Galaxy Groups and Clusters - Stony Brook University · 2011. 5. 3. · Galaxy Groups and Clusters I Half of galaxies are in groups or clusters I Half of members in a volume less than

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

I Clusters contain ∼ 50 luminous members in inner Mpc

I Being a member alters evolution of a galaxy: they fall in throughhot gas and pressure strips away cool gas in outer parts

I Groups are dominately formed of spirals

I Clusters are dominately formed of ellipticals and S0’s, predominatelygiant 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 beintercluster cool gas

I Most mass is dark

J.M. Lattimer AST 346, Galaxies, Part 7

Nearby Galaxy Groups


Stephan’s Quintet

A rare compact group, galaxiesalmost touch, 85 Mpc distantand 80 kpc across.

Long tails of starshave been pulled from the disks.

About 109M� in hot gas withTX ∼ 107 K, consistent with thevelocity dispersion of thegalaxies of 300 km/s.

About 1010M� in cool gas,mostly outside the galaxies,apparently stripped out.

NGC 7318b, recently arrived,tore out the tail from NGC 7319.

A smaller spiral, NGC 7320c,passed through 500 Myr ago andwill return.

HST

SST

7319

7320, not a member

7318B 7318A

7317


M81 Group

Sparse group (> 34members),connectionsof long HI streamerstorn from galactic disks.

Distance is 3.6 Mpc,total mass 1012M�.

M81

NGC 3077

M82


NGC 1550 GroupHas about 15 members within 1 Mpcof the S0 galaxy NGC 1550, includingtwo ellipticals.

Radiates 4× 109 L� in X-rays (10times that of Stephan’s Quintet).

Metallicity about 0.1 solar.

Galaxy velocity dispersion σr = 310km/s, approximate distribution with aPlummer model with a = 100 kpc.

3σ2r

2=

KEM

= − PE2M

=3π

64

GMa

LX = n2Λ(TX ),Λ ∼ 3×10−27T1/2X erg/s

n ∝ r−β , IX ∝ LX R ∝ r1−2β

Hydrostatic equilibrium:

M(< r) = −kNo

µ

r2

Gn

d(nT )

dr

NGC 1550 group

X-ray emission

NGC 1550


Veclocity Dispersions in Groups

Assume a Plummer model for groups with the same a and mass for eachgalaxy. The Virial Theorem predicts

σ2r ∝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 thesame as the stellar velociities within galaxies. Dynamical friction istherefore important.


Dynamical Friction and Mergers

A galaxy of mass M moves past a starof mass m at velocity V . M acquiresa speed ∆V⊥ = 2Gm/(bV )perpindicular to V . We requireb >> 2GM/V 2.

The star acquires an equal andopposite momentum. The total KE inperpindicular motions is

∆KE⊥ =M2

(2Gm

bV

)2

+m

2

(2GMbV

)2

=2G 2mM(M+ m)

b2V 2.

This energy comes from the forwardmotion of the galaxy, which changesby ∆V‖. To lowest order

−∆V‖ =∆KE⊥MV

=2G 2mM

b2V 3.

The average rate at which it slows is

−dV

dt=

∫ bmax

bmin

nV2G 2mM

b2V 3

=4πG 2Mnm

V 2ln Λ

n is the stellar density. Can also beapplied to a small galaxy orbitingwithin a dark halo of density nm.Using the dark halo potentialnm = ρH ' V 2/(4πGr2),

F‖ = −GM2

r2ln Λ =Mdr

dt

Integrating:

tsink =r2V

2GM ln ΛJ.M. Lattimer AST 346, Galaxies, Part 7

Mergers and Simulations

NGC 4676 ”the Mice”

R band, HI contours


Simulations


Starbursts

Mergers often have 109 − 1010M� of dense molecular gas broughtinward to center which is gravitationally compressed and leads to violentstar formation.

If dust is present, it intercepts the stellar light and re-radiates it in theinfrared.

—


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× 108M� will be exhausted in τff = 100 Myr


Starbursts: Arp 220

Luminous and ultraluminous infrared galaxies(ULIRG) form stars at rate

M∗ ∼LFIR

6× 109 L�M� yr−1.

Most powerful ULIRG have 1000M�/yr rate.

Half of ULIRG also haveactive galactic nuclei.

Arp 220 is a close-bymerging pair 75 Mpcdistant, withM ∼ 200M�/yr.

Has 109M� H2 ina 20 pc gas disk.

Can’t sustain activityfor more than 1 Gyr.

Rounder cores, morerandom motions, lessrotation: form ellipticals?


Nearby Galaxy Clusters


Properties of Clusters

5-10% of luminous galaxieslive in clusters.

Most members are dwarfs.

Virgo central regions have0.5 L�/pc2

Virgo core radius is about0.5 Mpc

Fornax cluster has 1/5 asmany members, but ismore compact, with twicethe luminosity density, butless hot gas, relatively.

The core of a galaxy likeNGC 1399 is 107 times asdense as the center of theFornax cluster.

tota

l

#w

ith

in[M

B,M

B+

1]

Virgo


Rich Clusters

Examples are Coma, Perseus Clusters.

As clusters become more massive,theybecome denser; radii hardly change.

Infalling clumps add 10% every fewGyr, but will cease in 2-3 Hubble timesas the expansion of the universe willoverwhelm a cluster’s gravity.

Spirals excluded from the centers.

Galaxies fall supersonically intoclusters; shocks leave gas behind.

By observing novae and planetarynebulae, it is estimated ∼ 10− 20% ofstars are intercluster, probably tornout of infalling galaxies.

Virial estimates of masses∼ 2− 7× 1014M� for Virgo–Coma.Hot gas indicates masses 50% larger.

Coma

X-ray contours

◦ ellipticals? spirals


Hot Cluster Gas

Mass in hot gas equals stars inpoor clusters, but 10 times starsin a rich cluster. It can be tracedto larger radii than stellar light.

Temperature of gas increaseswith cluster luminosity, consistentwith galaxy velocity dispersion.As new clumps added, TX grows.

Models suggest TX increasesfaster than L, so high z clustersshould be cooler for a given L;not observed, indicating earlyenergy sources (starbursts andactive nuclei).

Cooling time is ∝ nX TX/LX , or

tcool =3nkT

3× 10−27n2√

T

≈ 14

(10−3cm−3

n

)√107K

TGyr

Since cool gas and star formation notobserved in central galaxy, gas mustbe reheated by supernovae or radiosources. Gas in outer regions doesn’tcool quickly and does not form stars.

Lx∝ T

3X


Cosmic Baryonic Budget

Hot gas accounts for 0.1 of themass of a luminous cluster, butmuch less in smaller systems.Together with stars, accountsfor about 1/6 of total mass.

But baryons are moreconcentrated in galaxies (lessthan half of mass inside solarcircle is dark).

Dense gas in the dampedLyman-α clouds (neutral andatomic) is half the mass of hotgas.

A large amount of ionized gascould be hidden; it’s low densityprevents it from cooling. Thisdiffuse gas is in the Lyman-αforest.

Fukigita & Peebles 2004


Did Galaxies Grow By Mergers?

I Largest red galaxies (cD andellipticals) live in dense regionswhile star-forming spirals andirregulars fill less dense regions.

I At z = 1, about 5-10% of galaxiesare in major mergers, so thatwithin last 5 Gyr, 2/3 of luminousgalaxies have had a merger.

I If ellipticals formed from mergers,their stars are older. Clumps areideal sites for mergers because oflow random velocities, and sodense with ellipticals.

I In a major merger of two equalmasses, disks are destroyed andcool gas is lost; star-formationterminates. Remnant will haveonly middle-aged and old stars.

I A merged system will become lessdense. A system of size R with Ngalaxies of mass M has energyPE/2= −GNM2/(2R). Aftermerger, and virialized, the energyis PE/2= −G (NM)2/(2Rg ) soRg = NR. Merged systems areless dense by 1/N2.


Did Galaxies Grow By Mergers?

I If merged systems stillcontained some cool gas, itwould settle to center andtrigger star formation.

I Merged galaxies thereforedevelop metal-rich centers.

I With a small, dense, innerdisk, these galaxies wouldrapidly rotate, and resemble”disky” ellipticals.

I When these merged systemsmerge again, more luminoussystems are formed, and tendto be triaxial, so resemble”boxy” ellipticals.

I Problems:

I Where does ”fundamental plane”relationship come from?

I Why are luminous red galaxies notrare at high redshifts? More efficientstar forming?


Gravitational Lensing

I Microlensing by a compact(point) source

α ≈ 4GMbc2

I Lensing by extended objectsSources near the Einstein radius

α(b) = ∇ψL(b)

ψL(b) =4G

c2

∫Σ(b′) ln |b− b′|dS ′

I Weak lensingSources are well outside theEinstein radius

Image

Source

Lens


Gravitational MicrolensingUse small angle approximations:

β = y/dS

θ = x/dS = b/dLens

α = (x − y)/dLS

θ − β = αdLS/dS

=4GMθc2

dLS

dLensds≡ θ2

E

θIf ds = NdLens

θE = 0.002

√1 kpcdLens

N − 1

N

MM�

.

Image

Source

Lens

Solving θ2 − βθ − θ2E = 0: θ± =

(β ±

√β2 + 4θ2

E

)/2

When dLens << dS , α ≈ θ − β = θ2E/θ.

Images are magnified and brightened (I (x) is unchanged):

Fimage,±

Fsource=Aimage,±

Asource=

xdx

ydy=

∣∣∣∣ θβ dθ

dβ

∣∣∣∣ =1

4

(β√

β2 + 4θ2E

+

√β2 + 4θ2

E

β± 2

)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) =dψL

db, ψL =

4GMc2

ln b.

Summing the effect from a collectionof point masses:

α(b) = ∇ψL(b)

ψL(b) =4G

c2

∫Σ(b′) ln |b− b′|dS ′

If axisymmetric, one finds

α(b) =4G

bc2

∫ b

0

Σ(R)2πRdR

=4G

c2

M(< b)

bThis is proven by noting that a ray passing through a uniform circularring is not bent, and a ray passing outside is bent the same as from apoint mass at the center.


Extension to Asymmetric Galaxy Clusters

θ − β = α(θ)dLS

dS

=4GM(< b)

θc2

dLS

dLensdS

Since b = θdLens

β = θ

[1− M(< b)

πb2Σcrit

]Σcrit =

c2

4πG

dS

dLensdLS

Plummer

potential

dark halo

potential

units are a/dLens

If Σ(0) > Σcrit , an image at β = 0 will be an Einstein ring of angular sizeθE = bE/dLens , where M(< bE ) = πb2

E Σcrit .

If dS , dLS >> dLens

Σcrit ≈ 2× 1014

(100 Mpc

dLens

)M� pc−2

M(< θE ) ≈(

dLens

100 Mpc

)(θE

1′′

)2

1010M�.


Weak Lensing

Galaxies behind a cluster but welloutside of its Einstein radius haveweakly magnified tangential images.The radial axes are in the ratio

x

y:

dx

dy,

∣∣∣∣dβdθ∣∣∣∣ :

∣∣∣∣βθ∣∣∣∣

Shear γ measures compression.Assuming b >> θE dLens ,

γ =1

2

(dβ

dθ− β

θ

)=M(< b)/(πb2)− Σ(b)

Σcrit.

In the event that Σ(R) is constant,θ ∝ β.

Measuring average shapes of manygalaxies in the background allows anestimate of shear and distribution ofmass.

Studies of halos of bright galaxiesshow they are larger and more massivethan rotation measures imply.

Trying to determine how dark matteris distributed between clusters is acomplex calculation becausse the lightis bent by many clusters along the lineof sight.


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Galaxy Groups and Clusters - Stony Brook University · 2011. 5. 3. · Galaxy Groups and Clusters I Half of galaxies are in groups or clusters I Half of members in a volume less than