UNCERTAINTIES ON THE BLACK HOLE MASSES AND CONSEQUENCES FOR THE EDDINGTON RATIOS Suzy Collin Observatoire de Paris-Meudon, France Collaborators: T. Kawaguchi (Tokyo), B. Peterson (Ohio U), M. Vestergaard (Steward obs), C. Boisson, M. Mouchet (Paris)

I.Uncertainties on direct mass determinations II.Indirect mass determinations: super-Eddington accretion rates

IN 35 SEYFERT AND LOW REDSHIFT QUASARS BH MASSES ARE DETERMINED DIRECTLY BH MASSES ARE DETERMINED DIRECTLY BY THE “REVERBERATION MAPPING METHOD” 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 Line Region. Assuming that the BLR is gravitationally bound (certainly true for the Balmer line emitting region), the mass of the BH,, is then: where is the dispersion velocity, and a scale factor. It is usually assumed (Peterson & Wandel 1999, Kaspi et al. 2000) that which correspond to an isotropic BLR with a random distribution of orbits. which correspond to an isotropic BLR with a random distribution of orbits. M(BH) = f (c  V 2 /G) = f (Virial Product)  M(BH), M(BH), R(BLR) Vf V = FWHM, and f = 3/4 IN ALL OTHER OBJECTS (EXCEPT ONE) THE MASSES ARE DETERMINED INDIRECTLY USING THIS EMPIRICAL RELATION by-product:  an empirical relation between R(BLR) and L(optical) I. UNCERTAINTIES ON THE MASS DETERMINATIONS

VARIOUS UNCERTAINTIES 1.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). 2. What is the best choice for measuring V? The FWHM (all works) or  line ?  line seems more reliable (Peterson et al. 2004), but it is generally not measured. 3.Is it better to use the RMS or the mean spectrum? Etc…

Peterson et al. 2004: use  (line) instead of FWHM, RMS spectrum instead of mean spectrum, and changed the factor f (scaled on the bulge masses by Onken et al. 2004) Sample of reverberation mapped objects Example of systematic uncertainties

Collin, Kawaguchi, Peterson, Vestergaard (2006) Reverberation mapped objects, all datasets broad flat topped lines Mean spectra RMS spectra NGC5548 narrow peaked lines Gaussian profile THE SCALE FACTOR IS NOT A CONSTANT

Pop 1 Pop 2 Pop A Pop B similar to Sulentic et al. Collin et al. Scale factor determined by fitting M(BH) to M(  * ), M(BH) being FWHM-based Remember: f = 0.75 is used f = 2.4  1 f = 0.85  0.15

THE INCLINATION OF THE BLR PLAYS A ROLE a fraction of Pop1 objects should be seen at small inclination: their masses can be underestimated by factors up to ten (NGC4051, Mrk590, NGC7469…) Assuming that the velocity includes a plane rotational plus an isotropic part V obs =V Kep (a 2 + sin   ) 1/2 and using the distribution of M(  * ) /M(RM), we found that

BH MASSES DETERMINED IN LARGE SAMPLES BH MASSES DETERMINED IN LARGE SAMPLES INDIRECTLY BY THE EMPIRICAL RELATION Kaspi et al. 2000, revised by Kaspi et al Allows to determine M(BH) for single epoch observations, simply by measuring Lopt (= L at 5100A) and the FWHM Determination of Lbol/Ledd Lbol: generally deduced from Lopt, assuming Lbol ~10 Lopt

CAUTION! 1.IT ELIMINATES THE INTRINSIC DISPERSION OF THE L-S RELATION 2.THE SCALE FACTOR CAN STILL BE WRONG 3.THE INCLINATION CAN STILL AFFECT THE WIDTHS

Example: from the SDSS, McLure & Dunlop 2004 The relation leads to very high M(BH) for luminous quasars (~10 10 Mo, Netzer 2003, Vestergaard 2002). Narrow line objects L/Ledd=1

II. EXISTENCE OF SUPER-EDDINGTON ACCRETION RATES Collin, Boisson, Mouchet, et al Reverberation mapped sample of Kaspi et al “Are quasars accreting at super-Eddington rates?”

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) STRONG DECREASE OF BUT THERE ARE OTHER SAMPLES, WITH BH MASSES DETERMINED INDIRECTLY

cos  =0.7, Corr-bol=10 L/Ledd=1 L/Ledd=0.1 Let assume that Lopt is due to a thin accretion disk (as usually accepted) In the optical, the AD radiates locally like a BB (Hubeny et al. 2001)  FOR SMALL MASSES AND LARGE LOPT, THE EFFICIENCY  SHOULD BE VERY SMALL THE ACCRETION RATE MUST NOT BE CONFUSED WITH THE LUMINOSITY!

example of super-Eddington accretion rates: Collin & Kawaguchi, 2004 BH masses deduced from the size-luminosity relationship

Another example of super-Eddington accretion rates Collin & Kawaguchi, 2004

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

L/Ledd=1 McLure & Dunlop 2004 After correction for the efficiency

COULD THERE BE ANOTHER EXPLANATION? 1. Super-Eddington accretion rate (not large, ≤ 1 Mo per year) at large distance from the BH, but super-Eddington relativistic wind at small distance (Pounds et al. 2004, Gierlinski & Done 2004, Chevallier et al. 2006). 2. The optical-UV emission is not due to the accretion disk, even taking into account a non-gravitational external heating: but to what else? 3. The empirical L-R(BLR) relation may not be valid at large L/Ledd and small masses. 4. Alternatively, we observe really super-Eddington accretion rates. Indeed… 3. The empirical L-R(BLR) relation may not be valid at large L/Ledd and small masses. 4. Alternatively, we observe really super-Eddington accretion rates. Indeed…

Super-Eddington accretion rates are well explained by slim disks Collin & Kawaguchi, 2004

COSMOLOGICAL CONSEQUENCES OF SUPER-EDDINGTON ACCRETION RATES 1.During their low mass phase, the growth time of the BHs is not Eddington limited (but most probably mass supply limited); it is thus much smaller than the Eddington time (Kawaguchi et al. 2004). 2. It implies that the BH/bulge mass relationship for NLS1s may be more dispersed than for other objects. Super-Eddington accretion can explain the rapid early growth of BHs Super-Eddington accretion can explain the rapid early growth of BHs

SUMMARY 1.There are both random (factor 3) AND systematic uncertainties (in particular in the scale factor) in the determination of M(BH) using reverberation mapping technique. 2.These uncertainties are exported to the masses determined indirectly through the L-R(BLR) relationship in the other AGN. Moreover it is not clear whether this relationship can be extrapolated to large and small masses and to large Eddington factors. 3.If it can be extrapolated to large Eddington factors (~1), it implies that the accretion rates should be strongly super- Eddington in low mass objects ( below 10 8 Mo). 4.It can have important consequences for the cosmological growth of BHs.

NLS1 A very tight correlation appears, due to the neglect of the error bars on the empirical relation RM objects RM objects Boroson et al 04 Boroson et al 04 Grupe et al 99 Grupe et al 99 Grupe et al 03 Grupe et al 03 Veron et al 01 Veron et al 01 Lopt < ergs/s Lopt < ergs/s x Example: Collin & Kawaguchi, 2004