1. Dark Matter in galaxies !
Refining the free function of MOND
B. Famaey
(Strasbourg Observatory, France)

2. Large-Scale « Geography »
of the whole world
• Earth: diameter = 13 000 km,
distance from Sun = 149 millions km
(= 1 Astronomical Unit)
• Distance Earth-Mars between 0.4
and 2.7 A.U.
• c = 300 000 km/s (7.5 revolutions
around the Earth in 1 second)
• Moon = 1.3 light-second
• Sun = 8 light-minutes
• Solar System = 6 light-hours
• Closest star (Proxima Centauri) = 4.2
light-years

3. The Milky Way
Our Galaxy Sun’s
(artist view) neighbourhood
1011 stars
100 000 ly

5. Everything is in motion
• Earth goes around the Sun at 30 km/s
• Sun rotates at 220 km/s with respect to the
center of the Milky Way (one orbit each 200
million years = Sun aged of ~25 galactic
« years »)
• Milky Way moves at 600 km/s with the Local
Group w.r.t. the Hubble flow
• Universe expands

6. Gravitation
• Newton (1686) : F = G m1 m2/ r2
• Newton (1686): a = F/m
• Equivalence principle: inertial mass IS gravitational charge
 General Relativity (Einstein, 1915), gravitation is not
really a force, just a deformation of space-time, natural state
is free-fall (like astronauts in space stations)
• Weakest « force » of Nature, but only one acting at long
ranges (no screening)
= governs the dynamics of the Universe on large scales

7. Equivalence principle

8. The old missing mass problem
• 1781: William and Caroline
Herschel discover Uranus
• 1792: Delambre publishes orbit
of Uranus, non-Newtonian even
after taking the perturbations of
other planets into account
• 1834: Hussey proposes new
planet, Airy believes in new • 1859: perihelion precession of
gravitational law
Mercury of 43 arcsec per
• 1846: Le Verrier calculates the century, Leverrier postulates the
position of the new planet
existence of the small planet
Vulcan
Galle discovers Neptune
But correct answer for Mercury found by Einstein in 1915

9. The modern-day missing mass
• 1933: Zwicky observes • End of the 1970s: Bosma
velocity dispersion of and Rubin: 21 cm line of HI
individual galaxies in the allows them to measure the
Coma cluster, and finds asymptotically FLAT
M/Mvis ≈ 20
rotation curves instead of
Keplerian 1/√r falloff
Doppler Shift: (λ-λ0)/λ0 = Vr / c

10. • Not only the amplitude but the shape is abnormal:
Vc = cste = M(r) ∝ r
• M( r ) = ∫ 4 π r2 ρ(r) dr
= ρ(r) ∝ r -2
• BUT ρvis(r) ∝ e-r/r0 /r

11. Dark Matter halo
=85% to
95% of
the mass

12. The Large Scale Structure

14. The ΛCDM model of the Universe
- Cosmic Microwave Background at 2.7 K (Planck), variations of 1/100 000
= 85% of the matter is dark … + accelerated expansion (dark energy)

15. Direct detection?
Many experiments such as XENON100
(liquid Xenon) or Cryogenic Dark Matter Search
(CDMS): try to detect a direct collision
between a dark particle and a nucleus in a
Germanium-Silicium crystal = NO LUCK…
but can exclude certain masses and « cross-
sections »

16. Could gravitation also be wrong?
…. Maybe…
• Gravitational acceleration at the edge of
galaxies is 100 billion times smaller than on
earth! = impossible to test in the lab!
• Direct relation between distribution of dark and
normal matter in galaxies = unexplained!

17. Tidal dwarf galaxies
Tidal dwarf galaxies in
the NGC 5291 system
Bournaud et al. (2007)
Gentile, Famaey et al. (2007)

18. Milky Way and Andromeda:
disks of satellites
Milky Way Andromeda
Kroupa et al. (2010)
Ibata et al. (2013)

19. Conclusion
• Whatever the solution to the dark matter problem, it will lead
us to one of the biggest revolutions in physics
• Either new particles, or new law of gravitation, or some subtle
combination of both (if I had to bet I’d bet on the 3rd, but
Nature does not care about anyone’s bet…)
We should not consider the present favoured cosmological
model as a dogma, but should also not discard it for purely
aesthetical personal reasons. On large scales, a plethora of data
are supporting it, on galaxy scales, we do not understand what is
happening
= In Science, experiment is the ultimate judge! Not one’s
own intuition or « preference »… Exciting future 