1. AY202a Galaxies & Dynamics Lecture 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. LF in
Other
Properties
From
Blanton
SDSS
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 11α
L* E E E E+11
phi* E E E E-3
Lsum E E E E+08
Ngal
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 , 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 Broad lines in NGC1068
Seyfert 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. vesc = c at the Schwarzschild radius rS
Black Holes
Laplace 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. rBH/D ~ 0.1” (M● /106M)(σ /100 km/s)-1 (DMpc)-1
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. L(V,t) = ∫ (V,τ) C(t-τ) dτ
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 Lyα, 26 CIII], 50 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) = (σ/200 km/s)

41. Barth,
Greene
& Ho

42. BH Mass Function
Greene & Ho ‘07