Title

UDF #3492

Coma Cluster
2 KE

PE

1 d
2
I
2 dt
2
(Zwicky 1937)

NGC 3198
Ngc 3198
(Begeman 1989)

MO dified
N ewtonian
D ynamics a n

GM ( r ) r
2
 v
2 r a n


(  ) a
M

(

(

1

 r x
) r )
(  x
 x r r a
0

1
1
)
(Milgrom 1983)
(Kent 1987)

The Tully Fisher Relation
In “deep MOND,” a
 a n a
0
 v
2 r

GM a
0 r
2

L

M
 v
4
Tully-Fisher

a n

GM ( r ) r
2
 v
2 r

M ( r )
 r
 
( r )
 r

2
(Kent 1987)

In Situ Measurements
In the Solar neighbourhood, we have:

1.1

70 M a pc -2 Total mass within 1.1 kpc of the Galactic plane
(Kuijken & Gilmore 1991)
 bar
1.1

50 M a pc -2
Census of mass in baryons within 1.1 kpc of the
Galactic plane (Olling & Merrifield 2001)
 DM
1.1

20 M a pc -2

0.4
 bar
1.1
whereas more globally in the Milky Way:
M(R
0
)

9.5 × 10 10 M a
Total dynamical mass within the Solar circle
M bar (R
0
)

5.5 × 10 10 M a
Census of mass in baryons within the Solar circle (Olling & Merrifield 2001)
M DM (R
0
)

4.0 × 10 10 M a

0.7 M bar (R
0
)
Dark matter more spherically distributed than baryons

Measuring Halo Shape
One measure of the shape of the halo can be made using the thickness of a galaxy’s gas layer, assuming that it is in hydrostatic equilibrium:
Flatter halo dark matter concentrated closer to plane
Vertical gravitational pull reduces scaleheight of gas layer

q = c/a
1.0
0.8
0.6
0.4
0.2
(Olling & Merrifield 2000)

NGC 720
(Buote & Canizares 1996)

Milky Way

Moore et al.
(2003)

Milky Way
(Dubinski 1994)

Title

Where Have All the Satellites Gone?
Invisible Galaxies?
• Never formed stars
MOND?
• Destroyed by dynamical friction


MOND
DM

1

2
M
DM
M
MOND
(Ciotti & Binney 2004)
(Minchin et al. 2005)
• First star blew out gas, stopping star formation
For a typical galaxy-scale halo,
M
DM
M
MOND

25



MOND
DM

0 .
05


NFW
( r )
 r r s


 s r s

2

M
( r )

 r r
M

1 .
5


1
M

 r r
M

1 .
5

Navarro et al. (2004)

(Klypin, Zhao & Somerville 2002)

NGC 6822

N6822 rotation curve: the prediction
(de Blok 2004)

MOND Again
(Sanders & McGaugh 2002)

NGC 4472
Elliptical Galaxies

PNe
Romanowsky et al. (2003)

Combined dispersion profiles
NGC 821 (Romanowsky et al 2003)
NGC 3379 (Romanowsky et al 2003)
NGC 4494 (Romanowsky et al 2003)
NGC 4697 (Méndez et al. 2001)
Isothermal halo
MOND
(Sanders & McGaugh 2002)
Isotropic no dark matter model
(Romanowsky et al. 2003)

Explanation for “Naked” Ellipticals
We have been able to rule out:
• Systematic problems with data
• Face-on highly-flattened systems
• Strong radial bias in orbits
 CDM prediction
(Bullock et al. 2001)
Which leaves:
• Lost dark matter halos
• MOND
• Low concentration halos
More data on the way…

Conclusions
There is overwhelming evidence that, on the scale of galaxies, dynamically-inferred masses exceed the observed baryonic masses
For the last twenty years, the paradigm has been that the deficit is made up by non-baryonic dark matter
It is by no means clear at this point that Occam’s
Razor supports this interpretation (c.f. MOND)

Summary

Clusters of Galaxies