Galaxy%20formation

1

• Gave this is Sta Bar on Nov/08 got to the end
  but spoke for about 65 mins
• For Dur on Jan/09 I shortened the intro, but
  still took 65 mins
• To prepare for CERN on Feb/09, I added new
  slides from Vogelsberger paper
• Thus, this is now a full collection of slides on
  this topic

2
The galactic dark matter halo
Carlos S. Frenk Institute for Computational
Cosmology, Durham
3
The cosmic power spectrum
CMB
k-1 (comoving h-1 Mpc)
10
1000

• Convert angular separation to distance (and k)
  assuming flat geometry
• Extrapolate to z0 using linear theory

WMAP
LCDM
Power spectrum P(k) (h-1 Mpc)3
wavenumber k (comoving h-1 Mpc)-1
4
The cosmic power spectrum from the CMB to the
2dFGRS
CMB
k-1 (comoving h-1 Mpc)
10
1000

• Convert angular separation to distance (and k)
  assuming flat geometry
• Extrapolate to z0 using linear theory

z0
WMAP
2dFGRS
Power spectrum P(k) (h-1 Mpc)3
? LCDM provides an excellent description of mass
power spectrum from 10-1000 Mpc
Sanchez et al 06
wavenumber k (comoving h-1 Mpc)-1
5
The cosmic power spectrum from the CMB to the
2dFGRS
CMB
k-1 (comoving h-1 Mpc)
10
1000

• Convert angular separation to distance (and k)
  assuming flat geometry
• Extrapolate to z0 using linear theory

z0
WMAP
2dFGRS
Power spectrum P(k) (h-1 Mpc)3
? LCDM provides an excellent description of mass
power spectrum from 10-1000 Mpc
Sanchez et al 06
wavenumber k (comoving h-1 Mpc)-1
6
2df galaxy survey
7
The cold dark matter model
Detecting cold dark matter
8
The cold dark matter model
Detecting cold dark matter
9
Cold dark matter searches
Astrophysical input normally assumed for direct
searches
10
Non-standard halo models
Analytic models
Massive substructures and streams ? large boost
factor
caustic ring model
Van Bibber, IDM (2008)
11
The structure of cold dark matter halos

• Need N-body simulations

12
Initial conditions for simulations of cold dark
matter halos
The linear power spectrum (power per octave)
Assumes a 100GeV wimp Green et al 04

• Predictions for detection expts depend on CDM
  distr on scales far below those accessible to
  sims
• We require a good theoretical understanding of
  mixing and small-scale structure

k3P(k)
k h Mpc-1
13
The cold dark matter power spectrum
The linear power spectrum (power per octave )
Assumes a 100GeV wimp Green et al 04
k3P(k)
k h Mpc-1
14
Testing the CDM paradigm
dr/r 10-5
Small scales
Initial conditions LCDM
z0
dr/r 1-106
15
Detection of cold dark matter
Many of these issues can be addressed with high
resolution simulations of the formation of
galactic dark halos from CDM initial conditions

• Predictions for detection experiments depend on
  the CDM distribution on scales far below those
  accessible to simulation
• We require a good theoretical understanding of
  mixing and small-scale structure

16
Detectability issues for CDM distribution

• Laboratory experiments
• - What is the expected CDM distribution in
  space and in velocity on the scale of the
  apparatus?
• Small-scale clumping
• - How much ?-emission comes from small clumps?
  - Which strucures should be most
  easily detected?
• Unbound phase-space structure
• - How much ?-emission comes from caustics?
  
• Galactic Centre
• - How much ?-emission comes from the black
  hole's cusp?

17
The Aquarius programme
18
z 0.0
19
Galactic halos (without the galaxies)

• Halos are extended
• Extend to 10 times the 'visible' radius of
  galaxies and contain 10 times the mass in the
  visible regions
• Halos are triaxial ellipsoids (not spherical)
• more prolate than oblate
• axial ratios greater than 2 are common
• Halos have nearly universal cuspy" density
  profiles
• dlnr / dln r g with g lt -2.5 at large r
• ??????????????????????????????????????????g gt
  -1.2 at small r
• Halos are clumpy
• Substantial numbers of self-bound subhalos
  containing 10 of the halo's mass

20
z 0.0
21
The Aquarius programme

• 6 different galaxy size halos simulated at
  varying resolution, allowing for a proper
  assessment of numerical convergence and cosmic
  variance

Springel et al 08
22
The Aquarius programme
C. Frenk, A. Helmi, A. Jenkins, A. Ludlow, J.
Navarro, V. Springel, M. Vogelsberger, J.
Wang, S. White
23
(No Transcript)
24
Images of all Aquarius halos (level-2)

• The Aquarius Billennium halo simulation. A dark
  matter halo with 1 billion particles within the
  virial radius.

500 kpc
Play Movie
25
Galactic cold dark matter halos

• The central density structure of halos

26
The Density Profile of Cold Dark Matter Halos
27
Explanations for the core/satellite "crises"

• The dark matter is warm
• The dark matter has a finite self-scattering
  cross-section
• The primordial density power spectrum has a
  break (or running spectral index)
• There is no dark matter -- gravity needs
  modifying
• Astrophysics baryon effects, black holes, bars
• The comparison of models and data is incorrect

28
Density profile r(r)
z0
Orignal NFW simulations resolved down to 5 of
rvir
NFW
29
Density profile r(r)
z0
30
Density profile r(r) convergence test
z0
The spherically averaged density profiles show
very good convergence, and are approximately fit
by a NFW profile
31
Deviations from NFW
The density profile is fit by the NFW form to
10-20. In detail, the shape of the
profile is slightly different.
32
Universality of the mass profile
6 HALOS LEVEL 2 RESOLUTION
density ? r2
circular velocity
scaled radius
Slight but significant deviations from
similarity. A third parameter needed to
describe accurately mass profiles of CDM halos.
Einasto
Virgo Consortium 08
33
Pseudo-phase-space density profile
r-1.875
log ????
log radius

• All halos have the same phase-space density,
  ?/?3, structure a power-law
• with the same exponent as Bertschingers
  secondary infall similarity solution
• This seems to reflect a fundamental structural
  property of CDM halos

34
The structure of the cusp
slope
slope
Moore etal
Moore etal
NFW
NFW
Einasto
Einasto
radius
scaled radius
Logarithmic slope scales like a power-law of
radius the Einasto profile Innermost profile
shallower than r-1
Virgo Consortium 08
35
The cusp maximum asymptotic slope
Moore etal
Moore etal
maximum asymptotic slope
maximum asymptotic slope
NFW
NFW
Einasto
Einasto
radius

• Maximum asymptotic slope of the cusp shallower
  than r-1

Virgo Consortium 08
36
Density profile r(r)
log r(r) r2
37
Slope of the density profile
Density profile becomes shallower towards the
centre
No obvious convergence to a power law
profile Innermost slope is shallower than -1
Virgo Consortium 08
38
Velocity structure convergence test
Velocity dispersion
Velocity anisotropy
radius

• Excellent numerical convergence down to radius
  where the collisional relaxation time approaches
  the age of the universe

Virgo Consortium 08
39
Universality of velocity structure
Velocity dispersion
Velocity anisotropy
scaled radius

• Slight but significant deviations from
  similarity
• Deviant systems in mass are also deviant in
  velocity
• Note similarity in shape between density and
  velocity dispersion

40
A Cold dark matter universe
N-body simulations show that cold dark matter
halos (from galaxies to clusters) have
Cuspy density profiles
Does nature have them?
Look in galaxies and clusters
41
The density profile of galaxy cluster dark halos
Johnston et al 09
Total
NFW
BCG
Weak lensing for 130,000 groups and clusters from
SDSS
Projected surface density
Model contributions from brightest central
galaxy, cluster dark halo and neigbouring dark
halos
r h-1Mpc
r h-1Mpc
r h-1Mpc
42
The density profile of galaxy cluster dark halos
Concentration-mass relation
concentration
NFW
Neto et al 07
Weak lensing for 130,000 groups and clusters from
SDSS
Johnston et al 09
43
Summary of halo mass structure

• The mass profile of CDM halos
• not strictly self-similar, and deviates slightly
  but significantly from the formula proposed by
  NFW.
• It is well approximated by the Einasto profile
  dln?/dlnr ? ra
• The Cusp
• ? ? r-1.2 (or steeper) cusps ruled out,
• cusp must be shallower than ???? r-1
• The phase-space density
• seems to be a fundamental structural property of
  CDM halos.
• A simple power law, with the same exponent as the
  self-similar secondary infall model, approximates
  well the profiles of all halos,
• ????? ? r-1.875

44
Summary of halo mass structure

• Halo profiles not strictly self-similar
• The NFW formula fits spherically averaged
  profiles of most objects to within 10 out to at
  least 2rs
• The Einasto formula fits better its additional
  shape parameter varies systematically with mass
• Scatter among halos larger than the Einasto-NFW
  difference
• The cusp
• ? ? r-1.2 (or steeper) cusps ruled out,
• cusp must be shallower than ???? r-1
• There is no indication of any asymptotic inner
  power law
• Observational evidence for NFW profiles in
  clusters

45
Halo structure conclusions

• Halos extend to 10 times the 'visible' radius
  of galaxies and contain 10 times the mass in the
  visible regions
• Halos are triaxial ellipsoids (not spherical)
• Halos have nearly universal cuspy" density
  profiles
• Cusps are inferred in cluster halos

46
Halo substructures
47
The Aquarius programme

• 6 different galaxy size halos simulated at
  varying resolution, allowing for a proper
  assessment of numerical convergence and cosmic
  variance

Springel et al 08
48
z 1.5

• N2003?106

4003 run
49
z 1.5

• N20094?106

12003 run
50
z 1.5
N200750?106
24003 run
51
The mass function of substructures
N(M) ? Ma
a -1.90
The subhalo mass function is shallower than M-2
dN/dMsub Mo

• Most of the substructure mass is in the few most
  massive halos
• The total mass in substructures converges well
  even for moderate resolution

Msub Mo
300,000 subhalos within virialized region in
Aq-A-1
Springel, Wang, Vogelsberger, Ludlow, Jenkins,
Helmi, Navarro, Frenk White 08
Virgo consortium Springel et al 08
52
The mass function of substructures
N(M) ? Ma
a -1.90
The subhalo mass function is shallower than M-2
dN/dMsub Mo

• Most of the substructure mass is in the few most
  massive halos
• The total mass in substructures converges well
  even for moderate resolution

Msub Mo
MASS PER LOG INTERVAL
Msub2 dN/dMsub h-1 Mo
Virgo consortium Springel et al 08
Msub Mo
53
The substructure circ velocity function
We find 3 times as many subhalos as Diemand et al
find for VL I, but VLII is close to our ensemble
54
The substructure circ velocity function
We find 3 times as many subhalos as Diemand et al
find for VL I, but VLII is close to our ensemble
Differences in the DM distributions of VLII and
Aquarius are NOT significant for the problem at
hand
55
The substructure circ velocity function
CUMULATIVE NUMBER OF SUBSTRUCTURES AS A FUNCTION
OF VMAX,
We find 3 times as many subhalos as Diemand et al
find for Via Lactea I
VLI
VLII
The velocity function of substructures is close
to a power law

• Cosmic variance? - No
• Substructure finding algorithm? - No
• Different cosmological parameters? - unlikely

N(gtVmax/V50)
Crucial for interpretation of abundance of Milky
Way satellites and annihilation signal from
substructures
Vmax/V50
56
Galactic halos (without the galaxies)

• Halos are extended
• Extend to 10 times the 'visible' radius of
  galaxies and contain 10 times the mass in the
  visible regions
• Halos are triaxial ellipsoids (not spherical)
• more prolate than oblate
• axial ratios greater than 2 are common
• Halos have nearly universal cuspy" density
  profiles
• dlnr / dln r g with g lt -2.5 at large r
• ??????????????????????????????????????????g gt
  -1.2 at small r
• Halos are clumpy
• Substantial numbers of self-bound subhalos
  containing 10 of the halo's mass

57
How lumpy is the halo?
58
z 0.1
A galactic dark matter halo
1.1 billion particles inside rvir
Springel, Wang, Volgensberger, Ludlow, Jenkins,
Helmi, Navarro, Frenk White 08
24003 run
59
The subhalo number density profile
n(r)/ltngt

• The spatial distribution of subhalos (except
  for the few most massive ones) is independent of
  mass
• Most subhalos are at large radii -- subhalos
  are more effectively destroyed near the centre
• Most subhalos have completed only a few orbits
  dynamical friction unimportant below a subhalo
  mass threshold
• Subhalos are far from the Sun

r kpc
dfn(ltr)/dlog r
Enclosed no. fraction of substructures of
different mass
Sun
r kpc
60
The cold dark matter power spectrum
The linear power spectrum (power per octave )
Assumes a 100GeV wimp Green et al 04
k3P(k)
k h Mpc-1
61
Direct cold dark matter searches
How smooth is the dark matter mass distribution
at the solar position?
62
How lumpy is the MW halo?
Mass fraction in subhalos as a fn of cutoff mass
in CDM PS
The Milky Way halo is expected to be quite smooth!
Mass fraction in subhalos within Rsun lt 0.1
63
Substructure conclusions

• The total mass in subhalos converges only weakly
  at small mass
• Substructure is primarily in the outermost parts
  of halos
• The radial distribution of subhalos is almost
  mass-independent
• Subhalos contain a very small mass fraction in
  the inner halo

64
Halo structure conclusions
Overall structure

• Halos extend to 10 times the 'visible' radius
  of galaxies and contain 10 times the mass in the
  visible regions
• Halos are triaxial ellipsoids (not spherical)
• Halos have nearly universal cuspy" density
  profiles
• dlnr / dlnr? gt -1.2 at small r observed in
  clusters

65
Halo substructure conclusions

• Total mass in bound subhalos converges (weakly)
  at small mass
• Substructure is 7 of mass and is primarily in
  outer part of halo
• Subhalos contain a very small mass fraction in
  the inner halo

66
Direct searches for cold dark matter
67
CDM distribution around the Sun
Density prob distribution fn around solar circle
10 kpc gt r gt 6 kpc

• Estimate ? at a point by adaptive smoothing w.
  64 nearest particles
• Fit to smooth r profile stratified on ellipsoids

Smooth component
Subhalo population
Prediction for uniform point distribution
r / rmean
Vogelsberger et al 09
68
CDM distribution around the Sun
Density prob distribution fn around solar circle

• The chance of a random point lying in a
  substructure is lt 10-4

10 kpc gt r gt 6 kpc
Smooth component
Subhalo population
Prediction for uniform point distribution
r / rmean
Vogelsberger et al 09
69
CDM distribution around the Sun
Density prob distribution fn around solar circle

• The chance of a random point lying in a
  substructure is lt 10-4
• The rms scatter about smooth model for the
  remaining points is 4

10 kpc gt r gt 6 kpc
Smooth component
Subhalo population
Prediction for uniform point distribution

• With gt99.9 confidence, the DM density near the
  Sun differs from smooth mean value by lt 15

r / rmean
Vogelsberger et al 09
70
Direct cold dark matter searches
What is the dark matter velocity distribution at
the solar position?
71
Local velocity distribution
Velocity distribution in a 2kpc box at solar
circle

• Velocity histograms for particles in a typical
  (2kpc)3 box at R 8 kpc
• Distributions are smooth, near-Gaussian, and
  different in different directions
• No individual streams are visible

72
Energy space features - fossils of formation
Nearly universal shape at high binding energy
Density of states

• The energy distr. in (2 kpc)3 boxes shows bumps
  which
• - repeat from box to box -
  stable over Gyr timescale - different
  for different halos
• These are potentially observable fossils of the
  formation process

Large fluctuations at lower binding energies
Vogelsberger et al 09
73
Effect on detector signals
Differences relative to multivariate Gaussian
WIMP recoil spectrum
Axion microwave spectrum
Power x 106
R/RGauss
b x 10-6
b x 10-6
b(v/c)
74
Conclusions for direct detection experiments

• With more than 99.9 confidence the Sun lies in
  a region where the DM density differs from the
  smooth mean value by lt 15
• The local velocity distribution of DM particles
  is similar to a trivariate Gaussian with no
  measurable lumpiness due to individual DM
  streams
• The energy distribution of DM particles should
  contain broad features with 20 amplitude which
  are the fossils of the detailed assembly history
  of the Milky Way's dark halo

? Dark matter astronomy
75
Indirect CDM detection through annihilation
radiation
Supersymmetric particles annihilate and lead to
production of g-rays which may be observable by
GLAST/FERMI
? Theoretical expectation requires knowing r(x)
? Accurate high resolution N-body simulations of
halo formation from CDM initial conditions
76
A blueprint for detecting halo CDM
To calculate annihilation luminosity need
contribution from 4 components

1. Smooth emission from main halo
2. Smooth emission from resolved subhalos
3. Emission from unresolved subhalos in main halo
4. Emission from substructure of subhalos

77
A galactic CDM halo
2 myths about the galactic halo
78
A blueprint for detecting halo CDM
Supersymmetric particles annihilate and lead to
production of g-rays which may be observable by
GLAST/Fermi
Converges for ?(r) with slope shallower than -1.5
79
Convergence of annihilation luminosity of main
halo

• Distribution converged at level for main halo
• Most emission comes from 0.5 lt r/kpc lt 20
• Emission is not converged for most subhalos but
  scales as V4max / rmax
• Estimate converged for Vmax gt 1.5 km/s
  rmax gt 165 pc

dL/dlnr Mo2/pc3
r kpc
Springel et al 08
80
More on substructure convergence
Convergence in the size and maximum circular
velocity for individual subhalos cross-matched
between simulation pairs. Biggest simulation
gives convergent results for
Vmax gt 1.5 km/s rmax gt 165
pc Much smaller than the halos inferred for even
the faintest dwarf galaxies
ln(Vmax,1200/Vmax,2400)
Vmax, 2400km/s
ln(rmax,1200/rmax,2400)
rmax, 2400kpc/h
Virgo Consortium 2008
81
Mass and annihilation radiation profiles of a MW
halo
gt 105M?
gt 108M?
main halo Lum
main halo Mass
subhalos (smooth) Lum
82
Mass and annihilation radiation profiles of a MW
halo
gt 105 M?
gt 108 M?
main halo Lum
main halo Mass
subhalos (smooth) Lum
83
A blueprint for detecting halo CDM
To calculate L need contribution from 4
components

1. Smooth emission from main halo
2. Smooth emission from resolved subhalos
3. Emission from unresolved subhalos in main halo
4. Emission from substructure of subhalos

84
A blueprint for detecting halo CDM
Emission from substructure of subhalos

• Assume all material beyond rt is removed
• Scale from main halo (within scaled rt)
• Correct for luminosity below (scaled) mass limit

Tidal radius
85
Subhalo lum profile Vmax 10 km/s

• MW subhalos above Earth mass contribute 230
  times as much L within 250 kpc as the smooth halo
  mass distribution
• The projected surface brightness of the subhalo
  population is almost uniform
• When a small object falls into the MW, tides
  remove its subhalos but do not affect its smooth
  emission
• Substructure does not much boost halo
  luminosities in the inner galaxy (rlt30kpc)

86
The Milky Way seen in annihilation radiation
87
The Milky Way seen in annihilation radiation
88
The Milky Way seen in annihilation radiation
89
The Milky Way seen in annihilation radiation
90
The Milky Way seen in annihilation radiation
Aquarius simulation N200 1.1 x 109
Springel et al 08
91
A blueprint for detecting halo CDM
S/NF/(?2h??psf)1/2
S/N for detecting subhalos in units of that for
detecting the main halo. 30 highest
S/N objects, assuming use of optimal filters
(S/N)/(S/N)main halo

• Highest S/N subhalos have 1 of S/N of main halo
• Highest S/N subhalos have 10 times S/N of known
  satellites
• Substructure of subhalos has no influence on
  detectability

92
The Milky Way seen in annihilation radiation
93
Conclusions about clumping and annihilation

• Subhalos increase the MW's total flux within 250
  kpc by a factor of 230 as seen by a distant
  observer, but its flux on the sky by a factor of
  only 2.9 as seen from the Sun
• The luminosity from subhalos is dominated by
  small objects and is nearly uniform across the
  sky (contrast is a factor of 1.5)
• Individual subhalos have lower S/N for
  detection than the main halo
• The highest S/N known subhalo should be the LMC,
  but smaller subhalos without stars are likely to
  have higher S/N

94
Conclusions about clumping and annihilation

• Subhalos increase flux on sky by x 2.9 as seen
  from Sun. (Flux within 250kpc is increased by
  x230 as seen by distant observer)
• The luminosity from subhalos is dominated by
  small objects and is nearly uniform across the
  sky (contrast is a factor of 1.5)
• Individual subhalos have lower S/N than the
  main halo
• The highest S/N known subhalo should be the LMC,
  but smaller subhalos without stars are likely to
  have higher S/N

95
A galactic CDM halo
5 Myths about the galactic halo annihilation
signal from the Milky Way

• Halo DM is mostly in small (e.g. Earth mass)
  clumps

• Halo DM is self-similar distribution of nested
  subhalos (fractal)

• Small (Earth mass) clumps dominate observable
  ?-ray signal

• Dwarf spheroidals/subhalos are best targets for
  detecting signal

• Subhalo ?-ray emission boosted by
  sub-substructure

96
Myths about small-scale structure and DM detection

• Halo DM is mostly in small (e.g. Earth mass?)
  clumps ---gt direct detectors
  typically live in low density regions
• DM streams ---gt non-Maxwellian, clumpy f(v)
  ---gt direct detectors will
  see an irregular energy distribution
• Small (Earth-mass?) clumps dominate observable
  annihilation signal
• Dwarf Spheroidals/subhalos are best targets for
  detecting annihilation (and are boosted by
  sub-substructure)
• Smooth halo annihilation emission is dominated
  by caustics

97
Myths about small-scale structure and DM detection

• Halo DM is mostly in small (e.g. Earth mass?)
  clumps ---gt direct detectors
  typically live in low density regions
• DM streams ---gt non-Maxwellian, clumpy f(v)
  ---gt direct detectors will
  see an irregular energy distribution
• Small (Earth-mass?) clumps dominate observable
  annihilation signal
• Dwarf Spheroidals/subhalos are best targets for
  detecting annihilation (and are boosted by
  sub-substructure)

98
Conclusions LCDM on small scales

• Predictions from LCDM for dark matter are well
  established
• Dark halos of all masses have cuspy density
  profiles, with inner slope shallower than -1.
• X-rays/lensing ? Evidence for cusps in relaxed
  cluster halos
• Total mass in bound subhalos converges (weakly)
  at small mass

• Near the Sun, the DM density differs from mean
  value by lt 15
• The local velocity distribution of DM is
  trivariate Gaussian with no measurable
  lumpiness due to individual DM streams
• The energy distribution of contains broad
  (fossil) features

• g-ray annihilation may be detectable by FERMI
  which should first detect smooth halo (if
  background can be subtrated)

99
Inelastic scattering
2008 Xmas card from the Finkbeiners
100
Conclusions LCDM on small scales

• Many small substructures, with convergent mass
  fraction
• the distribution of DM is not fractal nor is it
  dominated by Earth-mass objects

• The satellites problem probably explained by
  gal formation

101
Conclusions LCDM on small scales

• Predictions for galactic dark matter in LCDM
  well established
• N-body simulations of LCDM predict
• cuspy halo profiles, with inner log slope
  shallower than -1 well fit by NFW, better by
  Einasto
• many small substructures, with convergent mass
  fraction
• DM distribn not fractal nor dominated by
  Earth-mass objects

• g-ray annihilation may be detectable by FERMI
  which should

• First detect smooth halo
• Then (perhaps) detect dark subhalos with no
  stars
• Sub-substructure boost irrelevant for detection

? Confirm fundamental prediction of CDM model
102
Summary of halo mass structure

• The mass profile of CDM halos
• not strictly self-similar, and deviates slightly
  but significantly from the formula proposed by
  NFW.
• It is well approximated by the Einasto profile
  dln?/dlnr ? ra
• The Cusp
• ? ? r-1.2 (or steeper) cusps ruled out,
• cusp must be shallower than ???? r-1
• The phase-space density
• seems to be a fundamental structural property of
  CDM halos.
• A simple power law, with the same exponent as the
  self-similar secondary infall model, approximates
  well the profiles of all halos,
• ????? ? r-1.875