The Demographics of broad-line quasars

1. The Demographics of broad-line quasars Yue Shen(CfA) Collaborator: Brandon Kelly (UCSB) Shen & Kelly, ApJ, (2012), 746, 169

2. Quasars and AGNs: • accreting supermassive black holes • active counterparts of the local dormant SMBHs at the center of almost every bulge-dominant galaxies • likely interacted with the host galaxy via feedback processes, as inferred from tight scaling relations between BH mass and bulge properties in local dormant SMBHs • Topics of quasar/AGN studies: • Demographics (abundance of quasars -- LF, BHMF) • Spatial distribution (quasars as dark matter tracers) • Quasar host galaxies • Physical properties (BH mass, SED, emission line regions, feeding and feedback mechanisms, etc.) • Binary SMBHs • Quasar as a backlight (absorption line systems)

3. What happened in the past decade • Large-scale surveys and Multi-wavelength campaigns – rapidly increasing statistics • Sophisticated Simulations of structure formation and galaxy evolution • We now have a basic picture of the cosmological evolution of the SMBH population SDSS DR7

4. Quasar luminosity function and downsizing The space density of bright quasars peaks around z~2-3 Richards et al. (2006, SDSS DR3)

5. Quasar luminosity function and downsizing • Downsizing in quasar LF: the number density of fainter quasars peaks at later times • Discovered in X-ray surveys, and now confirmed in optical surveys as well. Optical LF from 2SLAQ, Croom et al. (2009)

6. Estimating quasar BH masses The broad-line region (BLR) is assumed to be virialized BLR size (reverberation mapping) Virial velocity Reverberation mapping is time consuming, and we only have BLR size measured this way for ~40 AGNs

7. Reverberation mapping  R~Lb b~0.5, Consistent with predictions of photoionization models Bentz et al. (2009)

8. Single-epoch virial BH masses Use continuum luminosity as the surrogate for BLR size; use line width (such as FWHM) as the surrogate for BLR virial velocity. Both quantities are measured from the single-epoch spectrum Continuum luminosity Broad line width

9. Dibai (1980) The mass-luminosity plane Shen et al. (2008)

10. Carnegie Lunch Talk Quasar demographics in the mass-luminosity plane • Two major problems: • Flux limit of the sample • Scatter in BH mass due to errors in mass estimates Virial masses

11. Issues of single-epoch virial BH masses • General concerns of the virial method • Is the virial assumption valid? • Evidence of virial motion in a handful of AGNs (Peterson & Wandel 2000; cf. Krolik 2001) • Disk wind? Perhaps more relevant to CIV (BALQSOs, blueshifts) • Radiation pressure? (Marconi et al. 2008) • Is the virial coefficient f determined properly? • Onken+04 and Woo+10 are consistent, but Graham+10 claimed differently • the value of f depends on the normalization/slope of the M-sigma relation. • Is the RM sample representative of the whole AGN/quasar population? No. • The high-luminosity regime is not sampled well • sub-populations of AGNs may not be included in the RM sample (<~40) • RM BLR size best measured for Hbeta, but not so much for CIV and MgII. • Practical issues with the single-epoch virial mass estimators • how do you measure the line-width and continuum luminosity? Virial BH masses are NOT true masses!

12. Statistical uncertainties of (single-epoch) virial BH masses Scatter matters!! More smaller BHs will be scattered into a high-mass bin by errors in mass estimates than larger BHs being scattered out, leading to a Malmquist-type bias Vestergaard & Peterson (2006)

13. i.e., the virial mass estimate is unbiased, but has a scatter around the true mass (uncertainty) What happens if we fix luminosity? • LogMvir ~ 0.5LogL + 2LogFWHM • P(Mvir|Mtrue) != P(Mvir|Mtrue,L) • A simple example: take a collection of BHs with the same true mass. Uncorrelated variations Correlated variations in luminosity and FWHM G0, G1 and G2 are independent Gaussian random deviates with zero mean and constant dispersion

14. The case of NGC 5548 Collin et al. (2006)

15. When • sigma_L=0.4, sigma_FWHM=0.15 and sigma_corr=0.2  total dispersion in LogL is 0.45 dex, total dispersion in LogFWHM is 0.16 dex, and the uncertainty of the virial mass estimate is 0.36 dex A non-zero term will lead to a luminosity-dependent bias at fixed true mass Luminosity: FWHM: Virial mass:

16. If we observe BHs at fixed luminosity The dispersion of virial mass at fixed luminosity is 0.3 dex, i.e., smaller than the virial uncertainty 0.36 dex. If we observe all BHs, i.e., no constraints on luminosity logL logFWHM logMvir logMvir logMvir

17. Again, P(Mvir|Mtrue) != P(Mvir|Mtrue,L)

18. The virial masses are biased even at fixed luminosity! The impact on the observed evolution of the scaling relations between Mbh and bulge properties Shen&Kelly (2010)

19. Modeling the demographics of broad line quasars using SDSS DR7 • ~58,000 homogeneously selected quasars • Virial BH masses from the Shen et al. (2011) quasar catalog

20. A quick look of the BHMF with virial BH masses • Not the true BHMF! • No correction for the flux-limit • No distinction between true and virial masses.

21. Forward Bayesian modeling in the mass-luminosity plane: accounting for the flux limit and the difference between true and virial masses The model “true” BHMF: mixture of log-normals The model luminosity (Eddington ratio) distribution at fixed true mass

22. Incorporating the luminosity-dependent bias of virial BH masses The posterior distribution of model parameters We perform Bayesian inference with MCMC to derive the posterior model distribution. I.e,, mapping the joint distribution of true masses and luminosities to the “observed” plane of virial masses and luminosities We model in different redshift bins to probe any redshift evolution in the model parameters.

23. An example for the redshift bin at z=0.6 Posterior checks: the observed distributions of luminosity and virial masses were reproduced

24. The distinction between virial BH masses and true masses Black contours: virial BH masses Red contours: true BH masses Flux limit A cautionary note on the “sub-Eddington boundary” claimed by Steinhardt & Elvis, which is based on virial masses and flux-limited samples

25. LF and BHMF at z=0.6

26. The LF is tightly constrained above the flux limit, and makes reasonable prediction to fainter luminosities.

27. The BHMF is difficult to constrain in most redshift bins.

28. Uncertainties and Evolution of Model Parameters

29. Downsizing in LF and BHMF of broad line quasars

30. But the mass density in broad line quasars is always negligible compared to the total mass density in all SMBHs at all times

31. Conclusions • It is useful and important to study the demographics of quasars in the mass-luminosity plane, which offers more information on the evolution of the population • Single-epoch virial BH masses are NOT true masses, and there is evidence for a luminosity-dependent bias, as expected from the imperfect relation between luminosity and line width utilized in virial mass estimators • The flux limit, the scatter (and the luminosity-dependent bias) between true and virial masses, change the distribution in the mass-luminosity plane significantly. • A much larger sample of RM AGNs is needed to fully understand the systematics of these single-epoch mass estimators.