AY202a Galaxies & Dynamics Lecture 13: LF Con’t, Galaxy Centers

1. AY202a Galaxies & DynamicsLecture 13: LF Con’t,Galaxy Centers

2. Stepwise Maximum Likelihood 1988 Efstathiou, Ellis & Peterson introduced SWML to get the form of the LF w/o “any” assumption about its shape. Parameterize LF as Np steps φ(L) = φk Lk – ΔL/2 < L < Lk + ΔL/2

3. ln L = ∑ W((Li-Lk)ln k - ∑ ln {∑ j L H[Lj-Lmin(zi)]} + C Where N = number of galaxies in sample W(x) = 1 for - L/2 < L < +L/2 = 0 otherwise H(x) = 0 for x - L/2 = x/ L + 1/2 for -L/2 < L < +L/2 = 1 for x > L/2 Normalization via several techniques.

4. CfA1 Marzke et al. (1994)

5. LF in Clusters Smith, Driver & Phillips 1997 α = -1.8 at the faint end….

6. LCRS 1996 Lin et al. 1996

7. Current State of LF Studies 2dF blue photo ~250,000 gals, AAT Fibers SDSS red++ CCD, ~650,000 gals SDSS Fibers 2MASS JHK HgCdTe, 40,000 gals one of + 6dF fibers Stellar Masses from population synthesis

8. SDSS Mass Function vs Density Blanton & Moustakas (2009)

9. SDSS LF in Other Properties From Blanton Galex HI

10. Another Bias ---- we are in a special place There is excess clustering of galaxies around galaxies described often in terms of the correlation function ξ(r) = (r/r0)γ So the excess # of galaxies can be described by NE/N = 4 ∫ r2-γ r 0γ dr with this description we can correct the effective volume around US Vc = cV0 where c = 1 + 4 r0γ /(3-γ) 2r0 3-γ/V0 V0 = 4/3 r3

11. 2MRS

12. 2MRS

13. 2MRS LF E/S0s EarlySP LSP All Types -7 to -1 0 to 5 6 to 11 M* -24.37 -23.85 -24.12 -24.23 α -0.84 -0.78 -1.62 -1.00 L* 1.20E+11 7.45E+10 9.55E+10 1.06E+11 phi* 1.29E-03 2.92E-03 1.51E-04 3.54E-3 Lsum 1.45E+08 1.98E+08 3.08E+07 3.77E+08 Ngal 9414 10466 904 20934 If M/L ~ 1, then the Mass Density = the Luminosity Density but one should apply the appropriate M/L vs type, etc.

14. SDSS Baldry et al.

15. NED

16. LF by Type NED; Trentham

17. The field galaxy baryonic mass function. The data points are for all galaxies, while the lines show spine fits by Hubble Type. The CDM mass spectrum from the numerical simulations of [Weller et al. 2004] is also shown. Overlaid are parameters for a Schechter fit to the total mass function. NED

18. Caveats & Questions 1. How location dependent is (L)? 2. What is the real faint end slope? 3. Is the Schechter function really a good fit? At the bright end? At the faint? 4. What is (T), φ(L,U-B), φ(L,B-B) …? 5. How much trouble are we due to surface brightness limitations? Galaxies have a large range of SB, color, morphology, SED, etc.

19. This week’s paper: The Optical and Near-Infrared Properties of Galaxies. I. Luminosity and Stellar Mass Functions, by Bell, Eric F.; McIntosh, Daniel H.; Katz, Neal; Weinberg, Martin D. 2003, ApJS 149, 289.

20. Bell et al.

21. Bell et al. 2003 M/L versus Color for B- and K-band

22. Bell et al. 2003 log10 (M/L) = a λ+ bλ (color)

23. B-V vs Type Buzzoni et al.

24. JPH 1977

25. AGN Huchra & Burg

26. Galaxy Centers History AGN Discovered way back when --- Fath 1908 Broad lines in NGC1068 Seyfert 1943 Strong central SB correlates with broad lines Growing evidence over the years that there was a central engine and that the central engine must be a black hole! And, what about galaxies that are not AGN?

27. Black Holes Laplace 1795 escape velocity vesc = (2GM/r)½ vesc = c at the Schwarzschild radius rS rS = 2GM/c2 = 2.95 x 105 cm (M/M) This radius is named after Karl Schwarzschild. For the Sun’s mass it is about 3 km. Even a 109 M BH would have a radius of only 3x1012 m or 10-6 pc How do we search for them?

28. Three basic techniques: Photometric Cusps Kinematic Cusps / Maps Reverberation mapping Generally based on the radius of influence of the BH take rotation velocity around a BH = (GM/r )1/2 rBH = GM●/σ2 ~ 0.4 (M● /106M)(σ /100 km/s)-1 so the angular scale we expect to see kinematic effects around a BH is then θBH = rBH/D ~ 0.1”(M● /106M)(σ /100 km/s)-1(DMpc)-1

31. NGC3115 kinematics

32. HST Study by the “Nuker” team, Magorrian et al 1998 log (M●/M) = (-1.79 ±1.35) + (0.96 ±0.12) log(Mbulge/M)

33. Masers in NGC4258 microarcsec proper motions with VLBI

34. Reverberation Mapping Blandford & McKee ’82,  Peterson et al. Assume 1. Continuum comes from a single central source 2. Light travel time is the most important timescale τ = r/c 3. There  a simple (not necessarily linear) relation between the observed continuum and the ionizing continuum.

35. Continuum light curve relative to mean L(V,t) = ∫ (V,τ) C(t-τ) dτ Velocity delay map

37. N5548 Lag relative to 1350A = 12 days @ Lyα, 26 days @ CIII], 50 days @ MgII

38. Kaspi et al R vs L & M vs L From Reverberation Mapping

39. Greene & Ho SDSS AGN M● vs σ

40. Greene & Ho Push to low M Log (M●/M) = 7.96 + 4.02 (σ/200 km/s)

41. Barth, Greene & Ho

42. BH Mass Function Greene & Ho ‘07