Mass and Light distributions in Clusters of Galaxies - Henry A ...

1.1 Clusters of Galaxies
and a gravitational radius
R G ≡ 2M 2 tot
[ ∑
i≠j
m i m j
r ij
] −1
≈ 2M 2 tot
[ ∑
i≠j
m i m j
r ⊥,ij
] −1
. (1.7)
The approximation gives R G in terms of the observable projected galaxy
separation r ⊥,ij in the plane of the sky (Limber & Mathews 1960). The
velocities can be evaluated from the radial velocity distribution 〈v 2 〉 = 3σ 2 r,
where σ r is the radial velocity dispersion. Substituting this in eq. 1.6 we have
M tot = 3R [
]
Gσr
2 2 [ ]
G = 7 × σ r RG
1014 M ⊙ . (1.8)
1000 km/sec Mpc
For a typical rich cluster, σ r ∼10 3 km/sec and R G ∼1 Mpc, so the mass is of
order M tot ∼ 10 15 M ⊙ .
1.1.2 The “Missing Mass Problem” - Dark Matter
Analyses of clusters measure surprisingly high masses, especially compared
to the typical total luminosity of a cluster, L tot ∼ 10 13 L ⊙ . Commonly, mass
is compared to luminosity by calculating the mass-to-light ratio, typically,
( M
L
)
tot
( )
M⊙
≃ 300 h . (1.9)
L ⊙
This exceeds the value of luminous galaxies which ranges from M/L B ≈
1 − 12 M ⊙ /L ⊙ by more than a factor of 10. This discrepancy means less
than 10% of the cluster mass is in stars in luminous galaxies. This is the
“missing mass” problem, first suggested by Zwicky (1933), who measured
the nearby Coma cluster mass from galaxy velocity dispersions.
Zwicky
(1937) postulated that there is a need for a non-standard mass component
to explain these measurements. Current measurements indicate that about
85% of the mass is made of this dark component. As of yet, the nature of
DM is unknown, but is fairly certain to be non-baryonic, non-radiating, cold
matter interacting practically through gravitation alone.
5
Quantifying the