1. On the inconsistency between the SMBH Mass Function from velocity dispersion and luminosity E. Tundo 1,2, M. Bernardi 2, R. K. Sheth 2 J. B. Hyde 2, A. Pizzella 1 J. B. Hyde 2, A. Pizzella 1 (1) Dipartimento di Astronomia, Universitá di Padova, Italy (2) Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, USA June 2nd, Ohio State University GLCW8

2. Search for SMBHs Class of Objects: Quiescent Galaxies AGNs Primary methods: Stellar kinematics Megamasers Gas kinematics Reverberation Mapping Today we have about 50 detections, but only three are SURE detections of SMBHs

3. SMBHs correlations Fundamental empirical relations: M bh - L bulge ; M bh - σ * Figure from Gebhardt et al. (2000); but see also Ferrarese & Merritt (2000), Tremaine et al. (2002), Magorrian et al. (1998)

4. What can we learn from these correlations? Black holes and galaxy formation/evolution are linked We can obtain local black hole mass function, Φ(M bh ), from measures of velocity dispersion or luminosity ● Φ(M bh ) is needed as a cosmological test for modern models for formation and evolution of galaxies.

5. : scaling relations SMBHs mass function: scaling relations M bh -σ, M bh -L relations from Häring & Rix (2004) early type sample log(M bh )=(8.21±0.06)+(3.83±0.21)∙log(  /200) Σ=0.22±0.06 dex log(M bh )=(8.68±0.10)-(1.30±0.15)(M r +22)/2.5 Σ=0.34±0.09 dex

6. Comparation of Φ(>M bh ) from the two predictors More than an order of magnitude of difference at 10 9.3 M bh /M ☼ ! Blanton+Hyde, with scatter Sheth+bulge, with scatter From velocity dispersion From luminosity Tundo, E., Bernardi, M., Sheth, R. K., Hyde, J. B., Pizzella, A. 2006, ApJ in press (astro-ph/0609297)

7. We obtain different Φ(>M bh ) even starting from the same luminosity function! Comparation of Φ(>M bh ) from the two predictors From L to Mbh From L to σ to Mbh Sheth et al. 2003 + bulges Tundo, E., Bernardi, M., Sheth, R. K., Hyde, J. B., Pizzella, A. 2006, ApJ in press (astro-ph/0609297) L-based and σ-based cumulative mass functions should give the same result: Φ(M )=∫Φ(O)p(M |O)dO If this is not, something is wrong! L M bh σ

8. Slope s of σ-L relation is different in SDSS and Häring&Rix sample: s HR = -0.14 s SDSS = -0.1 Tundo, E., Bernardi, M., Sheth, R. K., Hyde, J. B., Pizzella, A. 2006, ApJ in press (astro-ph/0609297) A selection effect in the local SMBHs sample

9. Tundo, E, Bernardi, M, Sheth, R. K., Hyde, J. B., Pizzella, A. 2006, ApJ in press (astro-ph/0609297) Taking into account the bias… If we ‘brutally’ correct Ls to make them follow the SDSS L-σ relations, and refit M bh -L the two predictor give the same cumulative mass function.

10. Simulations Bernardi, M., Sheth, R. K., Tundo, E., Hyde, J. B. 2006, ApJ in press (astro-ph/0609300) An empirical model for the selection effect let us reproduce observed relations M bh -σ, M bh -L, σ-L Agreement is non trivial: a change of 5% in selection parameters produce significative differences.

11. Bernardi, M., Sheth, R. K., Tundo, E., Hyde, J. B. 2006, ApJ (astro-ph/0609300) Simulations σ –based Φ(>M bh ) is in better agreement with intrinsic distribution.

12. Conclusions L-based and σ-based cumulative mass function are different, because the L-σ relation is different for the sample in which we measure M bh -L and M bh -σ correlations. If it is caused by selection effects, this bias affects mailnly the luminosity, so it could be safer to use σ-based SMBH mass function. ……. Thank you!!!!!