dark matter and dark energy components chapter...
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Dark Matter and Dark Energy components
chapter 7
Lecture 3
The early universe chapters 5 to 8
Particle Astrophysics , D. Perkins, 2nd edition, Oxford
5. The expanding universe 6. Nucleosynthesis and baryogenesis 7. Dark matter and dark energy components 8. Development of structure in early universe
exercises
Slides + book http://w3.iihe.ac.be/~cdeclerc/astroparticles
Overview
• Part 1: Observation of dark matter as gravitational effects
– Rotation curves galaxies, mass/light ratios in galaxies
– Velocities of galaxies in clusters
– Gravitational lensing
– Bullet cluster
• Part 2: Nature of the dark matter :
– Baryons and MACHO’s
– Standard neutrinos
– Axions
• Part 3: Weakly Interacting Massive Particles (WIMPs)
• Part 4: Experimental WIMP searches
• Part 5: Dark energy (next lecture)
2013-14 Dark Matter lect3 3
Previously
• Universe is flat k=0
• Dynamics given by Friedman equation
• Cosmological redshift
• Closure parameter
• Energy density evolves with time
2013-14 Dark Matter lect3 4
2
2 8
3
NR t G
R ttH t totρ
0
01 0R t
z z tR t
c
tt
t
2 3 4 22
0 01 1 1r kH t H z t z z00m ΛΩ t Ω t
Ωk=0
Dark matter : Why and how much?
2013-14 Dark Matter lect3 5
luminous 1%
dark baryonic
4%
NeutrinoHDM <1% cold dark
matter ~24%
dark energy ~70%
• Several gravitational observations show that more matter is in the Universe than we can ‘see’
• It these are particles they interact only through weak interactions and gravity
• The energy density of Dark Matter today is obtained from fitting the ΛCDM model to CMB and other observations
5
0
0
10
0.30
rad
matter
t
t
2 3 42
0 0 0 01 1m rH t H t z t z t
Planck, 2013
Dark matter nature
• The nature of most of the dark matter is still unknown
Is it a particle? Candidates from several models of physics beyond the standard model of particles and their interactions
Is it something else? Modified newtonian dynamics?
• the answer will come from experiment
2013-14 Dark Matter lect3 6
PART 1 GRAVITATIONAL EFFECTS OF DARK MATTER
Velocities of galaxies in clusters and M/L ratio
Galaxy rotation curves
Gravitational lensing
Bullet Cluster
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Dark matter at different scales
• Observations at different scales : more matter in the universe than what is measured as electromagnetic radiation (visible light, radio, IR, X-rays, -rays)
• Visible matter = stars, interstellar gas, dust : light & atomic spectra (mainly H)
• Velocities of galaxies in clusters -> high mass/light ratios
• Rotation curves of stars in galaxies large missing mass up to large distance from centre
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1 10 500MW cluster
MW cluster
M M M
L L LThere must be missing mass
Dark matter in galaxy clusters 1
• Zwicky (1937): measured mass/light ratio in COMA cluster is much larger than expected
– Velocity from Doppler shifts (blue & red) of spectra of galaxies
– Light output from luminosities of galaxies
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Optical (Sloan Digital Sky Survey)
+ IR(Spitzer Space Telescope NASA
COMA cluster
1000 galaxies 20Mpc diameter
100 Mpc(330 Mly) from Earth
v
Dark matter in galaxy clusters 2
• Mass from velocity of galaxies around centre of mass of cluster using virial theorem
• Proposed explanation: missing ‘dark’ = invisible mass
• Missing mass has no interaction with electromagnetic radiation
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COMA SUN
M M
L L
10
7
1
2
( ) 10500
10 cluster sun
KE GPE
M velocities M M M
L LL L
Mv
Part of the mass is not seen
Galaxy rotation curves
• Stars orbiting in spiral galaxies
• gravitational force = centrifugal force
• Star inside hub
• Star far away from hub
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2
2
Mmmv
r r
r G
v r
1v
r
NGC 1560 galaxy
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Optical emission from stars
HI 21cm radio emission from gas
Universal features
• Large number of rotation curves of spiral galaxies measured by Vera Rubin – up to 110kpc from centre
• Show a universal behaviour
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Dark matter halo • Galaxies are embedded in dark matter halo
• Halo extends to far outside visible region
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HALO
DISK
There is a halo of dark matter in each galaxy
Dark matter halo models
• Density of dark matter is larger near centre due to gravitational attraction near black hole
• Halo extends to far outside visible region
• dark matter profile inside Milky Way is modelled from simulations
Dark Matter lect3
15
Solar system
DM
Den
sity
(G
eV c
m-3
)
Distance from centre (kpc)
2013-14
Milky Way halo models
At the position of the solar system the dark
matter density is around 0.3 GeV/cm3
From models of halo profiles
Gravitational lensing
• Gavitational lensing by galaxy clusters -> effect larger than expected from visible matter only
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Gravitational lensing principle
• Photons emitted by source S (e.g. quasar) are deflected by massive object L (e.g. galaxy cluster) = ‘lens’
• Observer O sees multiple images
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Lens geometries and images
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Observation of gravitational lenses
• First observation in 1979: effect on twin quasars Q0957+561
• Mass of ‘lens’ can be deduced from distortion of image
• only possible for massive lenses : galaxy clusters
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Images of distant quasars are distorted
Lens = Abell 2218 galaxy cluster
Different lensing effects
• Strong lensing:
– clearly distorted images, e.g. Abell 2218 cluster
– Sets tight constraints on the total mass
• Weak lensing:
– only detectable with large sample of sources
– Allows to reconstruct the mass distribution over whole observed field
• Microlensing:
– no distorted images, but intensity of source changes with time when lens passes in front of source
– Used to detect Machos
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Collision of 2 clusters : Bullet cluster
• Optical images of galaxies at different redshift: Hubble Space Telescope and Magellan observatory
• Mass map contours show 2 distinct mass concentrations
– weak lensing of many background galaxies
– Lens = bullet cluster
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Cluster 1E0657-56
0.72 Mpc
Bullet cluster in X-rays • X rays from hot gas and dust - Chandra observatory
• mass map contours from weak lensing of many galaxies
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Bullet cluster = proof of dark matter
• Blue = dark matter reconstructed from gravitational lensing
• Is faster than gas and dust : no electromagnetic interactions
• Red = gas and dust = baryonic matter – slowed down because of electromagnetic interactions
• Modified Newtonian Dynamics cannot explain this
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Alternative theories
• Newtonian dynamics is different over (inter)-galactic distances
• Far away from centre of cluster or galaxy the acceleration of an object becomes small
• Explains rotation curves
• Does not explain Bullet Cluster
• example:
• For mass mg = stars and gas, at small r
• At large distance r from galaxy centre
a << a0 and F becomes small
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0
g
g
aµ
a
F m a
F m a
PART 2 THE NATURE OF DARK MATTER
Baryons
MACHOs = Massive Compact Halo Objects
Standard neutrinos
Axions
WIMPs = Weakly Interacting Massive Particles →Part 3
2013-14 Dark Matter lect3 25
What are we looking for?
• Particles with mass – interact gravitationally
• Particles which are not observed in radio, visible, X-rays, -rays, .. : neutral and possibly weakly interacting
• Candidates:
• Dark baryonic matter: baryons, MACHOs, primordial black holes
• light particles : primordial neutrinos, axions
• Heavy particles : need new type of particles like neutralinos, … = WIMPs
• To explain formation of structures majority of dark matter particles had to be non-relativistic at time of freeze-out
Cold Dark Matter
2013-14 Dark Matter lect3 26
BARYONIC MATTER
Total baryon content
Visible baryons
Neutral and ionised hydrogen – dark baryons
Mini black holes
MACHOs
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Baryon content of universe
• measurement of light element abundances
• and of He mass fraction Y
• And of CMB anisotropies
• Interpreted in Big Bang Nucleosynthesis model
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106.047 0.074 10BN
N
2BΩ h = 0.02207 0.00027
He mass fraction
D/H abundance
ΩBh2=.022
PDG 2013
Baryon budget of universe
• From BB nucleosynthesis and CMB fluctuations:
• Related to history of universe at
z=109 and z=1000
• Most of baryonic matter is in stars, gas, dust
• Small contribution of luminous matter
• 80% of baryonic mass is dark
• Ionised hydrogen H+, MACHOs, mini black holes
• Inter Gallactic Matter = gas of hydrogen in clusters of galaxies
• Absorption of Lyα emission from distant quasars yields neutral hydrogen fraction in inter gallactic regions
• Most hydrogen is ionised and invisible in absorption spectra form dark baryonic matter
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0.01lum
0.05baryons
Ly forest and neutral hydrogen gas
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Hydrogen atoms Absorb UV light
Emission of UV light by quasar = 1216 Ǻ Lyman transition in H
Measurement of absorption spectra yields amount of neutral H
Tiny black holes
• Primordial black holes could make up dark matter if created early enough in history of universe and escaped BB nucleosynthesis phase
• If present in Milky Way halo they would be detected by gravitational microlensing (see MACHO’s, next part)
• no events were observed
• Primordial black holes with
• Could make up DM halo, but not all of it
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13 83 10 3 10BHM M M
MACHOS
Massive Astrophysical Compact Halo Objects
Dark stars in the halo of the Milky Way
Observed through microlensing of large number of stars
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Microlensing • Light of source is amplified by gravitational lens
• When lens is small (star, planet) multiple images of source cannot be distinguished : addition of images = amplification
• But : amplification effect varies with time as lens passes in front of source - period T
• Efficient for observation of e.g. faint stars
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Period T
Microlensing - MACHOs
• Amplification of signal by addition of multiple images of source
• Amplification varies with time of passage of lens in front of source
• Typical time T : days to months – depends on distance & velocity
• MACHO = dark astronomical object seen in microlensing
• M 0.001-0.1M
• Account for very small fraction of dark baryonic matter
• MACHO project launched in 1991: monitoring during 8 years of microlensing in direction of Large Magellanic Cloud
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2 2
1 / 12 4
x xx x
TA
t
2013-14 Dark Matter lect3 35
Optical depth – experimental challenge • Optical depth τ = probability that one source undergoes
gravitational lensing
• For ρ = NLM = Mass density of lenses along line of sight
• Optical depth depends on – distance to source DS
– number of lenses
• Near periphery of bulge of Milky Way
Need to record microlensing for millions of stars
• Experiments: MACHO, EROS, superMACHO, EROS-2
• EROS-2: – 7x106 bright stars monitored in ~7 years
– one candidate MACHO found
– less than 8% of halo mass are MACHOs
2013-14 Dark Matter lect3 36
2
23
Gc
SD
7per source 10
Example of microlensing
• source = star in Large Magellanic Cloud (LMC, distance = 50kpc)
• Dark matter lens in form of MACHO between LMC star and Earth
• Could it be a variable star?
• No: because same observation of luminosity in red and blue light : expect that gravitational deflection is independent of wavelength
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Blue filter
red filter
To do
• Meebrengen naar examen
2013-14 Dark Matter lect3 38
STANDARD NEUTRINOS AS DARK MATTER
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Standard neutrinos
• Standard Model of Particle Physics – measured at LEP
→ 3 types of light left-handed neutrinos
with Mν<45GeV/c2
• Fit of observed light element
abundances to BBN model (lecture 2)
• Neutrinos have only weak and gravitational interactions
2013-14 Dark Matter lect3 40
2.984 0.009fermion familiesN
3.5neutrino speciesN
Relic standard neutrinos
• Non-baryonic dark matter = particles
– created during radiation dominated era
– Stable and surviving till today
• Neutrino from Standard Model = weakly interacting, small mass, stable → dark matter candidate
• Neutrino production and annihilation in early universe
• Neutrinos freeze-out at kT ~ 3MeV and t ~ 1s
• When interaction rate W << H expansion rate
2013-14 Dark Matter lect3 41
sweak interaction , ,i ie e i e
Lecture 2
Cosmic Neutrino Background
• Relic neutrino density and temperature today
• for given species (e, , ) (lecture 2)
• Total density today for all flavours
• High density, of order of CMB – but difficult to detect!
• At freeze-out : relativistic
2013-14 Dark Matter lect3 42
0T t 1.95K meV
-3113N cmN
3340N cm
p FO m
Neutrino mass
• If all critical density today is built up of neutrinos
• Measure end of electron energy spectrum in tritium beta decay
2013-14 Dark Matter lect3 43
2
, ,
47e
m c eV 2
νm <16eV c1c
2m eV c
3 3
1 2 eH He e
Co
un
t ra
te
Electron energy (keV)
Neutrinos as hot dark matter
• Relic neutrinos are numerous
• have very small mass < eV
• Were relativistic when decoupling from other matter at kT~3MeV
• → can only be Hot Dark Matter – HDM
• Relativistic particles prevent formation of large-scale structures – through free streaming they ‘iron away’ the structures
• → HDM should be limited
• From simulations of structures: maximum 30% of DM is hot
2013-14 Dark Matter lect3 44
2013-14 Dark Matter lect3 45
simulations Hot dark matter warm dark matter cold dark matter
Observations 2dF galaxy survey
See eg work of Carlos Frenk http://star-www.dur.ac.uk/~csf/
AXIONS
Postulated to solve ‘strong CP’ problem
Could be cold dark matter particle
2013-14 Dark Matter lect3 46
Strong CP problem
• QCD lagrangian for strong interactions
• Term Lθ is generally neglected
• violates P and T symmetry → violates CP symmetry
• Violation of T symmetry would yield a non-zero neutron electric dipole moment
• Experimental upper limits
2013-14 Dark Matter lect3 47
15 16. . . 10 .
predictede d m e cm
experiment 25. . . 10 .e d m e cm
QCD quark gauge standardL L L L 2
216
a aS Fg TF FL
1010
Strong CP problem
• Solution by Peccei-Quinn : introduce higher global U(1) symmetry, which is broken at an energy scale fa
• This extra term cancels the Lθ term
• With broken symmetry comes a boson field φa = axion with mass
• Axion is very light and weakly interacting
• Is a pseudo-scalar with spin 0- ; Behaves like π0
• Decay rate to photons
2013-14 Dark Matter lect3 48
1010~ 0.6A
A
GeVm meV
f
2
216
a aS FA
A
g TF
fFL
2 3
64
A AA
G m
Axion as cold dark matter
• formed boson condensate in very early universe during inflation
• Is candidate for cold dark matter
• if mass < eV its lifetime is larger than the lifetime of universe
stable
• Production in plasma in Sun or SuperNovae
• Searches via decay to 2 photons in magnetic field
• CAST experiment @ CERN: axions from Sun
• If axion density = critical density today then
2013-14 Dark Matter lect3 49
production decayA
6 3 210 10Am eV c1 A
cA
2 3
64
A AA
G m
Axions were not yet observed
2013-14 Dark Matter lect3 50
Axion mass (eV)
Axi
on
-γ c
ou
plin
g (G
eV-1
)
Combination of mass and coupling below CAST limit are still allowed by experiment CAST has best sensitivity
Axion model predictions Some are excluded by CAST limits
PART 3 WIMPS AS DARK MATTER
Weakly Interacting Massive Particles
2013-14 Dark Matter lect3 51
luminous 1%
dark baryonic
4%
NeutrinoHDM <1% cold dark
matter ~24%
dark energy ~70%
summary up to now
• Standard neutrinos can be Hot DM
• Most of baryonic matter is dark – MACHO? PBH?
• cold dark matter (CDM) is still of unknow type
• Need to search for candidates for non-baryonic cold dark matter in particle physics beyond the SM
2013-14 Dark Matter lect3 52
0.05 0.01 00.24 .30CDMmatter Baryons HDM
2013-14 Dark Matter lect3 53
Non-baryonic CDM candidates • Axions
– To reach density of order ρc their mass must be very small
– No experimental evidence yet
• Most popular candidate for CDM :
• Weakly Interacting Massive Particles : WIMPs
• present in early hot universe – stable – relics of early universe
• Cold : Non-relativistic at time of freeze-out
• Weakly interacting : conventional weak couplings to standard model particles - no electromagnetic or strong interactions
• Massive: gravitational interactions (gravitational lensing …)
2 6 310 10Am c eV
2013-14 Dark Matter lect3 54
Weakly interacting and massive
• Massive neutrinos: – The 3 standard neutrinos have very low masses – contribute to
Hot DM – Massive non-standard neutrinos : 4th generation of leptons and
quarks? No evidence yet
• Neutralino χ = Lightest SuperSymmetric Particle (LSP) in R-
parity conserving Minimal SuperSymmetry (SUSY) theory
– Lower limit from accelerators > 50 GeV/c2
– Stable particle – survived from primordial era of universe
• Other SUSY candidates: sneutrinos
• New particles from models with extra space dimensions
• …….
MSSM
Expected mass range
• Assume WIMP interacts weakly and is non-relativistic at freeze-out
• Which mass ranges are allowed?
• Cross section for WIMP annihilation vs mass leads to abundance vs mass
2013-14 Dark Matter lect3 55
2 2
22
1) 4 ~ ~
1 12) 4 ~ ~
M s M
Ms M
2W
2W
s > M
s < M
0
1~
vt
24
f f
s M
Expected mass range: GeV-TeV
• Assume WIMP interacts weakly and is non-relativistic at freeze-out
• Which mass ranges are allowed?
• Cross section for WIMP annihilation vs mass leads to abundance vs mass
2013-14 Dark Matter lect3 56
MWIMP (eV)
2 2
22
1) 4 ~ ~
1 12) 4 ~ ~
M s M
Ms M
2W
2W
s > M
s < M
HDM neutrinos
CDM WIMPs
0
1~
vt
2013-14 Dark Matter lect3 57
WIMP annihilation rate at freeze-out
• WIMP with mass M must be non-relativistic at freeze-out
• gas in thermal equilibrium
• Annihilation rate
• Cross section depends on model parameters : weak interactions
AnnihilationW T N T χv
2
32
2
Boltzman gas
number density2
MckT
kT Mc
MTeTN
, ...f f
Could be neutralino or other weakly interacting
massive particle
WIMP velocity at FO
TFO
2013-14 Dark Matter lect3 58
Freeze-out temperature
• assume that couplings are of order of weak interactions
• Rewrite expansion rate
• Freeze-out condition
• f = constants ≈ 100
• Set solve for P
2
Fv G M
1* 221.66
PL
g TH T
M
22
322
2
~F
PL
MTc
ke G
M
TMT M f
2
~ 25FO
cP FO
k
M
T
FO FOW T H T
GF = Fermi constant
2
PM
T
c
k
2
~25
FO
M ckT
2013-14 Dark Matter lect3 59
P=M/T (time ->)
Nu
mb
er d
ensi
ty N
(T)
today
Increasing <σAv>
Depends on model
P~25
2013-14 Dark Matter lect3 60
Relic abundance today Ω(T0) - 1
• At freeze-out annihilation rate ~ expansion rate
• WIMP number density today for T0 = 2.73K
• Energy density today
3
0 FO
A
T
vT
T0N
2
FO PLT M
A FOv H TFON T
3
000
A
N TT
T Mv
O
PL
FP
M
253
0
110
c FO
m sv
t c
0 T
L
FO
P
P
M
3
3
0
FOR T
RT
TFON T0N
311
0
6 10
A
T GeV sv
2013-14 Dark Matter lect3 61
Relic abundance today Ω(t0) - 2
• Relic abundance of WIMPs today
• For
• O(weak interactions) weakly interacting particles can make up cold dark matter with correct abundance
• Velocity of relic WIMPs at freeze-out from kinetic energy
FOv ≈ 0.3 c
35 210X cm O pb1
253 1
0
10~
FO
t cm sv
2 31
2 2
FOkTM v
12
3~ 0.3v
c FOP
WIMP miracle
Experimental sensitivity
2013-14 Dark Matter lect3 62
Lines: No WIMP signal observed Set 90% C.L. upper limit on velocity weighted annihilation cross section
Areas: observed abnormal signal in gamma ray (Fermi) and positrons (Pamela) can be interpreted as originating from WIMP annihilation. Data hint at masses and velocity weighted annihilation cross sections inside surface areas.
SUPERSYMMETRY : POPULAR CANDIDATES
Neutralino is good candidate for cold dark matter
SUSY = extension of standard model at high energy
2013-14 Dark Matter lect3 63
What are we looking for?
• Particle with charge = 0
• With mass in [GeV-TeV] domain
• Only interacting through gravitational and weak interactions
• Stable
• Decoupled from radiation before BBN era
• Has not yet been observed in laboratory = accelerators
2013-14 Dark Matter lect3 64
2013-14 Dark Matter lect3 65
Why SuperSymmetry
• Gives a unified picture of matter (quarks and leptons) and interactions (gauge bosons and Higgs bosons)
• Introduces symmetry between fermions and bosons
• Fills the gap between electroweak and Planck scale
• Solves problems of Standard Model, like the hierarchy problem: = divergence of radiative corrections to Higgs mass
• Provides a dark matter canndidate
217
19
1010
10
W
PL
M GeV
M GeV
Q fermion boson Q boson fermion
2013-14 Dark Matter lect3 66
SuperSymmetric particles
• Need to introduce new particles: supersymmetric particles
• Associate to all SM particles a superpartner with spin 1/2 (fermion ↔ boson) sparticles
• minimal SUSY: minimal supersymmetric extension of the SM – reasonable assumptions to reduce nb of parameters
• Neutralino as dark matter
• Parameters = masses, couplings - must be determined from experiment
• Searches at colliders: so particles seen yet
M accessible range production sensitivity
Expected abundance vs mass
2013-14 Dark Matter lect3 67
Neutralino mass (GeV)
h
2
=[.05-0.5]
• variation of neutralino density as function of mass
• Allowed by collider and direct search upper limits on cross sections
• Expected mass range 50GeV – few TeV
Ω= [0.04 – 1.0]
M GeV
2h
Every dot shows the prediction from 7-parameter MSSM calculations
Calculation gives cross section. This yields the abundance Ω
PART 4: EXPERIMENTAL WIMP SEARCHES
The difficult path to discovery
2013-14 Dark Matter lect3 68
Where should we look?
• Search for WIMPs in the Milky Way halo
Indirect detection: expect WIMPs from the halo to annihilate with each other to known particles
Direct detection: expect WIMPs from the halo to interact in a detector on Earth
2013-14 Dark Matter lect3 69
Dark matter halo
Luminous disk
Solar system
© ESO
2013-14 Dark Matter lect3 70
three complementary strategies