Dark Matter:
What is it? Where is it?
Do we need it? How much?
History:
1937: like many things in astronomy, dark matter was first
postulated by Fritz Zwicky.
Apply virial theorem to indiv. galaxies in the Virgo cluster  Mgalaxy
Apply virial theorem to cluster as a whole  Mcluster
Zwicky found M/Lcluster ~200 ?? M/Lgalaxy~8
~1970: Vera Rubin, Ken Freeman and others explore rotation curves
and (re-)find the need for dark matter (formerly called missing).
Actual diagnosis: gravity acts stronger than expected on the basis
of the identified mass (=sources of gravity)
Reading: J Peacock, Cosmological Physics, Cambridge Press p367-386
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Vatican 2003 Lecture 26 HWR
Dark Matter on Different Scales
• Basic hypotheses to test:
– there is universal “dark matter”, which
• was initially distributed like all known matter
• interacts with the observed matter (and itself)
mostly through gravity
– OR,
• there is a universal modification to the laws of gravity
(Newton AND Einstein) that acts at large scales and/or
weak accelerations.
• Dark Matter appears to be needed in:
–
–
–
–
–
–
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Dwarf spheroidal galaxies: 500 pc
Large galaxies: 20 kpc
Galaxy halos: 50-500 kpc
Galaxy Clusters: 1 Mpc
Large-Scale Structure: 20 Mpc
Cosmic Microwave Background
Vatican 2003 Lecture 26 HWR
Dark Matter Evidence Nearby:
the Draco dwarf galaxy
Sky image of Draco
Stellar density contours of Draco from SDSS
Odenkirchen et al 2001
 Draco is a bound system in equilibrium
Dsun
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 70 kpc
Vatican 2003 Lecture 26 HWR
Radial Profile and Kinematics of Draco
Stellar density profile of Draco
Modelling options
1)
Stars only tot(r) = *(r)
2)
Stars + DM: tot(r) = *(r)
+ DM(r)
Giant stars with velocities measured
•
Estimate *(r) from stellar distribution
•
Giant stars as kinematic tracers
- need velocity precision of  3 km/s
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Vatican 2003 Lecture 26 HWR
Mass Modelling of Draco
Velocity dispersion profile
Expected (M/L)* ~ 2
 Draco is dark matter dominated
Jeans equation model
Enclosed mass
Try models with different DM profiles
 M (<10‘) well constrained
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Vatican 2003 Lecture 26 HWR
Rotation Curves of Spiral Galaxies
•Rotation curves show that DM is
needed
•Total (stars,gas,DM) rotation curve is
v~const. for 2-8 Rexp
•A so-called non-singular isothermal
(s=const.) DM distribution often fits
2
well: r (r )  r0 / 1  r / rc 
•But, is this dark matter profile
•Physically motivated?
•Physically plausible?
•Expectation from cosmological
simulations: NFW
profile
r~r-1 at small radii and
r~r-3 at large radii
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Vatican 2003 Lecture 26 HWR
Degeneracies in Fitting Rotation Curves
Rotation curves do not contain
enough information to:
Determine the ratio of star to DM mass
Distinguish the radial profile of DM
Van Albada et al 1985,
ApJ, 295, 305
Navarro 1997
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Dark matter at small radii is poorly
understood!
Vatican 2003 Lecture 26 HWR
Dark Matter in Galaxy Halos
Satellites to the Milky Way
Prada et al 2003
 tracers of the mass in the halo
SDSS sample: isolated MW-like galaxies
0.5 satellites per galaxy x 1000 galaxies
 Synthetic galaxy with 500 satellites
MW-like galaxies are at
the center
ofsystems
dark
unbound
matter halos that extend
to >200 kpc
•
identify satellite candidates
•
make a conservative rejection of unbound
systems
•
calculate resulting velocity dispersion of
satellites
•
compare to cosmological halo formation
models  good match
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DM density profile in
the outer parts r~r-3
Vatican 2003 Lecture 26 HWR
Dark Matter in Galaxy Clusters
In galaxy clusters the masses can be measured three ways
• Galaxy clusters contain hot gas ( bound by dark matter?)
• Galaxy velocity dispersion
• Gravitational lensing
T = 106 K  X-ray emission
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Vatican 2003 Lecture 26 HWR
X-Ray Gas in Hydrostatic
Exquilibrium
dP
GM ( r )

r
2
dr
r
M ( r )  
kT
d ln g d ln T
(

)
 mH g d ln r d ln r
Mstars~Mgas~3x1013MSun
Mtot,cluster(Rvirial)~1015MSun
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Vatican 2003 Lecture 26 HWR
Other Lines of Evidence For Dark Matter
• Gravitational lensing (Hans-Walter, next week)
 dark matter clumping on largest scales
• The Cosmic Microwave Background and the curvature of
space (Rachel, Friday) 
WM~0.27
• The growth of small fluctuations to strong fluctuations
(Rachel, next week)
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Vatican 2003 Lecture 26 HWR
Alternatives to Dark Matter
• MOND: Modified Newtonian Dynamics (Milgrom 1980s-)
Ansatz:
for accelerations a less than a0,
gravity behaves as a(a/a0) =
GM/r2
 as a(r) ~ 1/r of a < a0:
flat rotation curves
Note:
• a < a0 untested in the lab
• single value of a0 works for all
rotation curves
But:
• No relativistic version of
MOND
• MOND has trouble explaining
DM in cluster and far out in
halos
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Vatican 2003 Lecture 26 HWR
Summary: Dark Matter Evidence
•
A wide range of dynamical phenomena cannot be explained through
the known (baryonic) mass content of the universe alone.
•
All (well, almost all) these problems can be solved if we make one
radical assumption:
85% of all matter with rest mass (WM  0.25) is in a form
(dark matter) that was
– initially distributed as ordinary matter
– interacts with the rest (almost) only through gravity
– acts like a collisionless “fluid”
•
is cold, i.e. consists of non-relativistic particles
•
Stars,gas are now more concentrated/clumped than DM
•
We also need a “cosmological” constant (vacuum energy), i.e. a longdistance ‘repulsive’ force
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– galaxies sit at the center of much larger DM halos
– Note: rbaryon ~8 x rstars
Vatican 2003 Lecture 26 HWR
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Vatican 2003 Lecture 26 HWR
Nature of the Dark Matter
• Non-baryonic, to reconcile WM ~0.27 with primordial
nucleosynthesis Wb~0.018 and large-scale structure growth
• Cold: must not escape from potential wells
• (Cold) Dark Matter Candidates:
– Black holes
– Low-mass objects (“MACHO”s, free-floating planets)
– Elementary particles
Massive Black Holes as Dark Matter Candidates
– (one) plausible mass range: ~106 Msun
(Lacey and Ostriker, 1985)
– But, such massive black holes cannot be the dark matter in dwarf
galaxies (Rix and Lake, 1985).
– E.g. c.a. 80 BH’s in Draco, they would disrupt the galaxies!
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Vatican 2003 Lecture 26 HWR
• MACHO’s: Massive Compact Halo Objects
– Potential mass range: 0.08 MSun (stellar limit) to MEarth
Observational test: gravitational microlensing
• (MACHO and OGLE) experiments.
Idea:
• if all the dark matter in the Milky Way’s halo was MACHOS
• there is a 10-6 chance that a star (e.g. in the Magellanic
Cloud) has a MACHO exactly along the line of sight
• focussing  brightening of the stars’ image
• as stars move  dime dependent light curve.
Implementation: monitor 106 stars
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Vatican 2003 Lecture 26 HWR
Microlensing Searches
Large Magellanic Cloud
Micro-Lensing Cartoon
Lensing Lightcurve
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Vatican 2003 Lecture 26 HWR
Are MACHOs the Dark Matter?
•MACHO’s make up (at most)
15% of the Milky Ways halo
mass
MACHO Mass
•Inferred mass range: 0.4MSun
Why would they be invisible?
MACHOs are an enigma, but
certainly not the solution to
the dark matter problem
Halo Mass Fraction in MACHOs
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Alternative: lensing by ordinary
stars in the LMC or MW
Vatican 2003 Lecture 26 HWR
WIMPS as Dark Matter Candidates
• “cold” Dark Matter: must become non-relativistic already at
T >> 104K  clumping
• supersymmetric theories (SUSY) can naturally create
particle (pairs with their SUSY partner)
- lightest SUSY particle stable: neutralino, gravitino,
higgsino, etc.
• axions: hypothesized, very light particle; may arise in
quantum chromodynamics
 WIMPS are a plausible, but not firm, consequence of several
theories in particle physics
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Vatican 2003 Lecture 26 HWR
Towards detecting WIMPS
• WIMPS: may have exceedingly rare elastic scattering
events with crystals and one may measure the recoil.
• However: many other particles/processes interact with
crystals  high false detection rate.
• Reduce background  deep tunnels (e.g. Gran Sasso)
• Search for seasonal signature
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Vatican 2003 Lecture 26 HWR
A first detection? … Or not
The DAMA experiment
in the Gran Sasso
claimed to have found a
seasonal variation
? 50 GeV particles
Other experiments seem
to rule out DAMA
PROBLEM: cross-section could be
1000 times smaller than current limits
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Vatican 2003 Lecture 26 HWR
Dark Matter Up-Shot
• Cold, collisionless ‚Dark Matter‘ with WDM 
0.25 explains a wide range of phenomena (not
only rotation curves)
•„universal dark matter“ works
•Stars/cold gas are concentrated/clumped than DM
•DM poorly understood inside galaxies
• Nature of Dark Matter unknown
•We only know what it is NOT!
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Vatican 2003 Lecture 26 HWR