1. Demographics of SDSS Quasars in Two-Dimension
Yue Shen
Carnegie Observatories
In collaboration with Brandon Kelly (UCSB)

2. Motivation
The abundance (and clustering) of quasars are key to understand the evolution of quasars/SMBHs in the hierarchical structure formation paradigm
Abundance measurements form a basis for any cosmological quasar models
Likely tied to formation and evolution of galaxies
Key science goal in many current and upcoming extragalactic survey programs

3. Quasar Luminosity Function Evolves strongly with redshift
The space density of bright quasars peaks around z~2-3
Richards et al. (2006, SDSS DR3)

4. Z=
For bright quasars, the abundance follows a “pure luminosity evolution” (PLE)  a fading, long-lived quasar population?
PLE
Such a simple picture doesn’t fit other observations.
SDSS DR7 LF (Shen & Kelly 2012)

5. Quasar clustering measurements suggest low-z quasars are not simply the descendants of high-z quasars
Dashed lines: predicted evolution of the linear bias for a passive population
z~2 quasars should end up in cluster-sized environment at z~0.5
YS, McBride, White, Zheng, et al. (2013)

6. Quasars evolve in the mass-luminosity plane
A better representation of the evolution of the quasar population
Contains richer information about the growth of SMBHs
Virial masses

7. 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

8. Reverberation mapping  R~Lb (Kaspi et al. 2000)
b~0.5, Consistent with naive predictions of photoionization models
Bentz et al. (2009)

9. Single-epoch virial BH mass estimators
Continuum luminosity
Broad line width
Vestergaard & Peterson(2006), McLure & Dunlop (2004), Greene et al. (2005), and many more …
Currently the only practical method to estimate BH mass for large spectroscopic quasar samples
Many physical and practical concerns that need to be addressed (Shen 2013): we are extrapolating from ~40 local AGNs with reverberation mapping data to high-z, high-luminosity quasars
Large uncertainties for individual BH mass estimates: ~ a factor of 3 (~0.5 dex)

10. Quasar abundance in the mass-luminosity plane
The sample used: ~58,000 uniformly selected DR7 SDSS quasars, with good spectra to estimate BH mass
Two major problems:
Flux limit of the sample
Scatter in BH mass due to errors in mass estimates
Virial masses

11. Forward modeling in the mass-luminosity plane (Shen & Kelly 2012, Kelly & Shen 2013)
Flux limit and mass errors are more easily accounted for
More information is preserved
True BH masses

12. LF
BHMF
Caveats:
SDSS only probes the tip of the quasar population, poorly constraining the faint-end of the LF and the low-mass end of the BHMF – need deeper data
Systematic uncertainties of quasar BH mass estimates have dramatic effects on the BHMF estimates – need to improve the BH weighing method

13. Downsizing in terms of quasar luminosity and BH mass

14. Properly accounting for the selection effect of flux-limited samples and errors in the virial BH mass estimates
Eddington limit
Interpret the “observed distributions” with caution
Flux limit
Red: true mass
Black: virial mass estimates

15. Summary
Instead of measuring LF and BHMF separately, measure 2D density in the M-L plane (if you have a spectroscopic sample); this gives you more information on the evolution of the quasar population
Forward modeling in the M-L plane makes it easier to account for the sample flux-limit and errors in mass estimates
The “observed” distribution in the M-L plane is biased; don’t interpret it directly!
There is urgent need to improve quasar BH mass weighing methods (~0.5 dex error is inconvenient)