Galaxy Groups and Clusters
I
Half of galaxies are in groups or clusters
I
Half of members in a volume less than 1 Mpc3
I
Gravitationally isolated from Hubble flow
Clusters contain ∼ 50 luminous members in inner Mpc
I
I
Being a member alters evolution of a galaxy: they fall in through
hot gas and pressure strips away cool gas in outer parts
I
I
Groups are dominately formed of spirals
Clusters are dominately formed of ellipticals and S0’s, predominately
giant or dwarfs.
I
Groups and clusters are younger than the oldest stars
I
Motions are too slow for more than 1 or 2 transit times so far
I
Much baryonic mass is hot gas, emitting X-rays, but most might be
intercluster cool gas
I
Most mass is dark
J.M. Lattimer
AST 346, Galaxies, Part 7
Nearby Galaxy Groups
J.M. Lattimer
AST 346, Galaxies, Part 7
HST
Stephan’s Quintet
A rare compact group, galaxies
almost touch, 85 Mpc distant
and 80 kpc across.
7319
7318B
Long tails of stars
have been pulled from the disks.
7317
About 109 M in hot gas with
TX ∼ 107 K, consistent with the
velocity dispersion of the
galaxies of 300 km/s.
About 1010 M in cool gas,
mostly outside the galaxies,
apparently stripped out.
7320, not a member
SST
NGC 7318b, recently arrived,
tore out the tail from NGC 7319.
A smaller spiral, NGC 7320c,
passed through 500 Myr ago and
will return.
J.M. Lattimer
7318A
AST 346, Galaxies, Part 7
M81 Group
Sparse group (> 34
members),connections
of long HI streamers
torn from galactic disks.
Distance is 3.6 Mpc,
total mass 1012 M .
M82
M81
NGC 3077
J.M. Lattimer
AST 346, Galaxies, Part 7
NGC 1550 Group
Has about 15 members within 1 Mpc
of the S0 galaxy NGC 1550, including
two ellipticals.
Radiates 4 × 109 L in X-rays (10
times that of Stephan’s Quintet).
Metallicity about 0.1 solar.
NGC 1550 group
Galaxy velocity dispersion σr = 310
km/s, approximate distribution with a
Plummer model with a = 100 kpc.
KE
PE
3π G M
3σr2
=
=−
=
2
M
2M
64 a
1/2
LX = n2 Λ(TX ), Λ ∼ 3×10−27 TX
n ∝ r −β ,
X-ray emission
NGC 1550
erg/s
IX ∝ LX R ∝ r 1−2β
Hydrostatic equilibrium:
M(< r ) = −
kNo r 2 d(nT )
µ Gn dr
J.M. Lattimer
AST 346, Galaxies, Part 7
Veclocity Dispersions in Groups
Assume a Plummer model for groups with the same a and mass for each
galaxy. The Virial Theorem predicts
σr2 ∝ Mtot /a ∝ N/a
where N is the number of galaxies in a group.
The speeds of group galaxies 100 km/s < σr < 500 km/s, about the
same as the stellar velociities within galaxies. Dynamical friction is
therefore important.
J.M. Lattimer
AST 346, Galaxies, Part 7
Dynamical Friction and Mergers
∆KE⊥
2G 2 mM
=
.
MV
b2 V 3
The average rate at which it slows is
Z bmax
2G 2 mM
dV
=
nV
−
dt
b2 V 3
bmin
−∆Vk =
A galaxy of mass M moves past a star
of mass m at velocity V . M acquires
a speed ∆V⊥ = 2Gm/(bV )
perpindicular to V . We require
b >> 2G M/V 2 .
The star acquires an equal and
opposite momentum. The total KE in
perpindicular motions is
2
2
m 2G M
M 2Gm
+
∆KE⊥ =
2
bV
2
bV
2
2G mM(M + m)
.
=
b2 V 2
This energy comes from the forward
motion of the galaxy, which changes
by ∆Vk . To lowest order
J.M. Lattimer
4πG 2 Mnm
ln Λ
V2
n is the stellar density. Can also be
applied to a small galaxy orbiting
within a dark halo of density nm.
Using the dark halo potential
nm = ρH ' V 2 /(4πGr 2 ),
G M2
dr
Fk = − 2 ln Λ = M
r
dt
Integrating:
r 2V
tsink =
2G M ln Λ
=
AST 346, Galaxies, Part 7
Mergers and Simulations
NGC 4676 ”the Mice”
R band, HI contours
J.M. Lattimer
AST 346, Galaxies, Part 7
Simulations
J.M. Lattimer
AST 346, Galaxies, Part 7
Starbursts
Mergers often have 109 − 1010 M of dense molecular gas brought
inward to center which is gravitationally compressed and leads to violent
star formation.
If dust is present, it intercepts the stellar light and re-radiates it in the
infrared.
—
J.M. Lattimer
AST 346, Galaxies, Part 7
M82 – A Starburst Galaxy
Makes 2 − 4M /yr of new stars, same as Milky Way, in 600 pc region.
Radio-bright knots where stars ionize the gas, produce free-free radiation.
Supply of 2 × 108 M will be exhausted in τff = 100 Myr
J.M. Lattimer
AST 346, Galaxies, Part 7
Starbursts: Arp 220
Luminous and ultraluminous infrared galaxies
(ULIRG) form stars at rate
LFIR
M yr−1 .
Ṁ∗ ∼
6 × 109 L
Most powerful ULIRG have 1000M /yr rate.
Half of ULIRG also have
active galactic nuclei.
Arp 220 is a close-by
merging pair 75 Mpc
distant, with
Ṁ ∼ 200M /yr.
Has 109 M H2 in
a 20 pc gas disk.
Can’t sustain activity
for more than 1 Gyr.
Rounder cores, more
random motions, less
rotation: form ellipticals?
J.M. Lattimer
AST 346, Galaxies, Part 7
Nearby Galaxy Clusters
J.M. Lattimer
AST 346, Galaxies, Part 7
Most members are dwarfs.
Virgo central regions have
0.5 L /pc2
to
5-10% of luminous galaxies
live in clusters.
ta
l
# within [MB , MB + 1]
Properties of Clusters
Virgo core radius is about
0.5 Mpc
Fornax cluster has 1/5 as
many members, but is
more compact, with twice
the luminosity density, but
less hot gas, relatively.
The core of a galaxy like
NGC 1399 is 107 times as
dense as the center of the
Fornax cluster.
Virgo
J.M. Lattimer
AST 346, Galaxies, Part 7
Rich Clusters
Coma
Examples are Coma, Perseus Clusters.
As clusters become more massive,they
become denser; radii hardly change.
Infalling clumps add 10% every few
Gyr, but will cease in 2-3 Hubble times
as the expansion of the universe will
overwhelm a cluster’s gravity.
◦ ellipticals
? spirals
X-ray contours
Spirals excluded from the centers.
Galaxies fall supersonically into
clusters; shocks leave gas behind.
By observing novae and planetary
nebulae, it is estimated ∼ 10 − 20% of
stars are intercluster, probably torn
out of infalling galaxies.
Virial estimates of masses
∼ 2 − 7 × 1014 M for Virgo–Coma.
Hot gas indicates masses 50% larger.
J.M. Lattimer
AST 346, Galaxies, Part 7
Hot Cluster Gas
Mass in hot gas equals stars in
poor clusters, but 10 times stars
in a rich cluster. It can be traced
to larger radii than stellar light.
Temperature of gas increases
with cluster luminosity, consistent
with galaxy velocity dispersion.
As new clumps added, TX grows.
≈ 14
10−3 cm−3
n
J.M. Lattimer
107 K
Gyr
T
Since cool gas and star formation not
observed in central galaxy, gas must
be reheated by supernovae or radio
sources. Gas in outer regions doesn’t
cool quickly and does not form stars.
Models suggest TX increases
faster than L, so high z clusters
should be cooler for a given L;
not observed, indicating early
energy sources (starbursts and
active nuclei).
Cooling time is ∝ nX TX /LX , or
3nkT
√
tcool =
3 × 10−27 n2 T
r
3
L
∝ TX
x
AST 346, Galaxies, Part 7
Cosmic Baryonic Budget
Hot gas accounts for 0.1 of the
mass of a luminous cluster, but
much less in smaller systems.
Together with stars, accounts
for about 1/6 of total mass.
Fukigita & Peebles 2004
But baryons are more
concentrated in galaxies (less
than half of mass inside solar
circle is dark).
Dense gas in the damped
Lyman-α clouds (neutral and
atomic) is half the mass of hot
gas.
A large amount of ionized gas
could be hidden; it’s low density
prevents it from cooling. This
diffuse gas is in the Lyman-α
forest.
J.M. Lattimer
AST 346, Galaxies, Part 7
Did Galaxies Grow By Mergers?
I
Largest red galaxies (cD and
ellipticals) live in dense regions
while star-forming spirals and
irregulars fill less dense regions.
I
At z = 1, about 5-10% of galaxies
are in major mergers, so that
within last 5 Gyr, 2/3 of luminous
galaxies have had a merger.
I
If ellipticals formed from mergers,
their stars are older. Clumps are
ideal sites for mergers because of
low random velocities, and so
dense with ellipticals.
I
In a major merger of two equal
masses, disks are destroyed and
cool gas is lost; star-formation
terminates. Remnant will have
only middle-aged and old stars.
J.M. Lattimer
I
A merged system will become less
dense. A system of size R with N
galaxies of mass M has energy
PE/2= −GNM2 /(2R). After
merger, and virialized, the energy
is PE/2= −G (NM)2 /(2Rg ) so
Rg = NR. Merged systems are
less dense by 1/N 2 .
AST 346, Galaxies, Part 7
Did Galaxies Grow By Mergers?
I
I
I
If merged systems still
contained some cool gas, it
would settle to center and
trigger star formation.
I
Where does ”fundamental plane”
relationship come from?
I
Why are luminous red galaxies not
rare at high redshifts? More efficient
star forming?
Merged galaxies therefore
develop metal-rich centers.
With a small, dense, inner
disk, these galaxies would
rapidly rotate, and resemble
”disky” ellipticals.
I
When these merged systems
merge again, more luminous
systems are formed, and tend
to be triaxial, so resemble
”boxy” ellipticals.
I
Problems:
J.M. Lattimer
AST 346, Galaxies, Part 7
Gravitational Lensing
Image
I
Microlensing by a compact
(point) source
α≈
I
4G M
bc 2
Source
Lens
Lensing by extended objects
Sources near the Einstein radius
α(b) = ∇ψL (b)
Z
4G
ψL (b) = 2
Σ(b0 ) ln |b − b0 |dS 0
c
I
Weak lensing
Sources are well outside the
Einstein radius
J.M. Lattimer
AST 346, Galaxies, Part 7
Gravitational Microlensing
Use small angle approximations:
β = y /dS
Image
θ = x/dS = b/dLens
α = (x − y )/dLS
Source
θ − β = αdLS /dS
θ2
4G M dLS
≡ E
2
θc dLens ds
θ
If ds = NdLens s
1 kpc N − 1 M
θE = 0.002
.
dLens N M
=
Lens
p
Solving θ2 − βθ − θE2 = 0: θ± = β ± β 2 + 4θE2 /2
When dLens << dS , α ≈ θ − β = θE2 /θ.
Images are magnified and brightened (I (x) is unchanged):
!
p
θ dθ 1
β 2 + 4θE2
Fimage,±
Aimage,±
xdx
β
p
=
=
=
=
+
±2
Fsource
Asource
ydy
β dβ 4
β
β 2 + 4θE2
J.M. Lattimer
AST 346, Galaxies, Part 7
Gravitational Lensing by a Collection of Point Masses
For one point source, we can write
α(b) =
4G M
dψL
, ψL =
ln b.
db
c2
Summing the effect from a collection
of point masses:
α(b) = ∇ψL (b)
Z
4G
ψL (b) = 2
Σ(b0 ) ln |b − b0 |dS 0
c
If axisymmetric, one finds
Z b
4G
α(b) = 2
Σ(R)2πRdR
bc 0
4G M(< b)
= 2
c
b
This is proven by noting that a ray passing through a uniform circular
ring is not bent, and a ray passing outside is bent the same as from a
point mass at the center.
J.M. Lattimer
AST 346, Galaxies, Part 7
Extension to Asymmetric Galaxy Clusters
dLS
dS
4G M(< b) dLS
=
θc 2
dLens dS
θ − β = α(θ)
Plummer
potential
dark halo
potential
Since b = θdLens
units are a/dLens
M(< b)
β =θ 1−
πb 2 Σcrit
c2
dS
Σcrit =
4πG dLens dLS
If Σ(0) > Σcrit , an image at β = 0 will be an Einstein ring of angular size
θE = bE /dLens , where M(< bE ) = πbE2 Σcrit .
If dS , dLS >> dLens
100 Mpc
Σcrit ≈ 2 × 10
M pc−2
dLens
2
dLens
θE
M(< θE ) ≈
1010 M .
100 Mpc
100
14
J.M. Lattimer
AST 346, Galaxies, Part 7
Weak Lensing
Galaxies behind a cluster but well
outside of its Einstein radius have
weakly magnified tangential images.
The radial axes are in the ratio
dβ β x dx
:
,
dθ : θ y dy
Shear γ measures compression.
Assuming b >> θE dLens ,
β
1 dβ
−
γ=
2 dθ
θ
M(< b)/(πb 2 ) − Σ(b)
=
.
Σcrit
In the event that Σ(R) is constant,
θ ∝ β.
Measuring average shapes of many
galaxies in the background allows an
estimate of shear and distribution of
mass.
J.M. Lattimer
Studies of halos of bright galaxies
show they are larger and more massive
than rotation measures imply.
Trying to determine how dark matter
is distributed between clusters is a
complex calculation becausse the light
is bent by many clusters along the line
of sight.
AST 346, Galaxies, Part 7