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.