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Lectures
• Lecture I• Basis of cosmology• An overview: the density budget and the concordance
model
• Lecture II• The dark matter
• Lecture III• The CMB
• Lecture IV• The dark energy
Lecture IIDark matter
• Evidence for dark matter– Galaxies, clusters and lensing
• Measuring the matter density• The large structure • Cosmological perturbation theory (basis)• Structure formation • Dark matter candidates• Future measurements
4
Evidence for dark matter
Experimental probes to measure m
dynamics ( galaxies)
dynamics ( galaxies)
From x-ray
From x-ray large structure (LSS)
large structure (LSS)
(cluster of galaxies)
(cluster of galaxies)
lensing effect
lensing effect
6
Our Galaxy:The Milky Way
The mass of the galaxy:
1210
1210 solar masses
There is little evidence for the presence of considerable amounts of dark matter near the Galactic plane
Rotation of galaxies
Balance between gravitational pull and centrifugal force implies:
m v2 / R = G m M(R) / R2
v = [ G M(R) / R]1/2
From the visible matter distribution in galaxies one expects that M(R) ~ constant for large R, leading to the 1/R1/2 behavior plotted in the diagram. This is clearly not in agreement with the observational curve. Apparently there is more matter than can be seen!
The rotating disks of the spiral galaxies that we see are not stableDark matter halos provide enough gravitational force to hold the galaxies togetherThe halos also maintain the rapid velocities of the outermost stars in the galaxies
New Evidence: X-ray Observations of hot gaz in Clusters
Optical Image X-ray Image from the ROSAT satellite
Without dark matter, the hot gas would evaporate.
10
11
Gravitational lensing
12
Gravitational lensing
3 regimes:•Strong lensing with giant arcs and multiple images•Arclets where there is distorsion but not multiple images•Weak lensing where the distorsion is weak and isrecover in a statistical way
13
14
Measuring the matter density
The baryon densityThe total matter density
m 8G m
3H2b
8G b
3H2
15
Big Bang Nucleosynthesis Theory vs. Observations:
Remarkable agreement over 10 orders of magnitudein abundance variation
Deuterium: strongest constraint
4He
b
It is all baryonic components …( visible or
not…)
Concordance region:b h2 = 0.023For h=0.7, b = 0.04.
16
Measuring m
• Two approaches:• Local approach ( look at some galaxies or clusters)
– Measure mass to luminosity or mass to baryon content ratio
• Statistical approach– Map a large portion of sky and measure the statistical
properties of the objects» Correlation function in structures» Weak lensing measurement (see annexe)
17
measure Hot Gas in Galaxy Clusters
• Emits X-rays– Scattering of electrons off nuclei
produces X-rays called bremsstahlung..
• Interacts with the CMB– ~1% of CMB photons passing
through cluster scatter off hot electrons (inverse Compton)
– Called Sunyaev-Zel’dovich Effect (SZE) ..
• Combining observations of two processes allows one to measure the size of the cluster! Then can give the mass
X-ray Image of Abell 262
SZE Image of MS 1054
CMB coolest in cluster center
SZ C
olla
bora
tion
18
Ω m From Baryon Fraction
HYPOTHESIS
Fraction of baryon and DM areUniversal
Clusters are potential wellsX rays in equilibriumMX = Mb
mm
b
023.0
7.01.005.0
5.1
hhM
M
m
b
m
b
tot
b
23.01.0
023.0 m
nucleosynthesis
19
Ω m From Luminosity
• Mesure masse M by virial method
hDV
DL
L
M LM
m 1500
In cluster : M/L > 250h = > m > 0.2
Difficulty is to know where the cluster stop
20
LOCAL DYNAMICS (NO DE)
LOCAL LENSING (NO DE)
BARYON FRACTION (NO DE)
RELIABILITY AND DE ??
POWER SPECTRUM
0.15 < Ω m < 0.3
FROM PEEBLES (THE « POPE »)
Synthesis of current measurements
Large scale structures
LSSSDSS/ 1 million of galaxies in 6 color + spectra
23
Density distribution of luminous matter of late type galaxies in the Sloan Digital Sky Survey. Superclusters are seen as high-density regions (red). Faint galaxy filaments are seen in low-density regions (voids).. There is more late type galaxies In low density region. Structures are formed after galaxies. Fine structure forms only in models of Cold Dark Matter
24
Overview of LSS picture• Galaxies are not uniformly distributed
– There is structures of some ~ 10 Mpc ( wall …)– Vacuum of 50 Mpc to 70 Mpc – Density contrasts are small – Galaxies seems older than structures
• Dark matter exists, should play a role in structure formation
• Tools to quantify this picture– Correlation function of galaxies– Matter Power spectrum
• And a model to explain the formation of these structures…
25
Measuring the amplitude : definitions
Contrast of density:
in comoving coordinate where x = a(t) r
2-point correlation function:
rxxr
rnrnb
1
(r)(r)
ξ(r) quantify the excess probability from a Poisson case of finding a neighbor galaxy at a distance r.It is a statistical measurement
26
Ω m Correlation Function of Galaxies
• The probability of finding a pair of objects separated by distance r, in each occupying volume elements dV is: dP = n2 [1+ξ(r) ] dV1dV2
Studies done from redshift surveys
BUT:
Z = distance + peculiar velocity
Although redshift (velocity) corresponds to true distance according to the Hubble Law, small peculiar velocities not associated with the Hubble flow can cause distortions in redshift space.
The most evident of these is the Fingers-of-God effect, where long thin filaments in redshift space point directly back at observer.
27
Ω m From Correlation FunctionWhen computing ξ(r) in redshift space, the r coordinate is separated into the transverse component σ and the radial component π.
The transverse component σ is a true measure of distance, while π is distorted by peculiar velocities as explained above.
Ω m 0.3
If no peculiar motion: circular shape is expected
Distorsion is a measure of velocity and of (Ω m
0.6 / b) => for b ~ 1 … b is a bias parameter..
28
Cosmic shearCosmic shear
First detection Van Waerbeke et al.(2000); Wittman et al. (2000); Bacon et al. (2000); Kaiser et al. (2000)
Distortion of distant-galaxy images by the weak lensing effect
Background galaxydeformed deformed image!!image!! Large-scale structure
Powerful future cosmological tool probing Dark matter distribution
Cosmological parameters
The important cosmological information can be obtained by quantifying the non-Gaussianity of weak lensing fields.
29
To complete the m evaluation at large scale ..CMB give also a very precise value ( see lecture 3 for details on interpretation and assumption…)
m = 0.27 0.04
30
Warning on interpretation ….
As soon as we measure large scales, we are more sensitive to m but also to fluctuations (statistical measurement)quantified by 8
(typical size of fluctuation for galaxies)
We can conclude than m < 0.5 Two other proofs with CMB and supernovae (lecture 3 and 4) be explain later
8
31
COSMOLOGICAL FLUCTUATIONSAND
STRUCTURE FORMATION
32
Density Fluctuations in the Universe
•Observations of the distribution of galaxies in the nearby universe–provide direct measurements of the density fluctuations when the
universe is 13 billion years old–current accurate measurements lie between scales of 1 and
several hundred million light years
+ Observation of the CMB (next lecture) (fluctuation ~ 10-5)
•Structure formation models–can we produce structure like that we see today from a universe
that is consistent with the CMB observations when it was ~300,000 years old?
33
From Homogeneity to Structure
• Structure Evolution is a Basic Component of the Big Bang model–well constrained observationally–sensitive to cosmological parameters and the nature of dark
matter• can provide way of addressing these outstanding issues
Gravity amplifies inhomogeneities, even in an expanding universe
Structure evolutionThe picture:
• Structures are formed from gravitational instability of small primordial fluctuations
• Fluctuations are assumed to be
– Scale invariant
– Gaussian
– Adiabatic (compared to isocurvature )
– With Scalars et tensor modes ….
Fluctuations are generated by a mecanism :the inflation and with initial density conditions (see lecture 3)
35
Gravitational Instability
Small departures from uniformity are amplified in an expanding universe
Overdense regions
greater deceleration of expansion leads to greater overdensityexpand more slowly than typical part of the universeeventually collapse if sufficiently overdense
Underdense regions less deceleration of expansion leads to even larger underdensities regions expand faster than typical part of the universe underdense regions grow and form voids
36
Gravitational Instability•General relativity provides solutions for the evolution of density perturbations
Increasing TimeIn
crea
sin
g S
ize
Life and Times of 4Density Perturbations
lowest amplitude
highest amplitudeOverdensity of very small perturbations grows linearly with the expansion of the universe until perturbations become large
Power spectrum
• Define the fourier transform of the density contrast -> k
The power spectrum is the fourier transform of the correlation function
= 2 a(t)/k
Each mode can evolute in time independently of others. is constant but is increasing with the expansion
xkkk
x .iexp2 2/3
3
d
)(x
What mean power?
Power is the amplitude
Scale is the wavelength
This exemple has power at large scalesAnd small power at small scales
39
Why study P(k)?: test of all hypotheses including inflation CDM…
• Shape depends on– m total matter content
– b baryon content
– DE dark energy content
Probed by galaxy surveys: 2dFGRS, SDSSThe link with CMB which gives the same on large scales ! (in lecture 3)
Why this shape ???
Level of amplitudeOf the fluctuations
Can be define for each scale at a given time
Or can be define at a time which depend of the scale (for example when the scale enter the horizon)(often use later)
Power spectrum of SDSS
LuminosityIs decreasing
Small scalesLarge scales
The modelling
• start with primordial fluctuations adiabatic (fixe the initial condition in density (b,k = CDM,k = ¾ ,k = ¾ ,k)
• Physics affect fluctuations which are inside the horizon
• primordial fluctuations can only be observed with the CMB for size > hubble radius ( > 1°)
• Primordial fluctuations are otherwise modified by a transfer function
Transfer function
P(k,t) = P0(k) D2(t) T2(k)
Transfert function
Initial spectrum
nkkP all the fluctuations are entering horizon with the same amplituden=1(No privileged scales)
Growth factor
The growth depend of the time (expansion )
Calculated from
hydodynamic in RG
Will depend of the kind of component (DM, baryons, etc…)
The linear growth of fluctuation(basis)
• Hydrodynamic equation in an expanding universe (eq of continuity, Euler and Poisson)
Consider small fluctuations around the homogeneous solution in a pertubated metric
= > Express in term of contrast of density …linear << 1
expansion Gravitational instability
45
Solutions
Matter domination: (t) t2/3 a(t) 1/(1+z) croissance ~ a
Radiation domination: (t) t a2(t) croissance ~ a2 (true outside horizon)
Inside the horizon, need to add the radiation pressure =>
Jeans scale … fluctuation can grow or can oscillate ( will be explain in more details in lecture 3)
46
What mean scale inside horizon?
Power is the amplitude
Scale is the wavelength
This exemple has power at large scalesAnd small power at small scalesOnly small scales are inside horizon
rH
Evolution of a density perturbationBefore horizon… P(k) = k correspond to fluctuations growing as a2 after horizon, grows as a if there is matter domination …
Small scales can enter horizon before matter domination, then are frozen until zeq we see them with a default of amplitude of =a2 compare to large scales
2 = a4
=>P(k) = k / a4
= k-3
After zeq
Turn over dependof Zeq
=> Depend of m
48
Key summary of the shape
Slope at small k~/ k Slope at large k
~/ k-3
Dependence of turnoverposition on m
Baryon supression and wiggles
49
Dark matter and the model of structure formation
Dark matter is needed to start early enough gravitational clustering to form structure.
SOME DARK MATTER SHOULD BE NON BARYONIC
If DM is non-baryonic then this helps to explain the paradox of small temperature fluctuations of cosmic microwave background radiation
Non baryonic =>No pressureNot interacting Only sensitive to gravitation
50
Why we need DM?
R or t
Radiation dominated
CDM dominated
Post-recombination
Dark m
atter
Baryons
Plasma -baryon Interaction oscillation
radiation-DM equalityCold DM no pressuregravitationnels
Recombinaison baryons fall in DM Structures can start
Zeq ~ mh2Zdec 1100
51
Numerical Structure Formation Simulations
• Model matter in universe as collection of particles that interact gravitationally (and perhaps hydrodynamically)
• 100 million particles is current maximum– one chooses particle mass by choosing a simulation volume
– for cosmological simulations the typical particle mass is around the mass of a galaxy or somewhat less (~1012 solar masses)
• Simulation process– distribute particles in early universe
– account for underlying expansion and turn gravity loose!
• Compare properties of simulated universe with those of the observed universe!
Movies from structure formation simulations available at http://www.astro.princeton.edu/~gbryan/
Formation of Structure: Numerical Simulations
Dark Matter particles come together to make galaxies, clusters, and larger scale structures
Dark matter : the candidates
ModifiedGravity
Low MassStars
Black Holes
Light Particles (eg axions) 10-5 - 10-2 eV
Tau NeutrinoMass 10 - 30 eV
Weakly interactingmassive particles 10-1000GeV
Examinewith dark energy
59
There are two types of matter:• baryonic can be luminous galaxies and clusters
but also can have massive none luminous objects inside galaxies…
• non-baryonic in dark halos
60
b ~ 0.023 h-2 ~ 0.01 - 0.09
•Visible matter is only * ~ 0.003 (M/L/5) h-1
(+0.006 h-1.5 for gaz inside the cluster)
=> 90% of baryons are dark…
61
Search for baryonic dark matter
• Compact objects : search for brown dwarfs and black holes using gravitational effects
A single image is amplified
Collaborations MACHOS, EROS: (Alcock et al 2001, Lasserre et al 2000)After 6 years ~ 10 millions stars of LMC13-17 candidats (>> 2-4 expected from visible stars in 34-230 days)
<20% of DM (< 50kpc) can be MACHOS to the best….
62
Non baryonic
• Hot dark matter• Relativistic• As neutrinos
• Cold dark matter– Non interacting– No pressure– massive
They give different predictions on the structure formation
weakly interactive particles ( WIMPS )were suggested (Peebles 1982, Bond, Szalay, Turner 1982, Sciama 1982).
LSP (neutralinos, axinos)AxionsSupermassives relics….
Cold or hot???
63
Degenerate with m
Why not neutrinos ?
• Pseudo scalar (proposed to solve the strong CP problem)• Pseudo Nambu Golston boson• Very weakly interacting with matter: interactions are
1012 weaker than ordinary weak interaction• Extremely light particles, with masses in the range of
10-3 eV/c2 to 10-6 eV/c2
• Axions may be detected when they convert to low energy photons after passing through a strong magnetic field
Axions
WIMPS
• Weakly Interacting Massive Particles (WIMPs)
• Non relativistic
• WIMPS arise in some Supersymmetric (SUSY) theories of particle physics and are the lightest neutral SUSY particle (LSP)
•WIMPs would have been easily detected in accelerators if M < 15 GeV/c2
Neutralino: the elegant candidate
• The lightest WIMP would be stable, and could still exist in the Universe, contributing most if not all of the Dark Matter
• Cross-sections for various interactions can be calculated if the WIMP is assumed to be a neutralino (from mSUGRA for instance).
• Very small
68
10 WIMPlog GeVM
log 10
(/p
icob
arns
)
Les particules candidatesLes particules candidates
SUSYM
GUTSM
PLANCKM
PQf
IH
coldthermalrelics w
imp
zilla
gravitino
axionQCD
WEAK" "
69
Direct searchs for Wimps…
Nuclear recoil elastic scattering (germanium detectors, scintillating crystals)
70
Some results
Need to increase sensitivity with a factor 100
71
Prospectives
72
• Increase the sky coverage of cluster surveys
new tools promising•Weak lensing•Baryon oscillation
Go to space…
73
The latest: 2dF and SDSS
• 2dFGRS:– 250,000 galaxies with redshifts– galaxies selected from APM– Median redshift 0.17– Final data released in summer 2004
• SDSS GRS– aims at 1,000,000 redshifts– DR3 was 11 days ago– >5000 square degrees– 141,000,000 objects– 374,000 galaxy spectra
74
SD
SS
Pro
ject
Dire
ctor
Joh
n P
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at
suns
et in
fro
nt o
f th
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5-m
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Sur
vey
tele
scop
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cate
d at
Apa
che
Poi
nt
Obs
erva
tory
in N
ew M
exic
o.
Imag
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edit:
Dan
Lon
g, A
pach
e P
oint
Obs
erva
tory
Imag
e di
strib
uted
by:
Fer
mila
b V
isua
l Med
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ervi
ces
75
Ongoing galaxy redshift surveys
• Completion of SDSS
• 6dF
• DEEP 2 (like 2dFGRS at z~1)
• VIRMOS VLT Deep Survey – (VVDS)
• UKIDSS
76
Scientific Promise of Weak Lensing
• Mapping of the distribution of Dark Matter on various scales
• Measurement of the evolution of structures
• Measurement of cosmological parameters, breaking degeneracies present in other methods (SNe, CMB)
• Explore models beyond the standard osmological model (CDM)
From the statistics of the shear field, weak lensing provides:
Jain, Seljak & White 1997, 1x1 deg, SCDM
77
PSF anisotropy
Very soon dominate by systematic effects => space is required
78
Weak Lensing Power Spectrum
CDM
CDM(linear)
OCDM
SNAP WF survey [300 deg2; 80 g arcmin-2; HST image quality]
Future surveys:CFHT, Keck, WHT, Subaru, ACS/HST
Future Instruments:Megacam, VST, VISTA, LSST, WHFRI, SNAP, GEST
Measure cosmological parameters (8, m, , , w, etc) very sensitive tonon-linear evolution ofstructures
79
Cosmological Implications
13.097.03.0
68.0
8
m
07.000.13.0
60.0
8
m
Shear Variance: (CDM)8.07.02.1
8 mm z
WHT+ Keck measurement:
Clusters: Pierpaoli et al. 2001
Clusters: Seljak 2001
06.075.03.0
44.0
8
m
Bacon et al. 2002
80
Future SurveysSurvey Diameter
(m) FOV (deg2)
Area (deg2)
start
DLS 24 20.3 28 1999
CFHTLS 3.6 1 172 2003
VST 2.6 1 x100 2004
VISTA 4 2 10000 2007
Pan-STARRS 41.8 44 31000 2008
LSST 8.4 7 30000 2012
SNAP 2 (space) 0.7 300 2014
81
The long term future
• CMB (next lecture)
• plus cosmic shear and velocities
• will tell us all about dark matter and early universe
• Galaxy surveys will tell us about galaxy formation.
• …
82
• Sunyaev-Zel’dovich Effect surveys : deg2 #amas SZA (Carlstrom et al.) Olimpo 2004 AMI, Ameba ~12 ~200 APEX, ACT (Page) ~200 ~2,000 SPT (Carlstrom et al.) ~4,000 ~20,000 Planck ~20,000 ~10,000 2007
• X-ray surveys:
REFLEX (Boehringer) ~4 ~1,000 XMM ~103 ~2,000 running DUET (Petre et al.) ~104 ~20,000
Futur large Surveys
83
Baryon Oscillations in the Matter Power Spectrum
Standard ruler:
ratio of wiggle scale to sound horizon H(z)
Just like CMB – simple, linear physics
Eisenstein astro-ph/0301623
kobs / kA ~ H(z) s H(z) / (mh2)1/2
84
annexe
85
From X measurement to mass
• X Flux : fX = L/4dL2 ( dL = (1+z)2 d )
• fx T3
• SZ viriel theorem => relation betweel M-T (m , z, )
2A
virvir2
CMB
2d
TMTkndl
cm
σ
T
ΔTΔS eBe
e
T
R
dA
dA R
(Still works for elliptical clustersas long as there is a large sample)
86
Ω m From Local dynamics:
e.g: Virgocentric infall as pedagogical example • Density fluctuations in the
Universe produce velocity perturbations of galaxies which are located near them.
• The linear approximation to this perturbation, which works in the limit of small / is the following:
• The unperturbed velocity in this case is given by v = Hr where r is the distance from the source which is causing the perturbation.
• We can apply this equation to the case of Virgo Infall as schematically shown below:
CMB DIPOLE
87
The Virgo cluster is a nearby cluster or region of mass overdensity. The diagram above shows three components:
* Our infall to Virgo * The CMB Dipole Anisotropy --> note that its direction is not pointed at Virgo and the amplitude is larger than our Infall into Virgo. Therefore, the Virgo cluster alone is not causing this motion.
* Possible motion of the entire Local Supercluster towards the next nearest supercluster, Hydra-Centaurus ( GREAT ATTRACTOR CONTROVERSY) For now ,let's just consider our infall into Virgo.
* The distance to Virgo is 15 Mpc. If we use H = 100, then the predicted expansion velocity is 1500 km/s.
* The observed velocity of Virgo, however, is 1200 km/s
* The difference represents our infall of 300 km/s to Virgo
* v/v = 300/1500 = 0.2
* We can now determine Ω (Ωm !!!!) if we can measure / that is interior to us
in the direction of Virgo.
88
But we can only measure / in light ( in fact N/N) when it is really / in mass that is causing our velocity perturbation.
Hence bias or the b parameter (or more generally a function ) becomes important.
The measured / in light is 1.9. If we assume there is no bias then we have with :
=> 0.2 = (1/3)(1.9) Ω 0.6
which yields Ω (Ωm !!!!) = 0.15 !!!!!!! Very far from Ωtot =1 !!!!
SO : Suppose there is a bias such that we really area measuring
0.2 = (1/3)(1.9) (Ω 0.6 / b)
and hence we only have (Ω 0.6 / b) = 0.15
For Ωtot = 1 this would require b = 6.6 - which is a huge bias !!!
Recent data, however, strongly suggests that b is not larger than 1.5 which is
Ωm = 0.23
89
Hot Gas and Galaxies
• Measure the mass of light
emitting matter in galaxies in the cluster (stars)
Measure mass of hot gas - it is 3-5 times greater than the mass in stars
Calculate the mass the cluster needs to hold in the hot gas - it is 5 - 10 times more than the mass of the gas plus the mass of the stars!
90
Distribution of early (top) and late (bottom) type galaxies in SDSS Northern equatorial strip.
Dark blue – galaxies in low-den environmentRed – galaxies in high-den environment
91
Biasing
• Relation of galaxies to mass ≡ “bias”
• Comparision of different galaxy types there must be some bias
• Theoretical models speculative
• Do galaxies tell us about cosmology…– or about galaxy formation??
92
AND about Bias
≡ galaxy power spectrum is a constant multiple of the matter power spectrum
– Pg(k) = b2 P(k)
– 8g = b 8
• Assumed for 2dFGRS and SDSS cosmological parameter analyses
• Could more generally have b(k)= non-linear bias eg. b=b0 + b1 k
93
Local dark matter
• Local dark matter …Local density of matter near the Sun from velocity and matter density dispersions near the plane of the Galaxy using Poisson equation
Density of matter in the disk of the Galaxy is equal to the density of stars (no dark matter in Galactic disk).
94
Black Hole at Center of Galaxy
At the center of every galaxy is a very massive black hole, as massive as a million suns.
These massive black holes form from mergers and are NOT the dark matter.
95Averaged shape: 0e γe
The underlying assumption is that the position angles are random in the absence of lensing. At some level intrinsic alignments will complicate things (can be dealt with using photometric redshifts).
no lensing lensing
Introduction: what is weak lensing?Introduction: what is weak lensing?
96
Weak Gravitational Lensing
Distortion Matrix:
Direct measure of the distribution of mass in the universe, as opposed to the distribution of light, as in other methods (eg. Galaxy surveys)
jij
iij zgdz
2
)(
Theory
97
Cosmic shearCosmic shear
First detection Van Waerbeke et al.(2000); Wittman et al. (2000); Bacon et al. (2000); Kaiser et al. (2000)
Distortion of distant-galaxy images by the weak lensing effect
Background galaxydeformed deformed image!!image!! Large-scale structure
Powerful cosmological tool probing Dark matter distribution
Cosmological parameters
The important cosmological information can be obtained by quantifying the non-Gaussianity of weak lensing fields.
98
Principles of Weak Lensing
Distortion matrix:
Convergence:
Shear:
Critical surface density:
221
crit
212221121
1 ;)(
lsol
oscrit DD
D
G
c
4
2
22
21
1
1
j
iij
Weak lensing regime: << 1 (linear approximation) Measure shear and solve for the projected mass
99
Measuring the Shear
)()(2 xIxwxxxdQ jiij
Ellipticity:2211
122
2211
22111
2,
Q
12
A measurement of the ellipticity of a galaxy provides an unbiased but noisy measurement of the shear:
observed = intrinsic
Quadrupole moments:
100
Status
Mellier et al. 2002
Mass-to-light ratio:<M/L> 400 h Mo/Lo
corresponding to:m 0.3in agreement withother methods
Use for shearmeasurements
101
Cosmic Shear Measurements
2()=<2
>Bacon, Refregier & Ellis 2000Bacon, Massey, Refregier, Ellis 2001Kaiser et al. 2000Maoli et al. 2000Rhodes, Refregier & Groth 2001Refregier, Rhodes & Groth 2002van Waerbeke et al. 2000van Waerbeke et al. 2001Wittman et al. 2000Hammerle et al. 2001*
Hoekstra et al. 2002 *
Brown et al. 2002 *
Hamana et al. 2002 * * not shown
Shear variance in circularcells:
102
Primordial fluctuations
Adiabatic Fluctations
Changes number density of photons and matter particles equally but their mass densities change differently
( predicted by inflation)
103
Size of fluctuation
nk kkP 2
all the fluctuation are entering horizon with the same amplitude
Fluctuation are growing with timeThe growth depend of the time(expansion ) and size (scale)
No privileged scales
=>Spectrum is scale invariant (Harrison-Zeldovich) n=1(mean no dependant of scale and time)
104
Some remarks on a pertubated metric
• General form– Scalar perturbation 2 scalar fcts s– Vectorial perturbations 1 vector wi
– tensorial 1 tensor hij with 3 indices
• Minimal perturbation of the metric g g = a2 2 -i B -i B 2[ij - i j E] With 4 scalars , , B et E
• For a fluid,with T diagonal, we can choose a jauge with B = E = 0 et = (Newtonian)
105
Correlation function and normalisation
8 ~ amplitude of P(k) at k ~ 2 /8 Mpc-1 corresponding at = 1
Vacuum => fluctuation
Often used to fix amplitude of primordial fluctuations, A in P(k) = A kn
106
Growth of DM and horizon
a
dtrH
1kEnter the horizon at
Horizon of a particle
For scales greater than horizon:
growth ~ a2
For scales smaller than horizon: it depends if the matter dominates ( STAGNATION/MESZAROS EFFECT) then: growth ~ a(more the scale is small, more has beenaffected by this in the past)
107
Theoritical
Zeq
108
Power spectrum
P(k)
k
Horizon à zeq
Dissipation
TURN OVER IN THE POWER SPECTRUM DEPENDING ON m VIA Zeq
kPtDkP init2
linéaire )(
Growth of the fluctuation
109
CFHT Legacy SurveyCFHT Legacy Survey
Megacam: FOV 1 square degree
110
The Canada-France-Hawaii Telescope Legacy Surveyis a five year project, with three major components:
Very wide/shallow survey: solar system• ~1500 square degrees• around ecliptic (strip)
Wide/deep survey: weak lensing• ~140 square degrees (3 fields)• 5 filters (u,g,r,i,z’)• i<24.5
Ultra deep: type Ia supernovae • 4 square degrees (4 fields)• repeated observations in 5 filters• expect ~1000 supernovae!
CFHT Legacy SurveyCFHT Legacy Survey
111
Further ahead: Pan-STARRSFurther ahead: Pan-STARRS
PANoramic Survey Telescope And Rapid Response System
4x1.8m telescopes 3 square deg FOV each Orhogonal Transfer CCDs
112
Further ahead: LSSTFurther ahead: LSST
8.4 meter diameter 7 square deg. FOV
Large Synoptic Survey Telescope