Padova Lecture Series 2007Lecture 4 41

Global Scaling Relations of Galaxies

!

VVir

2"M

Vir

RVir

Courteau et al.

2007

! For a virialized DM halo:

!

a = (1+ z)"1

! At early times, with:

!

MVir

RVir

3" a

#3

!

VVir" a

#1/ 2M

Vir

1/ 3

!

RVir" aM

Vir

1/ 3

! Constant M/L :

!

L"MVir

!

Rdisk

" #RVir

!

Vobs"V

Vir

!

Vobs" a

#1/ 2L0.33

!

Vobs"L

I

0.30±0.02

!

Rdisk

" aL0.33

!

Rdisk

"L0.38±0.02

Observed:

! N-body simul :

Padova Lecture Series 2007Lecture 4 42

!CDM Formation Models! Failures:

" LF normalization & TF zero-point simultaneously

Navarr

o &

Ste

inm

etz

(2

000+

)

MI – 5 log(h)

Lo

g V

rot (k

m s

-1)

Padova Lecture Series 2007Lecture 4 43

!CDM Formation Models! Failures:

" LF normalization & TF zero-point simultaneously

" Disk size (angular momentum “problem”)

Navarr

o &

Ste

inm

etz

(2000+

)

log Vrot (km s-1)

log

jd

isk (

km

s-1

h-1

kp

c)

(Courteau 1997)

Padova Lecture Series 2007Lecture 4 44

log Rotation Velocity

I-ban

d A

bsolu

te M

ag

nitude

But what about the Governato et al. 2007 simulations?

… looks good. But just how did they compute V?

Padova Lecture Series 2007Lecture 4 45

3.5 B-band scale lengths, 2.2 B-band scale lengths

Rotation Curves of the Governato et al. 2007 simulated galaxies

These don’t look like typical spiral galaxy rotation curves

Radius [kpc]

Rota

tio

n V

elo

city [

km

/s]

Padova Lecture Series 2007Lecture 4 46

Rota

tio

n V

elo

city [

km

/s]

2.2 K-band scale lengths,

Radius [kpc]

2.2 B-band scale lengths

Rotation Curves of the Governato et al. 2007 simulated galaxies

V2.2K is much higher than V2.2B

Padova Lecture Series 2007Lecture 4 47

V2.2K

log Rotation Velocity

I-ba

nd

Ab

so

lute

Mag

nitu

de

Plot V2.2K, and now the galaxies rotate too fast

Just like ENS 2001. …and another problem…

Padova Lecture Series 2007Lecture 4 48

Vvir

V2.2K

log Rotation Velocity

I-b

an

d A

bsolu

te M

ag

nitu

de

…the Vvir are too small: V2.2 /Vvir~2

…and another problem…

Padova Lecture Series 2007Lecture 4 59

The Courteau-Rix (1999) Argument

exp

2

R

)/(~V

LLM! ""For pure exponential stellar disks

exp

2

R

)/(~V

LM! ""For a given luminosity

2/1

expR~V !! ""and if M/L vs r is self-similar

in bright spirals

5.0)M(logR

)M(logV

rexp

r !="

"Therefore

Padova Lecture Series 2007Lecture 4 60

! At a given mass, a !Rexp of 20% yields

" 10% change in Vdisk

" 30% offset in luminosity from mean TFR

" Such an effect should be detectable

" DM halo (especially if cuspy) will reduce

this effect

The Courteau-Rix (1999) Argument

Padova Lecture Series 2007Lecture 4 61

TFR as a Tracer of DM

Pure self-gravitating exponential disks should have

but empirically we find

5.0)M(logR

)M(logV

rexp

r !="

"

!

"logV2.2

"logRexp

= #0.08 ± 0.05

Padova Lecture Series 2007Lecture 4 62

Residual Correlations

Courteau et al. 2007

Slope=-0.5

Padova Lecture Series 2007Lecture 4 63

Comparison With Models

! Simple exponential disk embedded in a DM halo

! Use density profile for collisionless !CDM simulationsof halo formation (NFW)

! Assume adiabatic invariance

! Use stellar disks of various M/L ratios and Rexp = 3 kpc,and compute the disk-halo contributions to the rotationcurve.

! Get ! logV2.2 / ! logRexp for each value of Vdisk/ Vtot

! Test with bulge and isothermal halos

Padova Lecture Series 2007Lecture 4 64

Comparison With Models

" Vdisk / Vtot = 0.55 ± 0.05 at R = 2.2Rexp

Courteau & Rix (1999); Courteau et al. 2007

Padova Lecture Series 2007Lecture 4 65

2237+0305

(Huchra Lens, z = 0.0394, zQSO = 1.695)

Geometry of

gravitational lens

system + rotation

curve can be used

to decompose the

mass distribution of

the lensing galaxy.

Vdisk/Vtot = 0.57±0.03

Trott & Webster

(2002)

Evidence for Sub-maximal

Disks

Padova Lecture Series 2007Lecture 4 66

Evidence for Sub-Maximal Disks

! Predicted by analytical models of galaxy formation(e.g. Mo, Mao, & White 1998). (Assumes AC)

! Bottema (1997): stellar kinematics of galactic disks

! Courteau & Rix (1999): TF residuals (Assumes AC)

! Kranz, Slyz & Rix (2002): gas kinematics and structureof spiral arms

! Kregel et al. (2002): disk flattening of edge-on galaxies

! Trott & Webster (2002): lensing + rotation curveconstraints

Vdisk/Vtot ! 0.6 MDM/Mtot " 0.7

(on average at 2.2 disk scale lengths)

Padova Lecture Series 2007Lecture 4 67

# = halo spin c = halo conc.

mg = disk mass $I = disk M/L

Assumes log-normal scatterDutton etal 2007

Semi-Analytic Models of Disk Galaxies

Padova Lecture Series 2007Lecture 4 68

# = halo spin c = halo conc.

mg = disk mass $I = disk M/L

Assumes log-normal scatter Dutton et al 2007

Semi-Analytic Models of Disk Galaxies

(after Courteau & Rix 1999)

Padova Lecture Series 2007Lecture 4 69

Galaxy scaling relations

Dutton etal 2007Allowing for halo expansion

Padova Lecture Series 2007Lecture 4 70

Three problems for

three solutions

! Lower stellar mass-to-light ratio

But need an extreme top-heavy IMF, or maybe

lots of dust

! Lower initial halo concentration

need initial c200#3, which seems inconsistent with CDM

! Turn off halo contraction

“But every goddamned simulation indicates that

there is substantial compression”

Anatoly Klypin (Irvine 2007)

Padova Lecture Series 2007Lecture 4 71

Reversing Halo Contraction

is not so Crazy

! Halo contraction is NOT a prediction of CDM

CDM says nothing about the baryonic physics of

galaxy formation

! Halo contraction is a prediction of dynamics

If the potential well deepens through the formation of a galaxy

at the center, and the halo has time to respond, it will contract.

! But this does not prevent other processes from

reducing or reversing its effects

Since cosmological simulations fail to make realistic disk galaxies,

something must be missing (e.g. resolution and/or physics).

This may result from non-spherical, clumpy gas accretion,

where dynamical friction transfers energy from the gas to the DM.

Padova Lecture Series 2007Lecture 4 72

Reversing Halo Contraction

is not so Crazy! Feedback: Slow infall + fast outflow = halo expansion

(e.g. Gnedin & Zhao 2000; Read & Gilmore 2005).

Also explains the small fraction (~20%) of the universal

baryons in galaxies.

! Angular Momentum Exchange: baryons lose AM to halo through dynamical friction (bars, mergers)

(e.g. Weinberg & Katz 2002; El Zant et al. 2004;

Mo & Mao 2004; Sellwood 2006; Tonini et al. 2006)

potential problems:

if baryons lose too much AM => disks too small

more concentrated baryons => halo contraction

! Maybe AMEX+FB together can expand the halo?

Padova Lecture Series 2007Lecture 4 73

Comparison With Models

" Vdisk / Vtot < 0.6 at R = 2.2Rexp with AC (Courteau & Rix 1999)

" Vdisk / Vtot = 0.72 ± 0.05 at R = 2.2Rexp without AC

Padova Lecture Series 2007Lecture 4 75

Summary

! Reproducing the Tully Fisher relation, disk sizes

and number densities, simultaneously, is still

a problem for disk galaxy formation models

Dutton et al. 2007

! Three solutions: low stellar M/L; low initial halo concentration;

reverse halo contraction.

! V2.2 /VVir is a powerful constraint on halo

contraction models, provided we know average

disk sizes and stellar masses.

! Speculation: Halo contraction might be reversed

by a combination of angular momentum

exchange and mass ejection through feedback.