Constraints on Broad Line Quasar Black Hole Masses, Eddington Ratios, and Lifetimes

1. Constraints on Broad Line Quasar Black Hole Masses, Eddington Ratios, and Lifetimes Brandon C. Kelly (CfA) Marianne Vestergaard (DARK, Denmark), Xiaohui Fan (Arizona), Philip Hopkins (Berkeley), Lars Hernquist (CfA), & Aneta Siemiginowska (CfA) Brandon Kelly, bckelly@cfa.harvard.edu

2. Black Hole Growth and Galaxy Evolution • Tight correlation between MBH and host galaxy bulge properties implies that supermassive black holes (SMBH) and galaxy evolution is linked (e.g., Merritt & Ferrarese 2001, Tremaine et al. 2002) • Can be explained if black hole growth is self-regulated (e.g., Wyithe & Loeb 2003, Di Matteo et al. 2005) • If growth is SR, then broad line phase for bright quasars occurs at end of growth Aller & Richstone (2007) Brandon Kelly, bckelly@cfa.harvard.edu

3. What do We Hope to Learn from Studying the Broad Line Quasar SMBH Mass and Eddington Ratio Distributions? • Distribution and Evolution of SMBH Mass and L / Ledd is a fundamental observational quantity for comparing with theoretical models • Can compare with local mass function of all SMBHs to estimate lifetime of BLQSO phase • Investigate how much growth occurs during BLQSO phases, test self-regulated growth model Brandon Kelly, bckelly@cfa.harvard.edu

4. Correcting for Mass Uncertainty and Incompleteness (Kelly et al. 2009) • Can derive mass estimates from L and FWHM (e.g., Vestergaard & Peterson 2006) • Mass estimates have a large statistical scatter (~0.4 dex), broaden inferred BHMF • Complicated incompleteness, even high mass end can be incomplete Brandon Kelly, bckelly@cfa.harvard.edu

5. Sample Summary • Used the SDSS DR3 Sample of Richards et al. (2006) with measurements taken from Vestergaard et al.(2008) • Only kept objects at 1 < z < 4.5 • Used Mg II for 1 < z < 1.6, and C IV for z > 1.6 • Left with ~ 10,000 sources Brandon Kelly, bckelly@cfa.harvard.edu

6. Quasar BHMF at 1 < z < 4.5 Volonteri & Natarajan (2009) Black Solid: Our Estimated BHMFs Green Solid: Best-fit BHMF Dashed Black : Local BHMF for all SMBHs (Merloni & Heinz 2008) Red Solid: BHMF from Vestergaard et al.(2008) Brandon Kelly, bckelly@cfa.harvard.edu

7. Eddington Ratio Distribution and Fractional Growth Most Broad Line Quasars are not accreting at or near the Eddington Limit Most of the contribution to the local BH mass density is from objects that we currently see as obscured Brandon Kelly, bckelly@cfa.harvard.edu

8. Inferred Lifetime of Broad Line Phase • Lifetime too short to grow a BH seed of MBH ~ 106 MSUN to MBH ~ 109 MSUN • Lifetime + L / Ledd Distribution Imply that most growth occurred in an earlier obscured phase of Eddington-limited growth Brandon Kelly, bckelly@cfa.harvard.edu

9. Maximum Mass of a SMBH Sijacki et all (2009) • If SMBH growth is self-regulated, this should be representative of the most massive SMBH • Consistent with maximum mass seen in cosmological simulations (Sijacki et al. 2009) and that expected from self-regulation arguments (Natarajan & Treister 2009) Brandon Kelly, bckelly@cfa.harvard.edu

10. Summary • First work to rigorously and self-consistently correct for statistical uncertainty and incompleteness in the broad line quasar mass function • BLQSO BHMF qualitatively in agreement with cosmological model of self-regulated black hole growth • Most BL quasars are not accreting at or near L / Ledd • SMBHs cannot experience all of their growth in a BL phase • Maximum SMBH mass is ~ 1010 – 1011 MSUN • Uncertainty in mass estimates may be ~ 0.2 dex, or correlated with luminosity Brandon Kelly, bckelly@cfa.harvard.edu

11. How uncertain are the Mass Estimates? Assuming Scatter of 0.4 dex When we fit the Scatter Red is the model Distribution Black is the observed distribution Standard value of 0.4 dex implies a mass estimate distribution that is too broad, implies: - Statistical error is correlated with luminosity? (Shen & Kelly 2010) - Uncorrected radiation pressure? (Marconi et al. 2008) - Broad line mass estimates are meaningless at this L and z? Brandon Kelly, bckelly@cfa.harvard.edu

12. Future work • Incorporate more flexible L / Ledd distribution • Investigate if error in mass estimates is correlated with luminosity, and include in application to DR7 data set (Shen & Kelly, in prep) • Apply technique to COSMOS and other multiwavelength data sets to better determine Eddington ratio distribution and BHMF (Kelly & Trump, et al.) • Reverberation mapping of higher z and L sources to better determine uncertainties (Elvis and Trump, et al.) Brandon Kelly, bckelly@cfa.harvard.edu

13. Mass-Luminosity Plane Blue: Intrinsic Distribution Red: Model Distribution of Mass Estimates Black: Observed Distribution of Mass Estimates Brandon Kelly, bckelly@cfa.harvard.edu

14. Downsizing of SMBHs Brandon Kelly, bckelly@cfa.harvard.edu