported to the masses determined These uncertainties are exported to the masses determined indirectly through the L-R(BLR) relationship in the other AGN. indirectly through the L-R(BLR) relationship in the other AGN. Moreover it is not clear whether this relationship can be Moreover it is not clear whether this relationship can be extrapolated to large and small masses and to large Eddington extrapolated to large and small masses and to large Eddington factors.factors.

3.3. If it can be extrapolated to large Eddington factors (If it can be extrapolated to large Eddington factors (~1)~1), it , it implies that the accretion rates should be strongly super-implies that the accretion rates should be strongly super-Eddington in low mass objects ( below 10Eddington in low mass objects ( below 1088Mo).Mo).

4.4. It can have important consequences for the cosmological It can have important consequences for the cosmological growth of BHs.growth of BHs.

1 0-31 0-21 0-11 001 031 04F WH M (H b )L (5 1 0 0 )/L e d dO P E N S Y M B O L Sb lu e s q u a re s : B o 0 3g re y d ia mo n d s : G ru 0 3re d o p e n c irc le s : G ru 9 9g re e n c ro s s e s : V V GF IL L E D S Y M B O L S : K a s p i e t a l. s a mp letria n g le s : L (5 1 0 0 ) < 5 1 04 3 e rg s /sL 5 1 0 0 /L e d d

10-3

10-2

10-1

100

103 104FWHM(Hβ)

/Lopt Ledd

5100/L Ledd

NLS1NLS1

A very tight A very tight correlation appears, correlation appears, due to the neglect of due to the neglect of the error bars on the the error bars on the

empirical relationempirical relation

RM objects RM objects

Boroson et al 04Boroson et al 04

Grupe et al 99Grupe et al 99

Grupe et al 03Grupe et al 03

Veron et al 01Veron et al 01

Lopt < 5 10Lopt < 5 104343 ergs/s ergs/s

x

Example: Collin & Kawaguchi, 2004Example: Collin & Kawaguchi, 2004